Quantitative gas chromatography: for laboratory analyses and on-line process control

JOURNAL OF CHROMATOGRAPHYLIBRARY- volume 42

quantitative gas chromatography for laboratory analyses and on-line process control

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JOURNAL OF CHROMATOGRAPHY LIBRARY - volume 42

quantitative gas chromatography for laboratory analyses and on-line process control Georges Guiochon Distinguished Scientist, University of Tennessee, Knoxville, and Oak Ridge National Laboratory, Oak Ridge, TN, U.S.A. and

Claude L. Guillemin lnghieur E. S.C.M., Centre de Recherches Rhone-Poulenc, Aubervilliers, France

ELSEVlER Amsterdam - Oxford - New York - Tokyo

1988

ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat25 P.O. Box 2 1 1, 1000 AE Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 52, Vanderbilt Avenue New York, NY 10017, U.S.A.

tibnry of Conprr Cltd~nginPubliationLbta

Cuiochon, Ceorges, 1931Quantitative gas chromatography. (Journal of chromatography library ; V . 4 2 ) Includes bibliographies and index, 1. G a s chromatography. 2. Chemistry, Analytic-Quantitative. 1. Cuillemin, Claude L., 192911. Title. 111. Series. 88-3911 90117.C515C85 1988 543' .0896 ISBN 0-444-42857-7

ISBN 0-444-42857-7 (Vol. 42) ISBN 0-444-4 16 16- 1 (Series) 0 Elsevier Science PublishersB.V.. 1988 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./ Physical Sciences & EngineeringDivision, P.O. Box 330, 1000 AH Amsterdam, The Netherlands.

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Special regulationsfor readers in the USA This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred t o the publisher. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods. products, instructions or ideas contained in the material herein. Although all advertising material in this publication is expected to conform t o ethical (medical)standards, inclusionin this publication does not constitute a guarantee or endorsement of the quality or value of such product or of the claims made of it by its manufacturer. Printed in The Netherlands

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. . . and so there ain't nothing more to write about, and I am rotten glad of it, because if I'd a knowed what trouble it was to make a book I wouldn't a tackled it and I ain't going to no more. Mark Twain The Adventures of Huckleberry Finn (Chapter XLIII)

This book is dedicated to our masters in the arts and science of gas chromatography, to our friends, with whom countless fruitful discussions lead us to clarify our ideas, to those who inspired us, to our coworkers whose work and pertinent questions helped us to progress. To those who came to hear our talks and who shared their problems with us and to all around us who provided the so essential support:

Thank YOU

VII

CONTENTS Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 1 Introduction and definitions .......................................... Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Definition and nature of chromatography .................................. I1. Phasesystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Schematic description of a gas chromatograph ............................... IV. Chromatographic modes .............................................. V. The chromatographic process ........................................... VI . Direct chromatographic data ........................................... VII. Data characterizing the gas flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII . Data characterizing the retention of a compound ............................. IX . Data characterizing the column efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X Data characterizing the separation of two compounds .......................... XI . Data characterizing the amount of a compound .............................. XI1. Data characterizing the column ......................................... XI11. Practical measurements ............................................... Glossaryofterms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literaturecited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1 2 2 3 4 6 7 10 12 13 16 20 21 28 30 32 33

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Chapter 2 Fundamentals of the chromatographic process Flow of gases thmugh chromatographic edumns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Outlet gas velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Column permeability . . . . . . . . . . . . . . ........................ I11. Gasviscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Velocity profile . . . . . . . . . . . . . . . . . ........................ V. Average velocity and gas hold-up time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . On the use of very long columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI . VII . Case of open tubular columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII . Measurement of carrier gas velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determination of the column gas volume ................................... 1X. X. Case of a non-ideal carrier gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI . Flow rate through two columns in series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI1. Variation of flow rate during temperature programming ........................ XI11. Flow rate programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossaryofterms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literaturecited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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XI

35 35 31 38 39

40 41 44 45 41 48 48 49 51 52 53 54

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Chapter 3 Fundamentals of the duomatographic process The thermodynamics of retention in gas chromatography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. The thermodynamics of retention in gas-liquid chromatography . . . . . . . . . . . . . . . . . . A.1. Elutionrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.11. Capacity ratio of the column ...........................................

55 55 56 51 51

VIII A.111. Partition coefficient .................................................. A.IV. The practical importance of the activity coefficient ............................ A.V. Specific retention volume .............................................. A.VI. Influence of the temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.VI1. Relative retention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.VIII. Influence of the gas phase non-ideality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.IX. Mixed retention mechanisms. Complexation ................................ A.X. Mixed retention mechanisms. Adsorption .................................. A.XI. Adsorption on monolayers and thin layers of stationary phases . . . . . . . . . . . . . . . . . . . B. The thermodynamicsof retention in gas-solid chromatography . . . . . . . . . . . . . . . . . . . B.I. The Henry constant and retention data .................................... B.11. Surface properties of adsorbents and chromatography .......................... B.111. Influence of the temperature ............................................ B.IV. Gas phase non-ideality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.V. Adsorption of the carrier gas ........................................... B.VI. The practical uses of GSC ............................................. C. Application to programmed temperature gas chromatography .................... C.I. The prediction of the elution temperature .................................. C.11. Optimization of experimentalconditions ................................... Glossaryofterms ......................................................... Literature cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 4 Fundamentals of tbe chromatographicprocess Chromatographicband broadening . . . . . Introduction . . . . . ....................................................... I. Statistical study of the source of band broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. The gas phase diffusion coefficient ....................................... I11. Contribution of axial molecular diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Contribution of the resistance to mass transfer in the gas stream . . . . . . . . . . . . . . . . . . V. Contribution of the resistance to mass transfer in the particles .................... VI . The diffusion coefficient in the stationary phase .............................. VII . Contribution of the resistance to mass transfer in the stationary phase . . . . . . . . . . . . . . VIII. Influence of the pressure gradient ........................................ IX. Principal properties of the H vs u curve ................................... X The reduced plate height equation ........................................ XI . Influence of the equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI1. Band profile for heterogeneous adsorbents .................................. XI11. Relationship between resolution and column efficiency ......................... XIV. Optimization of the column design and operating parameters ..................... Glossaryofterms ......................................................... Literature cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 5 Fundamentals of the chromatographicprocess Column overloading . . . . . . . . . . . . . . . Introduction . . . . . ....................................................... I. The effects of finite concentration ........................................ I1. The mass balance equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Moderate sample size: column overloading ................................. IV. Large sample size: stability of concentration discontinuities ...................... V. Large sample size: propagation of bands ................................... Glossary of terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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60 60 61 63 65 66 70 73 75 77 77 78 80

81 82 82 83 84

87 88 90 93 93 94 95 96 98 100 100 101 102 105 111

113 117 117 118 123 124 127 127 128 135 138 147 148 150

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Chapter 6 Methodology Optimization of the experimental conditions of a chromatographic separation using packed columns

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. The first step: an empirical approach ......................................

153 153 155

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The second step: optimization of the main experimental parameters . . . . . . . . . . . . . . . . I1 I11. Selection of materials and column design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossaryofterms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 7 Methodology Advanced packed columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Modified gas-solid chromatography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Steam as carrier gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 8 Methodology Open tubular columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Classification of open tubular columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Preparation of open tubular columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Evaluation of open tubular columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Open tubular column technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Guidelines for the use of open tubular columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossaryofterms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 9 Methodology.Gas chromatographic instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Description of a gas chromatograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Pneumatic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Sampling systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Columnswitching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Ancillary equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 10 Methodology Detectors for gas chromatography . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. General properties of detectors . . . . . . . . . . . . ................... I1 . The gas density balance . . . . . . . . . . . . . . . . . ....................... I11. The thermal conductivity detector . .................................... IV . The flame ionization detector . . . . . . . . . . . . . . . . ....................... V. The electron capture detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI . The thermoionic detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII . The flame photometric detector . . . . ............................. .............. VIII . The photoionization detector . . . . . . IX . The helium ionization detector . . . . . . . . ...................... Literaturecited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 11.Qualitative analysis by gas chromatography The use of retention data . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Characterization of compounds by retention data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Precision in the measurement of retention data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I11 . Comparison between retention data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1V. Classification and selection of stationary phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

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Chapter 12.Qualitative analysis Hyphenated techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. The use of selective detector response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. The use of on-line chemical reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

164 181 201 208 211 211 213 233 244 241 248 251 253 219 286 304 310 311 319 320 320 321 321 340 384 390 393 395 391 411 423 431 441 451 463 466 412 411 481 482 483 490 500 515 526 531 532 533 538

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I11 The coupling of mass spectrometry to gas chromatography ...................... IV. The coupling of infrared spectrophotometry to gas chromatography . . . . . . . . . . . . . . . . Literaturecited ..........................................................

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543 557 561

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Chapter 13 Quantitative analysis by gas chromatography Basic problems, fundamental relationships, mePmvemeatdthesamplesize ........................................... Introduction ............................................................ I. Basic statistics. Definitions ............................................. I1. Fundamental relationship between the amount of a compound in a sample and its peak size ............................................................. I11 Measurement of the sample size ......................................... Literaturecited ..........................................................

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563 563 564 570 575 586

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Chapter 14 Quantitntive analysis by gas chromatography Response factors, determination. a m rpcyandprefisioo .........................................................

Introduction ............................................................ I. Determination of the response factors with conventional methods . . . . . . . . . . . . . . . . . I1. Determination of the response factors with the gas density balance . . . . . . . . . . . . . . . . . 111. Stability and reproducibility of the response factors ........................... Literaturecited ..........................................................

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587 587 589 601 609 626

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Chapter 15 Quantitativeanalysis by gas duomatogmphy Measurement of peak area and derivation ofsamplecomposition ......................................................

Introduction ............................................................ I. Measurement of the peak area by manual integration .......................... I1. Measurement of the peak area by semi-automaticmethods ...................... I11. Measurement of the peak area by computer integration ......................... IV Area allocation for partially resolved peaks ................................. V. Analytical procedures for the determination of the composition of the sample . . . . . . . . . Literaturecited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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629 629 631 635 638 646 650 658

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Chapter 16. Quantitative analysis by gas chromatography sourceS of errors, accuracy and precision ofchwbgqMcmepPurement0 ............................................. Introduction ............................................................ I. Sources of errors in chromatographic measurements ........................... I1. The general problem of instrumental errors ................................. I11. Pressure and flow rate stability .......................................... IV. Temperaturestability ................................................. V. Stability of the detector parameters ....................................... VI . Other sources of errors ................................................ VII. Global precision of chromatographic measurements ........................... Literaturecited ..........................................................

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Chapter 17 Applicatioas to process cootml analysis ................................. Introduction ............................................................ I. Description of an on-line process gas chromatograph .......................... I1. Methodology ...................................................... I11 The deferred standard concept .......................................... IV. Examples of on-line industrial analyses .................................... Literaturecited ..........................................................

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661 661 662 613 675 678 679 684 684 687 689 690 690 694 703 718 139

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741

Subjertlndex ...........................................................

169

Appendix.ChmmatograpbyLexicon

Journal of Chromatography Library (other volumes in the series)

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795

XI

FOREWORD Gas chromatography has reached maturity. The number of scientific papers published yearly in this area is decreasing. Although there are still a few unresolved issues, many of these papers belong more to the realm of technological development than to the pursuit of science. After well above ten thousand valuable papers and many books have been published on gas chromatography, why have we written another one, and one this size? Gas chromatography is now firmly established as one of the few major methods for the quantitative analysis of complex mixtures. It is very fast, accurate and inexpensive, with a broad scope of application. It is likely to stay forever in the analytical chemistry laboratories. Although the source of scientific literature dealing with gas chromatography is slowly drying up, the sales of gas chromatographs are still increasing. Besides replacing obsolete instruments, chromatographs are purchased to expand existing laboratories and to create new ones. Gas chromatography has become complex and involved. Over two hundred stationary phases, more than ten detector principles and several very different column types are available for the analyst to choose from among the catalogs of over a hundred manufacturers and major retailers. Like other modem techniques of measurements, gas chromatography makes considerable use of computer technology. Digital electronics, data processors, programs for data acquisition and handling must be familiar to the analyst. Their integration to the chromatograph makes it a sophisticated piece of equipment. These progressive changes in the nature of gas chromatography as well as its now ubiquitous use have created new needs for information which are not satisfied by the literature presently available. The analyst needs an easy way to find out about the technique as he wants to use it: how to rapidly, simply and inexpensively carry out the quantitative analyses he has to perform. He needs help in finding methods to solve his daily problems and he does not have time to seek the primary literature and to digest it. Reviews published by scientific journals are an excellent solution, but they are scattered through hundreds of volumes, are published with no logical plan and are of uneven scope and quality. Most recent books are dedicated to specialized topics and none of them discusses the specific problems of quantitative analysis. The general books and treatises available are now aging. None of them deals seriously with the practical aspects of quantitative analyses, although it is the main issue in modem gas chromatography. We have written the present book in an attempt to fill these needs. It has always been surprising, if not shocking, to both of us that, although gas chromatography is essentially used to provide quantitative analyses, this topic is almost completely neglected in treatises, books, handbooks or textbooks. It is rarely talked about at

XI1

meetings, as if calibration were a dirty business and errors a plague and not a topic worthy of scientific discussions. We have striven to provide a complete discussion of all the problems involved in the achievement of quantitative analysis by gas chromatography; whether in the research-laboratory,in the routine analysis laboratory or in process control. For this reason the presentation of theoretical concepts has been limited to the essential, while extensive explanations have been devoted to the various steps involved in the derivation of precise and accurate data. This starts with the selection of the proper instrumentation and column, continues with the choice of optimum experimental conditions and then with careful calibration and ends with the use of correct procedures for data acquisition and calculations. Finally, there is almost always something to do to reduce the errors and an entire chapter deals with this single issue. Numerous relevant examples are presented. Although we have tried to be reasonably complete, and to present the most important and pertinent papers on each issue dealt with, we are sure that we have missed a few of them. We apologize in advance to the authors and to our readers for these lapses, which in part are due to the extreme abundance of the literature. We would like them to be brought to our attention. We shall appreciate all comments and especially those which could be useful for a further edition. Finally we want to thank here all those who have helped us in this endea\our: those who have provided us inspiration and understanding, those who have worked with us, those who have given us ideas or clues, those who have discussed these problems with us during the years when gas chromatography was in the making and the many authors whose papers we read with delight. Their names are found in our book and they are too many to be listed here. We are especially grateful to Prof. Daniel E. Martire who read the theory section and made many constructive comments, to Mrs. Lois Ann Beaver who read the whole manuscript and made many helpful suggestions for its improvement and to Mrs. H.A. Manten who turned our set of ASCII files into a book. Concord Tennessee, January 1988

GEORGES GUIOCHON CLAUDE L. GUILLEMIN

1

CHAPTER I

INTRODUCTION AND DEFINITIONS

TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Definition and Nature of Chromatography 11. PhaseSystems.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Schematic Description of a Gas Chromatograph . . . IV. Chromatographic Modes . . . . . . . . . . . . 1. Elution Chromatography . . . . . . . . . . . . . . . . . . 2. Frontal Analysis . . . . . . . . . . . . . . . . 3. Displacement Chromatography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. The Chromatographic Process ...................... V1. Direct Chromatographic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. The Retention Time, r R . . 2. The Gas Hold-up Time, t , 3. The Peak Width, w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. The Peak Height, h . . . . . . . ... ..................... 5. The Peak Area, A . . . . . . . . ............................. VII. Data Characterizing the Gas Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Data Characterizing the Retention of a Compound ...................... 1. The Retention Volume, VR . .......................

2 3

7

I 10

I1 12 12

.......................

13 13 13

1. The Standard Deviation, u . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. The Different Standard Deviations . .................................

16

4. The Relative Peak Width, f . . . . . . . . . . . . . . . 5 . The Number of Theoretical Plates of the Column, N

18 18

8. TheFrontalRatio, R

...............

............. ..........................

6. The Number of Effective Theoretical Plates, N,, . . 7. The Height Equivalent to a Theoretical Plate, HET

1. The Relative Retention, a

5 . The Effective Peak N

XI.

....

...................

Data Characterizing the 1. ThePeakHeight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. ThePeakArea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

2 XII. Data Characterizing the Column .......................................... 1. The Column Length, L .............................................. 2. The Column Inner Diameter, d , ........................................ 3. TheParticleSie, d , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. The Coating Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. The Gas Hold-up, V, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . ThePhaseRatio, /3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIII. Practical Measurements ................................................ Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28 28 28 28 29 29 29 30 32 33

INTRODUCTION Gas chromatography is one of many modes of chromatography. Described for the first time in 1952 (1) it has become extremely popular because of the rapidity and ease with which complex mixtures can be analyzed, because of the very small sample required and because of the flexibility, reliability and low cost of the instrumentation required. During the last 35 years an enormous amount of literature has been published in the field. A large number of journals publish several papers dealing with gas chromatography in every issue (2). Two journals publish only abstracts of papers published elsewhere (3,4); although striving to be complete they cannot be exhaustive. A great number of books has been published. Those most favored by the authors at some time or another in their lives are cited (5-13). This list represents a small sample of those which may be found on University library bookshelves. In the following, we shall quote, to the best extent of our knowledge, only the most important or relevant contributions. I. DEFINITION AND NATURE OF CHROMATOGRAPHY Chromatography is a separation process which utilizes the difference between the equilibrium coefficients of the components of the mixture to be separated between a stationary phase of large specific surface area and a moving fluid which percolates across it (5). There are four important concepts in this definition which, together, effect the profound originality and the considerable separation power and versatility of the method. First chromatography uses two different phases: one fixed and one mobile. Second, the mobile phase percolates across the stationary phase, and this phase has a large specific surface area. These two conditions together guarantee very fast mass transfers between the phases and rapid local equilibrium. Third, the components of the analyzed mixture must be soluble in the mobile phase and there must be a physico-cheqical process of some sort which causes the components of the analyzed mixture to have some moderate affinity for the stationary phase and to equilibrate between the mobile and stationary phases. Finally, the equilibrium coefficients of

3

the different components of the mixture must differ sufficiently to permit their separation. In other words, the mixture to be analyzed is dissolved in a fluid which percolates across a stationary phase. The components of the mixture equilibrate between the two phases, but a real, conventional, static equilibrium is impossible because the motion of the carrier fluid constantly displaces the equilibrium. The compounds are carried downstream by the moving fluid and separate at the same time. Since it is possible to design and build a system where components will experience a very large number of successive such equilibria, chromatography is an extremely powerful method of separation. Since physical chemistry provides a large number of equilibrium processes between two different phases, the method is very flexible. The stationary phase can be either a solid or a liquid. In the first case adsorption is the main equilibrium process used. In the second case, to avoid the potentially disastrous effects of convective mixing, and to permit rapid exchange between the two phases, the liquid is dispersed on a solid support. This support will have a rather large specific surface area, to promote fast exchanges between the phases and rapid equilibrium, but must be inert or almost so, in order not to contribute by an adsorption process to the nature of the equilibrium between the mobile and stationary phases. This condition will be more-or-less rigidly enforced depending on the aim of the analyst: if the additional contribution of the support contributes to the separation, the so-called ‘mixed mechanism’ will be gratefully accepted. The mobile phase can be either a gas or a liquid. In this book we study only gas chromatography, whose particular characteristics result from the use of a low-density, compressible fluid, of low viscosity, in which diffusion coefficients are large (1). In almost all applications it will be assumed that the behavior of the gas mobile phase is ideal. In a few cases a correction is made, using the second virial coefficient. Solubility in the mobile phase, of course, means volatility, and the components of the analyzed mixture must have a significant vapor pressure in the conditions of the analysis. There is no clear-cut threshold, and this question is discussed in more detail later, but it is quite difficult to analyze by gas chromatography (GC) compounds whose vapor pressure is not at least a few torr at the temperature at which the analysis is carried out (10). Conversely, the stationary phase must have an extremely low vapor pressure, in order to permit the achievement of a significant number of analyses under reproducible conditions.

11.

PHASE SYSTEMS

This term designates the combination of mobile and stationary phases used for a given chromatographic application. In gas chromatography the mobile phase has only a very small influence on the retention data, so the choice of the proper stationary phase is of paramount importance. In some rare instances, a change of carrier gas may alter the resolution pattern to a significant degree. References on p. 33.

4

The stationary phase is made of solid particles, preferably of narrow size distribution. Their average size is usually between 0.1 and 0.3 mm, although smaller particles have been used in some cases, to achieve very large efficiencies. From the point of view of their chemical composition, the stationary phases used can be classified into three groups: - Adsorbents, usually with a very large specific surface area (50 to 1000 and more m2/g). Silica, alumina, molecular sieves, activated charcoal, and graphitized carbon black have been used. Gas-solid chromatography is not a very popular method, except for the analysis of gases, or for the solution of special problems. - Neutral, or so-called inert, supports are usually derived from diatomaceous materials, sometimes from polymers. They are impregnated with a liquid of very low vapor pressure and high thermal stability under the conditions that the column is used. There is a large variety of such liquids which have been tested, and whose characteristics are reported in the literature. The properties of these phases and the principles of stationary phase selection are discussed in Chapter 3. Changing the nature of the liquid changes the solubility of the sample components and permits the adjustment of the selectivity, i.e. of the relative position of the bands of these compounds. Dissolution of additives in the stationary phase which result in the formation of labile complexes with some of the compounds to resolve is another approach to the change of selectivity. Gas-liquid chromatography is by far the most popular method in current use. - Adsorbents impregnated with a small amount of a low vapor pressure liquid have also been used with extremely good success to achieve difficult separations. The method is then usually referred to as gas-adsorption layer chromatography or modified gas-solid chromatography (see Chapter 7). .The mobile phase is an inert gas, such as helium, nitrogen, argon, or a gas like hydrogen, which is considered to be inert under the conditions of gas chromatography. Other gases or vapors have been used in some special cases, like steam (see Chapter 7) or anhydrous ammonia. The chemical composition of the carrier gas has only a very small effect on the retention of compounds and on their resolution. This effect is due to the variation of the second virial coefficient of interaction in the gas phase and can be neglected, except when working with very high efficiency open tubular columns. On the other hand, the physical properties of the mobile phase, and especially the large compressibility of gases, the large value of the diffusion coefficient and the major difference between partial molar volumes in the mobile and stationary phase have a profound influence and are the reason for the considerable differences between gas chromatography and liquid chromatography. 111. SCHEMATIC DESCRIPTION OF A GAS CHROMATOGRAPH

There have been many implementations of the principles of gas chromatography, but all GC quipment is very similar in its basic principles (1-4). A schematic description is given in Figure 1.1 (see also Chapter 9, Section I). The basic components are as follows:

5

1

Carrier gas

- - - 3

2

Injector

I

4

Column

1

6

I

Data collection and handling

!

Detector

I I I

Figure ! . I . Schematic of a modular chromatograph. 1 - Source of carrier gas, at constant flow rate or constant pressure. 2 - Introduction of the sample into the carrier gas stream. 3 - Chromatographic column. 4 - Detection system.

5 - Temperature controlled oven. 6 - System for data collection and handling.

- A carrier gas supply unit, which delivers a steady stream of the carrier gas selected. The most popular systems use a flow rate controller. The mass flow rate of the carrier gas through the controller is kept constant. In other words, the number of moles of gas passing through the column per unit time is constant. - A sampling system, which permits the injection in this stream of gas, just upstream of the column, of the proper amount of sample. This sample must be vaporized in a short enough time and introduced into the column as a cylindrical plug of vapor diluted by the carrier gas. - The column, which is contained in a temperature-controlled oven. The temperature selected usually lies in the range ambient temperature to 35OoC, although analyses have been reported in the much larger range (- 180 O C to 1000 O C). - A detector, which delivers a signal function of the composition of the carrier gas. Ideally this signal is zero when pure carrier gas exits from the column and is proportional to the concentration of any compound different from the carrier gas. Such a detector is called linear. If the proportionality coefficient is the same for all compounds the detector is called ideal. In practice, an ideal detector does not exist. The components of a mixture, known as solutes, injected at the column inlet are carried downstream by the carrier gas. They migrate at a speed which is proportional to the carrier gas velocity, but is slower, and depends on the strength of the interaction of each of these components with the stationary phase. Accordingly, if the stationary phase has been properly selected, each component exits or, is eluted, at a different time and is resolved from the other ones. The signal of the detector permits the identification of each component from the time of elution of its band (also called its retention time), and its quantification from the size of the detector signal (its height or area). This is the ideal situation, which is rarely encountered in practice without strenuous efforts, but is one which all chromatographers strive to achieve. The chromatographic process is thus a sequential one. To every injection corresponds a separation followed by a detection. Whatever the implementation, the response time of the analytical system cannot be shorter than the retention time of

+

References on p. 33.

6

the compound one is interested in. If the control of a unit in a chemical plant depends on the concentration of a certain component of the exit stream, the retention time of this compound on the process control chromatograph must be shorter than the response time required for the control loop. The transfer time between the unit and the sampling system of the chromatograph must also be taken into account.

IV.CHROMATOGRAPHIC MODES There are three different modes of chromatography: elution chromatography, frontal analysis and displacement chromatography. The first is used only for analytical applications; its implementation is discussed in detail in subsequent chapters (1-4). The principles of the other two modes are briefly described. 1. Elution Chromatography

In elution chromatography, the sample is injected just upstream of the column inlet, as a cylindrical plug of vapor which is diluted in the camer gas. Each component of the mixture migrates as if it were alone, and elutes as a narrow band. If the conditions of the analysis are properly chosen, all these bands are resolved from each other, each compound is separated from the other ones, but its dilution in the carrier gas has increased. The time width of the plug must be small compared with the distance between the two most closely eluted bands of the mixture, so that these bands do not interfere. In fact, during their elution through the column, the bands of the mixture components do broaden and their maximum concentration decreases, so the plug width needs to be rather small compared to the average width of the two closest bands. Band broadening is due to molecular diffusion and to resistance to mass transfer, which is discussed further in Chapter 4, while dilution results from band broadening, and is required by the Second Principle of Thermodynamics: the chromatographic separation of the mixture components is accompanied by their simultaneous dilution in the carrier gas, so there is no net decrease of entropy during the chromatographic process. When the sample is not diluted enough in the carrier gas, the assumption of the independence of behavior of the different components of the mixture does not hold any longer, and the retention time of one compound depends to some extent on the amount of the other ones (see Chapter 5). Except in some cases encountered mostly in trace analysis, this situation, described as non-linear chromatography is carefully avoided in analytical applications. 2. Frontal Analysis

In frontal analysis, the stream of pure carrier gas is replaced suddenly, at given starting time, by a stream of gas containing diluted sample vapor. If the vapor is

diluted enough the behavior of each component can again be considered to be independent. At the column exit the composition of the eluted gas changes by successive steps, until the composition of the eluate is the same as that of the mixture entering the column. It can be shown that, within the framework of linear chromatography, the signal recorded is proportional to the integral of the signal obtained in elution chromatography. The advantage of this method over elution chromatography is the larger signal. The drawbacks are the requirement of a very much larger volume of sample, the difficulties in vaporizing it and preparing a mixture of constant composition, and difficulties in handling the data with the conventional methods using a strip chart recorder and a digital integrator. The sampling problems remain quite cumbersome, so the method finds use only in the determination of equilibrium isotherms; in this case, the requirement that the sample be dilute, which is necessary in analytical applications, in order to work in linear chromatography no longer applies.

3. Displacement Chromatography In displacement chromatography an amount of sample, more-or-less dilute, is introduced into the column and the carrier gas stream is immediately replaced by a stream of a mixture of this gas and of a vapor which interacts with the stationary phase more strongly than any component of the mixture. This vapor pushes the sample in front of it and each component of this sample displaces the components which interact less strongly than itself with the stationary phase. At the column exit, the successive elution of the bands of the mixture components takes place. These bands closely follow each other, with some interference between each neighbor. For proper displacement behavior, a relatively large concentration of sample is required. For these reasons, the method is more suited to preparative applications than to analytical ones. Furthermore, regeneration of the column, with elimination of the displacement agent, is required before a second run can be made. This may need time. As the present book deals only with analyses carried out by gas chromatography, we do not discuss further the problems of frontal analysis or displacement chromatography, nor those of preparative chromatography.

V. THE CHROMATOGRAPHIC PROCESS There are three different approaches to account for the chromatographic process: (i) the stochastic method which uses probabilities to describe the behavior of the molecules of a compound during their elution and is best illustrated by the random walk model (see Chapter 4), (ii) the use of mass-balance equations, the classical method of chemical engineering (see Chapter 5), (iii) the analogy with the Craig machine, which is a cascade of liquid-liquid extractors. Each of these approaches is best suited to a different purpose. The analogy to the Craig machine, although it is somewhat arbitrary, illustrates very well some of the basic concepts of chromatography. The random walk approach permits an excellent, References on p. 33.

8

although somewhat elementary, discussion of the influence of the resistance to mass-transfer on band broadening. The analytical solution of the set of mass-balance equations is not possible in cases which are of real practical interest, so the method can give only the necessary numerical solutions, but does not supply the concepts or images which are required to understand the chromatographic processes. In this section, we give an outline of the Craig machine, in order to illustrate the basic concepts of chromatography (5-11). We do not give a detailed presentation of its theory, however, as it does not really apply to chromatography and does not readily extend to it.

16.

G

1601

I

I

I .8

G

1601

I L

. 8 4.

14.

4.

14.

.2

14.

12.

4.

2.

14.

. 2

1. 1.

13.

3 8

13.

3.

I

3. .3

38

3.

. 2 .2

1601

I G

G

@

13.

-1-H

12. 12.

0 E

.1

'1.

L

12.

3.

L

1.2.

160

G L

I I

1. 1.

160

G L

1.

160

1.

G L

1=

160

G

L

Concentration

Figure 1.2. Schematic of the chromatographic process, considered as an automatic Craig machine. Succession of transfer steps (T) and equilibrium steps (E). G denotes the gas phase, L the stationary phase in a chromatographic column. The lower curve gives the concentration profiles of the two compounds in the Craig machine.

9

Let us divide the column into a series of short reactors, each of unit volume. In each of these reactors, equilibrium of the sample composition between the two phases takes place. The continuous chromatographic process is thus replaced by a succession of a number of two-step processes. In the first step, a volume of gas is transferred from each reactor to the next one; the first reactor is filled with pure carrier gas. In the second step, the reactors are left still, so that equilibrium can be reached in each of the reactors. The sequence is repeated a sufficient number of times to permit elution of all sample components. Although we somewhat arbitrarily introduced a discontinuity in the process, this model correctly identifies the two basic phenomena which underlie chromatography: downstream transfer by the mobile phase and equilibrium between the two phases. If we assume, for example, that we have (cf Figure 1.2) 32 molecules in a sample of a mixture, 16 black ones and 16 white ones, with partition coefficients 0.5 and 0.0 respectively, a very crude assumption indeed, the process takes place as follows (cf Figure 1.2).

First step During the first transfer, the 32 molecules are introduced into the first reactor. During the first equilibrium, the white molecules are not soluble in the liquid stationary phase. They all stay in the gas phase, while the black molecules partition between the two phases, and at equilibrium there are 8 black molecules in the gas phase, 8 in the stationary phase.

Second step Second transfer: The gas phase of the first reactor is transferred to the second one, with the 16 white molecules and the 8 black ones it contains. The other 8 black molecules stay in the stationary phase of the first reactor. The proper volume of pure carrier gas is introduced into this reactor. Second equilibrium: In the first reactor there remain no white molecules. The black ones equilibrate between the two phases, 4 molecules on average are in the gas and 4 in the stationary phase. In the second reactor the 16 white molecules remain in the gas phase, while the 8 black ones partition between the two phases. At equilibrium there are 4 black molecules in the gas phase and 4 in the stationary phase.

Third step Third transfer: The gas phase of the second reactor is transferred to a third one with the 16 white and 4 black molecules it contains, the gas of the first reactor is transferred to the second one with the 4 black molecules it contains, and the first reactor is filled with pure carrier gas. References on p. 33.

10

Third equilibrium: In the first and second reactors there art? no white molecules. They are all in the third one, where they stay in the gas phase since they are not soluble in the liquid phase. The first reactor contains 4 black molecules and at equilibrium there are 2 in each phase. The second reactor is already at equilibrium, with 4 black molecules in each phase. The third reactor also contains 4 molecules, 2 in each phase. Fourth step Fourth transfer: The gas phase of the third reactor is transferred to a fourth one, with the 16 white molecules and the 2 black ones it contains. The gas phase of the second reactor is transferred to the third one, with its 4 black molecules and the gas phase of the first reactor is transferred to the second reactor with the 2 black molecules it contains. The first reactor is filled with pure carrier gas. Fourth equilibrium: Only the fourth reactor contains the non-soluble white molecules. The black molecules are now distributed between the four reactors as follows: 2 in the first one (1 in each phase), 6 in both the second and third reactors (3 in each phase, in each reactor), and 2 in the fourth reactor (1 in each phase). A distribution curve of the two compounds is given in Figure 1.2. The progressive dilution of the retained compounds, their separation when their distribution coefficients are different and the shape of their distribution among the different reactors now appear clearly. Their profile is given by the binomial distribution (5). When the number of reactors is large this distribution tends towards the Gaussian law. Assuming a large number of reactors and a Gaussian distribution, it is possible to relate the number of reactors to the properties of the profile. This number is given by the classical relationship: 2

N = 16(

$)

where t , is the time of the maximum of the distribution and w its base width. By analogy to distillation columns and other systems where continuous separation processes take place, this number has been called the number of equilibrium stages or, more classically, the number of theoretical plates.

VI. DIRECT CHROMATOGRAPHIC DATA

From the data recorded during a chromatographic analysis, five parameters can be measured for each peak, assuming it is well enough resolved from its neighbors (cf Figure 1.3). From these parameters, which vary a great deal when experimental conditions are changed, a number of more fundamental data can be calculated (cf next section).

11

4

I----tR

I I I

I I

I I

1

I

r,

AtR

d

Figure 1.3. Idealized chromatogram showing the ‘air’ peak and the peaks of two compounds. This illustrates the chromatographic symbols.

These five basic experimental data are: 1. The Retention Time, t ,

This is the time between injection of the sample and the appearance at the column’s exit of the maximum concentration of the band of the corresponding compound. 2. The Gas Hold-up Time, t,,,

This is the retention time of an inert compound which is not retained on the column, i.e. a compound not adsorbed or dissolved by the stationary phase. Such a compound is sometimes difficult to find. With most stationary phases air is not or is practically not retained. As air is not detected by some detectors, like the flame ionization detector, methane is often substituted. This is most often satisfactory, but not always. Methane is markedly retained by most adsorbents at room temperature. It is only very weakly soluble in many liquid phases. Other common names given to the gas hold-up are the ‘retention time of a non-retained compound’ and the ‘air retention time’. This last name, which refers to the ancient use of air with a thermal conductivity detector to determine the gas hold-up time, is obsolete and should be avoided.

3. The Peak Width, w

This is usually defined as the length of the segment of the base line defined by its intersection with the two inflection tangents to the peak. The peak width, either at half height or at some other intermediate height, is also used. References on p. 33.

12

4. The Peak Height, I, This is the distance between the base line and the peak maximum.

5. The Peak Area, A This is preferably measured by integration of the signal. The problems associated with the definition of the peak area and the precision and accuracy of its determination are discussed in Chapters 15 and 16. These parameters can be measured using either the lengths measured on the paper chart or, preferably, the units of the parameters measured, time and detector signal (current or voltage). They are rarely used as such but mostly as intermediate for the derivation of the data discussed in the following sections.

VII. DATA CHARACTERIZING THE GAS FLOW The average flow velocity of the gas stream is defined in chromatography as the ratio of the column length, L, to the gas hold-up time, t,:

As the whole pore volume inside the particles of the support or adsorbent is accessible to the air or inert compound, this parameters defines an average calculated over the entire fraction of the column cross-section occupied by the gas phase, whether mobile, around the particles, or stagnant, inside these particles. Thus the average velocity used in chromatography theory is different from the one classically used in chemical engineering. We assume that the permeability of the column is constant all along its length, i.e. that the packing density is constant, which is not a straightforward conclusion, at least for packed columns, considering their packing technology. Then it can be shown (1) that the outlet gas velocity, u,, again averaged over the cross-section available to the gas phase, is given by the following relationship: u, =j X

li =

2 ( ~3 1) li 3( P 2- 1)

(3)

where j is termed the James and Martin pressure correction factor, and P is the ratio of the inlet ( p i )to the outlet ( p o ) column pressures:

p = -Pi Po

(4)

13

These pressures are absolute pressures. Since manometers usually work with reference to atmospheric pressure, accurate measurements require the use of a precision barometer. Usually, P is the absolute inlet pressure in units equal to the local atmospheric pressure at the time of the measurement.

VIM. DATA CHARACTERIZING THE RETENTION OF A COMPOUND

There are two reasons to use data derived from the experimental retention time, rather than t R itself. First, t R varies considerably when the experimental conditions are changed, and it is practical to use data which are constant or more readily reproducible. Secondly, it is possible to derive a relationship between t R and the thermodynamic equilibrium constant. Data which are related to this constant make more sense and are easier to correct for changes in the ambient parameters. 1. The Retention Volume, VR The theory of chromatography shows that the retention time is related to the flow rate of mobile phase across the column. In liquid chromatography the product of the two is constant. Because of the very large compressibility of gases this simple relationship does not hold in gas chromatography, but nevertheless we can define the retention volume as follows:

where F, is the carrier gas flow rate measured at column outlet and at column temperature. If F, is not constant, VRcan be defined by an integral, but this does not result in a practical procedure of measurement. 2. The Dead Volume, V, The definition is the same, but uses the gas hold-up time: V , = t,,, X F,

The dead volume is also called the ‘gas hold-up volume’, the ‘retention volume of a non-retained compound’, which is long and somewhat self contradictory, and ‘the air retention time’, which is obsolete. 3. The True Retention Volume, V/

This is the volume of carrier gas flowing through the column while the compound is dissolved in or adsorbed on the stationary phase. Since all compounds move along the column at a speed 0 when they are interacting with the stationary phase and at a References on p. 33.

14

speed equal to that of the carrier gas when they are in the gas phase, this is the product of the carrier gas flow rate and the difference, tR - t,:

Similarly, t;P is the true retention time. 4. The Corrected Retention Volume,

vR

As explained above, when the carrier gas flow rate increases, the retention volume V, does not stay constant. An increase of the flow rate can be achieved only by increasing the inlet pressure. Thus the same amount of gas at the column inlet occupies a smaller volume, and a larger number of moles of carrier gas is required to elute a compound when the inlet pressure increases. The corrected or limit retention volume is the limit for pi=po of the retention volume (1). It can be shown (see Chapter 2) that:

where j is again the James and Martin factor.

5. The Net Retention Volume, V, This is also called the totally corrected retention volume. This is the true, corrected retention volume:

v,

By convention, VR, V;, and VN are measured at column temperature and at the column outlet pressure. While it is not too difficult to measure the flow rate at the outlet column pressure, a correction is necessary for the temperature. A correction for the water pressure is also required if the soap bubble flowmeter is used. 6. The Specific Retention Volume, Vg

This is the STP net retention volume, divided by the mass of liquid stationary phase in gas-liquid chromatography, or by the total surface area of adsorbent in gas-solid chromatography:

m ,is the mass of liquid phase, T, the column temperature (K) and pn the standard

pressure.

15

Like V i and V,, V, does not depend on the flow rate, but only on the column temperature, the phase system and the compound studied. V,, however, is a physical constant, directly related to the thermodynamic constant of the physico-chemical equilibrium used in the phase system (see Chapter 3). The accurate determination of any one of these parameters is difficult because it requires the measurement of the column flow rate, which can rarely be made with an error less than around 1%. For this reason relative parameters are often preferred in analytical work. Even in thermodynamical studies it is important to realize that the error made on the ratios of retention volumes, and hence on the ratio of the equilibrium constants, is often one order of magnitude smaller than the error made on the absolute value of these constants. Two parameters of this type are often used:

7. The Column Capacity Factor, k’ This is defined directly from the retention times:

k’ is the true retention time measured with the gas hold-up time as a unit. 8. The Frontal Ratio, R This is the ratio of the ‘air’ to the solute retention times:

Combining equations 11 and 12 gives: 1-R k ’ = - and R

1 R=1+k’

The theory of chromatography defines R as the fraction of the number of molecules in the mobile phase at a given time; of course 1- R is the fractional number of molecules in the stationary phase. As the molecules in the gas phase move at a speed equal to u and those in the stationary phase at a speed 0, the average speed of the molecules is Ru, hence equation 12. A more rigorous discussion is given in the literature (7). Thus, k’ is the ratio of the number of molecules present in the two phases and, accordingly, is proportional to the apparent thermodynamic constant of equilibrium. References on p. 33.

16

IX. DATA CHARACIXRIZING THE COLUMN EFFICIENCY

The larger the band width the more difficult it is to separate the components of a mixture, since there is less room to place them on the chromatogram. The analyst will thus strive to produce narrow, well-resolved peaks. Another advantage of narrow bands is that the maximum concentration of the eluate is large, which makes detection more sensitive with a given detector, a very useful feature in trace analysis.

1. The Standard Deviation, u In many cases, in analytical applications of chromatography, the peak profile can be assumed to be Gaussian. Accordingly, the chromatographic trace is described by the following equation:

The signal is equal to its maximum value, y, for t = t,, which is the definition of the retention time. Sigma is the standard deviation of the Gaussian curve. Its square, u2, is the variance of the Gaussian curve. These two parameters, the standard deviation and the variance, are used in the study of chromatographic band broadening. It must be emphasized that, while the standard deviation is defined only for a Gaussian profile, the variance can be defined for any distribution, and becomes equal to the square of u in the case of a Gaussian profile. The properties of the Gaussian curve have as a result that the inflection tangents define on the base line a segment of length w: w=4u

(15)

which relates the peak width to the standard deviation. The width of the Gaussian curve at each fractional height is related to the standard deviation. Equation 1 4 can be rearranged to give:

or :

where w, stands for the width at the fraction x of the peak height.

2. The Different Standard Deviations The standard deviation can be measured in different units at the column outlet, or at any place in the column. When the band resides inside the column, it is

17

distributed along a certain fraction of the column length, with a Gaussian profile. The standard deviation is then measured in length units. When the peak is recorded on a chromatogram, the standard deviation can be measured on this trace in time units. The relationship between these two values is: (11 = RUU,

(18)

We note in passing that, if the band profile is Gaussian inside the column, at a certain time (i.e., the plot of solute concentration versus abscissa along the column), the elution profile (i.e., the plot of solute concentration versus time at column exit) cannot be Gaussian. The sources of band broadening, such as diffusion or resistance to mass transfer, continue to act on the part of the profile which is not yet eluted, resulting in an unsymmetrical elution profile. We may consider this elution profile to be analogous to a Gaussian profile, but with a standard deviation which increases slowly with increasing time. The effect is small, however, and may be neglected. Finally, at column outlet, the band occupies a volume of mobile phase equal to: 401F, v = 4 a,,= 4 a, F, = Ru It is important to note that when they are used, uI is determined just before column exit, inside the column, while a,, is determined just after the column exit, in the gas stream. This explains the factor Ru in equation 19. The width of the peak profile is important, but mainly in comparison to the retention time, which gives the time scale of the chromatogram. For this reason several dimensionless parameters have been defined (see f, N , H , below). 3. Properties of the Variance

There are several properties of the variance which are discussed in greater detail in Chapters 2 and 13, but which are worth mentioning here, since they explain the importance attached to these parameters (14). Let us assume that we have a large number of molecules which can move in only one direction (i.e. the column axis; radial distribution is assumed here to be homogeneous). Their movements take place by random leaps and bounces of length 1. When each molecule has had the opportunity to achieve a large number, n, of leaps, the molecular distribution along the column axis will be Gaussian, with a variance given by: a: = n

x 1’

(20)

This is the equation of the unidimensional random walk (14). It can be used to calculate the contribution to the band variance of the various phenomena which tend to spread the distribution of the molecules of a compound (molecular diffusion, unevenness of the pattern of flow velocities, resistance to mass transfer, cf Chapter 4). References on p. 33.

18

The power and simplicity of this model result from the fact that if several independent random phenomena contribute to the band broadening, then the resulting variance is the sum of the variances of each independent phenomenon:

All that is necessary is a complete census of the various contributions to band broadening and the calculation of each individual variance. 4. The Relative Peak Width, f

This is the ratio:

5. The Number of Theoretical Plates of the Column, N

This number is given by the relationship:

):(

N = 16( $ ) 2 =

2

= 16f2

From equation 17, we can also write: 2

N = 5.54( 5) w0.5

which permits the derivation of the plate number from the width of the peak at half-height, often measured with more accuracy than the base line width (23). This parameter has been defined previously (cf Section V), using the plate theory. It is redefined here, independently of any theory, with the assumption of a Gaussian peak profile. This definition is not valid for an unsymmetrical peak, although the plate number is sometimes measured for such peaks, leading to data for which it is impossible to account and which are often controversial (15).

6. The Number of Effective Theoretical Plates, N , The definition is the same as for the theoretical plate number, but this time the true retention time, t;, is used:

$)

2

N-, = 16(

19

7. The Height Equivalent to a Theoretical Plate, HETP or H If the column of length L has a number of theoretical plates N,we can consider that, on the average, each plate has a height H such that:

-= L H

N

This is somewhat artificial, because these plates are not bound by physical limits in the column, they are merely theoretical, and defined artificially, because of the analogy with the Craig machine (cf Section V and equation 1)and because of a still more superficial analogy with distillation columns. The HETP is quite similar to the transfer unit length of chemical engineering. In fact it is possible to redefine the HETP in a more meaningful and useful way, by considering the local plate height, H(z), where z is the abscissa along the column (7). H ( z ) is defined as the proportionality coefficient between the distance dz and the differential increase in band width when the peak moves forward a distance dz from the abscissa z to the abscissa z dz:

+

daf=H(z)dz

(27)

If the local plate height were constant along the column (dH(z)/dz = 0), integration of equation 25 would give a result identical to equation 24, but it is always possible to define an average plate height:

JO

and then:

This problem is discussed in more detail in Chapter 4. The importance of the HETP results from the fact that it can be considered as the length of column necessary to achieve equilibrium between the two phases. Contrary to what happens in the theory of the Craig machine, however, the HETP does depend on the experimental conditions (cf Chapter 4). It should be emphasized here that if we apply the definition of equation 27 to the Craig machine, the value obtained for the HETP is not equal to 1 (plate), but to 1 - R (fraction of molecules in the stationary phase at equilibrium); consequently, the plate number is not equal to the number of reactors in the machine (25). This illustrates the inconsistency between the Craig machine model and the classical model of chromatography. As with most analogies, the Craig machine model should be used merely for its pedagogic value, not as a predictive tool. References o n p. 33.

20

AS=

BC AB

Figure 1.4. Definition of the band asymmetry. The asymmetry is usually defined as As=BC/AB, sometimes as As = B’C’/A’B’.

Time in seconds; concentration in arbitrary units.

8. The Band Asymmetry, As Peaks recorded in gas chromatography are not always Gaussian. In a number of cases the bands are quite unsymmetrical. There are several explanations for that fact, which are discussed in Chapter 4. It may then be useful to characterize the asymmetry, to study the influence of changes in experimental conditions and find trends and/or correlations. The most simple and useful parameter is the ratio of the two segments of the base line defined by its intersection with the vertical from the peak maximum and the two inflection tangents (A’B’/B’C’, Figure 1.4). The ratio of the two similar segments defined on the parallel to the base line at the peak half-width by the profile itself and by the vertical from the peak maximum is easier to measure, but usually much closer to unity (AB/BC, Figure 1.4).

X. DATA CHARACTERIZING THE SEPARATION OF TWO COMPOUNDS

Parameters relative to the characteristics of both peaks are used. They relate to the retention of and to the separation between the two peaks. These two peaks are referred to as #1 and # 2 in the following discussion. The most important parameters are the relative retention of two compounds, the retention index, the resolution between two compounds and the effective peak number or peak capacity of a column.

21

1. The Relative Retention, a This is the ratio:

It is defined and usually calculated so as to be larger than unity. In some cases, when a large number of compounds are referred to the same standard compound, or when a vanes with temperature, values smaller than unity may be considered. a depends on the stationary phase and is a function of the temperature. As a first approximation, it does not depend on the flow rate, the inlet pressure or the nature of the carrier gas (see Chapter 3). It is easier to calculate than the absolute retention data (specific retention volume or partition coefficient) and more accurate. Accordingly, it is frequently used. 2. The Retention Index, Z This is the most important retention parameter in practice, at least in the analysis of organic compounds (16). The retention index is related to the relative retention a [ X / n P Z ]of a compound, X , to the normal alkane eluted immediately before it, under the same conditions. z is the number of carbon atoms of this n-alkane. The retention index is: I ( X ) = 100

log( a X/HP,) log( a nP, + 1 / n P 2 )

+ 100 z

a nP, + l / n P , is the relative retention of two successive n-alkanes. It is practically constant when z exceeds 3 or 4 (see Chapter 11). The retention index system is now widely used, because of a combination of theoretical and practical advantages: - the system uses a reference scale based on the n-alkanes, which are well defined compounds, readily available, easy to elute in most cases, and covering a wide range of volatility, so it is almost always easy to find a pair of n-alkanes that are eluted just before and just after the studied compound. - a varies very rapidly with the temperature. Usually it is similar to an exponential function. Accordingly, I( X ) is an homographic function of temperature, but in a reasonable range, due to the mode of selection of the reference compounds, I ( X ) varies slowly enough and the dependence can be considered to a good approximation to be linear. The values dZ/dT are small for hydrocarbons, larger for compounds with polar groups, they can be tabulated to permit interpolation and supply some information for qualitative analysis. - although this does not readily appear from the definition, the system in fact uses a linear scale of free energies of dissolution in the fixed liquid phase or References on p. 33.

22

adsorption on the stationary phase. Because of this thermodynamic background, the retention index system enjoys some fundamental properties. For example, linear free energy relationships can be used to calculate the retention index of compounds which are not available, or for assisting in the identification of unknowns. A considerable amount of the literature deals with this problem (see Chapter 11). There are cases where the use of n-alkanes as reference compounds does not give satisfactory results, especially when the compounds studied are best resolved on strongly polar phases. Then n-alkanes are weakly soluble and mainly retained by adsorption at the liquid-gas interface. Their retention volume is not proportional to the amount of liquid phase, the retention index depends on the phase ratio, and the column loadability for n-alkanes may be extremely small. Then it is possible to replace the n-alkanes as the reference series by another homologous series such as the n-alkanols, n-alkyl phenols, fatty acid methyl esters, etc.

3. The Resolution, R,,2 The resolution between two peaks is defined by the equation:

It is the ratio of the difference between the two retention times to the average base line width of the two peaks. If the resolution is unity the tail inflection tangent

L

Figure 1.5. Idealized chromatograms showing two peaks with the same height and different values of their resolution. 1: R = 0.50; 2 : R = 0.75; 3: R = 1.00; 4: R =1.25; 5: R = 1.50; 6: R = 1.75. When the resolution is unity, the two inflexion tangents intersect on the base line. There is no return to base line for resolution smaller than ca 2.0. Time in seconds; concentration in arbitrary units.

23

of the first peak intersects the front inflection tangent of the second peak on the base line (cf Figure 1.5). There is no return of the recorder trace to the base line, but if the two peaks have equal size the valley trough is 27%of the common peak height. Interference is thus still too important to permit a good quantitative analysis. With a resolution around 1, difficult decisions must be made regarding peak area allocation between the two compounds. This cannot be done accurately for peaks of

0.8C ._ 0 0.7-

+

> 0.6C

al

2

0.5-

0

V

0.4 Q3 0.2

3 50

370

390

410

430

450

4 70

490

430

450

470

490

Time

0.260.240.22-

c

0.2-

0 .-+

0.18-

L

$

5

0.160.140.120.1

-

3 50

Figure 1.6

370

390

410

Tme

(Conhued on p . 24) References on p. 33.

24

The

-

1.0

0.9-

0.80.70 .u o .0.6-

u C

s

0.5-

0 a4-

0.3-

0.2-

-

0.1

o.o+ 350

370

390

410

430

450

470

490

Time

Figure 1.6. Influence of the relative peak height on the profile of a doublet with constant resolution. (A) R =1.00.Relative peak height: 1: 1.0; 2: 0.30;3: 0.10;4:0.03.

(B) R =1.50. Relative peak height: 1: 0.30; 2: 0.10;3: 0.030;4:0.010. (C)R =1.50. Relative peak height: 1: 1/10; 2: 1/100; 3: 1/1,OOO; 4: 1/1O,OOO; 5: l/lOo.OOO. (D)R = 2.00. Relative peak height: 1: 1/10; 2: 1/100; 3: 1/1,OOO; 4: 1/1O,OOO; 5: 1/100,OOO; 6: 1 /l,OOo,OOO. Time in seconds; concentration in arbitrary units.

25

unequal heights, when the resolution is less than 1.5 to 2, depending on the height ratio (see Figure 1.6). A good quantitative analysis requires a resolution of cu 1.5. When the resolution decreases below 1.0 the interference between the two peaks becomes stronger and stronger, and the valley disappears at R = 0.5. When the ratio of the two peak heights becomes very different from unity, those requirements change and become more drastic, especially for a proper quantification of the smaller peak (cf Figure 1.6). When the resolution between two compounds is great it is rarely measured, except perhaps for the derivation of the peak capacity. When it is small, it is possible to derive an important relationship between the resolution, the relative retention of the two compounds, the column capacity factor for one of them and the column efficiency, by making a simple approximation. Since the resolution is small, we can assume that the column efficiency is identical for the two compounds, hence:

Combination with equations 7, 11, 23 and 32, and assuming that tR,l and t R z are close enough and that tR,l+ t R , 2 is equivalent to 2 f R . 2 , give:

or :

fi x-xa-1

R=-

4

a

k‘ 1+k‘

(35)

where k’ stands for k ; , the capacity factor for the second compound (17). This relationship is very important because it permits the derivation of the plate number necessary to achieve the separation of a given pair of compounds, knowing their relative retention and the capacity factor of the column for the second one. It shows that no matter how efficient the column is, there is no separation if there is no resolution. In difficult cases, k’ should be optimized to ca 3-4, for rather large resolution power and a still reasonable analysis time. It has been shown that the minimum analysis time is achieved in conditions where k’ is around 1.5-2 for open tubular columns and 3 for conventional packed columns (24). Equation 35 also sets a minimum limit to the relative retention of two compounds which can be separated with a column of given efficiency. In t h s equation, a! and k’ for a given pair of compounds depend only on the phase system selected and to some degree on the temperature, but not on the column, while N depends essentially on the column length and the packing material used. The resolution of a given pair of compounds is thus proportional to the square root of the length of the column used. References on p. 33.

26

4. The Separation Factor, I:

This parameter was introduced by Giddings (7), but it has rarely been used. The definition is similar to that of the reso1ution;and it is easier to use when the plate numbers for the two compounds are markedly different. This is not a situation of practical importance, however.

When the two peaks are close and the column plate number is the same for both, F is equal to the square of the resolution. It is easy to show that: F-

(DK)’L 16H(p

+ K)’

(37)

where DK is the difference between the partition coefficients of the two compounds, K the average ( K , + K , ) / 2 , and B is the column phase ratio, V,/V;, the ratio of the volumes of gas and liquid phases contained in the column. This direct relationship between the separation factor and the thermodynamic constants of the phase system makes it interesting for theoretical studies. 5. The Effective Peak Number, EPN

This parameter which characterizes the separation power of a column in a particular range of retention is also called the separation number, TZ. It is defined as the maximum number of peaks of equal heights one can place between the peaks of two reference compounds, assuming a resolution of 1.0 between each one of these peaks (18). Obviously it is most convenient to select as reference compounds two successive n-alkanes or two successive homologs. If, as a first approximation, it is assumed that the base line width of these peaks varies linearly, we may write: EPN(1,2) =TZ(1,2) = R1,’- 1

(38)

It is important to realize that the separation number can change markedly from one pair of compounds to the next one, thus the linear approximation made in the derivation has only a coarse validity. This is especially true for open tubular columns. It is therefore necessary to indicate which pair has been used for the measurement. Furthermore the separation number also depends strongly on the column temperature, increasing rapidly with decreasing temperature, which explains why too many authors use unrealistically low temperatures to rate their columns. Although this parameter is useful to compare columns in strictly defined experimental conditions, it must be used very carefully, otherwise it may easily turn out to be a ‘rubber ruler’ (19).

21

XI. DATA CHARACTERIZING THE AMOUNT OF A COMPOUND There are two parameters which can be used for this purpose, the peak height and the peak area. I

1. The Peak Height

The peak height is the maximum deviation of the detector signal from the base line during the elution of the corresponding compound. This requires the interpolation of the background signal during this elution. The determination of the peak height is difficult if there is a significant base line drift during the analysis, as such a drift is usually not linear and the estimate of the value of the background signal at the time of the peak maximum may be inaccurate. In the case of closely eluting compounds it may become impossible to form any estimate of the background signal between the two peaks. Extrapolation is then necessary. If the two peaks interfere, each peak height may be biased by a contribution from the other compound. Such a contribution is 1%for two equal sized compounds distant by 3 standard deviations (resolution = 0.75). Thus, peak height measurement may be more accurate than peak area in the quantitative analysis of compounds which are poorly resolved, providing that the operating conditions, and especially the injection, remain strictly constant. The importance of this requirement must be stressed.

2. The Peak Area The peak area is the area under the signal. In principle the integration should be carried out from the injection time to infinity. Fortunately, the signal returns rapidly to zero after the peak maximum is eluted, and integration does not need to be performed over a range exceeding - 3 to 3 standard deviations. The peak area is proportional to the sample size as long as (i) all the sample is eluted, without decomposition, reaction or irreversible adsorption, and (ii) the detector is linear. This is true, even if the column is overloaded or for any other reason gives unsymmetrical peaks. This is an advantage over the peak height, which does not vary linearly with sample size under these conditions. If the detector used is linear, that is if the detector response is always proportional to the concentration of component in the stream of carrier gas, the peak size is proportional to the amount of compound contained in the injected sample. If the peak profile were Gaussian, the peak height as well as the peak area would be proportional to the amount of compound. There are, however, reasons other than non-linear detector behavior for the observation of peaks whose height is not proportional to the sample size. Furthermore, the fluctuations of experimental parameters do not affect peak height and peak area in the same way. The choice between height and area to base quantitative analysis is discussed in detail in Chapter 16, together with the sources of errors on both measurements.

+

References on p. 33.

28

The peak profile is often assumed to be Gaussian. Within the limits of validity of this assumption, the concentration at peak maximum is given by the following relationship:

rnfi

C,= -

(39)

VR&

The peak height depends on the plate number of the column and the retention volume of the analyte. This explains why, in trace analysis, better results are obtained under conditions where the retention time is relatively small, and the efficiency important. Dilution proceeds constantly during the chromatographic process, at a speed which is at least equal to that of pure molecular diffusion along the column axis. The shorter the analysis time, the lower the additional dilution of sample in the mobile phase. This is an important factor, because even'if the peak area is often the parameter measured to carry out quantitative analysis, the detection limit depends essentially on the peak height, and only a little on its width. Finally, it should be emphasized here that the peak area is the integral of the detector signal with respect to time, while the mass of a compound is the integral of its concentration with respect to the volume of carrier gas. Fluctuations of mobile phase flow rate and pressure (i.e. density) in the detector will introduce errors in quantitative analysis for this reason.

XII. DATA CHARACTERIZING THE COLUMN Although these data are not determined from the chromatogram, they are often necessary to evaluate the chromatographic data.

1. The Column Length, L 2. The Column Inner Diameter (abbreviated i.d.), d , These two dimensions are often supplied by the manufacturer. They may be difficult to measure, especially on a coiled prepared column. When packed columns are properly cut, d , may be measured by determining the size of the largest drill which can fit inside the column. For empty packed and open tubular columns, the inner diameter can be determined by weighing the column both empty and filled with water, a solvent of known density or mercury (which is better for open tubular columns (OTC)). 3. The Particle Size, d ,

For packed columns (PC), it is determined by sieving. The mesh sizes of sieves are normalized (cf Table 1.1). It can also be derived from measurement of the column permeability.

29

TABLE 1.1 Relationship between Normalized Sieve Mesh Size and the Average Size of the Particles which pass through them. Opening (mm) 0.080 0.083 0.100 0.104 0.124 0.125 0.147 0.149 0.160 0.175 0.177 0.200 0.208 0.210 0.246 0.250 0.295 0.297 0.315 0.351 0.400 0.417 0.420 0.500

USA ASTM E 11 39

USA WS Tyler Mesh

French AFNOR N F X MM

German DIN 4188

Japanese JIS Z 8801'

20 170

170

170

88

145

105

120

125

100

149

80

177

65

210

55

250

48

297

42

350

36 32

420 500

21 140

150 115

120

22

100 24 80 80 24 65 70 60 25

60

48 50 26 45

42 27 35

40 35

28

An accurate knowledge of either the column diameter (OTC) or of the average particle size (PC) is required for a proper assessment of the results of the determination of the column efficiency at various flow velocities of the carrier gas.

4. The Coating Ratio This is the weight of liquid phase with which a certain weight of the support is coated (w/w, W).

5. The Gas Hold-up, V, This is the retention volume of an inert compound. This is also the total volume of the column available to the mobile phase.

6. The Phase Ratio, /3 This is the ratio of the volume of stationary phase to the volume occupied by the mobile phase. References on p. 33.

30

XIII. PRACTICAL MEASUREMENTS In practice, there are three different methods to derive raw data from a chromatogram. The trace of a potentiometric recorder is measured with a ruler, the print-out of an electronic integrator is read, or data are acquired with a computer and processed automatically. The choice between these methods depends on the money available for investment, but also on the nature of the problem to be solved and it is important to understand the basic problem specific to each one of these three methods. The problems of quantitation are discussed extensively in the following chapters, so only a brief survey is supplied here. Direct measurements on the recorder trace are easy but tedious and time consuming. The precision is limited to a few percent, but fundamental errors are rare. A very simple method of determination of retention distances is illustrated on Figure 1.7 (20). The drawing of proportional triangles permits the rapid and precise (a few percent) determination of relative retention times. A straight line is drawn between the point on the origin of the signal scale at the time of the ‘air’ peak and the point on the signal full scale deflection at the retention time of the reference compound. Parallel lines are then drawn as shown on Figure 1.6. The relative retention times increase each time by one unit. The lines perpendicular to the base line through the peak maxima are drawn until their intersection with the line AC‘ or one of its parallels. The relative retention times are read on the vertical scale. Peak heights are also easy to measure. Proper calibration permits their use in quantitative analysis. Although the precision of such measurements is basically limited, it is not certain that the improvement in precision which can be achieved by turning to manual integration of the peaks justifies the considerable increase in the amount of work required. The various methods of manual integration have been studied in detail by Harris, Habgood and Ball (21). This problem is discussed further in Chapters 15 and 16. Electronic integrators work on-line, cannot keep the chromatogram in memory nor make decision based on later events, and operate according to decision made by their designers, which the analyst cannot change, which may be bad, and of which he is often not aware, which is much worse. For example the retention time is not the time when the derivative of the detector signal becomes zero, after a peak has been detected, but the time when this derivative becomes negative, and equal to the threshold indicating the end of a peak. The result is a systematic delay, which increases with increasing band width, and may be significant, especially in isothermal analysis, when retention times are most prone to be measured, because the band width increases regularly, with increasing retention, and so does the delay. Similarly, as shown by Bauman, there is a systematic error due to the influence of the base line drift correction on the measurement of the peak area (22). In principle the analyst who uses a computer can check the programs and adapt them to his problems. Unfortunately, this is often quite impractical, because the programs which are purchased are protected or at least often supplied in compiled language. Even a nice looking print-out of somebody else’s program is not easy to

31

23 min

Y

,I

0

0

A

Figure 1.7. Example of a simple chromatogram. Graphic determination of the relative retention times. Standard: toluene. Column: i.d. 4 mm, length: 4.0 m, packed with 15% triscyanoethoxypropae on Chromosorb P, 60/80 mesh, followed by 0.60 m of 15% Carbowax 20M on the same support. Temperature: column 100°C, injector and detector: 15OoC. Camer gas: Nitrogen, 3.0 l/h. Flame ionization detector: 2.0 I/h hydrogen and 15 l/h air. See list of compounds and retention times in Table 1.2.

TABLE 1.2 Relative Retention Times of the Compounds on the Chromatogram Figure 1.7 No.

Compounds

r;((x)/r;((toluene)

1 2 3

Methylene chloride Ethyl acetate Ethanol Methyl ethyl ketone Toluene Butyl acetate m-Xylene

0.23 0.39 0.47 0.14 1.00 1.47 2.54

4

5 6 7

NB. The standard compound, here toluene, should be chosen so that the relative retention times are between 0.1 and 10. Otherwise the precision of the measurements becomes poor.

understand and still more complex to modify. Strange results should be expected at the first attempt. Special attention should be paid to the methods of peak area allocation used in References on p. 33.

32

the case of incompletely resolved bands. Very large errors can be introduced by relying too heavily on the solutions programmed by computer scientists who have a limited understanding of chromatography and are only trying to help by interpolating base line or solvent peak profiles and using various algorithms of curve fitting to allocate the area measured. But in more cases than is presently realized by many, our experience is that these procedures are not legitimate, because the chromatographic process in such cases is not linear, as it is assumed in all those treatments. The actual solution is almost always in the achievement of a better resolution and a more accurate calibration. The problems encountered when using each one of these different approaches to the quantitation of chromatographic analysis are discussed in detail in the following chapters.

GLOSSARY OF TERMS

chi

Maximum concentration of a compound in the elution band. Equation 39 Difference between the partition coefficients of two compounds. Equation 37 Column diameter (i.d.) dc Average particle diameter dP EPN Effective peak number or peak capacity. Equation 38 F Separation factor. Equation 36 Carrier gas flow rate. Equation 5 F, Relative peak width. Equation 22 H Height equivalent to a theoretical plate. Equation 26 H ( z ) Local value of H. Equation 27 I Retention index. Equation 31 Correction factor for gas compressibility. Equation 3 j K Partition coefficient of a compound between the two phases. Equation 37 k' Column capacity factor. Equation 11 L Column length. Equation 2 I Average length of a step in the random walk model. Equation 20 Mass of liquid phase in the column. Equation 10 m, N Plate number. Equation 1 4, Effective plate number. Equation 25 n Number of steps in the random walk model. Equation 20 P Inlet to outlet pressure ratio. Equation 3 Inlet pressure. Equation 4 Pi Standard pressure. Equation 10 P" Outlet pressure. Equation 4 PO R Frontal ratio. Equation 12 Resolution between the peaks of two compounds. Equation 32 4 2 Column temperature. Equation 10 T, TZ Separation number. Equation 38 DK

L

33

Time. Equation 14 Gas hold-up time, or retention time of an inert compound. Equation 2 Retention time. Equation 1 True retention time of a retained compound. Equation 7 Carrier gas velocity. Equation 18 Average carrier gas velocity. Equation 2 Outlet carrier gas velocity. Equation 3 Inlet carrier gas velocity. Specific retention volume. Equation 10 Volume of liquid phase contained in the column. Equation 37 Dead volume. Equation 6 Net retention volume. Equation 9 Retention volume. Equation 5 True retention volume of a retained compound. Equation 7 Corrected retention volume. Equation 8 Peak width at base line. Equation 1 Peak width at half height. Equation 24 Peak width at the fraction x of its height. Equation 17 Fraction of the peak height. Equation 17 Detector signal. Equation 14 Peak maximum or maximum of the detector signal. Equation 14 Abscissa along the column. Equation 27 Relative retention of two compounds. Equation 30 Phase ratio of the column. Equation 37 Standard deviation of the peak, if Gaussian. Equation 14 Standard deviation of the contribution of a phenomenon to the band width. Equation 21 Standard deviation in length unit. Equation 18 Standard deviation in time unit. Equation 18 Standard deviation in volume unit. Equation 19

LITERATLJRE CITED (1) A.T. James and A.J.P. Martin, Biochemistry Journal, 50. 679 (1952). (2) All journals dedicated to chromatography and most general analytical chemistry journals. Journals dedicated to other techniques publish papers on ‘hyphenated’ techniques involving GC, while journals devoted to analytical chemistry problems publish reports on applications of GC. (3) Gas Chromatography Abstracts (1957-1969), Gas and Liquid Chromatography Abstracfs (1970-1985). Chromatography Abstracts (since 1986), now published semimonthly by Elsevier Applied Science Publishers, Barking, Essex, UK. (4) CA Selects: Gas Chromatography, published semiweekly by Chemical Abstracts Service, Columbus, OH. ( 5 ) A.I.M. Keulemans, Gas Chromatography, Reinhold, New York, NY, 1959. (6) R.L. Pecsok, Principles and Practice of Gas Chromatography, Wiley, New York, NY, 1959. (7) J.C. Giddings, Dynamics of Chromatography, M. Dekker, New York, NY, 1965. (8) L.S. Ettre and A. Zlatkis, The Practice of Gas Chromatography, Interscience, New York, NY, 1967.

34

(9) H.M. McNair and E.J. Bonelli, Basic Gas Chromatography, Varian, Walnut Creek, CA, 1969. (10) A.B. Littlewood, Gas Chromatography, Principles, Techniques and Applications, Academic Press, New York, NY, 2nd ed. 1970. (11) G. Guiochon and C. Pommier, Gas Chromatography in Inorganics and Organometallics, Ann Arbor Science Publishers, AM Arbor, MI, 1973. (12) D.J. David, Gas Chromatographic Detectors, Wiley, New York, NY. 1974. (13) Practical Manual of Gas Chromatography, J. Tranchant Ed., Elsevier, Amsterdam, 1969. (14) J.C. Giddings, in Chromarography, E. Heftmann Ed., Van Nostrand Reinhold, New York, NY, 1975,p. 27. (15) B. Bidlingmeyer and F.V. Warren, Ana!ytical Chemistry, 56, 1583A (1985). (16) E. sz Kovats, in Aduances in Chromatography,J.C. Giddings and R.A. Keller Eds., M.Dekker, New York, NY, I, 1965,p. 229. (17) J.H. Purnell, Journal of the Chemical Society, 1268 (1960). (18) R.A. Hurrell and S.G. Perry, Nature, 196, 571 (1962). (19) J. Krupcik, J. Garaj, J.M. Schmitter and G. Guiochon, Chromarographia, 14, 501 (1981). (20) C.L.A. Harbourn, BP Research Center, Sunbury on Thames, UK, 1957,private communication. (21) D.L. Ball, W.E. Harris and H.W. Habgood, Journal of Gas Chromotography, 5, 613 (1967). (22) F. Bauman and F. Tao, Journal of Gas Chromatography, 5, 621 (1967). (23)G. Guiochon and J. Schudel, in preparation. (24) E. Grushka and G. Guiochon, Journal of Chromatographic Science, 10, 649 (1972).

35

CHAPTER 2

FUNDAMENTALS OF THE CHROMATOGRAPHIC PROCESS Flow of Gases through Chromatographic Columns TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Outlet Gas Velocity 11. Column Permeabilit Ill. Gas Viscosity . . . . 1V. Velocity Profile . . . Average Velocity and Gas Hold-up Time . . V. VI. On the Use of Very Long Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Case of Open Tubular Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Measurement of the Carrier Gas Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX. Determination of the Column Gas Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X. Case of a Non-ideal Carrier Gas XI. Flow Rate through Two Columns ................................... XU. Variation of Flow Rate du .......... XIII. Flow Rate Programming. ......................................... GlossaryofTerms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

44 45

47 48 48 49

51 52 53 54

INTRODUCTION The injection of a certain amount of a pure compound into a chromatographic column is followed, after a certain time, by the elution of a peak, band or zone. (These names are given to the concentration profile of the compound as eluted from the column and recorded by the chromatograph.) The injection of a mixture results in the elution of a number of bands, ideally one for each component of the sample. In linear chromatography, i.e. in practice, in analytical applications of gas chromatography, the set of peaks recorded is the sum of the peaks which would be obtained as a result of the successive injections of the pure components in amounts equal to what exists in the injected sample of the analyzed mixture. In most cases, the time of the peak maximum and some parameter characterizing the band width are of major interest, while the profile itself is not studied in detail. The retention time depends on two independent series of parameters: those accounting for the flow velocity profile along the column, and those describing the thermodynamics of equilibrium between the mobile and the stationary phase (cf. Chapter 3). In addition the band width of peaks corresponding to small amounts of solute depends on the kinetics of mass transfer of the sample molecules in the mobile and the stationary phases and between these two phases (cf. Chapter 4). The band width and the profile of the elution bands of large samples are also functions of the equilibrium thermodynamics (isotherms: cf. Chapter 5). These relationships are important to a discussion of a good understanding of the References on p. 54.

36

basic phenomena observed in chromatography. They are presented in this chapter, as well as in the three following ones, but without much detail on the physico-chemical background involved, since it is not the aim of this book to present a detailed discussion of the theory of gas chromatography. The migration of a solute zone through a chromatographic column is made under the influence of the gas flow, which at the same time plays a determining role in band broadening (cf. Chapter 4). On the average the molecules of all compounds spend the same amount of time in the mobile phase. During that time they move along the column at the same speed as the carrier gas. During the time they spend in the stationary phase they do not move at all; their velocity is zero. Accordingly, the gas hold-up, or retention time of an inert compound, is an important parameter to consider. It serves as a convenient unit for the measurement of retention times (cf. definition of k ' in Chapter 1 and next chapter). The carrier gas flow can be characterized by either the volume flow rate or the linear flow velocity. For a given velocity the flow rate will be greater the larger the column diameter. Since the flow velocity is the important parameter from the standpoint of the chromatographic process, this is the one which should be considered. For the sake of precision it should be measured directly, not derived from the flow rate measurement, since the determination of the exact column diameter is often difficult, if not impossible, especially in the case of capillary columns. The mobile phase flows across the column. Whether this column is packed or is an open tube, it offers some resistance to the gas flow. This resistance is overcome by delivering the mobile fluid to the column under pressure. But gases are compressible: accordingly there is a pressure and a velocity profile along the column: i.e. the local velocity is a function of the position along the column. Of special interest are the outlet velocity and the average velocity, which is related to the retention time. We shall discuss these parameters in turn, then indicate how they are related and how they can be measured. The distribution of the true local gas velocity is extremely complex in a packed column, where the channels open to the gas flow are constantly changing shape and dimensions (1). Furthermore there is a distinction to be made between the stagnant part of the mobile phase which resides inside the particles of porous support used to disperse the stationary liquid phase and the really mobile gas phase which flows around these particles. It can be shown that the velocity inside the pores of the particles is negligible, while the gas flow surrounding the particles, although laminar, makes a large number of stable eddies, located between these particles at the places where the cross section of the channels available to the gas phase changes abruptly (1).With open tubular columns the flow structure is somewhat simpler. To a first approximation the column cross-section is constant, the flow stream lines are parallel to the column wall and the local velocity in a column cross-section is given by a parabolic relationship, maximum at the column center, zero at the wall (2). However, capillary columns are always coiled and the resulting centrifugal force creates a secondary radial flow which, if important, can significantly alter the distribution of flow velocities.

31

I. OUTLET GAS VELOCITY The gas flow velocity through a packed column is laminar (1,3). At moderate values of the gas velocity, normally used in practical applications of gas chromatography, the local velocity is related to the column characteristics by the Darcy law:

where: u is the local velocity, or velocity at point x, k is the column permeability, independent of the nature of the fluid used (gas, super critical fluid, liquid), is the carrier gas viscosity, dp/dx is the local pressure gradient. The minus sign indicates that the gas flows in the direction opposite to the pressure gradient, i.e. from high to low pressures. Equation 1 can be integrated between the inlet and the outlet of the column, whch supplies the value of the outlet velocity. If we assume that the carrier gas is ideal, we have the classical equation: PU = P O U O

where u, is the outlet gas velocity, while p and po are the local and the outlet pressure, respectively. The situation of a non-ideal carrier gas has been discussed by Martire and Locke (4). It applies to CO, used as a carrier gas at inlet pressures larger than cu 5 atm. Elimination of u between equations 1 and 2 gives a differential equation, easy to integrate into:

kP0

u o = - ( P 2 - 1)

2vL

(3)

where P stands for the inlet to outlet pressure ratio ( P= pi/po). In practice the outlet pressure is kept constant, equal to the atmospheric pressure. Then the outlet velocity increases much faster than the inlet pressure. This is due to the decompression of the carrier gas. It should be noted in passing that the Darcy law is empirical in nature. When the flow velocity increases, the permeability does not remain constant. Because it takes an increasingly large amount of energy to feed the eddies which appear between particles, the inlet pressure of a packed bed must increase faster than is predicted by Darcy law. It is indeed observed that, at flow velocities whch are large compared to typical GC values, there is an increasing deviation from the prediction of equation 3 (1). References on p. 54.

38

II. COLUMN PERMEABILITY In practice, the velocity of the carrier gas in a column is chosen so that the band broadening phenomena are minimized, or some compromise between a large column efficiency and a short analysis time is achieved (cf. below, Chapter 4). The required inlet pressure can be derived from equation 3. It is seen that this pressure increases with decreasing column permeability. The permeability of a packed column depends on two factors which are almost impossible to adjust so as to maximize the permeability: the mean particle size and the packing density (5). It depends little on the nature of the particles used, although it has been reported that columns packed with glass beads have approximately double the permeability of columns packed with brick powder, Chromosorb or similar material of the same average particle size (1). We do not know to what extent this fact is due to the uncertainty in measuring the average particle size of irregularly shaped particles and to what extent it really is an effect of the particle irregularity and roughness. For packings made in an identical manner, the permeability is reproducible within better than cu 10%(6) and is approximately proportional to the square of the particle size. The relationship should be rigorous, but is not, due to the difficulties in reproducing the packing density. From one column to another fluctuations of f10%are typical for columns packed successively in an identical manner. The most homogeneous packing possible is desirable to obtain columns of maximum efficiency. In practice this will be the packing with the highest density, and hence the lowest permeability. Under such circumstances the permeability is given approximately by the equation:

As we shall see in Chapter 4, it is desirable to use small particles to achieve a large column efficiency. Unfortunately, this results in columns having rather a low permeability, and as we shall see in the following sections, the retention time becomes very long, due to the effect of the carrier gas compressibility. Thus, although gas chromatography has been carried out with columns packed with particles as small as 20-30 pm (7), it is not recommended in practice to use particle sizes smaller than cu 100 pm. On the other hand, for reasons of efficiency (cf. Chapter 4), it is not advisable for the particles to be larger than ca 250 pm. Finally, the particle size distribution should be rather narrow, preferably between two successive standard screen sizes. This guarantees a somewhat higher permeability, due to the elimination of the very fine dust, and an improved efficiency, because of the elimination of the large particles through which mass transfer by diffusion is sluggish.

39 TABLE 2.1 Viscosities of Various Gases at Atmospheric Pressure (micropoise *) Gas

Temperature ( C) 0

H2 He Ar N2

co2

84 186 212 166 138

20 88 196 222 176 ** 147

50

loo

150

200

300

400

94 208 242 188 162

103 229 271 208 185 128

113 250 ** 297** 229 205 147

121 270 321 246 229 166

139 307 367 279 ** 268 201

154 342 410 311 235

H 2 0 (vapor) The C.G.S. unit of viscosity is the poise. Values obtained by interpolation.

**

111. GAS VISCOSITY

The viscosities at various temperatures of most gases likely to be used as carrier gases in gas chromatography are given in Table 2.1 (1,2,8). The pressure drop required to achieve a certain flow rate across a column increases with increasing gas viscosity. There is no way to change or adjust the viscosity of a gas, however. Furthermore the viscosity or the column inlet pressure is rarely a major factor in the optimization of experimental conditions. It should be noted, however, that hydrogen should be preferred to helium, because the viscosity of the former is more than two times lower than that of the latter. Similarly, nitrogen should be preferred to argon. The selection of the most convenient carrier gas should be made while taking into account other properties, such as the kinetics of mass transfer by diffusion, the required purity (especially the oxygen concentration) and the cost. This is discussed at the end of Chapter 4. As can be seen from Table 2.1, the viscosity of gases increases slowly with the temperature, the opposite of what happens with liquids. As a first approximation, the viscosity increases as the power 5/6 of the absolute temperature (2). Over a very large temperature range, exceeding the one used in gas chromatography, a more complex relationship, involving an activation energy gives better results (2). Consequently, when an analysis is carried out in temperature programming, the carrier gas velocity decreases with increasing temperature if a pressure controller is used. In the more frequently used schemes, when a flow rate controller is incorporated in the carrier gas line, the inlet pressure increases with increasing temperature. In both cases the average gas velocity does not remain constant. The carrier gas viscosity remains practically independent of the pressure in the range typically used in gas chromatography. The variation is smaller than 1%when the pressure increases from 1 to 10 atmospheres.

References on p. 54.

IV. VELOCITY PROFILE Because the compressibility of gases is very important, the velocity varies considerably along the column. When the local pressure decreases, the gas expands, the volume flow rate increases and, since the viscosity does not change with the pressure, the pressure gradient increases. It is possible to derive the value of the local velocity by integrating the differential equation obtained by the elimination of u between equations 1 and 2 (9). If the integration is carried out between the local point (abscissa x, velocity u, pressure p) and the column outlet (abscissa L, velocity uo, pressure po), instead of between the inlet and outlet of the column, we obtain:

where P is the inlet to outlet pressure ratio. Elimination of p between equations 2 and 5 gives the velocity profile:

Figure 2.1 shows the velocity profile for different values of the inlet to outlet pressure ratio, between 1.5 and 100. The velocity increases rapidly toward the end of the column, especially when the pressure ratio becomes larger than a few units. Such 1-

0.90.8-

0.3 -

0

0.2

0.4

x/

0.6

0.8

1

Figure 2.1. Velocity ProfiIes of the Carrier Gas in a Chromatographic Column. See equation 6.

41

large values of the inlet pressures are required only when long, very efficient columns are needed and their effect on the retention times, as discussed below, markedly reduces the separation power which can be expected from gas chromatography columns.

V. AVERAGE VELOCITY AND GAS HOLD-UP TIME Because of the rather large variation of the gas velocity along the column the component band moves along the column at an average velocity which is smaller than the outlet gas velocity. The average velocity is, by definition, the ratio of the column length to the gas hold-up time, or retention time of an inert compound, which is not soluble in the stationary phase and is thus not retained by it:

To calculate this inert compound retention (or, better, transit) time, we integrate the definition of the local gas velocity:

after eliminating u between equations 2 and 8, and d x between equations 1 and 8 and replacing u, by its value given by equation 3. The result is a differential equation relating d t and dp, which can be integrated. The results obtained are the following. The inert compound retention time, often called, in early publications, the air retention time because air was used as a marker for the measurement of t , when a thermal conductivity detector was used (now more appropriately named the column gas hold-up), is given by: tm =

417L2( P3 -Po')

(9)

3k( P? -Po'), where 17 is the carrier gas viscosity and k the column permeability. Combination of equations 3, 7 and 9 gives: ii =j u , with:

3P2-1 J=-2~3--1 ,

(11) References on p. 54.

42

-

21 2019

- \ re 17 -

-

16 15 14 13 12 11 10

-

9-

e7 6 5 4

-

321 -

0

I

I

1.2

I

I

1.4

I

I

I

1.6

Inlet to outlet

1

1.a

,

2

2.2

pressure ratio

Figure 2.2. Plot of the Gas Hold-up Time versus the Inlet to Outlet Pressure Ratio. See equation 9. Ordinate: r, (sec).

j is the James and Martin pressure correction factor (9). It accounts for the effects of the compressibilityof the mobile phase. It is most useful for the correction of the retention parameters and elimination of the pressure dependence. A table of values of j for values of the inlet to outlet pressure ratio up to 7 is given in Chapter 9 (Table 9.5). Equation 10 shows that the average velocity increases roughly as the pressure drop, whereas the outlet gas velocity and the gas mass flow rate (proportional to the product pouo) increase much faster. In fact assuming that the average velocity is proportional to the pressure drop, as it is in liquid chromatography, introduces an error of 33%at the maximum, which unfortunately occurs in the low pressure range which is most often the one used in practical applications of gas chromatography. Figure 2.2 shows the variation of the gas hold-up time with the inlet to outlet pressure ratio. Figures 2.3a and 3b illustrate the variation of the pressure correction factor with the inlet to outlet pressure ratio. Figure 2.3a deals with the low pressure range, where the plot is not very different from a straight line, while Figure 2.3b deals with the high pressure range where the plot curvature is marked. The derivation of the equations 3, 5, 6 and 9 to 11 is based on Darcy law (equation l), as mentioned at the end of Section I1 above. This is, however, an approximate equation, of empirical origin. Its range of validity has been discussed by Guiochon (1).It appears to be valid only at very low flow velocities, especially with packed columns, but deviations are most often small in the velocity range in which chromatography is carried out, as illustrated by precise measurements (1).

43

0.6

! 1

I

I

I

1.2

I

I

1.4

1.6

Inlet to outlet

0.1

!

1

I

1.8

pressure r a t i o

I

I

3

,

I

5

Inlet t o outlet

7

9

pressure r a t i o

Figure 2.3. Plot of the Compressibility Correction Factor, j , versus the Inlet to Outlet Pressure Ratio. The values of j are tabulated in Chapter 9, Table 9.5. (a) Low Pressure Range. (b) High Pressure Range.

They are sufficient, however, to explain some minor discrepancies. The conclusions of Lauer et al. (7) regarding the efficiency of long columns packed with very small particles would not be valid if the deviations were large. References on p. 54.

44

VI. ON THE USE OF VERY LONG COLUMNS As we have shown in Chapter 1 and will discuss further in the next Chapter, the retention times of all compounds are proportional to the gas hold-up time. Thus it is important to consider equation 9 and its implications (10). To separate two compounds characterized by their column capacity factors with a certain degree of resolution one needs a certain column efficiency, N , given by equation 35, Chapter 1. This requires the use of a column of length L = N H , H being the height equivalent to a theoretical plate, itself a function of the column characteristics and the carrier gas velocity, as we discuss in Chapter 4 . The selection of optimum structural and operating parameters will be the conclusion of this discussion. Some special problems arise, however, when the separation of compounds with relative retention very close to unity is required. Very efficient, and hence very long, columns are needed. If the column is long and the inlet pressure required to operate it at a reasonable velocity is high (cf. Section 7 , Chapter 4), we can assume that po is neghgible compared to p i . Then equation 9 simplifies into: t”

=

4qL2 3k~i

At the same time, equation 3 simplifies to:

Now we can eliminate p i between equations 12 and 13 (whereas it is not possible to eliminate p i be.tween equations 3 and 9). We obtain:

If we assume that the plate height is constant for columns of different lengths, but otherwise identical, which is a very reasonable assumption, we can rewrite equation 35 of Chapter 1 as: L=NH=16HR2

1+k’

Combining equations 13, 14 and 15 gives a relationship between the analysis time for a difficult separation (which requires a long column, i.e. a large camer gas pressure drop) and the parameters of the separation and of the column:

45

This equation gives the gas hold-up time for the analysis. The retention time of the second compound of the pair is obtained by multiplying t , by (1 k’) (see Chapter 3). It shows that, because of the effect of the gas compressibility (10): - the time necessary to obtain a certain degree of resolution between two compounds under given conditions increases as the cubic power of this resolution. - the duration of the analysis under given conditions (and constant resolution) increases as the third power of a - 1. Very rapid analyses are possible only for compounds having relatively large relative retention (a larger than cu 1.10). - permeable columns permit faster analysis: for the same outlet velocity the pressure gradient is smaller and the average velocity larger. This explains why open tubular columns (OTCs) are so much faster than packed columns in GC. The analysis time is proportional to the square root of the column permeability, which is 30 to 40 times larger for an OTC than for a PC packed with particles having the same diameter as the OTC. - similarly, carrier gases with low viscosity permit markedly faster analysis. For this reason hydrogen should be preferred every time when it may be used. - highly efficient columns (small H values) permit faster analysis: a reduction of H by 10% for example, permits the use of a 10% shorter column, with a lower pressure drop and pressure gradient. The analysis time is ca 15% shorter. - there exists an optimum value for the column capacity factor of the compounds the most difficult to separate: when k’ is large, the retention time is prohibitively long. When it is too small the separation becomes difficult. Most frequently this optimum value lies around 3 for packed column, somewhat below 2 for open tubular columns (27). - consequently there exists both an optimum degree of impregnation and an optimum temperature (maximum a). In practice it is often difficult to calculate these optimum values of the parameters and equally difficult to use the numerical results of these calculations. These general results, nevertheless, most often permit one to find suitable experimental conditions. In most cases the optima of chromatographic conditions are rather soft and a reasonable departure from the optimum values of the parameters does not entail an excessive cost in terms of analysis time or resolution.

+

VII. CASE OF OPEN TUBULAR COLUMNS We have, in the previous sections, shown the advantages of having highly permeable columns in gas chromatography (10). This is still more important than it is in liquid chromatography, because the pressure gradient has a direct influence on the retention times in gas chromatography whereas it has no such effect in liquid chromatography. To achieve highly permeable columns while retaining excellent efficiency, one can use open tubular columns (11,12). The technological developments made during the last few years, including the use of thin quartz tubes with an outside plastic coating resistant to oxidation at temperatures up to 350°C and of stationary phase References on p. 54.

46

coatings partly bonded to the inner wall surface and partly reticulated, as well as the variety of the chemical natures of these phases, make them extremely suitable for most analytical applications (13,14). The columns are extremely easy to handle, install and store, since the silica tubes are extremely strong, almost like steel. The immobilized layers of stationary phase are very forgiving, direct injections of sample solutions can be camed out, and column flooding is not prejudicial to the useful column life. These practical advantages make this type of column a very likely candidate for most types of practical applications in routine analysis nowadays. The general advantages of these columns stem from their extremely large permeability (1,lO). The permeability of an open tubular column is given by:

k = dL2 32

where d , is the column inner diameter. The HETP of such a column is of the order of its diameter, while the HETP of a packed column is at least twice the diameter of the particles used to make it. Thus, to achieve the same plate height, a permeability about 120 times greater is obtained. This permits the use of much longer columns with, nevertheless, a much smaller pressure gradient, and thus markedly larger values of j. It has been shown that, in order to achieve the same efficiency with a capillary column, one needs an analysis time about 12 times shorter than with a packed column (15). Furthermore, it is much easier to prepare very long columns and to achieve extremely high efficiencies when needed, if one uses open tubular columns. Finally, extremely rapid analyses can be achieved using narrow bore open tubes with thin films of stationary phase (16). The amount of sample one can inject into an open tubular column is much smaller than in a conventional packed column. In fact it is difficult to measure and handle the tiny volumes of liquid samples which are required. This drawback has been the major roadblock preventing the general use of these columns in routine quantitative analysis. New techniques have recently been developed for the solution of this problem and, as we said above, the use of immobilized layers of stationary phases permits the direct injection of a relatively large amount of dilute sample with no adverse short term (on the column efficiency) or long term (on the column life) effects. The band widths are usually very small and accordingly the detection limit is often comparable on both types of columns. All the results discussed in this section are applicable to capillary columns, with the only adjustments being required by their very large permeability. Thus it is only very long columns (several tens of meters) which exhibit significant pressure gradients, low values of the compressibility factor, j, and an average velocity inversely proportional to the pressure drop. If open tubular columns are tightly coiled their permeability decreases and becomes a function of the gas velocity. The rapid movement of the gas stream in a

41

coiled tube generates a secondary, radial flow under the influence of the inertia of the gas and the centrifugal force. This also generates a radial mixing whose use has sometimes been advocated for the preparation of columns exhibiting shorter HETP. Although it has been demonstrated that the peak obtained for a non-retained compound is markedly sharper with a strongly coiled column than with a loosely coiled one (17,18), the effect on retained compounds is much less significant and it does not seem that there is any possibility to further improve the efficiency of capillary columns in this regard (17).

VIII. MEASUREMENT OF THE CARRIER GAS VELOCITY Pressures and times are measured with a much better precision and accuracy than gas volumes and flow rates. Thus it is easier and more accurate to determine the average flow velocity of the mobile phase than its volume flow rate. The latter is measured using the soap bubble flow meter. A correction should be applied for the vapor pressure of water, but it is not very accurate unless one makes sure that the gas is really saturated with water vapor during its transit through the flow meter. The average velocity is determined from the retention time of an unretained compound. This raises the difficult question of the choice of the tracer to be used. Air gives satisfactory results with the TCD and the ECD but is not detected by the FID, the flame photometric detector nor the thermionic detector. Methane gives acceptable results in most cases with the FID, especially at high temperatures. It is somewhat retained on most liquid phases at moderate temperatures, giving values of the column capacity factor which rarely exceed 0.1. The average velocity is derived from t , using equation 7 and the outlet velocity is given by solving equation 10. This requires the measurement of the inlet pressure (the outlet pressure is most often atmospheric). Accurate measurements require the use of a barometer for the measurement of the atmospheric pressure and of a precision manometer connected to the carrier gas line as close as possible to the column inlet. There is a significant pressure drop between the pressure gauge of many instruments and the column inlet (and sometimes also between the column outlet and the atmosphere). When using equation 7 it must be remembered that the column length is not easy to measure, especially for a coiled capillary column, and is not always exactly what the manufacturer claims. Finally, we want to stress the following point, which we consider to be most important. The reading of instrument gauges (e.g. pressure, temperature) should never be trusted implicitly, whether they are analog devices or digital read outs. This is especially true of ball flowmeters which should rather be considered as indicators or two-bit read outs ( 0 = no flow, 1 =small flow rate, 2 =moderate flow rate, 3 =large flow rate). Whenever the exact value of a parameter is required, an independent sensor, of known accuracy, should be positioned properly and used for the measurements. At the very least the instrument gauges should be calibrated. References on p. 54.

48

M.DETERMINATION OF THE COLUMN GAS VOLUME For the application of a certain number of equations, the column gas volume or gas hold-up must be known (1,6,12,19). This is not equal to the retention volume of the inert peak as calculated from the product of the retention time of a non-retained compound by the volume flow rate. There is often a significant volume contribution of the sampling system, the detector and the connecting tubes between these two units and the column. If the column gas volume must be measured with accuracy, these volume contributions must also be measured. The best way is to use a zero-volume column, i.e. the shortest, finest tube available (20,21). The dead space, or correction looked for is the limit for a zero pressure drop of the inert compound retention volume on this column. When the correction determined this way is not really small, further corrections must be applied to take account of the contribution of the gas decompression on the various contributions to the equipment volume: the carrier gas velocity is not the same in the sampling system and in the detector.

X. CASE OF A NON-IDEAL CARRIER GAS

It has been shown that, except for carbon dioxide, the deviation from the ideal gas law (equation 2) is small and can be neglected in the pressure range over which gas chromatography is usually carried out, i.e. below 5 atm (4). At such larger pressures as have been studied, for example in the 20-50 atm range which must be used to operate columns packed with 20 pm- particles or capillary columns with 20 to 40 pm i.d., the deviations from ideal behavior may become more significant, but no serious problem has been reported by the few authors who have investigated these columns. It can safely be anticipated that, when the inlet pressure becomes large, the retention volumes corrected by the use of equation 8 in Chapter 1 will begin to vary with increasing flow rate, since the pressure correction factor, j , has been derived on the assumption that the mobile phase is an ideal gas. Since most gases are more compressible than is predicted by the ideal gas law in the conditions used in gas chromatography, the retention volumes will increase with increasing average column pressure. This effect is, however, largely offset by another one, also related to the non-ideal behavior of real gases. The fact that most carrier gases exhibit an ideal behavior as far as their mechanical properties are concerned does not mean that they also follow the same pattern for their mixing properties. Far from it; there are significant interactions between the solute vapors and the gas molecules, resulting in a variation of the partition coefficient with the average pressure of the gas in the column, as well as a change in the relative retention of some compounds which may be large enough in

49 1.32 -

-

1.3

1.28 1.26

-

1.24 1.22

-

1.2 1.18 -

1

3

5

Inlet t o outlet pressure r a t i o Figure 2.4. Influence of the Mobile Phase Compressibility on the Retention. Comparison between the

retention times of an inert compound in gas and liquid chromatography,assuming that the experimental conditions are such that the ratios of the column permeability to the mobile phase viscosity are the same for the two columns. Ordinate: ratio of t, on a GC column to I,,, in LC with the same column.

some cases, when very efficient columns are used, to result in an inversion of the elution order. This is discussed further in the next chapter.

XI. FLOW RATE THROUGH TWO COLUMNS IN SERIES It is not uncommon to connect two columns in series, either because it is too difficult to make a column of sufficient length and efficiency in one piece, or because two columns of different polarities are needed to achieve the desired separation. If the two columns have the same inner diameter and are at the same temperature, it is rather easy to determine the relationship between the inlet pressure and the outlet flow rate and to calculate the intermediate pressure at the junction point between the two columns (1).It is also easy to calculate the gas hold up time of the two column series and the apparent column capacity factor of the series, knowing the capacity factors of the two columns (Chapter 1, Section VIII, equation 11 and Chapter 3). If the two columns have a different diameter or if their temperatures are different (hence the gas viscosity is different in the two columns), the calculation is also possible, but becomes extremely tedious and the result is a very complex expression. A computer is best used in this case. The two columns cannot be very different, however, otherwise the flow rate, which is the same in both columns, could not be adjusted to a value permitting good performance of both columns. References on p. 54.

50

Considering that the flow velocity at the junction between two columns is the outlet velocity of the first column and also the inlet velocity of the second one (cf. equation 3 above) gives us a relationship between the inlet, the intermediate, and the outlet pressure of the column series from which the intermediate pressure can be derived (1,22):

In the case when the inlet pressure is rather large (i.e. larger than ca 3 to 4 atm) and the two columns have a comparable length, the contribution of the second column in the numerator of the RHS of equation 18 can be neglected. Knowing the intermediate pressure (inlet pressure to column 2, outlet pressure of column 1) it is easy to derive the average velocities of the two columns (equations 10 and 11) and the gas hold up time of each. The gas hold up time of the series is then:

t,=-

i

4q L 2 P 3 - P i 3k ' ( P 2 - P : )

2

+=: ( Ppa: -Po'), 3

3

1

The apparent capacity factor, k i p , , of a column series is defined by analogy to the capacity factor of a single column as: t,

= (1

+ kipp)frn

and it can be calculated by writing that the retention time is also the sum of the retention times on each of the columns of the series (22). 1t.becomes:

From equation 21 it is easy to derive an expression for the relative retention of two compounds on the column series which accounts for the variation of the relative retention with the flow rate (i.e. the intermediate pressure). This permits fine tuning of the separation between some pairs of compounds. When the two columns have different inner diameters and/or are operated at different temperatures, it is not possible to eliminate the pneumatic resistance of the columns in writing equation 21 and the results become much more complex, although the results are qualitatively the same: the relative retention times do depend on the mobile phase flow rate (because of the gas compressibility) and this effect may be used in some range to fine tune a separation.

51

MI. VARIATION OF FLOW RATE DURING TEMPERATURE PROGRAMMING During temperature programming the gas phase viscosity increases. Accordingly the flow rate is changing. We should note first that the flow rate is usually measured at room temperature, and the actual flow rate through the column is equal to the product of the measured flow rate by the ratio of the column absolute temperature to the room absolute temperature. If a pressure controller is used, the inlet pressure is kept constant. Accordingly, equation 3 shows that the outlet carrier gas velocity varies as the inverse of the viscosity, i.e. practically as the power -5/6 of the absolute temperature. Thus the measured flow rate decreases as the power -11/6 of the absolute temperature, which is large enough to be readily observed (1). The negative consequence is that, under these conditions, the column efficiency varies markedly with increasing temperature. This is due to the fact that the diffusion coefficient increases with the power 1.75 of the absolute temperature (see Chapter 4, Section 11). Thus, under constant inlet pressure the reduced-velocity (see Chapter 4, Section IX) decreases rapidly. We have:

where E is a proportionality coefficient which does not depend on the temperature. Equation 22 shows that the reduced velocity decreases as the power 2.5 of the absolute temperature, which is very important: for a column temperature increase from 80 O C (353 K) to 192' C (523 K), the reduced velocity decreases by a factor 2; for a temperature increase from 80°C to 275OC (548 K) it decreases by a factor 3. The consequence may be a large variation in the column efficiency. As a consequence, the initial flow rate should be large enough and the initial reduced velocity well above the optimum value of 3 to 5 , to avoid running the column at a reduced velocity below the value corresponding to the minimum plate height, when analysis time is long and overall column performances are poor. The situation is different when a mass flow rate controller is used. The mass flow rate controller is operated at constant temperature, usually room temperature (1). The inlet pressure will rise during temperature programming to compensate for the increase in apparent column pneumatic resistance (due to the increase in gas viscosity). The column outlet flow rate measured at room temperature will remain constant, reflecting the constant mass flow rate of gas flowing through the column. The actual gas velocity in the column increases in proportion to the column temperature. Now the reduced velocity decreases only as the power 0.75 of the column absolute temperature, which is a much weaker dependence. For the two temperature rises considered above (80 to 192" C and 80 to 275 O C), the reduced velocity decreases by a factor 1.23 and 1.40, respectively, which is much more easy to handle experimentally. References on p. 54.

52

This discussion explains why the use of flow rate controllers has become very popular in gas chromatography. They certainly afford better column performance in temperature programmed GC (see Chapter 9, Section 11). XIII. FLOW RATE PROGRAMMING Flow rate programming is of limited importance in chromatography because the use of extremely large inlet pressures would be required to achieve an attractive reduction in the analysis time of strongly retained compounds. But because the column efficiency drops rapidly at large flow velocities the column performance degrades rapidly. On the other hand, temperature programming in GC, gradient elution (mobile phase composition programming) in LC or pressure (or, better, density) programming in SFC provide the ability to reduce considerably the retention time of very strongly retained compounds without markedly modifying the column performance. Thus we shall not discuss the relationship between retention times and flow rate programming in great detail. Zlatkis et al. (23) have assumed that the retention time can be calculated by integration of the equation:

where the average velocity at each time is related to the instantaneous pressure by:

49 pi-Po= -Lu 3k This is a very approximate solution, however, because it assumes hydrodynamic steady state at each point in time (1).Unfortunately, it takes a time roughly equal to half the gas hold-up time for a pressure perturbation arising at the column inlet to result in a flow perturbation at the column outlet (24,25). This pseudo-time constant is large and explains the origin of major discrepancies between experimental data and values calculated by this method. Costa Net0 et al. (26) have observed that the corrected retention time is given by:

Accordingly they write:

Integration of equation 26 does not give the exact solution, however, because j varies with the inlet pressure at the same time as the outlet velocity (1).

53

A complete theory of programmed flow chromatography has still to be written (25). There is not much incentive to do so, however, as explained above. The problem is really complex, and the solution can be obtained only through the numerical integration of the proper mass balance equation for the carrier gas.

GLOSSARY OF TERMS Diffusion coefficient of the analyte in the mobile phase. Equation 22. Inner diameter of an open tubular column. Equation 17. Differential increase of the local pressure. Equation 1. Average particle diameter. Equation 4. Differential increase of the column abscissa. Equation 1. Proportionality coefficient in Equation 22. Carrier gas volume flow rate. Equation 25. Height equivalent to a theoretical plate. Equation 15. Correction factor for gas compressibility. Equation 10. Partition coefficient of a compound between the two phases contained in the column. Equation 25. Column permeability. Equation 1. Column capacity factor. Equation 15. Apparent column capacity factor when two columns are used in series. Equation 20. Column length. Equation 3. Lengths of two columns operated in series. Equation 18. Plate number. Equation 15. Inlet to outlet pressure ratio. Equation 3. Local pressure. Equation 1. Intermediate pressure, when two columns are used in series. Equation 18. Inlet pressure. Equation 9. Outlet pressure. Equation 2. Resolution between the peaks of two compounds. Equation 15. Frontal ratio. Equation 23. Gas hold-up time, or retention time of an inert compound. Equation 7. Corrected retention time. Equation 25. Retention time. Equation 20. Carrier gas velocity. Equation 1. Average carrier gas velocity. Equation 7. Outlet carrier gas velocity. Equation 2. Inlet carrier gas velocity. Volume of liquid phase contained in the column. Equation 25. Abscissa along the column. Equation 1. Relative retention of two compounds. Equation 15. Carrier gas viscosity. Equation 1. Reduced carrier gas velocity. Equation 22. References on p. 54.

54

LITERATURE CITED (1) G. Guiochon, Chromutogr. Reu., 8, M. Lederer Ed., Elsevier, Amsterdam, 1967,pp. 1-47. (2) E.A. Moelwynn-Hughes, Physical Chemistry, Pergamon, London, 1961. (3) N. Sellier and G. Guiochon, J. Chromatogr. Sci., 8, 147 (1970). (4) D.E. Martire and D.C. Locke, Anal. Chem.. 37, 144 (1965). (5) R.B. Bud, W.E. Stewart and E.N. Lightfoot, Transport Phenomena, Wiley, New York, 1962. (6) C. Landault and G. Guiochon, in Gas Chromatography 1964, A. Goldup Ed., The Institute of Petroleum, London, 1965,pp. 121-137. (7) H.H. Lauer, H. Poppe and J.F.K. Huber, J. Chromutogr., 132, 1 (1977). ( 8 ) Handbuch des Chemikers, VEB Verlag Technik, Berlin, 1956. (9) A.T. James and A.J.P. Martin, Biochem. J., 50, 679 (1952). (10) G. Guiochon, Anal. Chem., 38, 1020 (1966). (11) M.J.E. Golay, in Gas Chromatography 1958, D.H. Desty Ed., Buttenvorths, London, 1958,p. 36. (12) L. S. Ettre, Open Tubular Columns in Gus Chromatography, Plenum Press, New York, 1965. (13) R. Dandeneau. P. Bente, P. Rooney and R. Hiskes, Inr. Lab., November/December (1979) 69. (14) S.R. Lipsky and W.J. McMurray, J. Chromutogr., 279, 59 (1983). (15) G. Guiochon, in Advances in Chromatography,J.C. Giddings and R.A. Keller Ed., M. Dekker, New York, 1969,p. 179. (16) J. Gaspar, C. Vidal-Madjar and G. Guiochon, Chromatographia, 15, 125 (1982). (17) R. Tijssen, Chromatographiu, 3, 525 (1970); 5, 286 (1972). (18) F. Doue, J. Merle d’Aubigne and G. Guiochon, Chim. Anal., 53, 363 (1971). (19) P. Chovin, Informal Symposium of the Gas Chromatography Discussion Group, Liverpool, October 1960. (20) M. Goedert and G. Guiochon, Anal. Chem., 45,1188 (1973). (21) T.H. Glenn and S.P. Cram, J. Chromatogr. Sci., 8, 46 (1970). (22) J. Krupcik, J.M. Schmitter and G. Guiochon, J. Chromatogr., 213, 491 (1981). (23) A. Zlatkis, D.C. Fenimore, L.S. Ettre and J.E. Purcell, J. Gas Chromarogr., 3, 75 (1965). (24) L. Jacob and G. Guiochon, Nature, 213, 491 (1967). (25) L. Jacob, M. Bolon and G. Guiochon, Separ. Sci., 5, 699 (1970). (26) C. Costa Neto, J.T.Koffer and J.W. De Alencar, Anais Acad. Brasil. Cienc., 36, 115 (1964); J. . Chromatogr., 15,301 (1964). (27) E. Grushka and G. Guiochon, J. Chromatogr. Sci., 10, 649 (1972).

55 55

CHAPTER 33 CHAPTER

FUNDAMENTALSOF OF THE THE CHROMATOGRAPHIC CHROMATOGRAPHICPROCESS PROCESS FUNDAMENTALS The Thermodynamics Thermodynamicsof of Retention Retention in in G GaassChromatography Chromatography The TABLEOF OF CONTENTS CONTENTS TABLE Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............... .. . . . . . . . . . . . A. The Thermodynamics of Retention in Gas-Liqui phy . . . . . . ................. A.1 ElutionRate Rate .................................................... . . . . . . . ....... A.I Elution A.11 Capacity Ratio of the Column . . . . . . . . . . . . . . . . . . . . ...... A.II Capacity Ratio of the Column A.III Partition Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . ............ A.IV The Practical Importance of the Activity Coefficient . . . . A.V Specific Retention Volume ............................... A.VI Influence of the Temperature . . . . ........ ........... A.VII Relativ Relative Retention . . . . . . . . . . . . A.VII ........................................................ A.VIII Influen . . . . . . . . . . . . . ..... . . . . . ........... . . . . A.IX Mixed A.X Mixed . . . . . . . . . . . . . . ....... .. . . . . . A.XI Adsorption on Monolayers and Thin Layers of Stationary Phases . . . . . . . . . . . . . . . . . The TheThermodynamics Thermodynamicsofof Retention in Gas-Solid Chromatography . . . . . . . . . . . . . . . . . The . ... .. . . . . . . .. ....... . . . . . . . . . . . . . . . . . . . . TheHenry HenryConstant Constantand and Retention RetentionData Data. SurfaceProperties PropertiesofofAdsorbents Adsorbentsand andChromatography Chromatography....... . . . . . . . . . ........ . . . . . . . . Surface 1. Nature Natureofof the theMolecular Molecu Interactions Involved . . . . . . . . . . . . . . . . . . . . . 1. 2.2. Kinetics .............. ........... KineticsofofAdsorption-Desorption Adsorptio Homogeneityofof the theAdsorbent AdsorbentSurface Surface .... . . . . . . . . . . . . . . . ... .. . . . . . ......... .. . . . . 3.3. Homogeneity B.111 Influence Influenceofof the theTemperature Temperature . . . ...... .. .. . . . . . ............. .. .. .. .. .. .. .. . . . . . . . . . . . . . . . . . B.III B.IV Gas GasPhase PhaseNon-Ideality Non-Ideality ..... . . . . . . ......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. .. .. ..... B.IV B.V Adsorption Adsorptionofof the theCarrier CarrierGa Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. ................... .. . B.V B.VI The ThePractical PracticalUses UsesofofGSC GSC .. . . . .... . . . . . . ................................. .. .. . . . . . . . . . . . . . . . B.VI B. B. B.1 B.1 B.11 B.II

Application Application totoProgrammed ProgrammedTemperature TemperatureGas GasChromatography Chromatography . . . .............................. ThePrediction Predictionof of the theElution ElutionTemperature Temperature ........ .. . . . . . .. ........... . . . . . . . . . . . . . . . . . . The 1. Numerical NumericalSolution Solution .......... .. . . . . . . . . . . .... . . . . . . . ........................ 1. .................. . . . . . . . . . . . . . .... . . . . . . 2.2.Approximate ApproximateSolution Solutionand andthe theEq Equivalent Te ReducedTemperatu Temperature Scal ................. ........ 3.3. Reduced RetentionIndices Indices .... . . . ...... . . . . . . . . . . . . . . . . . . . . . 4.4. Retention C.11 Optimization Optimization ofof Experi Experimental . . . . . . . . . ............................ . . . . . . . . C.II Selectionofof the theStarting StartingTemperature Temperature ...................... . . . . . . . . ............. .. .. .. .. .. .. .. .. . 1.1. Selection Selectionofof the theProgram Program Rate Rate ...... . . . . . . . . . . . . . . ................................ . . . . . . . 2.2.Selection Glossary of Terms . . . ....................... . . . . . . . . . .. .. .. . . . . . . . . LiteratureCited Cited . . . . . . . . . . . . . . ..... .. .. .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature C. C. C.1 C.I

55 55 56 56 57

51 60 61 63 65 65 66 66 73 73

75 77

77 78 79 80 80

80 81 81 82 82 82 83 83 84 84 85 85 86 86 86 86 86 86 87 87 87 87 81 87 88 88 90 90

INTRODUCTION INTRODUCTION Chromatographyseparates separatessubstances substancesafter after the the differences differencesbetween between their their migramigraChromatography tion velocities velocitiesalong alongthe thecolumn. column.In In relative relativeterms, terms,these thesedifferences differencescharacterize characterize the the tion extent ofof separation separation afforded affordedby by the the column. column.They They depend depend entirely entirely on on the the interacinteracextent References on onp.p. 90. 90. References

56

tion-free energies of the compounds involved with the stationary phase. The gas flow velocity contributes only to the control of the absolute values of the migration velocities of the various components of a sample, i.e., the analysis time. Strictly speaking, since chromatography is a dynamic process, the phenomena that matter are the rates of adsorption and desorption (in gas-solid chromatography) and the rates of dissolution and vaporization (in gas-liquid chromatography). These rates depend on a large number of factors which are unknown or poorly understood (see Chapter 4). We know, however, that under the conditions where chromatographic separations are normally carried out, the kinetics of exchange of the molecules of analytes between mobile and stationary phases are very fast. Indeed, the column efficiency is related to the kinetics of phase exchange. If the kinetics were infinitely fast, the column efficiency would be infinite and the two phases constantly in equilibrium. This assumption leads to the model of ideal chromatography. The efficiency of actual columns is finite (see Chapter 4), but it is large. The deviation from equilibrium at the center of the peak or zone is usually very small. We assume in analytical chromatography that the kinetics of mass transfer between phases is fast and that equilibrium is essentially complete at all times at the center of the band. Furthermore, we assume that the concentrations of the analytes are small and that Henry’s law is valid in the entire concentration range involved in each band profile, i.e., that the equilibrium isotherm is linear. Deviations from this assumption are discussed in Chapter 5. In the present chapter we discuss the relationships between the retention times and volumes and the thermodynamic characteristics of the equilibrium of the analytes between the two phases. Gas-liquid and gas-solid equilibria are discussed in. the first two sections. In a third section we deal with the problems arising from programming the column temperature and changing continuously the Henry constant during the analysis. Throughout the chapter the discussion has been kept simple, with the needs of the analyst in mind. Those interested by more complete theoretical developments and by physicochemical applications of chromatography should consult the relevant literature (1, 2).

A. THE THERMODYNAMICS OF RETENTION IN GAS-LIQUID CHROMATOGRAPHY The retention parameters can be related simply to the thermodynamic partition coefficient between the gas and the liquid phase, provided the gas is assumed to exhibit an ideal behavior. If this assumption is not valid the calculation is much more complicated, since the molecular interaction is a function of the pressure, which varies all along the column and the effects of which must be integrated. In the vast majority of cases, however, the contribution of the gas phase non-ideal behavior to the retention volume is small and when the measurements carried out are not very accurate it can be neglected.

57

Thus we shall first describe the phenomena which control the retention in GC with the assumption that the mobile phase has an ideal behavior. We shall then discuss in a separate section (Section A.VII) how the results obtained are modified when this assumption is no longer valid.

A.1 ELUTION RATE If a very small sample of a pure compound is introduced in a chromatographic column, we observe that its molecules migrate as a band whose velocity is equal to Ru (cf Chapter 1, Section VIII), where R is independent of the flow velocity and of the sample size; R is a function of the temperature and of the nature of the chromatographic system. Since the gas moves at a velocity u, when a molecule of the sample is in the gas phase it also moves at the same velocity u, while it moves at a velocity equal to 0 when it is dissolved or sorbed in the stationary phase. We may thus assume that, at equilibrium between the gas phase and the solution, a fraction R of the molecules is in the gas phase, while the fraction (1- R ) is in the stationary phase. Since equilibrium is a dynamic process this also means that, on the average, a molecule spends a fraction R of its time in the gas phase and a fraction (1 - R ) of its time in the stationary phase. Therefore, the mean velocity of the molecules is Ru. Of course all the molecules do not move at the same velocity; some are faster than others. The band profile is the statistical distribution of the residence times of these molecules. As a first approximation this profile is Gaussian. In fact, in most cases, the band profile is more complex. In a separate Chapter (Chapter 4) we discuss the phenomena which may account for a skewed distribution profile.

A.11 CAPACITY RATIO OF THE COLUMN In this section we discuss the simple case when the retention is due entirely and only to dissolution of the compounds under observation in the stationary liquid phase. In complex cases, retention may be also due to other phenomena, for example, to adsorption on the solid support, at the liquid-gas interface, or to the formation of complexes with some additive dissolved in the liquid phase, just for that purpose (cf Sections A.VIII and A.IX). Most of the original work on the derivation of a relationship between the retention volumes and the equilibrium constant between the mobile and the stationary phase has been performed by Consden, Martin and James (3-5). The theory was further expounded for gas chromatography and its predictions compared with experimental results by Littlewood et al. (6), Keulemans et al. (7), Porter et al. (8), Pierotti et al. (9) and Kwantes and Rijnders (10). The capacity ratio has been defined in Chapter 1 (equation 11). It is equal to the ratio between the fractions of molecules which are at equilibrium in the stationary and in the gas phases (3-5). Thus it is also equal to the ratio of the numbers of References on p. 90.

58

moles of the compound which are at equilibrium in each phase: k ' = -1=- -R R

nL nG

Assuming that the solute is at infinite dilution in the liquid phase, we may write: nL=Xn,

where X is the mole fraction of solute dissolved in the liquid phase, n L and n, are the number of moles of the solute and the solvent (stationary liquid phase) in the column. The number of moles of the solvent is: PVL

ns=

M

(3)

where p is the solvent density, M its molecular weight and VL is the volume of liquid phase present in the column. The number of moles of the compounds in the gas phase at equilibrium is given by:

where V, is the volume available to the gas phase. Combining equations 1-4 we obtain (10):

Raoult's law gives a relationship between the mole fraction of any compound in solution and its partial pressure in the gas phase at equilibrium: p

= Xy*PO

(6)

where ym is the activity coefficient at infinite dilution and Po the vapor pressure. By combining equations 5 and 6 we finally obtain:

In equation 7 there are two groups of terms. The first one depends only on the liquid phase and the solute, while the second one is a characteristic of the column used for the analysis. The ratio VL/VG is called the phase ratio (cf Chapter 1, Section XII). It is directly related to the amount of liquid phase contained in the column, the coating ratio of the support. This ratio can be adjusted over a range of about 2 orders of magnitude with packed columns and about 1 order of magnitude with open tubular columns.

59

The major importance of chromatography as a method of studying physico-chemical problems was pointed out long ago by A.J.P. Martin (11). The validity of equation 7 has been extensively tested over the last twenty five years. Several reviews have been published on this topic, notably the one by Martire and Pollara (12), as well as numerous papers comparing the results of theoretical predictions and experimental determinations (6-10 and 12-15). It should be noted that equation 6 is the mole fraction based Henry’s law, expressing the fact that the partial pressure of the solute in the gas phase is proportional to its concentration (here, its mole fraction) in the solution at equilibrium. A similar law is found for gas-solid equilibria, expressing the fact that the amount of compound adsorbed is proportional to the partial pressure of the adsorbate (see section B.1 and equation 39). Finally, the practical consequences of equation 7 are considerable. It shows that on a given column (VL, VG,p, M are given), the retention of a compound depends on both its vapor pressure (the largest contribution) and its activity coefficient in solution in the stationary phase. When similar columns are prepared (the values of VL, V,, p are similar), and operated at the same temperature (same vapor pressure for the solutes), the retention data (e.g., k’) and the relative retention (a)depend on the activity coefficients,or on their ratio. Accordingly, gas chromatography is a very flexible method. A change in the stationary phase may, in favorable cases, change the elution order. More often, it will permit a readier achievement of separation. Ths phenomenon is illustrated in Figure 3.1, showing a change in the elution order of three very different organic compounds.

@

@

2

2

1

i

1

Apiezon

M

p, p’- Oxydipropionitrile

Figure 3.1. Influence of the nature of the stationary phase on the resolution of a simple mixture. 1 : Vinylidene chloride. 2: 2-Methylpentane. 3: Cyclohexane. A: Apolar stationary phase. Apiezon M on Chromosorb. B: Polar stationary phase. /3,/3’-Oxydipropionitdeon Chromosorb.

References on p. 90.

60

A.111 PARTITION COEFFICIENT The partition coefficient, K, is the equilibrium constant corresponding to the partition equilibrium of the solute vapor between the liquid and the gas phase: A (vapor) + A(in solution)

(8)

Accordingly, the partition coefficient is related to the column capacity factor (cf equations 11-13, Chapter 1 and equation 1 above), by the relation: VG K = kr VL

Combining equations 7 and 10 gives:

The partition coefficient, K, is a thermodynamic equilibrium constant. It is thus independent of all experimental conditions except the column temperature.

A.IV THE PRACTICAL IMPORTANCE OF THE ACTIVITY COEFFICIENT

The retention time is a linear function of the column capacity factor, k r (see Chapter 1, equation 11, which can be rewritten as: t R = t,(l + k’), with t,,, = L/U, equation 2). Combination with equation 11 above gives: (11 bis)

Therefore the retention time increases linearly with increasing amount of liquid phase contained in the column, increasing inverse of the vapor pressure at the column temperature and increasing inverse of the activity coefficient. The activity coefficient depends on both the solute and the solvent used. Considerable efforts have been spent trying to find out methods for its calculation from solute and solvent characteristics, with no simple solution having been found. If ym = 1 the chromatographic process is similar to fractional distillation, and the elution order is by decreasing vapor pressure and, in most cases, increasing boiling point.

61

If ym is different from unity, the chromatographic process is more similar to extractive distillation, and the elution order is influenced by the value of the activity coefficient. Figure 3.1 illustrates these effects. It shows the analysis of a mixture of vinylidene chloride, a polar vapor, with a boiling point of 37.5OC and of 2-methylpentane (b.p. = 60 O C) and cyclohexane (b.p. = 8 1 O C), two hydrocarbons. On Apiezon M, a non-polar stationary phase, the activity coefficients are controlled essentially by the molecular size, and the elution order is that of increasing boiling point. On 3,3’-oxydipropionitrile,a strongly polar phase, vinylidene chloride is strongly retained by polar interaction and elutes last. A close look at systematic experimental results shows that, even on phases considered to be non-polar, the retention time is not closely related to the vapor pressure. The activity coefficient is almost never equal to unity, but depends on the molecular size and shape. Furthermore, mixed mechanisms are not exceptional (see Section A.X).

A.V SPECIFIC RETENTION VOLUME Using the definition of the column capacity factor (equation 11 in Chapter l), combined with the definitions of the net retention and the specific retention volumes (equations 9 and 10 in Chapter 1, respectively) we can derive the following expression for the specific retention volume:

v=--K 273 P T ,

since the geometrical volume available to the gas phase is given by:

(cf equation 10 in Chapter 1). Combining equations 11 and 12 gives: 213R v,= ymP%

If VG is measured in mL, P o in Torr (mm Hg) and T in K, the units of R are mL (Torr)/(mole K), and its value is 62,370. If P o is measured in atm, the value of R is 82.07. The product ym Po in equation 14 is the mole-fraction-based Henry’s law constant. Thus, the specific retention volume appears as a parameter of direct thermodynamic significance. It is inversely proportional to the activity coefficient of the solute at infinite dilution in the stationary phase and to the solute vapor pressure, References on p. 90.

62

i.e. to the (mole-fraction-based) Henry’s law constant. Provided that the solute vapor pressure is known, the activity coefficient can be derived simply from a measurement of the retention volumes. Equation 14 has been verified by several authors, including Martire and Pollara (12) and is further discussed by Conder and Young (1). This is one of the simplest and most general methods of measurement of activity coefficients at infinite dilution in low vapor pressure solvents. In order for the determination of the specific retention volumes to be significant (cf equation 7 in Chapter l), the mass of stationary liquid in the column must be known accurately, and must be held constant during the entire series of measurements. Accordingly, the stationary phase used for these measurements must have a very low vapor pressure and a very small rate of decomposition, so that the losses of solvent are negligible. Clearly, only solvents which are chemically well-defined, i.e. pure compounds, not polymers, can be used for these measurements. Besides the obvious difficulties in defining the value of the activity coefficient of a solute in a polymer solution, it will often be difficult to find the proper value of M to introduce into equation 14, the number-average molecular weight of the stationary phase, which may vary greatly from one sample to another, even for products of identical origin. Although the molecular weight of the solvent (stationary liquid phase) appears in the denominator of the right-hand side (RHS) of equation 14, it should not be concluded that the use of high molecular weight solvents, or of polymers, is going to result in very low values of the specific retention volume, which could be of some interest in the analysis of high boiling compounds. When the retention volumes of compounds are measured on polymeric stationary phases derived from the same monomeric unit, but differing in their degree of polymerization, it is observed that, except perhaps for the first oligomers, the specific retention volume does not vary much and certainly remains finite. This is consistent with the finding of molecular thermodynamics that, for pure polymers, the product of the molecular weight and the activity coefficient at infinite dilution should be constant (16). The small residual fluctuations observed can largely be explained by variations in the distribution of molecular weights of the products used for the measurements. The awkwardness of utilizing an activity coefficient which approaches zero when the molecular weight becomes large has been pointed out by Kovats (26) and Martire (67) who suggested using instead a molality-based activity coefficient which remains finite. A detailed study of the dependence of this activity coefficient on the solvent molecular weight led Martire (67) to demonstrate that the specific retention volumes of alkanes increase linearly with increasing values of 1/M, the inverse of the molecular weight of the solvent, for polymers derived from the same monomer. This could lead to some confusion when one attempts to characterize liquid phases according to their polarity indices, since there is even a molecular weight dependence for relative retentions. One could be led to the erroneous conclusion that the ‘polarity’ of a polymeric stationary phase varies with its molecular weight, whereas what happens is merely a structural effect in the dilute solution (67). When two pure components having different ‘free volumes’ are mixed, the solute (low molecular weight) is in a more ‘expanded’ state than the solvent (large molecular weight).

63

A.VI INFLUENCE OF THE TEMPERATURE Both the vapor pressure and the activity coefficients in equation 14 depend on the column temperature. According to solution thermodynamics: d(ln P o ) =-AH, dT R T ~ and :

where AH, and A HE are respectively the variation of enthalpy associated with the vaporization of one mole of pure solute and the excess molar enthalpy of mixing (variation of enthalpy observed when mixing one mole of solute at infinite dilution in the liquid phase) (17). Equations 15 and 16 are equivalent to the more classical expressions:

and:

The molar enthalpy of vaporization of the solute from the infinitely dilute solution is:

Combining equations 14 to 17 gives the dependence of the specific retention volume on the temperature:

According to equation 18, the plot of In V, versus 1/T is a straight line of slope equal to A H,/R. This is, of course, assuming that the difference between the molar heat capacity of the vapor and that of the solute at infinite dilution has a negligible effect and that the total heat of vaporization does not change significantly with the temperature. In most cases the difference is indeed small and it is only when either extremely accurate measurements are carried out or when the determinations are made over a large temperature range that a curvature in the In Vg versus 1/T plot References on p. 90.

64

can be observed (18). From this curvature, the difference in the molar heat capacities can be derived. From equation 10 and the definition of the column capacity factor, the following relationship can be derived:

Since the dissolution enthalpy is usually between 5 and 15 kcal/mole, the correction (RT cu 0.5 to 1kcal/mole) is not negligible but remains rather small. Accordingly, the retention time of all compounds increases exponentially with decreasing column temperature. As a rough order of magnitude it is often estimated that the retention times double when the column temperature is decreased by 30 O C. This figure, however, depends very much on the nature of the compound considered since the dissolution enthalpy increases with the molecular weight and the polarity of the solute. Generally A H , is small compared to AH,, so it is the value of the vapor pressure which has to be considered in order to determine whether a compound can be analyzed successfully by gas chromatography at a given temperature. The nature of the liquid phase has great influence on the exact value of the retention time, but nevertheless if the vapor pressure is too small the elution will be impossible. As an example, let us consider didecyl phthalate ( M= 446),a classical stationary phase for the analysis of relatively light organic compounds of medium polarity (2). Using equation 14, we calculate that, for a compound of vapor pressure equal to 1 atm (760 mm Hg), with an activity coefficient of unity, the specific retention volume is 50 mL. If the boiling point of this compound is 100O C, the retention volume on a column containing 1 g of stationary phase will be 68.6 mL. If the vapor pressure is 10 Torr at 100OC, the retention volume at this temperature becomes equal to 5.2 L. In practice gas chromatography is carried out under experimental conditions such that the specific retention volume is between 10 and 1,OOO mL. The activity coefficient in solution in non-polymeric stationary phases is usually between 0.5 and 2.5, which barely changes the conditions of the exercise above. The column temperature must be chosen so that the vapor pressure of the analyzed compounds is between 10 Torr and a few atmospheres. With open tubular columns (OTC), which contain a much smaller amount of liquid phase, somewhat smaller vapor pressures can be used. A typical OTC column has an average film thickness of 0.1 pm and a diameter of 0.25 mm. The phase ratio is thus approximately VJV, = 4e/d = 0.0016 and the volume of liquid phase 0.0010 mL. With a vapor pressure of 1 Torr and an activity coefficient of 1, we will have a specific retention volume of 38 L and a k’ value of 41, which is very large and barely acceptable. Conversely, compounds with a vapor pressure larger than cu 100 Torr would be difficult to analyze with this column, since their retention will be too small. These comments and calculations do not mean that the influence of the activity coefficient is negligible; far from it. A change in retention volume by a factor equal

65

to several units, which can be easily observed when changing the liquid phase is considerable in gas chromatography; it can result in a change of the relative retention by 10 to 25% or more and make the difference between a very difficult separation bordering on the impossible and an easy separation. This is essentially because the relative retentions of the compounds to be analyzed are of primary importance in the determination of the necessary column efficiency and, accordingly, of its length and of the analysis time. These relative retentions can be vaned considerably by changing the stationary phase.

A.VII RELATIVE RETENTION The relative retention is defined by the following equation:

The relative retention of two compounds is therefore the ratio of their Henry’s law constants. The ratio of the vapor pressures, P,”/Pp, is given once the pair of compounds considered is chosen. If this ratio is close to unity the only way to achieve a good resolution of these two compounds in a reasonable time is by chosing a stationary phase which gives a value of the ratio ym.2/ym.1which is markedly different from unity. Combining equations 30 in Chapter 1 and 10 gives: RT In

=A(AGO)

(21)

where A(AGo) is the difference between the Gibbs molar free energies of vaporization of the two compounds from the solution at infinite dilution (19). Each of these Gibbs free energies of vaporization is of the order of 10 kcal/mole. A numerical calculation shows that a variation of the difference between these free energies of ca 5 cal/mole can transform an impossible separation ( a= 1.00) into a feasible one ( a= l.Ol), while a variation of 50 cal/mole, still no more than ca 0.5%of each free energy, will result in a facile analysis (a.=1.1). Thus the choice of the proper stationary phase is of paramount importance. Selecting for this role a solvent which gives relative retentions significantly different from unity for all pairs of components of the mixture will result in an easy and potentially rapid analysis, which is the main goal of the analyst. As the complexity of the mixture increases, however, this choice becomes more and more difficult. This explains why so many different liquids have been tried to solve analytical problems in gas chromatography. Because of the requirement of good stability at high temperature, the most important group of liquid phases used is high polymers. Previous studies have shown that the molecular weight of these products should be larger than ca 1,000 References on p. 90.

66

Daltons to ensure a low enough vapor pressure, while it should not exceed about 10,000 Daltons to avoid an excessive decomposition rate. This latter condition, however, does not apply to silicone products. Silicone greases are among the most stable stationary phases known, except for the carboranes (Dexsil). As mentioned above, the definition of the activity coefficient in equation 14 and related expressions presents some difficulties. Molecular thermodynamics suggests, however, that the product y"OM, the solute activity coefficient at infinite dilution and the solvent molecular weight, remains finite and varies only slowly with the molecular weight of the stationary phase. This is in agreement with the fact that retention volumes on families of liquid phases of a different degree of polymerization or polycondensation vary slowly (16,67). For further discussion, the reader is referred to the end of Section IV above. A.VII1 INFLUENCE OF THE GAS PHASE NON-IDEALITY The theoretical considerations developed above rely on the following assumptions (12): 1. The solute is infinitely dilute in the solvent and Henry's law is valid (i.e. the partial pressure of solute above the solution is proportional to the solute concentration or mole fraction in the solution). 2. Partition equilibrium of the solute between the gas and the liquid phase is achieved at all points along the column, at least around the concentration maximum of the band. 3. The behavior of the gas phase is ideal, from the point of views of both mechanics (Boyle-Mariotte law) and mixing. .4. The retention mechanism is pure: there is no contribution to solute retention by adsorption, either on the solid support or at the gas-liquid interface. 5. The carrier gas is not soluble in the liquid phase. Those are the conditions for the validity of equations 10 and 14 and those which are derived from them. The assumptions 1, 2 and 5 usually hold fairly well under normal chromatographic conditions. It can be assumed rather safely that in gas-liquid chromatography assumption 1 is valid as long as the maximum concentration of the solute in the elution band does not exceed 0.1 millimolar (see Chapter 5). Although equilibrium is actually not achieved at the front of the band (where the solute concentration in the gas phase is too large), nor at the band's tail (where it is the solute concentration in the liquid phase which is too large), it has been shown that the retention time of the band maximum is related to the partition coefficient (through equation 10) with a relative error which is of the order of a fraction of l/@, N being the plate number. This validates assumption 2. It is difficult to ensure that the phenomenon observed is pure gas-liquid partition, especially when one is working with polar compounds. Large coating ratios of solvent on a deactivated support have to be used. The preparation of supports which have a low surface energy, an homogeneous surface and which, nevertheless, are wetted by the classical solvents of gas-liquid chromatography, has

61

been the topic of intense research. It is difficult to satisfy assumption 4 when the polarity of the solute is markedly different from that of the solvent. If the solute polarity is large, there is probably some adsorption on the surface of the support. Whether it is much greater or much smaller than that of the solvent, there is most probably adsorption at the gas-liquid interface. These phenomena can be used with advantage in many analytical applications. For example on a very polar solvent like &P'-oxydipropionitrile or on tris-1,2,3-cyanoethoxypropanethe relative retention of aliphatic and aromatic hydrocarbons is a strong function of the phase ratio, because the retention of saturated hydrocarbons is essentially due to their strong adsorption at the gas-liquid interface. When the phase ratio increases, the retention of aromatics increases, but that of paraffins decreases, as does the surface area of the gas-liquid interface. Assumption 3, on the other hand, is far from valid, especially when high-efficiency columns are used (e.g. open tubular or capillary columns). Even hydrogen and helium have, under chromatographic conditions, a behavior which is far enough from ideal for the retention volumes of solutes and sometimes their relative retentions to vary with the column average pressure, i.e. the gas flow rate. For a real gas under moderate pressure, the virial equation of state gives satisfactory results: P V = n ( R T + B,)

(22)

In this equation the constant coefficient B, is the second virial coefficient of the gas phase, here the mixture of carrier gas and solute vapor. The mean second virial coefficient of this mixture can be calculated as a function of the composition of the mixture using the classical relationship: B,

= N:Bl,

+ 2 B 1 2 N l N 2+ N2B2,

where: - N, is the mole fraction of compound i in the gas phase, - B,, is the second virial coefficient of the pure gaseous compound i at the column temperature, and - B,, is the second mixed virial coefficient of compounds i and j at the same temperature. As usual, the index 1 corresponds to the carrier gas and the index 2 to the solute. The problem then becomes the evaluation of the mixed virial coefficient, more correctly called the mixed-gas second-interaction cross virial coefficient. This is usually obtained from the virial coefficients of the pure components of the mixture. The second virial coefficients of pure compounds can be calculated using the following, semi-empirical equation (20):

References on p. 90.

68

TABLE 3.1 Second Virial Coefficient of Common Carrier Gases

Gas

T (K)

B,, (cm3/mole) Calculated

He N2

H2 Ar

co2

300 400

300 400 300 400 300 400 300 400

'

. Experimental (21), at 320 K NA

0 0 1.28 8.9 13.9 14.45 - 9.5 2.6 - 125 - 60

0.44 13

- 9.9

-90

Data from Laub (68) 12.0 11.5 - 4.2 9.0 14.8 15.2 - 15.5 - 1.0 - 122.7 - 60.5

From equation 24.

where P,,,and Tc,i stand for the critical pressure and temperature of compound i , respectively. The values calculated from equation 24 for the gases most commonly used as mobile phases in gas chromatography are compared to experimental values in Table 3.1. A more general relationship has been studied by Laub (68), who has calculated the best values of the coefficients u0, a,, u 2 of the expansion: Bii = a0

+ul( T C,i )+

+) 2

u2(

K.i

by fitting this equation to the experimental data of Dymond and Smith (69). The agreement is satisfactory, except for water and HC1, for which a quartic fit was found to be necessary. Values of the virial coefficients obtained for some gases are also reported in Table 3.1. The values of the second virial coefficientsof conventional carrier gases are small and in practice their contribution to the mixed virial coefficient can be neglected compared to that of the second virial coefficient of the solute vapor. The mixed coefficient can be approximated using the following relationship:

More exact, but much more complex, relationships have been discussed by Laub (68). They can predict the value of the virial coefficient of a gas mixture as a function of its composition. Hence, a prediction of the variation of the relative retention of closely eluted compounds due to the introduction of a certain amount of a highly compressible vapor in the carrier gas appears to be possible, at least to some extent. The results predicted agree fairly well with experimental results (70).

69

Now, if we substitute the combination of equations 22 to 25 in the derivation of the partition coefficient to the classical Boyle-Mariotte equation, we obtain (22): In K ,

= In

RTp + -PO (U~-B~~)+ P- ( ~ B ~ ~ - U ~ ) RT RT POy"M,

where: - u: is the molar volume of the pure liquid solute at the column temperature, T. - u2 is the partial molar volume of the solute in the solution, which is generally replaced by u:, in the absence of accurate method of determination and because no acceptable method of estimate is available. - P is the column average pressure, Po/j (cf. Chapter 1, section VII and Chapter 2, equation 3). The last two terms of equation 26 have the same order of magnitude, as long as the column average pressure does not exceed a few atmospheres. The correction made to equation 14 cannot be neglected if accurate values of the activity coefficients are desired. In some cases, when highly volatile, polar solutes are studied, the correction can be very large, up to 50% of the value of ym. More generally, however, it does not exceed 3 to 5%. The difficulty in using equation 26 is to find an acceptable value for the virial coefficient of the vapor of the studied compounds. Equation 24a can be used if the values of the critical temperature and pressure are known. Equation 24b is more accurate, but has no predictive value, as long as virial coefficients data are not available. The virial coefficient can also be derived from the compressibility coefficient, Z, (23):

which can be measured experimentally. Values of B,, are also found in the literature. The validity of equation 26 has been thoroughly tested by Cruickshank et al. who have shown that the partition coefficient extrapolated to zero column pressure ( p o = 0, P(average) = 0, K , = Ki) is the same for several carrier gases which are insoluble in the stationary phase (24,25). Laub (70), too, has shown excellent agreement between calculated and measured values of the specific retention volumes of n-hexane on OV-1, measured with mixtures of hydrogen and Freon 11of variable composition, as mobile phase. He also observed under the same experimental conditions, a change of the elution order of benzene and 3,3-dimethylpentane. The problem of accounting for the non-ideal gas phase behavior when the carrier gas is soluble in the liquid phase, like CO,, is much more complicated. Martire and Boehm have recently developed a unified theory of retention which predicts the variation of the apparent equilibrium constant between mobile and stationary phases in fluid-liquid chromatography (82). The basic feature of this References on p. 90.

70

theory is to consider the mobile phase as a mixture of a poor and a strong solvent, as in liquid chromatography. At low mobile phase density the weak solvent is empty space. This model yields the conventional equations 11 and 26 when the density of the gas phase is low. It permits the prediction of the variation of the apparent partition coefficient with increasing average gas pressure, up to and beyond the critical state of the gas phase. It provides a transition to the known expression of the retention in supercritical fluid chromatography (82). The determination of accurate values of the activity coefficient is required for all studies of solution thermodynamics. From yoo, the Gibbs excess free energy can be derived (AGE= RT In y"), and from the variation of yoo with temperature, the excess enthalpy and entropy can be obtained. The determination of mixing, excess and vaporization enthalpy from gas chromatographic data, while correcting for non-ideal mobile phase behavior has been discussed thoroughly, with emphasis on precision and accuracy (26). Gas-liquid chromatography can provide a wealth of data in this field, as long as the experimental conditions required for the validity of assumption 4 above may be achieved. Detailed studies of the real accuracy of GC measurements have been made, including systematic comparisons between the values of y obtained for series of compounds, using different classical methods and gas chromatography (12). The method can be extended to the determination of the activity coefficient of a solute at infinite dilution in a mixture of non-volatile solvents, especially binary mixtures (27). It can also be used for the measurement of activity coefficients at finite solute concentration. The most promising experimental approach consists of using as mobile phase a mixture of pure, inert carrier gas and vapor of the studied compound at a known, adjustable concentration. When equilibrium is achieved the injection of a very small sample of the compound gives a retention time which can be related to the activity coefficient of the compound in the solution (28). Alternatively, the classical frontal analysis method can be used. Difficult experimental problems have to be solved (1).

A.IX MIXED RETENTION MECHANISMS. COMPLEXATION There are two main circumstances under which assumption 4, made at the beginning of Section A.VII above, is not valid. The most important is when the stationary phase is a solution, in a proper non-volatile solvent, of an additive or ligand capable of forming complexes with some of the analytes. Although these complexes must be labile and dissociate rapidly enough to permit the achievement of a good column efficiency, the complexation energy and the complexation constant may be sufficiently large for the presence of the additive to contribute markedly to the retention of some components of the analyzed mixture. The kinetics of the association-dissociation reaction must be fast compared to the migration rate of the band. An excellent presentation of the fundamental problems associated with the use of complexation in gas chromatography, current at the time of publication, can be found in the book written by Laub and Pecsok (29a).

71

Among the various reactions used in gas chromatography to selectively retard one compound or a chemical group, the most important are (1,29): 1. Reaction of the solute with an additive to form one or several complexes: A,Xm. (Solute = X,additive = A ) 2. Reaction of the solute with the solvent to form complexes: X,Sm. 3. Polymerization of the solute in solution. 4. Competition between the solute and an additive in order to form complexes with the solvent: A,Sm and XpSq. The first type of reaction is by far the most important and it has been studied in detail by several workers. The general case is the formation of 1 : 1 complexes between the solute and the additive. The equilibrium reaction is:

If we assume that: all solution interactions are neghgible, except the chemical interaction (formation of the complex), i.e. the activity coefficient of the solute in solution does not vary with increasing concentration of the additive, and - the partition coefficient of the solute between the gas and the liquid phase remains constant, then we can easily derive the following relationship (29): -

K,

=Kj(1+

KC,)

where: - C, is the additive concentration in the liquid phase, - K , is the partition coefficient over the solution, A , S . - K ; is the partition coefficient over the pure solvent S, and - K is the complexation constant. This relationship gives reasonably good results for the retention of olefins over solutions of Ag+ in polyglycols (30), but the method suffers several disadvantages (31-33): - the influence of changes in all physical interactions, other than chemical ones, is neglected; , - K ; for the uncomplexed species remains constant when the concentration of additive changes, although its structure is markedly different from that of the solvent; - the complexation constants as defined and measured have little meaning from a thermodynamic standpoint. A more accurate calculation, taking account of the variation of the activity coefficients of the components of the solution and of the molar volume of the solution with the concentration of the additive, has been derived by Eon, Pommier and Guiochon (31-33). References on p. 90.

12

The complexation constant is:

The partition coefficient, as defined and measured in chromatography, is not the thermodynamic constant of dissolution of the solute in the solvent, but the ratio: KR =

total concentration of X in the liquid phase concentration of X in the gas phase

The concentration of the solute in the gas phase, (C,,,), is given by Raoult’s law (cf section A.11 and equation a), assuming an ideal behavior for the gas phase (otherwise see section A.VI1):

The total concentration of the sample in the stationary phase is equal to the sum of the concentration of the uncomplexed solute and that of the complex:

cX.1 = - + - =NAx NX

us

us

[

Nx 1 + us

(33)

where us is the molar volume of the solution (different from the molar volume of the pure solvent, u,”). Combination of equations 31 to 33 gives:

Both the solute activity coefficient and the molar volume of the solution depend on the additive concentration, however, and this effect must be accounted for. It can be shown that, for weakly polar solutes, the main reason for these changes is the variation in the configurational excess entropy, which depends only on the molar volumes of the solvent, the solute and the additive. A detailed analysis of these phenomena leads to the relationship:

In equation 35 the activity coefficient of X is the coefficient at infinite dilution in the pure solvent; Kj is the partition coefficient with the pure solvent. The term which accounts for the entropy change just mentioned, is given by:

+,

13

When the solution contains highly polar compounds, the Keesom and Debye forces play an important role on its non-ideality and the term 1c, can no longer be calculated using equation 36 but it has to be measured using the counterpart method. Comparison between the results of the different approaches has been made by several groups (33-35). This problem has also been studied in detail by Martire (36) who derived, from theoretical considerations, an experimental protocol which permits the determination of meaningful complexation constants (37). The use of selective complexation can considerably improve some separations and markedly increase the speed of analysis. The use of Ag', mentioned above, as a component of the stationary phase is very useful for the enhancement of the relative resolution of compounds differing only by the position of a double bond. The use of charge transfer complexes has also been thoroughly investigated; for example the use of alkyl tetrachlorophthalates reported by Langer et al. (38). Numerous studies on the measurement of complexation constants by GC have also been performed (1). The method requires much smaller amounts of material than the competitive techniques of NMR or UV spectroscopy, so that true infinite dilution is achieved during measurements carried out with the former technique, whereas it is not with the other methods. The role of the solvent used, however, is critical (39).

A.X MIXED RETENTION MECHANISMS. ADSORPTION As we pointed out in a previous section, the retention of a solute is frequently due to several equilibrium phenomena which interact competitively and additively. Several adsorption phenomena may combine with the conventional dissolution in the liquid stationary phase. While adsorption at the gas-solid interface may in some cases contribute significantly, it is also possible, at least in theory, to considerably reduce this effect. On the other hand, adsorption at the liquid-gas interface is the necessary result of a marked difference between the polarities of the solute and the solvent. It always takes place when the activity coefficient exceeds a few units. Adsorption of polar solutes on the siliceous materials used as support in gas-liquid chromatography is a frequent occurrence. This phenomenon falsifies the determination of thermodynamic data, but does not interfere with the analytical usefulness of gas chromatography as long as the band profiles remain reasonably symmetrical. The extent of adsorption depends on the nature of the support and the treatments to which it has been subjected. The main drawbacks resulting from adsorption of the analytes on the support are the lack of reproducibility of the phenomenon, so that different columns made with the same solvent will have different selectivities and hence different resolutions for some pairs of compounds, and strong adsorption most often results in tailing peaks which cannot be used for the achievement of quantitative analysis. It also happens, when solute and solvent have markedly different polarities, that there is a strong degree of adsorption at the gas-liquid interface. As a consequence, the specific retention volume of these solutes does not remain constant when the References on p. 90.

14

results obtained with columns of different coating ratios are compared. The volume of the stationary phase increases proportionally to the phase ratio, but its surface area varies much less rapidly; sometimes it even decreases with increasing phase ratios. Then the relationship between KR and VR becomes more complex. It is conventional in these studies to determine the variation of the retention volume expressed for 1 gram of packing material (not 1 gram of stationary phase as for the determination of the specific retention volume). This quantity is related to the partition coefficient, KR, and the adsorption coefficient K, by (40):

V ,= KRVL + K , A ,

(374

where V, and A, are the volume and the surface area of the stationary phase, respectively. Equation 37a can be rephrased in terms of k', the column capacity factor, which gives, for independent retention mechanisms:

By changing the phase ratio and plotting VJV, versus AJVL it is possible to measure both the partition coefficient and the adsorption coefficient, which is defined as: K, =

Excess concentration of solute per unit surface area Concentration of the solute in the gas phase

(38)

A relationship between K , and the variation of the surface tension of the solution with the concentration of solute has been derived by R.L. Martin (40,41):

This equation has been discussed and checked in several publications (2). It gives results which are in good agreement with those of experimental measurements. This phenomenon, once understood, can be used with great advantage to improve the resolution between compounds which are difficult to separate, especially in complex mixtures. Since the retention of the compounds which have a polarity comparable to that of the stationary phase also have a retention volume which increases in proportion to the coating ratio, while the retention volume of those with a polarity markedly larger or smaller than that of the solvent have a retention volume which varies much less, it is possible to achieve group separation. For example, aromatic hydrocarbons can be separated from paraffins on a very polar nitrile phase, by using very large coating ratios. This method works much better in packed columns than in open tubular columns, because of the structure of the pore

75

volume. So far it is much less useful with capillary columns, because of the difficulties encountered in the preparation of stable columns with thick layers of polar phases. Eon and Guiochon have defined surface activity coefficients and developed an equation which relates these coefficients to the adsorption constant, K,, and the partition coefficient, K,. They have shown that the surface activity coefficients are mainly a function of the shape of the molecules, in analogy with gas-solid chromatography (42). Finally, Martire has raised the question whether the results determined with planar interfaces can be expected to correlate well with data from curved surfaces as obtained on supported liquids (71). The vapor pressure over a concave surface is lowered in accordance with the Kelvin equation. This phenomenon has been further discussed by Devillez et al. (43). It does not seem that the Kelvin effect plays a significant role in the determination of retention in gas-liquid chromatography (1,431.

A.XI ADSORPTION ON MONOLAYERS AND THIN LAYERS OF STATIONARY PHASES Serpinet has carried out important, systematic studies on the temperature dependence of the retention of various probe solutes by different organic stationary phases spread over conventional supports in a temperature range including the melting point of these solvents (72-78). At temperatures below the melting point of the liquid phase, retention takes place by adsorption on both the support surface and the surface of the solid organic compound. At temperatures well above the melting point, retention takes place essentially by dissolution in the bulk liquid phase, but also, depending on the circumstances, by adsorption at one or several of the interfaces: gas-liquid, gas-solid, liquid-solid, or ‘in’ the film of stationary liquid phase which may have spread over the support surface. Almost always, the plots of the logarithm of the specific retention volume versus the inverse of the absolute temperature are linear when the organic phase used is solid, i.e., below the melting point, and when it is a liquid, i.e., at temperatures well above the melting point. Around the melting point, however, the plots exhibit one or several more or less abrupt changes in the retention volume, related to the melting of the bulk of the organic solvent and/or of the films it may form on the surface (73). The study of these changes provides exceptionally interesting information regarding the structure of the film of stationary phase at the surface of the solid support. The results are very different, depending whether the underlying support has been silanized or not, prior to its coating by the stationary phase. The results demonstrate that there is a profound difference between the two types of support, in the distribution of the stationary liquid phase on their surface. This may have important consequences for the analyst. References on p. 90.

If the support has been silanized almost no solvent, not even hydrocarbons, can wet the surface (72). Its surface energy is too low compared to the surface tension of the stationary liquids used. Even squalane does not wet a silanized support. The stationary phase collects in pools on the surface of the support, forming a network of tiny liquid spheres. There is no film of solvent on the surface. When the temperature is raised, the plot of log V, versus 1/T is linear, with a negative slope, until the melting point is reached. Then an abrupt jump is observed, the bulk of the liquid phase becoming available for dissolution of the solutes, which are retained only by adsorption at lower temperatures. The gas-liquid interface seems to have an extremely small surface area, a fraction of 1 m2/g. Since the surface area of the gas-liquid interface is so small, the extent of selective adsorption at this interface is very small, and we cannot observe any change in the retention volumes of polar solutes with increasing coating ratio when we use a non-polar stationary phase coated on a silanized support (72). This is very different from what happens when a non-silanized support is used (see Section A.X, above). Unfortunately, it is not always possible to use a non-silanized support for the analysis of polar solutes with liquid phases of low polarity. On the other hand, if untreated supports are used, a much more complex situation prevails (74). The liquid phase wets the support well and spreads on it, where it may be found in thin films of different density and, if the phase ratio is large enough, in bulk. Even with heavily loaded columns, however, a significant fraction of the solvent is in the film form, up to 5-1096 (79, which may lead to severe difficulties in calculating accurate specific retention volumes (75). Plots of the logarithm of the retention volume versus the reverse of the temperature exhibit no transition for very low phase ratios. This is not a detection problem; the transition appears clearly at the melting point if a silanized support is used at the same low phase ratio (74). The liquid phase forms an expanded film. When the phase ratio increases, the density of this expanded film increases until a limit is reached, where a condensed film appears. At larger phase ratios the bulk liquid is formed. For octadecanol, the melting points of the condensed film and of the bulk are 84 O C and 58"C, respectively. Thus, two transitions appear on the log V, versus 1 / T plots (74). In certain cases a third transition corresponds to the melting of the liquid film at the liquid-solid interface (75). The relative amounts of the solvent under the different physical states may be determined by simple measurements. In this case, the ratio of the specific surface area of the gas-liquid interface to the mass of liquid phase varies greatly with increasing coating ratio. Since the interface area is large, adsorption of the analytes at this interface is significant, and its relative contribution to the retention volume varies with the coating ratio. The phenomenon discovered by Martin (40) and described in the previous section occurs. Serpinet has used the same method for the study of films formed by organic compounds, such as alkanes or alkanols, on the surface of various liquid substrates, themselves coated on an untreated diatomaceous support (76-78). The analytical applications of this work being limited, we refer the interested reader to the original publications.

B. THE THERMODYNAMICS OF RETENTION IN GAS-SOLID CHROMATOGRAPHY The most authoritative review of gas-solid chromatography has been published by Kiselev (44)who has also written a large proportion of the most important work carried out in this field. The definitions of the elution rate of a band and of the column capacity factor in gas-solid chromatography are the same as in gas-liquid chromatography. As far as the column capacity factor is concerned, this results essentially from the fact that, at the usual (low) pressures at which GC is carried out, the carrier gas is practically not adsorbed by the adsorbent used as stationary phase. Thus, as a first approximation, the adsorbent surface is free, and there is no competition of the carrier gas molecules with the sample components for adsorption: this situation is very different from the one encountered in liquid chromatography. Accordingly, in GSC there is no real difficulty in defining the gas hold-up time, or retention time of an inert, non-retained compound and in finding a suitable marker for the measurement of to. It must be noted, however, that there are some cases where this assumption does not hold (see Section B.V, below). The retention mechanism is no longer the dissolution of the studied compounds in a non-volatile solvent, and the molecular interaction forces between solvent and solute molecules, but it is rather the adsorption of these compounds on a solid of large specific surface area, and the interaction forces between a molecule in the gas phase and all the atoms or molecules which are staying on the other side of the solid surface (44).

B.1 THE HENRY CONSTANT A N D RETENTION DATA As long as the partial pressure of the vapor in the gas phase is small compared to the vapor pressure of this compound, the amount sorbed on the surface is proportional to the vapor pressure:

m=Kf

(40)

The coefficient K is called the Henry coefficient or constant of adsorption. Since the sorbed molecules make a monolayer on the adsorbent surface, the amount sorbed is proportional to the surface coverage, or proportion of a monolayer which is formed. When the partial pressure becomes larger, two phenomena complicate the result. On the one hand, the fraction of free surface (i.e. not covered by adsorbate molecules) decreases, on the other hand adsorbate-adsorbate interactions increase as the average distance between two sorbed molecules decreases. The equilibrium pressure, P,is given by the Kiselev equation (45):

P=

e K ( l - e)(l

+ K’B) References on p. 90.

78

where 8 is the coverage ratio, or fraction of the surface covered by adsorbed molecules. K and K ’ are numerical coefficients. Unfortunately equation 41 cannot be solved analytically for 8, although this is the form which would be most useful. A virial equation with three or four terms is also often used (46):

P = a exp( C,+ C,U + c3a2+ C,a4 + ... )

(42)

Linear chromatography takes place as long as the contribution of the curvature of the isotherm can be neglected. It should be born in mind, however, that a small deviation of the equilibrium isotherm from a linear behavior can result in markedly unsymmetrical peaks. Like the Henry constant, K, the coefficients K’, C,,C,, .. depend on the temperature. Accordingly, the heat of adsorption varies with the surface coverage. The retention data are usually reported to the unit mass of adsorbent used, and the specific retention volume is defined as in GLC. j/=B

VR ma

(43)

(VR is the retention volume on a column containing the mass m a of sorbent). It should be related to the unit surface area of the adsorbent used. This area is often difficult to measure accurately. Furthermore, there is no guarantee that adsorbents of the same chemical nature but having different surface areas will exhibit the same Henry constant for any given compound. Changes in the preparation procedure may result in marked changes in the surface chemistry at the same time as they produce adsorbents with different specific surface areas. Thus it is more cautious to relate both the specific retention volume normalized to the unit mass of adsorbent and the specific surface area. The retention volume related to the unit surface area of the adsorbent is equal to the Henry constant:

The value of the Henry constant depends both on the energy of interaction between the constituents of the surface of the adsorbent and the molecule of adsorbate, and on the geometrical structure of the adsorbate.

B.11 SURFACE PROPERTIES OF ADSORBENTS AND CHROMATOGRAPHY Two types of surface properties are important in chromatography. The nature and strength of molecular interactions which are involved during adsorption control the value of the Henry constant, hence the retention volume (cf. equation 42). The degree of homogeneity of the surface determines the adsorption-desorption kinetics and the elution band shape.

79

1. Nature of the Molecular Interactions Involved From the point of view of the nature of the molecular interactions involved, Kiselev has distinguished three types of adsorbents (44,47): 1. Adsorbents of type I are non-specific. Their surface contains neither polar functional groups nor ions. These are mainly graphitized carbon black, boron nitride, saturated hydrocarbons, and hydrocarbon polymers (e.g. polyethylene, polystyrene). They undergo only non-specific interactions with sorbed molecules, including the most polar ones. Water is eluted close to methane and ammonia. 2. Adsorbents of type I1 have on their surface polar groups like hydroxyls (silica) or small localized cations while the negative charge is distributed over a much larger volume, so strong local electric fields appear near the surface. This is the case of zeolites on the surface of which small exchangeable cations carry the positive charge, while the negative charge is spread over the large aluminate ions, AlO;, in the zeolite structure. Some salts, too (NaC1, etc.), belong to this group. These adsorbents give specific interactions with molecules having atoms, atomic groups or bonds on which the electronic density is highly concentrated, such as alcohols, ethers, ketones, amines, nitriles, thiols, and so on. 3. Adsorbents of type I11 carry localized negative charges carried by isolated atoms of oxygen (ethers), nitrogen (nitriles), by carbonyl groups, aromatic IT orbitals or small, localized exchangeable anions. These adsorbents are conveniently prepared by coating the surface of graphitized carbon black with a monomolecular layer of a polar polymer (e.g. polyglycol), of a dense homo or hetero PNA (copper phthalocyanin) or by chemical bonding on silica. Reticulated polystyrene/polydivinylbenzene also belongs to this group. These adsorbents may give strong selective interactions with alcohols and amines. A small number of adsorbent types have been used traditionally in gas chromatography: silica gel, alumina, molecular sieves, graphitized carbon black and porous polymers. Each of them permits the solution of a few well defined analytical problems. The recent development of a wide variety of adsorbents for HPLC has made available a wealth of new materials, some of which could be very useful for gas chromatography. Most chemically bonded silicas can be used up to temperatures around 250" C. This includes alkyl-bonded (C4, C,, CI2,C1,), perfluoropropyl-, cyanopropyl-, aminopropyl-, diol-, or phenyl-silicas.

2. Kinetics of Adsorption-Desorption The kinetics of adsorption-desorption (cf. Section B.VI) is another important property of adsorbents used in gas-solid chromatography. It depends in part on the geometrical structure of the particles, in part on the homogeneity of the surface. Adsorbents could be further classified by their pore structure, which determines the ease with which molecules can access the surface and diffuse back to the mobile phase around the adsorbent particles (44). 1. Non-porous adsorbents are made of very fine particles, which are usually agglomerated in a further step: the permeability of a bed made with these small References on p. 90.

80

particles would be much too small and would preclude their direct use in GSC. Graphitized carbon black is a typical example. The specific surface area is usually between 10 and 100 m2/g. The interparticulate pores inside the agglomerates are large and provide ready access to the surface. 2. Homogeneous, large pore adsorbents have pores larger than 100-200 A and specific surface area lower than 300-400 m2/g. They are mainly xerogels (silica gels or alumina) or macroporous glass particles. The regularity of this structure results from the formation of the silica gels as agglomerates of non-porous globules of relatively narrow size distribution. Such gels are very convenient for gas chromatographic analysis of low and medium boiling point compounds. 3. Homogeneous, micropore adsorbents have pores with dimensions which are of the same order as the molecules of analytes. They are useful for separations based on molecular size difference. Typical adsorbents belonging to that group are activated carbons (e.g. Saran) and zeolites. 4. Adsorbents having a wide pore size distribution. These are difficult to use because of the presence of a large number of micropores which strongly adsorb molecules having a size similar to theirs, resulting either in losses or very unsymmetrical band profiles. Silica gels obtained by precipitation from a silicate solution belong to that group. There are processes to reduce the specific surface area and enlarge the pores of these gels, which render them suitable for a number of GC applications. 3. Homogeneity of the Adsorbent Surface Finally, the homogeneity of the adsorbent surface is of great importance (48). If there are some adsorption sites for which the adsorption energy is much larger than on the rest of the surface, the retention of samples of small size will be very large, but when the partial pressure of the sample in the gas phase increases, the retention will fall sharply. This leads to band profiles which are extremely unsymmetrical (49,50).

B.III INFLUENCE OF THE TEMPERATURE The Henry constant of adsorption decreases rapidly with increasing temperature. Equation 18 applies to gas-solid chromatography as well as to gas-liquid chromatography (cf equation 44, Vg is proportional to the Henry constant). The adsorption enthalpy, however, is markedly greater than the vaporization enthalpy, especially at the low surface coverages encountered in analytical GSC, so the temperature dependence of specific retention volumes is much larger in GSC than in GLC. For the same reason, the relative retention of two compounds may change more rapidly with column temperature in GSC. Since there is often no practical limit to the column temperature which can be used, other than that set by the thermal stability of the sample, this permits the resolution of component pairs which would be difficult to achieve otherwise.

81

The separation of argon and oxygen on NaA zeolite (Molecular Sieve 5A) is a good example of the importance of adjusting the column temperature: this separation is very difficult at room temperature, not because the relative retention is small, but because the retention volumes of the two gases are very small. Since it increases rapidly with decreasing temperature, the resolution improves dramatically.

B.IV GAS PHASE NON-IDEALITY The theory of gas-solid chromatography relies on assumptions similar to those made in the theory of gas-liquid chromatography (cf Section A.VIII above): 1. The surface coverage of the adsorbent is very small and Henry’s law is valid (the amount of compound sorbed on the surface is proportional to its partial pressure in the gas phase). 2. Equilibrium of the analyte between the gas and the adsorbent surface is achieved at all points along the column, at least around the concentration maximum of the band. 3. The behavior of the gas phase is ideal, from the points of view of both mechanics (Boyle-Mariotte law) and mixing. 4. The retention mechanism is pure: there is only one adsorption mechanism. 5. The carrier gas is not sorbed by the stationary phase. Fulfillment of the first assumption requires the use of small sample sizes. The maximum sample size depends on the specific surface area, the linear range of the isotherm, and the extent of band asymmetry one is willing to accept. In practice, the detection of trace components remains possible. Assumptions 2 and 3 are valid within the same range of experimental conditions for GLC and GSC (cf their discussion in Section A.VII1). Assumption 4 is often valid, but requires surface homogeneity. If there are strong adsorption sites on the surface, or micropores, they would control retention at very low surface coverages (i.e. very small samples). As the proportion of the adsorbent surface they cover is small, they become saturated with samples having the size normally used in GC and strongly tailing peaks are observed, which are often difficult to quantify, even for pure compounds. In most cases, the carrier gas is sorbed to a significant extent. This means that a part of the surface is occupied by the molecules of the carrier gas, and is not available to the sample molecules (cf the theory of the Langmuir isotherm). This effect is much more important in GSC than it is in GLC (51). The effects of the non-ideal behavior of the mobile phase and of its adsorption on the stationary phase can be accounted for in an equation (51) which relates the ‘true’ specific retention volume, Vg,o (which would be observed with an ideal non-sorbed gas, or at zero gas pressure) to the specific retention volume measured, V,: log

v,

= log

vg,o+ RT

(45)

In this equation which is based on the assumption of an homogeneous adsorbent, B,, is the mixed second virial coefficient of the adsorbate and the carrier gas (cf References on p. 90.

82

Section A.VII1 and equation 25), P, the average column pressure ( P o / j ) , T, the column temperature, 9 and 0 the fractions of the adsorbate in the sorbed monolayer and in the gas phase at equilibrium, respectively. So, +/0 is the column capacity factor observed for the carrier gas. In the derivation of equation 45 it is assumed that this factor is small and thus that Henry's law is still valid for the carrier gas in the range of pressure used during the investigation, P must be small, so the extent of carrier gas adsorption remains negligible. B.V ADSORPTION OF THE CARRIER GAS

In some rare cases, the carrier gas used may be sorbed by the stationary phase. The camer gas may be a vapor or may contain a significant proportion of a vapor such as steam (see Chapter 7, section 11) or of a strongly sorbed gas like Freon 11 (70). In other cases, the inlet pressure may be large or the outlet pressure may be kept well above atmospheric pressure to raise the average pressure. Often a combination of these two factors will come into play. Then the nature, composition and pressure of the carrier gas all influence the retention volume of gases and vapors to a much greater extent than is predicted by the equations based on the mere consideration of the non-ideal behavior of the gas phase, as described in the previous section. As an example, when alkanes are eluted on Porasil C (80/100 mesh, 50-100 m2/g), using carbon dioxide as carrier gas at 80°C, with atmospheric outlet pressure, it is observed that the logarithm of the column capacity factor decreases linearly with increasing average pressure. A considerable decrease of 30 to 40% of the column capacity factor is measured when the pressure is raised from 1.3 atm to 5.1 atm (79). It can be estimated that about 15% of the surface of silica is covered with carbon dioxide at the corresponding average pressure (80). This effect could be used to advantage by innovative analysts. Other examples will be found in Chapter 7, where the use of a carrier gas containing steam is discussed. Pretorius has also used steam in the carrier gas and observed that the column capacity factors of some sterols decrease linearly with increasing steam partial pressure (81). B.VI THE PRACTICAL USES OF GSC

Gas-solid chromatography is not very popular. Its applications are limited to a small number of well-defined analyses which would be very difficult to achieve using gas-liquid chromatography. These are essentially analyses of gas mixtures: hydrogen isotopes (52), air and combustion gases (53), LPG (Cl, saturated, unsaturated and cyclic C2to C,, including most isomers), and many other gases. This is due to some major problems encountered in the use of adsorbents to analyze higher boiling, polar compounds. Most of the compounds just cited can be analyzed at temperatures much above their boiling point. Then their partial pressure in the column is a small fraction of

83

their vapor pressure and the equilibrium isotherm is still very close to its tangent at the origin. At the same time the slope of this tangent is very large, and the column capacity factors remain reasonable. For the analysis of higher boiling compounds, we find that deviation of the isotherm from linear behavior at the partial pressures normally achieved in analytical GC becomes increasingly important, while the column capacity factors increase rapidly. Smaller and smaller samples must be injected, giving broader and broader peaks, until detection becomes impossible. Reduction in the specific surface area of the sorbent used is a possibility. It permits the achievement of shorter analysis times, but requires the use of still smaller samples. Symmetrical peaks and good column efficiency can be obtained only if the adsorbents used have a very homogeneous surface, i.e. the adsorption energy is the same at all points on the surface. This is possible only for non-polar compounds, and, to some extent, for moderately polar compounds on non-polar sorbents, such as graphitized carbon black, treated with hydrogen at 1400O C (Carbopack, Supelco) (5433, and porous polymers (56). In other cases, the adsorption energy will vary widely from place to place on the surface. This results in band broadening, because the residence time of a molecule on the surface increases exponentially with the sorption energy. A wide distribution of residence times results in band broadening and possibly strongly skewed peaks for most energy distributions (cf Chapter 4). This effect, however, is negligible if the adsorption energy remains small enough for the residence times to be smaller than ca 0.1 msec. This is why strongly polar compounds such as SO,, SH, or even CO, can be analyzed on silica gel and H,O on graphitized carbon black or porous polymers. Major developments have been made in the preparation of homogeneous surface adsorbents. The surface chemistry of chemically bonded silicas has seen considerable progress. A great number of new adsorbents have been prepared for high performance liquid chromatography, which are potentially attractive for gas chromatography but have not been yet tested. Besides the analysis of gases already discussed above and further documented in the following chapters, the most important and best-studied application of gas-solid chromatography has been the separation of geometrical isomers, for which extremely large relative retentions have been observed (44).

C. APPLICATION TO PROGRAMMED TEMPERATURE GAS CHROMATOGRAPHY In many cases, the analyst must determine the composition of complex mixtures containing many components with widely different vapor pressures, vaporization energy and polarity. It is not possible to find an optimum temperature at which to operate a column that could separate these components properly in isothermal analysis. The temperature would be low enough to resolve the light, slightly polar components, and then the heaviest, most polar compounds would not be eluted within a reasonable time, or would give broad, flat bands, difficult to detect and to References on p. 90.

84

quantitate. Or the temperature would be high enough to afford proper elution of these late-eluting components as sharp, well-resolved bands, but then the light components would not be separated: the resolution between two peaks depends on the retention of the second one (see equation 35, Chapter 1). Since there is no acceptable column temperature another approach must be used, either the use of several columns and column switching durind the analysis (see Chapter 9, Section IV), or programmed temperature gas chromatography (PTGC). The former method is used in process on-line analysis, the latter for routine or research analyses carried out in the laboratory. PTGC is very widely used for the analysis of mixtures derived from natural sources, such as fats or fatty acid esters, amino acid derivatives, petroleum fractions, or in environmental or biochemical analysis. In all those applications the problems encountered are essentially in the determination of the peak areas for quantitative analysis. These problems are not specific to PTGC. It is just a little more difficult to achieve the proper control of the ambient parameters and limit the instrumental sources of errors, related to the fluctuations of flow rate or temperatures (see Chapter 9, Section V). Retention data are rarely used for identification in a modem laboratory, and never retention data obtained in PTGC. They are both too inaccurate and too difficult to account for. On the other hand, there is no special problem encountered in temperature-programmed operation of the chromatographic column of a combined instrument, such as a GC-MS or a GC-FTIR. For this reason, the determination of a relationship between the isothermal retention volume, or the entropy and enthalpy of retention, and the retention time in PTGC is not the main worry of the analyst. The only problems of practical importance are the selection of the optimum starting temperature and program rate. The final temperature is most often set equal to the temperature limit of the stationary phase used. For these reasons we thought that a separate chapter dealing with temperature programming was not necessary. The instrumental aspects of the method are discussed in Chapter 9, Section V. The theoretical problems are discussed in the present section. C.1 THE PREDICTION OF THE ELUTION TEMPERATURE

PTGC was suggested first by Griffiths, James and Phillips (57), as early as 1952. Ballistic programming was used at the time, resulting in non-linear programs, difficult to reproduce, even with a given chromatograph. Now modem instruments permit the use of linear programs or of a succession of linear temperature ramps and isothermal periods. The theory of PTGC was studied by Giddings (58) as early as 1960. An exhaustive book has been published by Harris and Habgood (59). Interesting work has also been published by Rowan (60) and, more recently, by Dose (61), who took advantage of the considerable advances made in computer technology during the last twenty years and revisited the issue.

85

In linear temperature programming, the only practical method of PTGC, the column temperature at time t is given by: T = To + rt

(46)

where To is the starting temperature, t the time and r the program rate. When the temperature increases, most of the physical constants vary. The partition coefficients decrease, the diffusion coefficients and the carrier gas viscosity increase. The carrier gas flow rate changes. It increases in proportion to the temperature if a flow rate controller is used (see Chapter 9, Section 11.4), it decreases with approximately the 0.8 power of the absolute temperature if a pressure controller is used (see Chapter 9, Section 11.3). The most important variation, however, is that of the partition coefficient. Harris and Habgood (59) have shown that, as a first approximation, we may assume that the average carrier gas flow rate remains constant. At a given time, the velocity of migration of the band is given by: dz

F(z) L

dt

VR

-=-

-

(47)

where: - F(z) is the gas flow rate at the abscissa z , - VR is the corrected retention volume of the

compound (see Chapter 1, equation 7), - L is the column length. Combining this equation with equation 6 of Chapter 2, which relates the local carrier gas velocity (hence, flow rate) to the outlet velocity, equation 46, and integrating between column inlet and outlet, on the assumption that the flow rate is constant, gives:

Equation 48 cannot be integrated analytically, because the corrected retention volume is the sum of the gas hold-up volume, which decreases in proportion to the reverse of the temperature, and the net retention volume, equal to A exp( A H/RT). This equation has been solved graphically and numerically by Harris and Habgood (59) and approximately by Giddings (58). Bauman et al. (62) have suggested a procedure to adjust the temperature scale and produce a unique curve for all analytes. Rowan (60) has presented a set of curves that permit calculations for constant pressure GC. Dose (61) has used computer integration. 1. Numerical Solution For each analyte, the corrected retention volume is measured at different temperatures. Then the RHS of equation 48 is calculated by numerical integration. References on p. 90.

86

It is practical to use the specific retention volume in equation 48. Then the flow rate Fo in equation 48 must be also related to the unit mass of stationary phase. The retention temperature, TR, is obtained as the abscissa of the intersection between the horizontal line y = r/F corresponding to the program rate and the flow rate selected for the experiment with the plot of the integral of dT/VR versus the temperature. The results obtained are in excellent agreement with experimental data (58). 2. Approximate Solution and the Equivalent Temperature

If the gas hold-up can be neglected compared to the retention volume, i.e., as long as the starting temperature is low and the program rate moderate, equation 48 can be solved by conversion to the sum of an exponential and an integral for which tabulated solutions are readily available. This approach, due to Rowan (60), has been rendered obsolete by the advent of the personal computer. By skillful manipulation of equation 48, Giddings (58) has shown that the retention temperature, TR, is such that the retention volume in temperature programming is approximately equal to the isothermal retention volume at a temperature called the significant or sometimes the equivalent temperature, equal to 0.85 TR (temperatures in K). This may be a very useful semi-empirical rule to determine, approximately but rapidly, the temperature at which to carry out an isothermal analysis giving almost the same retention time for a certain compound as the one observed during a temperature programmed analysis.

3. Reduced Temperature Scale .The graph obtained by plotting the integral of dT/VR from a starting temperature, To, to T versus the temperature T is called a characteristic curve. It is different for each compound and the necessity of determining a separate curve for each compound in order to derive retention temperatures from isothermal data makes the method very impractical. Baumann et al. (62) observed that the characteristic curves corresponding to a sufficiently low starting temperature are similar for all compounds. It is possible to adjust the temperature scale to make these curves coincide. A single curve could then be used. This method has obvious limitations, since it assumes that the retention enthalpies are similar for all compounds. Obviously this cannot be true, since it is well known that some pairs of compounds undergo a reversal of their elution order when the temperature is increased. 4. Retention Indices

It has been observed that the retention index calculated from the retention temperatures:

is approximately equal to the retention index obtained under isothermal conditions. As the retention index varies slowly with temperature, the selection of the proper temperature is critical for the systematic use of retention data obtained in programmed temperature. Van den Do01 and Kratz (63)observed a reasonable agreement with isothermal data measured at the retention temperature. Guiochon (64) claimed a better correlation with isothermal indices obtained at the equivalent temperature.

C.11 OPTIMIZATION OF EXPERIMENTAL CONDITIONS

1. Selection of the Starting Temperature Reversing the concept of equivalent temperature (see previous section), we see that an analysis is not carried out under the conditions of temperature programming if the retention temperature is not equal to or larger than 1/0.85 = 1.18 times the starting temperature (in K). As long as the resolution is sufficient, that has no importance, on the contrary, the retention being lower, the analysis time is shorter. If the resolution is insufficient, on the other hand, this is probably because retention is insufficient. If this is so, it can be improved by reducing the starting temperature, by increasing the program rate or by decreasing the flow rate. Adjustment of the flow rate is first carried out to optimize the column efficiency. Then the program rate is adjusted to optimize the resolution (see the next section). Finally, the starting temperature is selected to provide sufficient resolution for the early pairs that are difficult to separate. If the column length needs adjustment, either to increase the resolution or to reduce the analysis time, it should be born in mind that, since the corrected retention volume in equation 48 is proportional to the column length and the outlet flow rate is usually kept constant when the column length is changed, the program rate should be changed in proportion to the reverse of the column length: long columns must be operated with slow program rates, short columns with fast program rates.

2. Selection of the Program Rate Harris and Habgood (59) have demonstrated, both from a theoretical standpoint and by experimental results, that the program rate has a critical effect on the resolution between closely eluted bands. The column efficiency usually increases with increasing temperature, since diffusion coefficients, which control the kinetics of mass transfer, do increase with increasing temperature. Since faster radial mass transfer also means a larger optimum velocity (see Chapter 4), the use of flow rate controllers rather than pressure controllers is legitimate (see Chapter 9, section 11). The resolution can be divided into two parts, one related to the column efficiency, the other one to the thermodynamics of the interaction between the two References on p. 90.

88

compounds considered and the stationary phase. The resolution can be expressed as:

(see Chapter 1, equation 32). This can be written as:

m

R=R,-

4

with:

Fryer, Harris and Habgood (65) have shown that in most cases the intrinsic resolution increases with decreasing starting temperature. Exceptions occur when the initial temperature is already low or when there is an inversion of the elution order at some intermediate temperature. The intrinsic resolution tends towards 0 with increasing values of the ratio r / F . It usually (that is, except when there is reversal in elution order) happens that the intrinsic resolution is a maximum for values of r / F ’ around 0.1 ( F ’ is the carrier gas flow rate, STP, per unit mass of stationary phase in the column). Experimental data confirm these predictions, with an optimum for r / F ’ slightly below 0.1. Merle d’Aubigne and Guiochon reported a maximum in the intrinsic resolution of 2,2,3and 2,3,4-trimethylpentane for a ratio of r / F ’ of 0.3, with open tubular columns. ‘Accordingly, the program rate should be chosen so that the ratio r / F ’ lies between 0.1 and 0.3. This corresponds to values which are often markedly lower than those used by many analysts. Faster analysis would be obtained by shortening the column and using a program rate closer to the values recommended here.

GLOSSARY OF TERMS Specific surface area of the stationary phase. Equation 37. Mass of sorbate adsorbed on an adsorbent at equilibrium under a certain pressure. Equation 42. Second virial coefficient of a gas mixture. Equation 22. Bm Second virial coefficient of a pure gas or vapor 1 at the column temperBl 1 ature. Equation 23. Second mixed virial coefficient of compounds 1 and 2 at the column B12 temperature. Equation 23. Concentration of a complexing additive in the stationary phase. Equation CA 29. C , , C,, etc. Coefficients in the isotherm equation 42.

A, a

89

F'

j

K K,K' K,

PO PC.1

P Pn PO

R R R R; r SO

T

T, TC.1

TO TR t

Concentration of solute X in the gas phase. Equation 32. Total concentration of solute X in the stationary phase. Equation 33. Flow rate of carrier gas. Flow rate of carrier gas divided by the weight of stationary phase contained in the column. Local carrier gas flow rate, at abscissa t. Equation 47. Retention index of a compound X. Equation 49. Correction factor for gas compressibility. Equation 13. Complexation constant. Equation 29. Adsorption coefficients. Equation 41. Adsorption coefficient of a vapor on the surface of an adsorbent. Equation 37. Partition coefficient of a compound between the two phases. Equation 26. Partition coefficient over the pure solvent. Equation 29. Column capacity factor. Equation 1. Henry's constant of dissolution or adsorption. Equation 20. Column length. Equation 47. Molecular weight of the stationary liquid phase. Equation 3. Mass of adsorbent contained in a column. Equation 43. Plate number of the column. Equation 50. Mole fraction of compound A in the stationary phase. Equation 23. Number of moles of gas or vapor. Equation 22. Number of mole of solute in the gas phase at equilibrium. Equation 1. Number of mole of solute in the liquid (stationary) phase at equilibrium. Equation 1. Number of mole of solvent (stationary phase) in the column. Equation 2. Average column pressure (P o / j ) . Equation 26. Vapor pressure of the solute under study. Equation 6. Critical pressure of compound 1. Equation 24. Local pressure of the carrier gas. Equation 4. Standard pressure. Equation 13. Outlet pressure. Equation 13. Frontal ratio. Equation 1. Universal gas constant. Equation 4. Resolution. Equation 50. Intrinsic resolution. Equation 50. Program rate in temperature programmed gas chromatography. Equation 46. Specific surface area of an adsorbent. Equation 44. Absolute temperature of the stationary phase or the column. Equation 4. Column temperature. Equation 12. Critical temperature of compound 1. Equation 24. Starting temperature in temperature programmed GC. Equation 46. Retention temperature. Equation 48. Time. Equation 46. References on p. 90.

Carrier gas velocity. Volume occupied by n moles of a gas or vapor. Equation 22. Retention volume of compound 1. Equation 51. Specific retention volume. Equation 12. Ideal specific retention volume, observed with an ideal, non sorbed carrier gas. Equation 45. Geometrical volume available to the gas phase. Equation 4. Volume of liquid phase contained in the column. Equation 3. Retention volume of the 'air' peak. Equation 13. Retention volume expressed for 1 g of packing material. Equation 37. Corrected retention volume. Equation 47. Partial molar volume of a solute in a solution. Equation 26. Molar volume of the solution. Equation 33. Molar volume of the pure liquid solute 2 at the column temperature. Equation 26. Molar volume of the pure solvent at the column temperature. Equation 33. Base-line width of the peak of compound 1. Equation 50. Mole fraction of solute in the stationary phase. Equation 2. Compressibility coefficient of compound 2. Equation 27. Abscissa along the column. Equation 47. Relative retention of two compounds. Equation 20. Activity coefficient of the solute in solution in the stationary phase. Equation 6. Activity coefficient of compound A. Equation 30. Excess molar enthalpy of mixing of 1 mole of pure solute with the liquid stationary phase. Equation 15. Variation of enthalpy associated with the vaporization of 1 mole of solute at infinite dilution in the liquid stationary phase. Equation 15. Variation of enthalpy associated with the vaporization of 1 mole of pure solute. Equation 15. A ( A G o ) Difference between the Gibbs free energies of vaporization of two compounds whose resolution is under study. Equation 21. 9 Fraction of the adsorbate in the sorbed monolayer. Equation 45. G Correction coefficient in Equation 35. P Density of the stationary liquid phase. Equation 3. (I Surface tension of the stationary liquid phase. Equation 39. e Coverage ratio of the adsorbent. Equation 41. In the case of the discussion of the separation of two compounds, the subscripts 1 and 2 stand for the parameters pertaining for the two compounds involved.

LITERATURE CITED (1) J. R. Conder and C.L. Young, Physicochemical Measurement by Gas Chromatography, Wiley, New York, NY, 1979.

91 (2) A.B. Littlewood, Gas Chromatography, Principles, Techniques and Applications, Academic Press, New York, NY, 2nd Edition, 1970. (3) R. Consden, A.H. Gordon and A.J.P. Martin, Biochem. J., 38, 224 (1944). (4) A.T. James and A.J.P. Martin, Biochem. J., 50, 679 (1952). ( 5 ) A.T. James and A.J.P. Martin, The Analysr, 77, 915 (1952). (6) A.B. Littlewood, C.S.G. Phillips and D.T. Price, J. Chem. SOC.,1955, 1480. (7) A.I.M. Keulemans, A. Kwantes and P. Zaal, Anal. Chim. Acra, 13, 357 (1955). (8) P.E. Porter, C.H. Deal and F.H. Stross, J . Amer. Chem. SOC.,78, 2999 (1956). (9) G.J. Pierotti, C.H. Deal, E.L. Derr and P.E. Porter, J . Amer. Chem. SOC.,78, 1989 (1956). (10) A. Kwantes and G.W.A. Rijnders, in Gas Chromatography 1958, D.H. Desty Ed., Butterworths, London, UK, 1958, pp. 125-135. (11) A.J.P. Martin, The Analyst, 81, 52 (1956). (12) D.E. Martire and L.Z. Pollara, in Advances in Chromatography, Vol. I, J.C. Giddings and R.A. Keller Eds., Marcel Dekker, New York, NY, 1965, pp. 365-362. (12b) G.M. Vogel, M.A. Hamzavi-Abedi and D.E. Martire, J . Chem. Thermodyn., 15, 739 (1983). (13) R. Kobayashi, P.S. Chappelear and H.A. Deans, Ind. Eng. Chem., 59, 63 (1967). (14) C.L. Young, Chromatogr. Rev., 10, 129 (1968). (15) J.R. Conder, in Progress in Gas Chromatography, J.H. Pumell Ed., Interscience, New York, NY, 1968, pp. 209-270. (16) D.F. Fritz and E. sz Kovats, Anal. Chem., 45, 1175 (1973). (17) E.A. Moelwyn-Hughes, Physical Chemistry, Pergamon Press, London, 1961. (18) C. Vidal-Madjar, M.F. Gonnord, M. Goedert and G. Guiochon, J. Phys. Chem., 79, 732 (1975). (19) B.L. Karger, Anal. Chem., 39, 24A (1967). (20) G. Blu, L. Jacob and G. Guiochon, Bull. Centre Rech. S.N.P.A., Pau (France), 4 , 485 (1970). (21) L.M. Canjar and F.S. Manning, Thermodynamic Properties and Reduced Correlation for Gases, Gulf Pub., Houston, Texas, 1969. (22) D.H. Everett, Trans. Faraday Soc., 61, 1637 (1965). (23) E.A. Guggenheim, J. Chem. Phys., 13, 253 (1945). (24) A.J.B. Cruickshank, M.L. Windsor and C.L. Young, Proc. Roy. SOC.(London), A295, 259, 271 (1966). (25) A.J.B. Cruickshank, B.W. Gainey and C.L. Young, in Gas Chromatography 1968, C.L.A. Harbourn Ed., The Institute of Petroleum, London, UK, 1969, pp. 76-91. (26) G. Blu, L. Jacob and G. Guiochon, J. Chromatogr., 50, 1 (1970). (27) A.B. Littlewood and F.M. Willmott, Anal. Chem., 38, 1031 (1966). (28) J.R. Conder and J.H. Pumell, Trans. Faraday Soc., 64,1505 (1968); id. 64, 3100 (1968); id. 65, 824 (1969). (29a) R.J. Laub and R.L. Pecsok, Physicochemical Applications of Gas Chromatography, Wiley, New York, NY, 1978. (29) J.H. Pumell, in Gas Chromarography 1966, A.B. Littlewood Ed., Elsevier, New York, NY, 1967, pp. 3-18. (30) E. Gil-Av and J. Herling, J. Phys. Chem., 66, 1208 (1962). (31) C. Eon, C. Pommier and G. Guiochon, C.R. Acad. Sci. (Paris), 270C. 1436 (1970). (32) C. Eon, C. Pommier and G. Guiochon, Chromatographia, 4 , 235, 241 (1971). (33) C. Eon, C. Pommier and G. Guiochon, J. Phys. Chem., 75, 2632 (1971). (34) C. Eon and G. Guiochon, Anal. Chem., 46, 1393 (1974). (35) J.H. Pumell and O.P. Srivastava, Anal. Chem., 45, 1111 (1973). (36) D.E. Martire, J. Phys. Chem., 87, 2425 (1983). (37) D.E. Martire, Anal. Chem.. 46, 1712 (1974). (38) S.H. Langer, Anal. Chem., 44, 1915 (1972). (39) C. Eon and B.L. Karger, J. Chromatogr. Sci., 10, 140 (1972). (40) R.L. Martin, Anal. Chem., 33, 347 (1961). (41) R.L. Martin, Anal. Chem., 35, 116 (1963). (42) C. Eon and G. Guiochon, J. Colloid and Interface Sci., 45, 521 (1973). (43) C. Devillez, C. Eon and G. Guiochon, J. Colloid and Interface Sci., 49, 232 (1974).

92 (44) A.V. Kiselev and Ya.1. Yashin, Gas Solid Chromatography, Masson, Paris, France, 1968. (45) A.V. Kiselev, Kolloidn. Zh., 20, 388 (1958). (46) F.J. W h s , Proc. Roy. Sm., A164.496 (1938). (47) A.V. Kiselev, in Gas Chromatography 1964, A. Goldup Ed., Buttenvorths, London, UK, 1964, p. 238. (48) J.C. Giddings, Anal. Chem., 36, 1170 (1964). (49) C. Vidal-Madjar and G. Guiochon, J. Phys. Chem., 71, 4031 (1967). (50) J. Villermaux, J. Chromatogr., 83, 205 (1973); J. Chromatogr. Sci., 12, 822 (1974). (51) D.E. Martire, Private Communication, 1986. (52) C. Pommier and G. Guiochon, Gas Chromatography in Inorganics and Organometallics, Ann Arbor Science Pub., Ann Arbor, MI, 1973, chap. IX.2. (53) Ibid., Chap. 111.7. (54) A. Di Corcia and R. Samperi, J. Chromatogr., 77, 277 (1973). (55) A. Di Corcia and F. Bruner, Anal. Chem., 43, 1634 (1971). (56) O.L. Hollis, Anal. Chem., 38, 309 (1966). Also US Patent No. 3,357,158 (1967). (57) J.H. Griffiths, D.H. James and C.S.G. Phillips, Analyst, 77, 897 (1952). (58) J.C. Giddings, in Gas Chromatography, N. Brenner, J.E. Callen and M.D. Weiss, Eds., Academic Press, New York, NY, 1962, p. 57. (59) W.E. Harris and H.W. Habgood, Programmed Temperature Gas Chromatography, Wiley, New York, NY, 1966. (60) R. Rowan Jr., Anal. Chem., 33, 510 (1961). (61) E.V. Dose, Anal. Chem., 59, 2414 and 2420 (1987). (62) F. Baumann, R.F. Klaver and J.F. Johnson, in Gas Chromatography 1962, M. Van Swaay Ed., Butterworths, London, UK, 1962, p. 152. (63) H. Van den Do01 and P. Kratz, J. Chromatogr., 11,463 (1963). (64) G. Guiochon, Anal. Chem., 36,661 (1964). (65) J.F. Fryer, H.W. Habgood and W.E. Harris, Anal. Chem., 33,1515 (1961). (66) J. Merle d’Aubigne and G. Guiochon, in Gas Chromatographie 1965, H.G. Struppe Ed., Akademie Verlag, Leipzig, DDR, 1965. (67) D.E. Martire, Anal. Chem., 46, 626 (1974). (68) R.J. Laub, Anal. Chem., 56, 2110 (1984). (69) J.H. Dymond and E.B. Smith, The Virial Coefficients of Pure Gases and Mixtures, Clarendon Press, Oxford, UK,1980. (70) R.J. h u b , Anal. Chem., 56, 2115 (1984). (71) D.E. Martire, in Progress in Gas Chromatography, J.H. Purnell Ed., Interscience, New York, NY, 1968, pp. 93-120. (72) J. Serpinet, Anal. Chem., 48, 2264 (1976). (73) J. Serpinet, Chromatographin. 8, 18 (1975). (74) J. Serpinet, J. Chromatogr., 119, 483 (1976). (75) J. Serpinet, Nature Physical Science. 232(28), 42 (1971). (76) G. Untz and J. Serpinet, Bull. Soc. Chim (France), 1973, 1591. (77) G. Untz and J. Serpinet, Bull. Soc. Chim (France), 1973, 1595. (78) G. Untz and J. Serpinet, Bull. Soc. Chim. (France). 1976, 1742. (79) R. Laub. Private Communication, 1987. (80) D.E. Martire, Private Communication, 1987. (81) V. Pretorius, J. High Resolut. Chromatogr. Chromatogr. Commun., I , 199 (1978). (82) D.E. Martire and R.E. Boehm, J. Phys. Chem, 91, 2433 (1987).

93

CHAPTER 4

FUNDAMENTALS OF THE CHROMATOGRAPHIC PROCESS Chromatographic Band Broadening

TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . ............................... I. Statistical Study of the Source of Band Broa ng ............................. 11. The Gas Phase Diffusion Coefficient . . . . . . . . . . . . ........................ 111. Contribution of Axial Molecular Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Contribution of the Resistance to Mass Transfer in the Gas Stream . . . . . . . . . . . . . . . . . V. Contribution of the Resistance to Mass Transfer in the Particles ................. VI. The Diffusion Coefficient in the Stationary Phase . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Contribution of the Resistance to Mass Transfer in the Stationary Phase . . . . . . 1. Gas- Liquid Chromatography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Gas-Solid Chromatography . . .............................. VIII. Influence of the Pressure Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX. Principal Properties of the H vs u curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Open Tubular Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Packed Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................ 3. Variation of the Efficiency with the Column Length 4. Efficiency of Series of Coupled Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . X. The Reduced Plate Height Equation ......................... XI. Influence of the Equipment. . . . . . . . . . . . . . . . . . . . . . . . . ........ 1. Injection Systems. . . . . ................ 2. Connectors and Tubings ..................... 3. Detectors and Amplifiers 4. Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII. Band Profile for Heterogeneous Adsorbents . . . .......................... y ......................... XIII. Relationship between Resolution and Column Ef XIV. Optimization of the Column Design and Operating Parameters .................... 1. Selection of the Column Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Selection of the Particle Size (CPC) or Column Inner Diameter (OTC) . . . . . . . . . . . . . 3. Practical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature Cited . . . . . . . . . . . . ...........................................

93 94 95 96 98 100

102

110 111 113 114

117 117 118 120 121 122 123 124

INTRODUCTION The thermodynamics of gas chromatography deals with the partition or adsorption equilibrium between the gas and the stationary phase and relates the equilibrium constant to the retention time or volume of the compound. The retention data are usually referred to the elution time of the band maximum. It can be shown that, if equilibrium is not achieved but the kinetics of mass transfer between the two phases is controlled either by diffusion or by a first-order reaction or by a References on p. 124.

94

combination of both, the retention time of the mass center of the band is related to the equilibrium constant by the equations discussed in Chapter 3 (1,2). Thus, use of the retention time of the mass center, or the first moment of the chromatographic peak, to calculate retention data has been advocated. The advantage of this approach over the more traditional one has not been shown conclusively, however, probably because, when the assumptions on which it is based are valid, the bands are never far from being symmetrical. Nevertheless, the retention time should be viewed as an average residence time of the molecules injected in the sample (3). Around that average their residence times are spread more or less widely. Some molecules move along very fast, others more slowly. This effect can be related to the variance or the standard deviation of the residence time. The kinetics of chromatography studies the influence of the experimental parameters on this variance. There are several more or less independent contributions to band broadening. In what follows we review them and discuss their importance.

I. STATISTICAL STUDY OF THE SOURCE OF BAND BROADENING If we consider a reference system moving along the column at a speed Ru,the band appears to be immobile but the molecules spread around its center (3). We shall assume that the various sources of band broadening are independent and that their contribution can be described in this reference frame using the model of random motion (cf Chapter 1, Section IX, Properties of the Variance). Brownian motion is an example of random motion. The various sources of band broadening in this model will operate as an apparent increase of the diffusion coefficient, and the eluted band will have a Gaussian profile, provided the profile of the injected band is either symmetrical or very narrow compared to the eluted profile. As long as the sources of band broadening are random, the resulting profile must be symmetrical: there is no systematic effect in a random phenomenon, and nothing which can explain the fact that late molecules are further delayed, more so than early molecules. This is if we neglect the small contribution to band broadening and asymmetry which results from the fact that late eluted molecules stay longer in the column and experience diffusion for a longer time. Rigorously speaking, only the band profiles inside chromatographic columns are symmetrical; elution profiles are not. The difficulties and limitations of the method are now obvious. Certain contributions may be forgotten in our survey (3). The effect of others may be impossible to calculate, or several such sources may not be independent, so the resulting variance may be calculated incorrectly. Three effects have to be neglected here and will be discussed separately, because they cannot be treated adequately with this model. They are (i) the deviation of the phase equilibrium isotherm from a linear behavior in the concentration range experienced by the band considered (cf Chapter 3,(ii) the shape of the injection band which can rarely be made symmetrical and narrow enough (cf Section X,below) and (iii) the effect of mixed retention mechanisms and

95

more specifically of adsorption on high energy sites on the surface of either an adsorbent or of a liquid support (cf Chapter 3, Section A.IX, and Section XI, below). Excellent results, in good agreement with experimental results are, however, obtained by using a random motion model taking account of the effects of the following phenomena: 1. Axial, molecular diffusion. 2. Transfer of the gas molecules from the main stream of carrier gas to the inside of the particles and back. 3. Mass transfer by diffusion inside the pores of the packing particles, either in the gas or in the liquid phase. 4. The kinetics of adsorption-desorption when adsorption takes place, either as a main or a secondary retention mechanism and when this kinetics is fast. Calculation of these contributions can be done in three different ways. We can write the mass balance equation for the analyte in a chromatographic column and solve it. This is how the rigorous Golay equation for open tubular columns was obtained (4). Any deviation between experimental results and the predictions of the Golay equation must be explained by a discrepancy between the experimental conditions and the assumptions made in the derivation of the equation, such as tailing injection, mixed mechanisms including adsorption, non-cylindrical tube, etc. Another method for deriving contributions to band broadening applies the random motion model (cf equation 20, Chapter 1). Finally, the Einstein equation ( 5 ) relates the variance of a Gaussian profile to the diffusion coefficient and the time during which diffusion is allowed to take place. In the next two sections we discuss the derivation of the contribution of these sources of band broadening. 11. THE GAS PHASE DIFFUSION COEFFICIENT

Mass transfer in gas chromatography takes place through diffusion across the gas stream, to the porous particles of support or adsorbent, then through diffusion in the stagnant gas which impregnates these particles and finally through diffusion in the liquid phase or adsorption-desorption on the gas-solid interface. As will be shown later, the contribution of the gas phase diffusion to the kinetics of mass transfer, and hence to the band broadening, is of major importance. Molecular diffusion plays a major role in both the radial and the axial direction of the column. In all these cases the fundamental parameter which will control the kinetics is the diffusion coefficient. Diffusion in gases has not been much studied, except for the case of permanent gases mixtures; there are few data available on organic molecules. While it seems difficult at present to accurately calculate the diffusion coefficients of vapors in carrier gases, there is an empirical equation which permits the derivation of values of this coefficient which are in good agreement with experimental results. Diffusion in gases is not an activation process (6). Thus, in agreement with the prediction of simple gas dynamics, the diffusion coefficient increases as the power References on p. 124.

96 TABLE 4.1 Atomic and Structural Diffusion Volume Increments

v,* C H 0 N

c1 S Aromatic Ring

~~

~

v, **

16.50 1.98 5.48 5.69 19.50 17.00

25.40 0.80 6.30 8.60

- 20.20

- 50.20

Cf. Ref. 8. Cf. Ref. 7.TABLE 4.2

**

1.7 of the absolute temperature (the simple kinetic theory of gases predicts an exponent equal to 1.5 for hard-sphere molecules; the differenceis explained by the slight softness of the molecules: a grazing collision is no collision). Similarly, the diffusion coefficient is inversely proportional to the gas pressure. Finally, the diffusion coefficient varies slowly with the composition and, in GC, can be considered as being independent of the solute concentration (7,8). Fuller, Schettler and Giddings have shown that the diffusion coefficients of those gases and organic vapors for which they could find experimental data are well accounted for by the following equation (8):

where: - Ml and M, are the molecular weight of the solute and carrier gas, respectively, - Kl and V;., are the volume increments of the atoms or groups composing the solute and carrier gas, respectively. - P and T are the gas pressure (here in atm) and temperature (in K), respectively. The increments for the most important atoms are given in Table 4.1. For carrier gases, He = 5.4, H, = 11.1, N, = 22.5, CO, = 32.8. Other data are available. Their use permits an estimate within about 10% of the diffusion coefficient, which is quite satisfactory for the following applications.

111. CONTRIBUTION OF AXIAL MOLECULAR DIFFUSION

In elution chromatography, the sample is injected as a narrow plug into the mobile phase. Accordingly, there is a strong concentration gradient along the column axis and, following Fick's law of diffusion, a large flux of sample takes place, in an opposite direction to the concentration gradient (5). For this reason

97

short analysis times should be preferred, especially for trace analysis: the shorter the time spent inside the column, the lesser the extent of dilution by diffusion. In h s classical study of Brownian motion, Einstein has shown that in the case of a one-dimensional motion of molecules, the distribution profile after a time period t is Gaussian. The variance of this Gaussian profile is related to the time and to the diffusion coefficient, D , by the equation: 0:

= 2 Dt

(2)

Since the molecules remain in the gas phase for a time equal to L / u , we obtain the following contribution of axial diffusion to the band variance (3): 0: =

DL 2U

(3)

The velocity in equation 3 is the average velocity ( j u o ) . But the diffusion coefficient in this equation is an average coefficient. Diffusion coefficients in gases are inversely proportional to pressure. This relationship holds very well over the whole range of pressures used in gas chromatography. It can be shown that the diffusion coefficient to be used in equation 3 is the one measured under the average pressure. Since the carrier gas mass flow rate along the column is constant, the product of the average pressure and velocity is equal to the product of the outlet pressure and velocity. Hence:

where Dg is the diffusion coefficient of the analyte in the mobile phase under atmospheric pressure. Finally, there is still a correction to apply to equation 4 in the case of packed columns, because we have so far neglected the fact that the trajectories of the sample molecules when they move with the carrier gas extend around the packing particles and are longer than the column length (9,lO). On the average the velocity of the gas stream is larger by a factor l / y than if the trajectories were linear. The value of this tortuosity constant can be estimated by complex geometrical reasoning to be approximately 0.7, in agreement with experimental results (10). In conclusion, the axial, molecular diffusion contribution to band broadening is:

with y equal to 1 for open tubular columns and 0.7 for packed columns. We have neglected the contribution of axial diffusion in the stationary phase. While it is dissolved or adsorbed, the solute can also diffuse along the axis of the column. The constraint which promotes diffusion is the concentration gradient. As the equilibrium constant is often large, the concentration gradient in the stationary References on p. 124.

98

phase can be much larger than it is in the gas phase, which could compensate in part for the much smaller diffusion coefficient. The fact that the ratio of the diffusion coefficients in the gas and stationary phases exceeds a factor of 10,000, and the lack of data suggesting otherwise, however, makes it reasonable to assume a negligible contribution from axial diffusion in the stationary phase (7). If necessary, it could be taken into account by adding another term to the plate height, corresponding to the axial diffusion in the stationary phase (11).

IV. CONTRIBUTION OF THE RESISTANCE TO MASS TRANSFER IN THE GAS STREAM

The sample molecules are injected and eluted in the gas stream. They migrate along the column in the gas stream. When they are in the stationary phase, whether it is a packing of solvent coated support or of adsorbent, or a layer of solvent along the wall of an open tubular column, they are motionless. Accordingly, they must move in and out of the stationary phase, and across the gas stream. The actual gas velocity across the gas stream is not constant. The gas experiences two constraints. The difference between the inlet and outlet pressure tends to force it out of the column. As soon as it moves, however, viscous drags prevents the sliding of the gas along the wall, or of gas streamlines along each other. In the simple case of a cylindrical tube (as in an open tubular column) the net result of these forces is a parabolic velocity profile in the cross section (12). Along the wall the velocity is zero. It increases towards the center of the tube, where it is at a maximum. At a distance x from the center of the tube the local velocity is given by:

”

=2

4 1-

4)

where u is the cross section average velocity, i.e. the local velocity as used in chromatography, and r is the column diameter. In a packed column the velocity distribution is much more complex. There is a large number of interconnected channels which experience very fast changes in cross section. This explains why the permeability of a packed column is small compared to that of a cylindrical tube. Qualitatively, however, the situation is similar. The gas velocity is zero along the particles and increases rapidly towards the center of each channel. A molecule which is in the middle of a gas stream, whether in a packed or capillary column, can have access to the stationary phase only by diffusion across the gas stream. In the case of an open tubular column, Golay has shown rigorously that the contribution due to this phenomenon, called resistance to mass transfer, is given by (4):

4 = (1+ 6k‘+ 1lk’’)d:u

L 96(1+ / C ’ ) ~ D ~

(7)

99

where d , is the column diameter. This equation has been experimentally verified by many independent studies. Similarly, in a packed column there is a contribution due to the finite rate at which molecules can diffuse across the gas streams. It is given by a similar equation:

where d , is the particle diameter. The factor w is a function of k’ and of the geometry of the packing. Although theory does not provide a detailed relationship, it has been suggested that the k’ dependence of w would be well accounted for by the same fraction as in equation 7. There is, however, a second contribution which takes place in packed columns and has no equivalent in an open tubular column. This is due to the fact that the different channels in the packing have different lengths and, having widely different diameters, are traversed at different velocities (13). As a first approximation, using the random motion approach, we can calculate this second contribution: a:2 = 2hd,L

(9)

where h is a numerical coefficient, not very different from unity. The two phenomena which take place in a packed column, diffusion across the gas stream and distribution of the channels lengths and average velocity are not independent, however. The widest channels are also those which are travelled the fastest. Accordingly, Giddings (14) and Littlewood (15) have suggested the combination of these two terms, given by equations 8 and 9, in the following manner: a; =

1

-1 +1z 2

a/,1

a/,2

Thus, the mobile gas phase contribution in a packed column becomes: wdiuL

2

a/ =

D,

w + -dPu 2h

At low gas velocity this contribution is proportional to the gas velocity; it tends towards a constant limit at large mobile phase flow rates. Equation 11 is in very good agreement with experimental results (15,16). As far as open tubular columns are concerned, the Golay equation is in excellent agreement with experimental results (17-21). Attempts at reducing the resistance to mass transfer across the carrier gas stream have been made by tightly coiling the open tubular column (22,23).This promotes a References on p. 124.

100

radial, secondary flow. Under the stress due to the inertial effect, the gas which is in the center of the tube tends to flow towards the outside wall. A secondary circulation develops, two rotating cells appearing, one on each side of the plan perpendicular to the coil axis, through the center of the tube cross section. This radial flow promotes mixing of the gas phase and markedly reduces the variance of an unretained compound. Retained compounds, however, must still diffuse across the whole tube section and this takes time (22). The dependence of the resistance to mass transfer in the gas stream on k' is very strong and it does not seem that a considerable increase in the column efficiency is observed for retained compounds, which are those we want to separate (22). Probably for this reason strongly coiled columns have not found general acceptance.

V. CONTRIBUTION OF THE RESISTANCE TO MASS TRANSFER IN THE PARTICLES In packed columns, but not in open tubular columns, there is an additional intermediary between the gas stream and the stationary phase: the solute molecules must diffuse across the particles, in the stagnant gas phase which impregnates these particles, in order to gain access to the pools of liquid phases which are in some of the pores. This is the origin of another contribution to band broadening for which Giddings has derived an equation (24):

where p is a numerical factor which again is a function of k'.

VI. THE DIFFUSION COEFFICIENT IN THE STATIONARY PHASE The diffusion coefficient, D,, of a dilute solute in a solvent is given by the empirical Wilke and Chang equation (48), which is usually a satisfactory approximation:

where:

- M2 is the molecular weight of the solvent, - q2 is the solvent viscosity, T is the temperature (K), V, is the molar volume of the solute (to be rigorous, it should be the molar volume at infinite dilution in the solvent, but the precision of the correlation on -

101

which equation 13 is based permits the use of the molar volume of the pure solute instead). - $J2 is a constant which accounts for molecular association in the solvent; it is 1.0 for non-associated liquids, 1.5 for ethanol, 2.6 for water. For the GC applications of equation 13, $J2 will be assumed equal to 1. Equation 13 indicates that the diffusion coefficient is inversely proportional to the solvent viscosity. The obvious consequence, which was established very early on in the theory of gas chromatography (49), is the advice to avoid stationary phases with high viscosity. This misconception was reinforced by further theoretical developments (50,51). As was pointed out recently by Hawkes (27), the error arose from the fact that equation 13 is valid only for globular molecules, while most highly viscous stationary phases used are polymers (see Chapter 6). In the case of polymeric stationary phases, the situation is different (52). The small solute molecule “sees” only a short fraction of the polymeric chain, so the diffusion coefficient is related rather to the ease with which relative motions of the different segments of the chain take place, i.e., to the chain flexibility. Although little is known on the quantitative relationship between molecular structure and the diffusion coefficient, we know for example that the silicone chain is very flexible, much more so than a long alkyl chain, and this explains the superior quality of the results obtained with silicon phases in gas-liquid chromatography. Accordingly, the use of high molecular weight, viscous polymers, advocated by Grob and Grob (40,41), as a solution to the problem of mechanical stability of the liquid film layer on the wall of open tubular columns, is very sound. Also justified is the use of weakly cross-linked layers of stationary phase: provided the density of cross-linking is low enough not to significantly alter the local flexibility of the chains, the diffusion coefficient in the cross-linked polymer will be the same as in the untreated one. On the other hand, most polymers experience a vitreous transition. Below a certain temperature, the relative motions of the chain segments stop. These motions made possible the diffusion accross the polymer of analytes having the molecular size used in gas chromatography. Thus, below the glass temperature the polymeric phases behave as a solid material and retain analytes by adsorption on their surface. The determination of retention volumes of probe solutes as a function of temperature around the glass temperature usually shows a rapid jump in the retention volumes when access to the bulk becomes possible. Such determinations permit a study of the properties of the polymer. The method is called inverse gas chromatography and is widely used after the pioneering work of Guillet (55).

VII. CONTRIBUTION OF THE RESISTANCE TO MASS TRANSFER IN THE STATIONARY PHASE There are two different cases, depending whether the analyte is retained by dissolution in a liquid phase, coated on a solid support, or by adsorption on a solid surface. References on p. 124.

102

1. Gas-Liquid Chromatography

Using the random motion model, it is possible to show that if d, is the average size of the liquid phase droplets, the contribution to band broadening due to resistance to mass transfer in the liquid phase, i.e. to a finite diffusion coefficient, is given by the following relationship (3,7,11):

where v is a numerical coefficient, a function of k’, and depends on the geometrical structure of the particles. In the case of an open tubular column, the walls of which are coated by a liquid film of average thickness d,, the corresponding term, calculated by Golay (4) from the integration of the mass balance equation, is: u:

=

6k’

d/’

-UL

(1 + k ’ ) 2 Dl

where D, is the diffusion coefficient in the liquid phase.

2. Gas-Solid Chromatography In gas-solid chromatography we obtain an equation similar to equation 14 (53): :a

=

1 -UL (1+ k’)2 k, k’

where k , is the desorption rate constant ( 1 / k 2 is the average desorption time; this time is an exponential function of the adsorption energy). If the desorption time is small enough, lower than about 0.5 msec, the contribution given by equation 16 becomes negligible (54). When heterogeneous adsorbents are used, it is possible to determine, by two independent methods, the adsorption enthalpy on the low energy sites which cover most of the adsorbent surface and the average adsorption enthalpy on the high energy sites. The few results obtained show that it is possible to use this approach to characterize surfaces (54). In practice, by selecting a convenient adsorbent or by using thin films of stationary phase for open tubular columns, or a low coating ratio for packed columns, it is possible to achieve experimental conditions in which the contribution of the resistance to mass transfer in the stationary phase is negligible. VIII. INFLUENCE OF THE PRESSURE GRADIENT Combination of equations 5, 7 and 15 gives the variance of the band resulting from the different contributions which take place in an open tubular column. Using

103

equation 29 of Chapter 1, we can derive the HETP: H = -2+0 ,

+ l l l ~ ’-Ud:~ ) + 6k’ -Ud/’ 96(1 + k ’ ) 2 Dg (1 + k ’ ) 2

(1 + 6k’

U

Dl

This is the Golay equation (4). Combination of equations 5 , 11, 12 and 14 gives the variance of the band eluted from a packed column. The HETP of this column is (11):

wdp’u

2YDg H= +

w

D,+-d 2x

p

dp‘ d/’ +p-u+v-u DB Dl u

T h s equation is more complicated than the Golay equation because it depends on a number of empirical coefficients which cannot be predicted. It is not even possible to indicate which are the properties of the packing or of the particles which control the values of the parameters y, w , A , p or v, let alone to derive quantitative relationships permitting their calculation. From the data accumulated during 20 years of the study of gas chromatography, however, it seems possible to conclude that most packing materials suitable for GC give a very similar performance. The two equations given above for the HETP of packed and capillary columns (equations 17 and 18) have been derived with the assumption that the pressure gradient in the column is negligible. This is not always so, especially with packed columns and with open tubular columns having a large efficiency. We should consider that equations 17 and 18 give the local plate height (cf Chapter 1, equations 26-29). The local plate height is the proportionality coefficient between the differential increase of the band variance and the differential element of column length (3,7,25): do:

= H(z)

dz

(19)

Integration of this equation between column inlet and outlet gives the experimental or average plate height. When this integration is performed, it turns out that, in the equation of the local plate height, there are two kinds of terms: those which are independent of the local velocity and those which are proportional to it. The first two terms in equation 17, the first four in equation 18 depend on D,/u. Since D, is inversely proportional to the pressure (cf Section I1 above), these terms are a function only of the mass flow rate of carrier gas, which is constant along the column. When the band moves along the column, these contributions to the local plate height remain constant. There is only one effect of the pressure gradient on band broadening. When the band progresses along the column by the distance dx, there is a differential increase of the variance given by equation 19. Because of the pressure gradient, however, this volume contribution is expanded during further band elution, in the ratio p / p , , the ratio of local pressure to the outlet pressure. The References on p. 124.

104

Figure 4.1. Plot of the pressure correction factor, 1,versus the inlet-to-outlet pressure ratio.

integration of these effects results in a coefficient, f, by which the constant local plate height is multiplied in the derivation of the average plate height (25): 9 (~~-1)(~*-1)

f=,

( P 3 - 1)2

where P is the inlet-to-outlet pressure ratio. f varies between 1 (P= 1) and 1.125 (P infinite). For P = 6, which is a rather large value in practice, f is already equal to 1.10 (cf Figure 4.1). The last term in either equation 17 or 18 depends on the local velocity, but on no property of the gas phase (25). Integration yields a term which is now proportional to the average gas velocity. Accordingly, at large pressure gradients the contribution of the resistance to mass transfer in the liquid phase becomes negligible. The global result is:

where Hg and HIdenote the contributions to the average plate height originating in the gas and liquid phase, respectively. For an open tubular column we have: Hg=

(-+ :UZ

(1 + 6k’+ l l l ~ ’ ~ ) 96(1+ k’)*

D~

105

and :

6k’

HI = (1

df-

-24

+ k ’ ) 2 Dl

Similarly, for a packed column we obtain:

and:

These equations are in excellent agreement with the results of experimental investigations (25,26). The principle of the methods used to separate the two contributions, H, and HI,due to the resistances to mass transfer in the gas and the liquid phases is to carry out measurements of the column HETP in a range of mobile phase velocities, with several carrier gases having markedly different diffusion coefficients, such as hydrogen, helium, nitrogen and carbon dioxide. IX. PRINCIPAL PROPERTIES OF THE H VS u CURVE

Equations 20-23 (OTC) and 20, 24, 25 describe the relationships between the column efficiency and the various experimental parameters involved. Figures 4.2 and 4.3 give some illustrations of these results for open tubular columns. 1. Open Tubular Columns

When the pressure drop is negligible, i.e. for short, rather wide bore OTC columns, f in equation 22 is practically equal to unity and the plot H versus u is an hyperbola, with a vertical asymptote at u = O and a slanted asymptote going through the origin and having a slope equal to C, + C,, but in practice equal to C,: the modem OTC columns use rather thin stationary liquid films and, in spite of the cm2/sec), the very low diffusion coefficient in the liquid phase (2 to 10 X second term of equation 20 is most often negligible (17). It is worth noting that the diffusion coefficient of solutes in the stationary liquid phase does not decrease much with increasing molecular weight of the liquid phase. This is because the molecules of solutes which are small enough to be analyzed by gas chromatography cannot interact with the whole molecule of the stationary phase when it is a macromolecule (see Section VI). Only a number of segments of the References on p. 124.

106 0.11 0.1

0.09 0.08

-5

0.07

0.06

n

t-

W

I

0.05 0.04 0.03

0.02 0.01

0

I

I

I

200

I

I

400

I

I

I

r

I

aoo

600

I

1000

Gas velocity (cm/sec)

I

0

I

100

I

1

200 Gas velocity

1

1

300 (cm /sec )

400

5

Figure 4.2. Plot of the plate height versus the gas velocity for an open tubular column (Golay equation, no pressure correction). n-hexane in helium carrier gas (0,= 0.574). a. Effect of the column diameter (k' = 1). d , = (1) 0.1, (2) 0.25 and (3) 0.5 mm. b. Effect of the column capacity ratio ( d , = 0.25 nun). k' = 0, 1, 2, 5 and 10.

polymeric molecule may interact with the solute. Thus there is no adverse effect in using highly viscous polymers. The column temperature, however, must be above the vitreous transition (27).

107

Reduced

velocity

Figure 4.3. Influence of the pressure on the efficiency curve of an open tubular column. k ‘ = 0 . 5 . Reduced parameters. d , = (1) 0.25, (2) 0.10 and ( 3 ) 0.05 nun.

Accordingly, in many practical cases, the plate height equation for OTCs can be written:

The minimum value of the plate height is: H,,

= 2-

=

d,

2(1 + k’)

/

1 + 6k:

llk”

and is obtained at a velocity equal to: uopt =

1

+ 6k’ + i l k ”

It is of interest, for best performance, to adopt a flow velocity equal to the optimum value (equation 28), or if the column efficiency exceeds the amount required for the separation of all the compounds of interest, a somewhat higher value. Then a slight increase in carrier gas velocity does not cause a serious loss of efficiency (since d H/du = 0 at uOpt),but results in a proportional decrease in the analysis time. If u‘ denotes the ratio u/uopl, substitution in equation 26 gives:

References on p. 124.

108

For u’ = 1.5 the loss in efficiency is only 8% and for u’ = 2 it is still only 20%. In order to improve the efficiency of a column we have to reduce the value of the coefficients of equation 21 (see equations 21 to 23, combined). This should be done with discrimination, however. The first two coefficients are functions of the diffusion coefficient, but the product BCg is constant. Equations 27-29 demonstrate that the minimum plate height is independent of the nature of the carrier gas, but the corresponding velocity is proportional to the diffusion coefficient. Accordingly, for separations of a given mixture carried out at constant resolution with different carrier gases, the analysis time increases in the order hydrogen c helium < nitrogen < argon = carbon dioxide. The speed advantage of hydrogen over helium is still larger than the ratio between diffusion coefficients, because the former gas has a much lower viscosity than the latter; consequently the pressure drop for a given carrier gas velocity is much smaller and the pressure correction factor, j, is much closer to unity. The only practical possibility to reduce the plate height is to use a narrower column and a thin film of liquid phase. Then the third term of equation 17 disappears, as discussed earlier, and the second term is reduced. The result is both a smaller minimum HETP and a faster optimum gas velocity (cf equations 27 and 28). Attempts have been made in recent years to use narrow bore OTCs (20,21). Excellent results have been obtained in many laboratories with 0.10 mm i.d. columns, which are now commercially available. Unless very long columns are needed, no modification of the equipment is required. The use of very long columns often demands the replacement of the pressure or flow rate controller: the inlet pressure corresponding to a flow velocity 1.5 to 2 times greater than uOp,can be quite high. On the other hand short, narrow OTCs are very fast and their use may require a fast dedicated computer data acquisition system (20). Some scientists have been able to prepare and operate OTCs having diameters of 0.04 to 0.06 mm (20,21). In this case the inlet pressure becomes very large, above 20 atm, and the analysis time increases much more rapidly than the plate number, which creates a practical limit to the efficiencies which may be achieved by GC (28). Finally, it is seen in equations 27 and 28 that the minimum value of the HETP does not depend on Dg, i.e. on the nature of the carrier gas, so long as the term of resistance to mass transfer in the liquid phase is negligible; but the corresponding value of the velocity is proportional to Dg. This is the origin of the second reason why hydrogen is the best carrier gas in gas chromatography. It gives the same efficiencies as the other gases but at a much greater gas velocity. Since it is also the least viscous gas, the pressure drop is low. Accordingly analyses are carried out much more rapidly with hydrogen than with any other carrier gas, including helium.

2. Packed Columns Due to the second term of equation 24 (see equations 21, 23 and 24, combined), the shape of the plate height curve is much more complex with a packed column than with an OTC, even when the coefficient of resistance to mass transfer in the stationary phase is negligible. At very low velocities, where Dg is the dominant term

109

in the denominator of the second term of equation 24, we obtain an arc of a hyperbola. At large velocities, where Dg is negligible compared to the other term, the curve is asymptotic to another arc of a hyperbola. At intermediate values it cannot be represented conveniently by a simple equation. Around the minimum of the HETP curve, it is possible to write a three-term expansion: H=A

B ++ Cu, uo

(30)

The coefficients A, B and C are empirical, however, and cannot be related simply to the various terms of the more rigorous equations 24 and 25. Nevertheless, B depends essentially on the diffusion coefficient in the gas phase, while C depends on both the gas diffusion coefficient and the average particle size. Equation 30 is identical to the classical Van Deemter equation (29). Originally, it was derived using a simple random approach, and incorporating the sole contributions of axial diffusion (B), eddy diffusion (A) and resistance to mass transfer in the liquid phase (C). The resistance to mass transfer in the gas phase had wrongly been considered to be negligible due to a much larger diffusion coefficient. The difference in scale between the distances over which gas and liquid phase diffusion must operate in order to relax concentration gradients had been overlooked. There has been a considerable amount of work carried out on the optimization of experimental conditions for the analysis of mixtures by gas chromatography, including the selection of the column type, of the column design and operational parameters (3,7,11,17,28).The main results are summarized below. Examination of equations 24 and 30 shows that in order to improve the column performance we need to decrease the average particle size and the thickness of the pools of stationary liquid phase. We also need a very homogeneous packing. The coefficients p and w (equation 24) and A (equation 30) depend on the quality of this packing. As for the column diameter of an OTC, the reduction in the average particle size of the packing has two opposite effects on the performance of a GC column. The permeability decreases and so does the HETP. Furthermore the minimum HETP is achieved for a larger value of the flow velocity. Thus the inlet pressure should be increased greatly, to compensate for the decrease in column permeability and to take advantage of the increase in the optimum flow velocity. Accordingly, the pressure correction factor, j , decreases rapidly. This combination of effects results in a slower improvement in column performance when the particle size is reduced than is observed in liquid chromatography (28). In practice, there is an optimum particle diameter, which lies around 100-125 pm, but depends to some extent on the required column length: for short lengths somewhat smaller particles can be used. Very large efficiencies have been reported for columns packed with 30 pm silica particles (57). When the coating ratio of the support is decreased, a rapid decrease of the HETP is observed, due to a reduction of the term in equation 25. Below a ratio of 5-lo%, however, the coefficient of resistance to mass transfer in the liquid phase does not change much, if d, remains constant. Essentially this is related to the phenomenon References on p. 124.

110

of wettability. The liquid phase is most often spread as a pattern of tiny droplets in the porous support and fills certain pores. Its structure does not look much like a regular film. The use of surface-active agents sometimes leads to a marked improvement, although in many instances these compounds act more like tailing reducers, by poisoning active sites on the support surface, than like wetting agents (30). 3. Variation of the Efficiency with the Column Length There have been some controversies in the past regarding the variation of the column efficiency with the column length. It is certain that the validity of the concept of the height equivalent to a theoretical plate rests on the relative constancy of this parameter when comparing columns of different lengths, but otherwise identical and prepared in the same way, with the same material. We can already remark that equations 20-22 for open tubular columns and equations 20, 23 and 24 for packed columns show that the average plate heights measured for columns of different lengths will be different, even if the local plate height is the same for all of them, since the values of the correction factors, f and j, depend on the inlet pressure, i.e., for columns operated at the same outlet velocity, on the column length. On the other hand, for the comparison between plate heights to be valid, the columns must be operated at the same outlet velocity, so the camer gas mass flow rate must be the same, and the terms accounting for the contributions of the different sources of band broadening to the plate height must be identical (see equations 21 and 23 and note that the various terms depend on u / D g , i.e., they are independent of the local pressure). If the performance of several columns of different lengths are compared at constant average velocity, the outlet velocity will be different for each of them (see Chapter 2), the different contributions originating in the gas phase will be different (see equations 21 or 23), and the result will obviously be that the plate height varies with column length. On the other hand, the few authors who have taken the compressibility of the gas phase into account and compared column performance at constant outlet velocity have reported a constant plate height (57). This demonstrates that the reproducibility of the methods of preparation of packed columns and open tubular columns are satisfactory and that these methods produce reasonably homogeneous columns. 4. Efficiency of Series of Coupled Columns It is tempting to conclude from the previous results that the efficiency of a series of different chromatographic columns is the sum of the individual efficiencies. This would be a hasty conclusion. Things are more complex. What is additive is not the plate numbers, but the contributions of each column to the variance of the zone. This problem has been studied in detail by Kwok et al. (58). Their conclusion is that, in general, the plate number of the column series is lower than the sum of the plate numbers of the different columns. It is especially noteworthy that, if the distribution of the stationary liquid phase in a column becomes some function of

111

the column length, because of column weathering, the column efficiency decreases markedly, even if the local plate height does not change (e.g., because the resistance to mass transfer in the liquid phase is neghgible). In practice, there are two important cases. The first one is when several columns as identical as possible are prepared separately and connected to achieve the resolution of two components difficult to separate, and when it is not possible to prepare a single column of the required efficiency directly. In this case, the columns have nearly the same HETP and the same retention volume per unit length; under such circumstances the plate numbers are additive. If several columns made with different stationary phases are connected, because it is not possible to achieve the proper selectivity with a single one, the plate numbers are additive only if all columns have the same HETP and the same retention volumes, which can be true only for a few rare compounds. Otherwise, the efficiency of the column series is essentially determined by the efficiency of the column in which the analyte spends the larger fraction of its retention time. The efficiency of the column series depends on the compound used to measure it and even on the order in which the columns are placed, because of the compressibility of the mobile phase. A study of the efficiency of a series of two open tubular columns, having the same inner diameter, but prepared with different liquid phases, has been made by Gutierrez and Guiochon (59). They have derived an equation which permits calculation of the apparent plate height of a column series, taking into account the effect of the compressibility of the gas phase on the HETP (see equations 21 and 23). There is a fair agreement between experimental and calculated results.

X. THE REDUCED PLATE HEIGHT EQUATION It is often difficult to discuss the effect of a change in the nature of the carrier gas (change in D,), or in the average particle size (dp,PC) or column diameter (d,., OTC). Several plate height contributions are affected, and vary in opposite directions. Giddings (31) has shown that for columns carefully and reproducibly packed with materials having different particle size, using different methods, and operated with different mobile phases, a well-defined relationship exists between the reduced plate height:

H

j=-

dP and the reduced velocity:

For OTC the reduced parameters are defined in the same fashion, with reference to the column inner diameter. References on p. 124.

112

Furthermore, a more refined analysis of the resistance to mass transfer in the mobile phase leads to the replacement of the second term by a summation of several similar terms, corresponding to different scale levels in the column packing (heterogeneity of the packing at the particle size level, at the level of particle aggregates, etc. until the level of the column diameter; five such terms have been postulated (3)). A numerical simulation shows that this sum can be replaced by an exponential function of the reduced velocity (32). The final, semi-empirical equation:

+

+

2Y A v ” ~ CV h=Y

(33)

has been used very successfully in high performance liquid chromatography for the last 15 years (33). Its relevance to gas chromatography is similar. Its use permits a rapid assessment of the quality of a column and an easy discrimination between the influence on column performance of a poor packing methodology and a poor packing material. y should be approximately 0.7. For excellent columns, A is below 2; for good columns it is between 2 and 3. Values above 3 correspond to fair or bad packing homogeneity. Similarly C should be below 0.2. Figure 4.4 shows a few typical examples of plots of equation 33. For OTC the same equation applies, but now y is equal to unity and A to zero, C is given by the k’ part of the term of resistance to mass transfer in the gas phase of the Golay equation (equation 21). For k’ = 3 it is equal to 0.0768. It increases with k’, from 0.0104 ( k ’ = O ) to 0.115 (k’ infinite). 1.2

,

1.1

1 0.0

0.8 0.7

0.6 0.5 0.4

0.3 0.2

0

. 0.2

0.4

0.6

0.8

1

. 1.2

.

. 1.4

1.6

Loo (Reduced VelocHy)

Figure 4.4. Plot of the plate height versus the gas velocity for a packed column. Reduced parameters. Curves 1, 2 and 3: A = 1, 2 and 4, respectively, with C = 0.02. Curves 1, 4 and 5 : A = 1 with C = 0.02, 0.05 and 0.1,respectively.

113

The use of the reduced plate height equation simplifies discussion of the effect of the diffusion coefficient in the mobile phase and of the particle size (packed columns) or column diameter (open tubular column) on column performance. It also permits a quick assessment of the quality of a column, since reduced plate heights of about 2-3 should be obtained for well packed columns and about 1 for OTC.

XI. INFLUENCE OF THE EQUIPMENT It is not possible to use a column without ancillary equipment, and the very existence of this apparatus creates an additional contribution to band broadening. The main sources of loss of efficiency in the apparatus are the profile of the injection band, which depends on the volume of the injector, the rate of vaporization of the sample and its size, the volume and time constant of the detector, the size of the connecting tubes and the way connections are made. Especially detrimental to analytical performance is the existence of dead spaces through which the carrier gas does not flow but to which the vapors have access by diffusion. When the dead zone is passed, small amounts of vapor trapped in these dead volumes leak out very slowly and become a source of very long band tails. Probably one of the most lucid and most widely applicable contributions to this problem is the detailed study by Sternberg (34). The band profile recorded at the outlet of the column is the convolution product of the column contribution, which should be the largest one by far, with the various contributions of the equipment identified above. It is often impossible to carry out detailed calculations which precisely account for the exact band profile. Theoretical developments in this field aim more at deriving specifications that the equipment must satisfy than at calculating corrections to be applied to experimental data. 1. Injection Systems

There is a real paucity of data regarding the actual profile of the bands injected into a chromatographic column. Admittedly, such profiles are difficult to record. Paradoxically, however, the detailed performance of exotic systems such as the fluidic logic gate injection device (35-37) are much better known than those of classical sampling valves or syringe systems. The aim of the injection system is to introduce into the column a narrow, cylindrical or quasi-cylindrical plug-like band of the sample vapor. Most often the sample is a liquid, which requires the additional step of vaporization. Due to the slowness of heat transfer and the relatively large amount of heat required, it is difficult to expect the ready achievement of this requirement, unless the sample is really small. Otherwise differential vaporization may take place inside the syringe needle, with catastrophic consequences regarding the accuracy of the quantitative data thus obtained. In practice it is more realistic to expect an injection band profile with a very steep leading edge, followed by an exponential decay. The decay may result from References on p. 124.

114

slow vaporization, from mixing in the vaporization chamber or from a diffusion chamber, if the gas stream passes near an unswept, unstirred volume. In this case it can be shown (34) that the retention time is increased by an amount equal to the time constant, r, of the exponential decay, while the second moment of the elution band is increased by the square of the time constant. Thus the plate height, which is related to the zone variance expressed in length units, is increased by an additional contribution: H, =

r2uz

(1 + k’)’L

(34)

The time standard deviation is related to the length standard deviation by equation 18 in Chapter 1. The outlet velocity is used to account for the gas decompression, since the variance contribution which originates in the injection system is expanded in the ratio pi/po during the band elution. This contribution decreases rapidly with increasing retention, increasing column length and decreasing flow velocity. In most cases it is neghgible, unless extremely fast analyses are required or the time constant r is large. For reasonable performance T should be lower than about 0.3 sec. On the other hand, very fast injection devices with time constants of a few msec have been built (36,37) and operated for the systematic acquisition of analytical data (38) or for performance studies (39). The properties of these devices have been reviewed recently by Annino (66). Essentially, the injection time constant depends on the kinetics of vaporization of the sample and on the speed at which a gas stream can be switched. The operation of a vaporizer in a transitory state is difficult. The performance will depend most on the surface area of the heated tube, on the sample size and on the way it is applied on the heated surface. Best results are obtained with small samples. The contribution of the injection to band broadening becomes negligible when the injection is done with a cold column, followed by analysis in the temperature programming mode, because then the whole sample is frozen at the very top of the column. Various ingenious devices using similar techniques have been described, such as the on-column injection designed by Grob and Grob (40,41) for open tubular columns, based on secondary cooling, and the injection system designed by Poy and Cobelli (42) (see Chapter 8, Section IV). 2. Connectors and Tubings

Sternberg studied the contribution of connectors and tubings with the assumption that the Golay equation can be applied to describe band spreading in a connecting tube (34). Later Golay and Atwood (4344) showed, theoretically and experimentally, that the contribution of a short, empty, cylindrical tube is smaller than that predicted by equation 26 applied to a non-retained compound. This is because the number of theoretical plates which would be associated with such tubing is very small (it is short and the velocity is large since it is narrow), thus the

115

conditions for the development of a Gaussian profile are not met and the spreading is less than that predicted by Sternberg (34). When connectors which provide sharp diameter changes are used, additional band spreading takes place. The connector may be regarded approximately as a mixing chamber. The concentration profile at the exit of such a device is an exponential decay, which is extremely detrimental: at 1 mL/min (16.7 pL/sec), a mixing chamber of 16.7 yL has a time constant of 1 sec. This is the volume of a 2.5 cm long, 1 mm i.d. tube which would give a negligible contribution in laminar flow spreading. Accordingly, great care should be applied to the design of injector-to-column and column-to-detector connections which are very smooth, made out of narrow tubings, and rather short. The contribution of tubings is most often negligible in GC (44).

3. Detectors and Amplifiers The detector senses the variation of the concentration of solute in the carrier gas at the exit of the column. It cannot do that without adding some contribution of its own to the band profile, however. The sensing element of the detector operates in a finite volume and the response is adjusted to the constantly varying concentration after a finite time has elapsed. The instrument designer can strive to reduce these contributions. The efforts of manufacturers have been generally successful and performances are satisfactory, unless one is trying to achieve extremely high performance, especially when operating very fast and/or very narrow columns. The contribution of the detector cell volume is very similar to that of an injection system operated under the same conditions (i.e. plug flow or exponential mixing chamber). The contribution of the detector time constant is also given by equation 34, where 7 now stands for the response time of the detector. In most cases, the response time of the detector is essentially due to the response time of the amplifier used to adjust the signal supplied by an ion detector to the needs of recording devices. Although amplifiers and other ancillary electronic devices are not first order systems, it is a reasonably good approximation to discuss them as if they had an exponential response, with a constant response time. It is important to realize that the time constant contribution depends on the square of the carrier gas velocity and thus increases very rapidly with it. Accordingly, it is very difficult to achieve very fast analysis. Although the efficiency of narrow bore OTCs or of columns packed with very small particles could in theory be very large at high carrier gas velocities, the equipment contribution nullifies totally, or in large part, the gains thus achieved (37). This is especially important when choosing a detector. For example, when a flame ionization detector is operated at high sensitivity, a large impedance in the collecting electrode circuit is needed. This translates into a rather large time constant. The use of the Lovelock argon detector, which is only marginally more sensitive but supplies the electronics with a larger current and, thus, requires a lower amplification gain, permits the use of much smaller time constants. References on p. 124.

116

Detailed examples of the influence of the amplifier time constant on the performance of a fast gas chromatograph have been published (34,37-39). 4. Requirements

Open tubular columns offer the most serious challenge to instrument design. The column volume is small, the sample size is very small, the gas volume flow rate is low, the column efficiency is high and the analysis time is short. All these reasons combine to impose specifications which are difficult to meet. Long columns having an extremely large efficiency do not place strong demands on the performance of the system. We shall discuss here the requirements for a 15 m long column, and will use three different values of the diameter: 0.5 mm (i.e. the macrobore OTCs, used for their sample capacity), 0.25 mm (the standard column) and 0.1 mm (the advanced narrow bore OTC). The plate height of an OTC depends on the retention. It varies from 0.29 times the column diameter for unretained compounds to ca 2 column diameters for largely retained compounds. The corresponding gas velocity varies in the opposite direction, from ca 14 D J d , to about 4 DJd, (cf. equations 27 and 28 above). Since the chromatograph must be able to give good results even for early eluted peaks, we make further calculations for a compound with k’ = 1. Then the minimum plate height and corresponding velocity become 0.7 d , and 6 D,,,/d,, respectively. The time variance is derived from the following relationship:

Using equations 31 and 32 and neglecting the column pressure drop permits the derivation of an approximate solution:

The maximum contribution of the equipment should be small compared to the column band variance, so that the loss of efficiency remains reasonable. The maximum contribution of the equipment increases in proportion to the column length, to the cube of the column diameter and to the reverse of the square of the diffusion coefficient. If we require that the relative loss of efficiency be smaller than a certain factor 9, we must have:

Equations 35 and 37 permit the calculation of equipment specifications, depending on the column performance and on the way the burden is shared between the

117

TABLE 4.2 Equipment Specifications for an Open Tubular Column

**

Column i.d. (rm)

N

500 250 100 80

42857 85714 214286 267857

Outlet Velocity (cm/sW

Inlet Pressure (atm)

Retention Time (set)

Peak Variance (sec2)

12 24 60 15

0.032 0.231 2.011 3.093

254 140 109 114

1.5 0.1875 0.0120 0.0061

Exact calculation. h = 0.7; Y = 6; k’ = 1. Carrier gas, helium; q = 240 pP; Dg= 0.1 cm2/sec. ** Column length: 15 m.

different parts of the equipment. Numerical values resulting from an exact solution of equation 35 are given in Table 4.2. In general the specifications can be met by available commercial instruments, although the development of rapid analysis is still hampered by the lack of amplifiers with a short enough time constant.

XII. BAND PROFILE FOR HETEROGENEOUS ADSORBENTS When the surface of the adsorbent used in GSC, or even sometimes of the support used to spread liquid stationary phases in GLC, is heterogeneous, the elution bands become unsymmetrical. The molecules sorbed on a high energy site are markedly delayed (there is a relationship between the average residence time on a site and the energy of adsorption), and this phenomenon is systematic: the molecule will elute late. A dissymmetry has been introduced in the distribution of residence times. Giddings (45) and Villermaux (2,46) have studied this phenomenon and derived band profiles which would apply to situations where there are two different sites of adsorption, one with a rather low adsorption energy, covering most of the surface, and the other one with a large energy but covering a very small fraction of the surface. The band profile is then mostly Gaussian, but with a thin, long tail extending to a very long retention time and corresponding to the molecules desorbing slowly from the saturated high energy sites. A quest for a chromatographic system representing these models has been unsuccessful (47).

XIII. RELATIONSHIP BETWEEN RESOLUTION EFFICIENCY

AND COLUMN

The aim of the analyst is to achieve the separation of the components of a certain mixture in the shortest possible time. This requires the use of an efficient column, having a short HETP, at a high carrier gas flow velocity. Efficiency alone is insufficient, however, and the stationary phase selected to make the column must retain the components of the analyzed mixture (their k ’ s must be finite and different from 0), and exhibit enough selectivity, so that their relative retention References on p. 124.

118

differs significantly from unity. The combined influence of these three factors, column efficiency, absolute and relative retention, is described by the resolution equation (see Chapter 1, equation 35): fia-1 k’ R A . B= --4 a l+k’ The absolute retention is relatively easy to adjust, by changing the temperature. The analysis time, however, is proportional to 1+ k’ and increases rapidly with column length (see Chapter 1, equation 11 and Chapter 2, equations 14 and 16). The optimization of the column design and operating parameters becomes complex because of the intricacy of the various relationships involved (see next section). It is important to note, however, that, assuming we can keep the nature and energy of the molecular interactions involved constant, the resolution increases only in proportion to the square root of the plate number. Since the retention time increases in proportion to the power 3/2 of the column length (see Chapter 2, equation 16) it makes it an extremely costly proposition to increase the resolution by increasing the column length. Certainly very spectacular analyses of complex mixtures have been achieved by using extremely long columns (packed columns up to 30 m, open tubular columns exceeding 300 m), but the analysis times are then counted in hours. Whenever possible, the analyst should strive to reduce the column HETP as much as possible. This increases the plate number without changing the column length. The analysis time may increase, because a reduction in H will most often be obtained by using finer packing particles or a narrower column tubing (OTC), resulting in a lower column permeability and a higher pressure drop, hence a smaller value of j , but as long as the necessary inlet pressure can be met, the performance achieved will usually make the effort worthwhile.

XIV. OPTIMIZATION OF THE COLUMN DESIGN AND OPERATING PARAMETERS

In most cases, the optimization problem has been discussed for a pair of compounds. This problem is a simplification of the more realistic one, when the most difficult pair of compounds to be resolved is not the last pair of components of the mixture to be eluted. It is not too difficult to transform this second more general problem into the first, simpler one, as shown by Purnell (60). The resolution equation (equation 38) is applied to the pair of components, A and B, of the mixture which is most difficult to separate, introducing the column capacity factor k’ of the second compound, B, of the pair (see derivation of equation 35 in Chapter 1). Then the analysis time is expressed as t A = (1 ak‘)t,, where a is the relative retention of the last component eluted during the analysis, relative to the compound B. This slightly modifies the equations used for the optimization. For the sake of simplicity we have not discussed this problem further. We can distinguish two types of problem. In the first case, the analysis is to be

+

119

performed on some available column; only the column temperature and the carrier gas flow rate, possibly the temperature program, have to be optimized for the new separation. This is rather easy compared to the second case, when we want to design the column and have to choose the particle size or column diameter and the column length. The optimum column will then be operated at a predetermined temperature and carrier gas flow rate, derived during the optimization procedure. Practical strategies to optimize packed and open tubular columns are described in Chapters 6 and 8, respectively. Here we discuss the theoretical background of the problem and suggest solutions which are not necessarily those used in practice, where convenience and the desire to save on costs, time and effort impose restrictions. It must be stressed that most optima in gas chromatography are not very critical, the analysis time does not vary rapidly with departure from optimum conditions, and accordingly there is little pay-off for finding the exact value of the optimum conditions. The optimization problem of analytical chromatography can be described as the search for the minimum of a function (analysis time) with constraints (resolution between all components equal or larger than a certain threshold). The following independent relationships are available:

(38) See Eq. 1.35 t,

= (1

t,

=

+k’)t,

4VL2(P’ -Po’>

(39) See Eq. 1.11 (40)

See Eq. 2.9

(41)

See Eq. 3.7

3 k , d 2 ( p z -p:)’

L=NH

(42) See Eq. 1.26 (43) See Eq. 4.30

(44)

See Eq. 2.3

These equations contain eight parameters: the carrier gas viscosity, q , the specific permeability of the column, k , , the outlet pressure, p,, the coefficients of the plate height equation, A , B and C, which are given by identification of equation 43 (identical to equation 30), with either equation 17 (OTC) or 18 (CPC), the relative References o n p. 124.

120

retention a of the two compounds (it is in fact a function of temperature, as is the partition coefficient) and the desired resolution R. We have neglected the correction for carrier gas compressibility in the plate height equation for the sake of simplicity. The equations contain eleven unknowns, which are either intermediate variables, such as the plate number or the column capacity factor, the value of which will be determined by the optimization process, or independent parameters to be optimized. These unknowns are: the retention time, t,, the gas hold-up time, t,, the column capacity factor, k’,the partition coefficient, K (or rather the column temperature), the phase ratio, V,/V,, the average particle size, d (or the column diameter for an OTC), the column length, L, the plate number, N , the HETP, H , the outlet carrier gas velocity, u,, and the inlet pressure pi. Since there are seven equations (equations 38-44), there are four degrees of freedom. We can choose any one of the eleven unknowns and optimize it as a function of any three other unknowns. Many combinations do not make much sense, others have only a limited interest (e.g., minimizing the column length, the inlet pressure, the column temperature). If we elect to minimize the analysis time, we can still choose different combinations of parameters. Those which seem to make the more sense are the column length, the particle size, the inlet pressure and the column temperature. We now discuss the selection of the optimum values of these parameters. 1. Selection of the Column Temperature In the case of the separation of two compounds, or when the most difficult pair to separate is also eluted last, the optimization process results in a value of k’ which is around 3 for packed columns and about 2 for open tubular columns, for which the HETP increases strongly with increasing column capacity factor. For more complex mixtures, when the last component is eluted long after the most difficult pair to be resolved, the optimum column capacity factor for the second component, B , of this pair is slightly smaller, between 1.5 and 2, depending on the nature of the column and the conditions. The exact result also depends on whether the column has a large pressure drop or not (61-63). The analysis time does not depend much on the exact value of k’, between about 1.5 and 3.5, however. Since k‘ is the product of the partition coefficient (a function of the nature of the stationary phase and the temperature) and the phase ratio, there is a large flexibility in selecting these two parameters. One critical factor is the relative retention. Often it increases with decreasing temperature, which favors the selection of a low column temperature. There are cases, however, where the elution order reverses at some intermediate temperature. Then the choice of a high temperature, if it permits the elution of the lower concentration compound first, is to be preferred. Finally, the selection of the column temperature must result in an acceptable value of the phase ratio, permitting a reasonable value of k’. Phase ratios cannot exceed about 25 to 30%. The porosity of the support material would not permit a larger liquid phase content without loss of column efficiency due to excessive resistance to mass transfer in the stationary phase. At the other end, it has been

121

possible to prepare glass bead columns coated with about 0.1% (w/w) of liquid phase, which translates into a phase ratio around 0.003. Open tubular columns with a 0.3 mm i.d., and a liquid phase film thickness of cu 0.1 pm have been prepared. The corresponding phase ratio is 0.001. Although lower values are possible, the column performances are bound to change or decrease because of the occurrence of adsorption on an uncovered surface, loss of efficiency due to the lack of homogeneity of the stationary phase distribution in the column, decrease in the column loadability, resulting in poor peak symmetry and increasing detection limits, etc. 2. Selection of the Particle Size (CPC) or Column Inner Diameter (OTC) We tend to select conditions under which the plate height is as small as possible, by operating the column around the optimum flow velocity, and making the column either with small particles or with a narrow tube. The pneumatic resistance of the column will be high and it may be possible that we do not have the equipment available to apply the required inlet pressure. Then coarser particles or a wider tube have to be used. In the case of an easy separation, the lower limit to the analysis time that may be achieved will depend on the detector time constant and on the speed at which the data system may acquire the detector signal, so further discussion is irrelevant. In the case of a difficult separation, we know the column will be long and have a high pneumatic resistance. We may then neglect po compared to pi in equations 40 and 44,which simplifies them greatly. We thus obtain equations 12 and 13 in Chapter 2. Using the reduced plate height and velocity (see equations 31 and 32), and combining these with equations 12 and 13 in Chapter 2, we obtain: (45) and:

The first equation shows that the analysis time increases as the 3/2 power of the required plate number (see equation 16 in Chapter 2). It also increases as the 3/2 power of the reduced plate height. These dependences are very important. The selection of the stationary phase must be very carefully made in order to reduce the necessary value of N, while much effort (or money) must be invested in making available the best possible columns (low value of h). On the other hand, the analysis time decreases only as the square root of the particle size, which is a modest dependence and explains why, in gas chromatography, there has never been so headlong a rush towards fine particles as there has been in liquid chromatography. The dependence of the analysis time on /h3/k,explains why open tubular columns are so much faster than packed columns. Although the analysis time does not References on p. 124.

122

depend formally on the flow velocity, it is a function of this velocity, for a given column, through the value of h. The second equation shows that the inlet pressure is proportional to the square root of the required plate number and inversely proportional to the particle size. Normally a difficult analysis should be carried out at the highest pressure at which the chromatograph may be safely operated. The carrier gas should be hydrogen (lowest viscosity, see equation 45, highest diffusion coefficient, see equation 46). The particle size is then derived from equation 46, in which all other parameters are known, whence the column preparation procedure has been perfected. 3. Practical Procedure When the stationary phase has been selected and the best temperature chosen, giving the largest value of a, the phase ratio results from the condition that k’ be around 2. Then equation 38 gives the required plate number of the column. Knowing this number, the maximum value of the inlet pressure we may obtain or can afford, the general characteristics of the packed or open tubular columns available (i.e., specific permeability, k,, minimum reduced plate height, h, corresponding optimum reduced velocity, Y ) and the nature of the carrier gas we may use (hence the viscosity and the diffusion coefficient, see Section 11), it is possible to calculate the optimum particle size (CPC) or column diameter (OTC). If this size or diameter is considered to be too narrow, a larger value may be used. The inlet pressure will be lower, as will the camer gas velocity, and the analysis w ill take a longer time. The column length is calculated from equation 42, from the values derived for the required plate number, the selected particle size, and knowing the minimum value of the reduced plate height. Finally, equation 40 gives the retention time and equation 44 gives the outlet carrier gas velocity, hence the flow rate. We observe that, if we design and make the column for the analysis studied, we have to operate it at the optimum velocity, at which its efficiency is a maximum. Because of the compressibility of gases, the velocity is eliminated from equation 45. This conclusion would not be valid for easy analysis if the pressure drop is not large (then we cannot neglect p,, compared to pi in equations 42 and 44). It is not valid, either, if we use an available column. Then we operate it at the velocity which gives just the required efficiency, if the column is efficient enough to start with. Finally, we note that the equations discussed above, and our conclusions, are different from the system of equations used in liquid chromatography and the conditions arrived at using this technique (64). This reflects the very different behavior of the carrier mobile phase under pressure. Gases are highly compressible, while the compressibility of liquids is very small and has a negligible effect on retention in liquid chromatography, unless the pressure becomes very high; in excess of several hundreds of atmospheres (65).

123

GLOSSARY OF TERMS Coefficient in the plate height equation. Equation 30. Coefficient in the plate height equation. Equation 26. Coefficient in the plate height equation. Equation 30. Coefficient of the contribution of the resistances to mass transfers in the gas phase in the plate height equation. Equation 26. Coefficient of the contribution of the resistances to mass transfers in the liquid phase in the plate height equation. Diffusion coefficient. Equation 2. Diffusion coefficient of an analyte in the mobile phase. Equation 1. Diffusion coefficient of an analyte in the stationary liquid phase. Equation 14. Symbol used to denote either the average particle size or the column diameter when discussing general columns properties. Equation 40. Column diameter (i.d.). Equation 7. Average thickness of the stationary phase. Equation 14. Average particle diameter. Correction factor for the influence of gas compressibility on the efficiency of a chromatographic column. Equation 20. Height equivalent to a theoretical plate. Equation 17. Average value of the column plate height. Equation 21. Contribution to the plate height equation. Equation 34. Contribution to the average plate height originating in the gas phase. Equation 21. Contribution to the average plate height originating in the liquid phase. Equation 21. Local value of H. Equation 19. Miiimum value of the plate height of a column. Equation 26. Reduced plate height of a column. Equation 31. Correction factor for gas compressibility. Equation 3. ( u =ju,). Partition coefficient of a compound on the liquid phase. Equation 41. Column capacity factor. Equation 7. Desorption rate constant. Equation 16. Specific column permeability. Equation 40. Column length. Equation 3. Molecular weight of the solute and carrier gas, respectively. Equation 1. Plate number. Equation 35. Inlet to outlet pressure ratio. Equation 20. Local pressure. Equation 1. Column inlet pressure. Equation 40. Column outlet pressure. Equation 40. Resolution between two compounds, A and B. Equation 38. Radius of an open tubular column. Equation 6. Absolute temperature. Equation 1. References on p. 124.

2

Time. Equation 2. Gas hold-up time of the column. Equation 39. Retention time of a compound. Equation 35. Carrier gas velocity. Equation 3. Average carrier gas velocity. Equation 23. Outlet carrier gas velocity. Equation 4. Value of the carrier gas velocity corresponding to the minimum of the plate height of a column. Equation 28. Local velocity in an open tubular column. Equation 6. Volume increments of the atoms or groups composing the solute and camer gas, respectively. Equation 1. Molar volume of the analyte in the Wilke and Chang equation. Equation 13. Volume of liquid phase contained in the column. Equation 41. Dead volume of a column. Equation 41. Position of a point in the cross section of an open tubular column. Equation 6. Abscissa along the column. Equation 19. Relative retention of two compounds. Equation 38. Tortuosity of the column packing. Equation 5 . Viscosity of the liquid phase. Equation 13. Maximum relative loss of efficiency. Equation 37. Numerical coefficient in equation 9. Numerical coefficient in equation 12. Numerical coefficient in equation 14. Reduced carrier gas velocity. Equation 32. Numerical coefficient in equation 8. Association constant. Equation 13. Contribution of the equipment to the standard deviation of the elution band profile. Equation 37. Standard deviation in length unit. Equation 2. Standard deviation in time unit. Equation 35. Time constant of the detector. Equation 34.

LITERATURE CITED (1) E. Grushka, J. Phys. Chem, 76, 2586 (1972). (2) J. Villermaux, Chem. Eng. Sci., 27, 1231 (1972). (3) J.C. Giddings, in Chromatography, E. Heftmann Ed.,Van Nostrand Reinhold, New York, NY, 3rd Ed., 1975, pp. 27-44. (4) M.J.E. Golay, in Gas Chromatography 1958, D.H. Desty Ed., Butterworths, London, UK, 1956, p. 36. (5) B.L. Karger, C. Horvath and L.R. Snyder, Separation Theory, Wiley Interscience, New York, NY, 1974. (6) R.B. Bird, W.E. Stewart and E.N. Lightfoot, Transport Phenomena, Wiley, New York, NY, 1960. (7) J.C. Giddings, Dynamics of Chromatography, Marcel Dekker, New York, NY, 1965.

125

E.N. Fuller, P.D. Schettler and J.C. Giddings, Ind. Eng. Chem., 58 (5), 19 (1966). R. Kieselbach, Anal. Chem., 33, 23 (1961). J.H. Knox and L. McLaren, Anal. Chem., 36, 1477 (1964). R.A. Keller and J.C. Giddings, in Chromatography, E. Heftmann Ed., Van Nostrand Reinhold, New York, NY, 3rd Ed., 1975, p. 110. (12) G. Guiochon, Chromatographic Reuiews, 8, 1 (1966). (13) J.C. Giddings, J. Chem. Educ., 35, 588 (1958). (14) J.C. Giddings, Anal. Chem., 35,439 (1963). (15) A.B. Littlewood, Anal. Chem., 38, 2 (1966). (16) C. Landault and G. Guiochon, Chromatographia, 1 , 119 and 277 (1968). (17) L.S. Ettre, Open Tubular Columns in Gas Chromatography, Plenum Press, New York, NY, 1965. (18) D.H. Desty and A. Goldup, Gas Chromatography 1960, R.P.W. Scott Ed., Buttenvorths, London, UK, 1960, p. 162. (19) 1. Halasz and G. Schreyer, Chem.-1ng.-Tech.,32, 675 (1960). (20) G. Gaspar and G. Guiochon, Chromatographia, 15, 125 (1982). (21) C.P.M. Schutjes, C.A. Cramers, C. Vidal Madjar and G. Guiochon, J. Chromatogr., 279,269 (1983). (22) P. Doue and G. Guiochon, Chimie Analytique, 53, 363 (1971). (23) R. Tijssen, Chromatographia, 3, 525 (1970). (24) J.C. Giddings, J. Chromatogr., 13, 301 (1964). (25) J.C. Giddings and P.D. Schettler, Anal. Chem., 36, 1483 (1964). (26) C. Vidal Madjar and G. Guiochon, J . Phys. Chem., 71, 4031 (1967). (27) S.J. Hawkes, Anal. Chem., 58, 1886 (1986). (28) G. Guiochon, in Aduances in Chromatography, J.C. Giddings and R.A. Keller Eds., Marcel Dekker, New York, NY, 8, 179 (1969). (29) J.J. Van Deemter, F.J. Zuiderweg and A. Klinkenberg, Chem. Eng. Sci., 5, 271 (1956). (30) W. Averill, J. Gas Chromatogr., I (l), 22 (1963). (31) J.C. Giddings, J. Chromatogr., 13, 301 (1964). (32) J.H. Knox and M. Saleem, J. Chromatogr. Sci., 7, 614 (1969). (33) G. Guiochon, in Progress in HPLC, C. Horvath Ed., Wiley, New York, NY, Vol. 2, 1980, p. 1. (34) J.C. Sternberg, in Aduances in Chromatography, J.C. Giddings and R.A. Keller Eds., Marcel Dekker, New York, NY, 2, 205 (1966). (35) T.H. Glenn and S.P. Cram. J. Chromatogr. Sci., 8, 46 (1970). (36) G. Gaspar, P. Arpino and G. Guiochon, J . Chromatogr. Sci., 15, 256 (1977). (37) G. Gaspar, R. Annino, C. Vidal-Madjar and G. Guiochon, Anal. Chem., 50, 1512 (1978). (38) C.P.M. Schutjes, P.A. Leclercq, J.A. Rijks, C.A. Cramers, C. Vidal Madjar and G. Guiochon, J . Chromatogr., 289. 163 (1984). (39) G. Gaspar, C. Vidal-Madjar and G. Guiochon, Chromatographia, 15, 125 (1982). (40) K. Grob and K. Grob Jr., J. Chrornatogr., 151, 311 (1978). (41) K. Grob and K. Grob Jr., J. High Resolut. Chromatogr. Chromatogr. Commun., 1, 263 (1978). (42) F. Poy and L. Cobelli, J. Chromatogr., 279, 689 (1983). (43) M.J.E. Golay and J.G. Atwood, J. Chromatogr., 186, 353 (1979). (44)J.G. Atwood and M.J.E. Golay, J. Chromatogr., 218, 97 (1981). (45) J.C. Giddings, Anal. Chem., 35. 1999 (1963). (46) J. Villermaux, in Column Chromatography, E. Kovats Ed., Association of Swiss Chemists, Aarau, Switzerland, 1970. (47) A. Jaulmes, PhD Dissertation, Pans, 1985. (48) C.R. Wilke and P. Chang, Am. Inst. Chem. Eng. J., 1 , 264 (1955). (49) A.I.M. Keulemans and A. Kwantes, in Vapour Phase Chromatography, D.H. Desty Ed., Butterworths, London, UK, 1957, p. 22. (50) S.J. Hawkes and E.F. Mooney. Anal. Chem., 36, 1473 (1964). (51) J.M. Kong and S.J. Hawkes, J. Chromatogr. Sci., 14, 279 (1976). (52) J.E. Ferry, Viscoelastic Properties of Polymers, Wiley, New York, NY, 1970. (53) J.C. Giddings, J. Chromatogr., 3, 443 (1960). (54) C. Vidal-Madjar and G. Guiochon, J . !hys. Chem., 71, 4031 (1967). (8) (9) (10) (11)

126 (55) J.E. Guillet, J. Macromol. Sci. Chem., A4, 1669 (1970). (56) J.E. Guillet, in New Developments in Gas Chromatography, H. Purnell Ed., Wiley, New York, NY. 1973, p. 187. (57) H.H. Lauer, H. Poppe and J.F.K. Huber, J. Chromatogr., 132, 1 (1977). (58) J. Kwok, L.R.Snyder and J.C. Stemberg, Anal. Chem., 40, 118 (1968). (59) G. Guiochon and J. Gutierrez, J. Chromatogr., 406, 3 (1987). (60) J.H. Purnell and C.P. Quinn, in Gas Chromatography 1960, R.P.W. Scott Ed., Buttenvorths, London, UK, 1960, p. 195. (61) E. Grushka, Anal. Chem, 43, 766 (1971). (62) G. Guiochon, Anal. Chem., 38, 1020 (1966). (63) E. Grushka and G. Guiochon, J. Chromatogr. Sci., 10, 649 (1972). (64) G. Guiochon, in High Performance Liquid Chromatography, C. Horvath Ed., Wiley, New York, NY, 1980, Vol. 2, p. 1. (65) M. Martin, G. Blu and G. Guiochon, J. Chromatogr. Sci., 11, 641 (1973). (66) R. Annino, in Advances in Chromatography, J.C. Giddings, E. Grushka and P.R. Brown Eds., M. Dekker, New York, NY, 1987, Vol. 26, p. 67.

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CHAPTER 5

FUNDAMENTALS OF THE CHROMATOGRAPHIC PROCESS

Column Overloading TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. The Effects of Finite Concentration . . . . . . ......................... 1. The Sorption Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. The Isotherm Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Competition between Sorption and Isotherm Effects ................. 4. Viscosity.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................. 5. Gas Phase Non-ideal Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Temperature Effect . . . . . . . . . . . . . . . . . . . . . . 7. Resistances to Mass Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Column Flooding . . . . . . . . ................................... 11. The Mass Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Moderate Sample Size: Column Overloading . . . . . . . . . . . . . . . . . . . . . . . . . 1. Derivation of the Overloaded Band Profile . . . . . . ........................ 2. Discussion of the Characteristics of the Overloaded Profile . . . . . . . . . . . . . . . . . . a. Retention Time of the Band Maximum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Influence of the Sample Size on the Band Profile ....................... c. Influence of the Isotherm Parameters . . . . . . . . . . ............. d. Influence of the Apparent Diffusion Coefficient . . ............. e. Range of Validity of the Model . . . . . . . . . . . . . . .................... 3. Experimental Results . . . . . . ........................................ IV. Large Sample Size: Stability of C ntration Discontinuities . . . . . . . . . . . . . . . . . . . . . . . V. Large Sample Size: Propagation of Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary of Terms ... .. ... .... . Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

127 128

131 131 132 133 134

138 141 141 143 143 144 144 144 147 148 150 151

INTRODUCTION The simplifying assumptions made in Linear chromatography, which permit a satisfactory description of the retention time of the elution bands of solutes (see Chapter 3), and of their broadening and shape (see Chapter 4) are no longer valid when the concentration of solute in the mobile phase becomes large. Chromatography then is non-Linear and non-ideal and therefore much more difficult to account for than has been assumed in the previous chapters. This problem has been studied and discussed at length by many authors, following the pioneering work by Wilson (l),De Vault (2) and Glueckauf (3,4) who dealt with the simpler case of liquid chromatography. The GC problem is complicated by the compressibility of gases resulting in a non-linear pressure gradient along the column, and by the variation with pressure of several of the physico-chemical properties of gases. So it should not be surprising that there is still no general References on p. 151.

128

solution which permits a quantitative account of the peak shape observed when large samples are introduced into a GLC or a GSC column. Only recently, through the use of computers, has significant progress been made following developments made in the numerical solutions of non-linear .partial differential equations. An excellent treatment of the problem of general chromatography has been published by Helfferich and Klein (9, but the hodographic transform used by these authors cannot be applied in the case of the complex isotherms frequently observed in gas chromatography. So one has to rely on the more complex characteristics theory (6) or on still more involved mathematical approaches (7). Furthermore, the sorption effect (see Section 1.1, below) is much more important in gas chromatography than in liquid chromatography, and thus more difficult to deal with. We briefly describe the various effects that are responsible for the migration and change of shape of the bands of solutes at large concentrations, and we then discuss some of the approaches to solving the problem. Two different approaches can be used. If the sample size is large enough to result in the elution of markedly asymmetrical peaks, but the column is still not strongly overloaded, it is possible to obtain an approximate solution of the mass balance equation of chromatography which accounts for the onset of the overloading phenomenon (see Section 111, below). When the sample size becomes even larger still, this approach fails and the computer calculation of numerical solutions becomes the only method available (see Sections IV and V, below).

I. THE EFFECTS OF FINITE CONCENTRATION The increase of the concentration of solute vapor in the gas phase results in a variety of phenomena which contribute to the great complexity of the study of non-linear effects in gas chromatography. Some of these phenomena are of critical importance, central to the chromatographic process itself, like the sorption and the isotherm effects. Some are less important, like the variations of the gas viscosity and the diffusion coefficient with the gas composition or the heat effect. A complete theory should take all of them into account, which is probably too complex a requirement to be realistic. Nonetheless it is worthwhile listing and investigating these various effects. 1. The Sorption Effect

The partial molar volume of the solute dissolved in the stationary liquid phase or sorbed on the surface of the adsorbent is comparable to the molar volume of the pure solute in the liquid state at its boiling point. Its molar volume in the gas phase is 22.4 L at STP. Thus, the solute occupies a much larger volume in the gas phase than in the stationary phase. Accordingly, on the peak front, where the solute dissolves in the stationary phase or gets sorbed on it, the volume of the mobile phase decreases sharply. A similar but opposite effect takes place on the band tail. Consequently, the velocity of the mobile phase is much larger inside the band than before the front or after the tail.

129

Although the pressure profile along the column is smooth, there is a sharp increase of the gas velocity at the peak front and a correspondingly rapid decrease of this velocity at the band tail. This effect was first pointed out by Bosanquet and Morgan (8). It has been thoroughly discussed by Golay (9),Peterson and Helfferich (lo), Haarhoff and Van der Linde (11) and Jacob and Guiochon (6,12). It always results into a sharpening of the band front. The consequences of this effect are very important in gas chromatography, while they are almost negligible in liquid chromatography where the partial molar volumes of the solute in the two phases are usually very close, the difference being several orders of magnitude smaller than in gas chromatography. The larger the solute vapor concentration in the gas phase, the larger the local gas velocity. The region of the band where the concentration is large moves faster than the regions where it is smaller. The peak becomes unsymmetrical, with a sharp front and a more diffuse tail. The phenomenon, however, is different from conventional tailing. In the case of an important sorption effect, the tail profile is quasi-Gaussian, while the front is much sharper. 2. The Isotherm Effect At large concentrations the partition or adsorption isotherm is no longer linear. Figure 5.1 shows a classical plot of the vapor pressure of a solute above its solution versus its molar fraction. This conventional graph does not, however, properly describe the situation of the overloading of a chromatographic column (6). In the column the amount of stationary phase, i.e. of solvent, is constant. Thus, even with a very large sample, there is a practical limit to the maximum concentration of solute which may be reached. The isotherm effect was first studied by Wilson (1) and De Vault (2), then Glueckauf gave a detailed analysis of its consequences (3,4). The specific problems of gas chromatography have been discussed by many scientists (6-20). Figure 5.2 shows a plot of the mass of solute in the stationary phase versus the partial pressure of solute in the gas phase. In gas-liquid chromatography such a plot is always convex towards the partial pressure axis. Isotherms which are concave towards that axis, at least for low partial pressures, may occur in gas-solid chromatography, but they are rather rare and correspond to a very rapid decline of the amount of compound sorbed with increasing partial pressure in the gas phase (13). It should be noted here that, because of condensation in capillary tubes or small pores, which takes place at pressures slightly lower than the vapor pressure, the amount of compound contained in the stationary phase increases very rapidly when the partial pressure becomes close to the vapor pressure. As a consequence of this general shape of the equilibrium isotherm in gas chromatography, the amount of compound contained in the stationary phase increases faster than the partial pressure, i.e. the solubility increases with increasing partial pressure and the region of the solute bands where the concentration is large References on p. 151.

130 1

0.9 0.8

al 2 0.7 c

2

6

0.6

5In 0.5 ?Q

0.4

-

.0 0.3 c 0

a 0.2 0.1

0

0.2

0.4 0.6 Mole fraction of solute in solution

0.8

Figure 5.1. Solution equilibrium. Plot of the partial vapor pressure versus the molar fraction of the solute in the solution. Deviation from Raoult’s law. The plots have been generated using the Wilson equation.

0

Figure 5.2. Equilibrium between the gas and the stationary phase in gas chromatography. Plot of the amount of solute sorbed in the stationary phase at equilibrium, versus the ratio of the partial pressure of the solute to its vapor pressure.

131

tends to move more slowly than the regions where the concentration is small. Thus the band profile becomes unsymmetrical, with a slowly rising front and a steep tail.

3. Competition between Sorption and Isotherm Effects From what has been explained in the two previous sections it can be deduced that the isotherm and the sorption effects are generally antagonistic, the sorption effect tending to generate band profiles with a steep front and a slowly descending tail, while the isotherm effect tends to promote the formation of band profiles having the opposite shape. The isotherm effect dominates at low temperature, i.e. when the vapor pressure of the compounds under consideration is rather small. Then the solubility is important while the partial pressure, which has to be lower than the vapor pressure, is small and the sorption effect cannot be really significant. The opposite is true at high temperatures, or rather at temperatures where the vapor pressure of the studied compound is large. Then the sorption effect is very important and dominates the isotherm effect, since the solubility is relatively low and less influenced by the change in intermolecular interactions associated with the increase in concentration of the solute in the solution. There is an intermediate situation where the two effects have the same magnitude. Valentin has shown that the shift from the experimental conditions when the isotherm effect dominates to those when it is the sorption isotherm which imposes the band profile occurs when a well defined relationship, the Valentin condition (14,15), is satisfied. This usually corresponds to the column temperature being equal to the boiling point of the solute under a pressure equal to the column average pressure (Po/’). The temperature at which the shift takes place can thus be adjusted by changing either the inlet pressure or the outlet pressure, by operating the column exit under partial vacuum. This does not change the retention time nor the column capacity factor under analytical conditions, but it changes the shift temperature. In the region of experimental conditions around the shift temperature (or pressure), the two effects, isotherm and sorption effects, have comparable magnitudes. Then the bands obtained for large sample sizes are unusually symmetrical over a range of sample sizes which can be much larger than at either lower or higher temperatures (14,15). This phenomenon should be used to advantage in trace analysis, where it is useful to be able to inject large sample sizes without experiencing very strong broadening and distortion for the main compound of the mixture, for which the column is overloaded. 4. Viscosity The viscosity of vapors is appreciably less than the viscosity of most common carrier gases, except hydrogen. Accordingly, the viscosity of the mixture of carrier gas and solute vapor which is encountered inside the band during its migration is lower than that of the pure carrier gas found upstream and downstream. This results in a somewhat larger gas velocity inside the bands, increasing the magnitude of the References on p. 151.

132

sorption effect, and also in a reduced pressure gradient inside the band. The overall effect is limited, however, because the band occupies only a small fraction of the column volume. This conclusion is in agreement with observations reporting that the pressure profile remains constant during the elution of the band (16,17). It does not seem that the variation of the gas viscosity inside the band is a major factor influencing the band profile. It probably does hardly more than slightly modify the magnitude of the sorption effect. The influence of the solute concentration on the gas Siscosity can be almost cancelled by using hydrogen as a carrier gas, a practice which is recommended any time it is compatible with local safety rules, since the use of this carrier gas permits the achievement of the fastest analysis or separations. 5. Gas Phase Non-ideal Behavior As we have discussed in Chapter 3, the gas phase does not have an ideal behavior. Even if the carrier gas follows the Boyle-Mariotte law closely enough, this may not be the case for the gas mixture of carrier gas and solute vapor found inside the bands at large concentrations. Thus, the compressibility of the gas phase may appear to increase somewhat during the elution of a large band, although as in the case of the effect of the change in viscosity (cf section above), the fact that the band occupies only a small fraction of the column volume may considerably reduce the practical consequences. No report found in the literature points to this possibility as yet. More importantly, the molecular interactions in the gas phase alter the value of the equilibrium constant (see Chapter 3, Sections A.VII and B.IV). This phenomenon seems to be well understood in the framework of linear chromatography (18). The simple treatment discussed previously (Chapter 3) does not apply when the concentration of vapor becomes large and the non-linear behavior cannot be accounted for by a development limited to the second virial coefficient. The only detailed discussion of this problem which has been published so far (17) applies to the problem of the step and pulse method (also called elution on a plateau). This method has been used for the determination of isotherms. Insofar as the discussion here is limited to problems having their origin in column overloading in analytical chromatography, such as those encountered in trace analysis, with the bands of the main components of the sample, it is possible to consolidate the effect caused by the non-linear behavior of the gas phase with the isotherm effect.

6. Temperature Effect

The elution of a chromatographic band generates a local heat signal which is difficult to analyze in detail. Several phenomena interact. The sample injection band is brought into the column by the carrier gas as a volume of vapor more or less diluted in this gas. When it enters the column the pulse of vapor is partly sorbed by the stationary phase, a process that generates heat in the column packing. When the band migrates, the front part is warmer than the

133

rest of the column, since there the gas phase concentration of the solute tends to be larger than the value corresponding to equilibrium and accordingly, vapor sorbed by the stationary phase. The tail part, where the solute vaporizes from the stationary phase, is correspondingly colder. The interaction between this temperature profile, which is more complex than the concentration profile, and the band profile itself results in a trend towards a broadening of the band profile. This results from the fact that the equilibrium constant decreases with increasing temperature and is thus smaller on the band front than on its tail. Superficially, it appears that the process could be adiabatic, the same amount of heat being generated locally on the band front, when vapor is sorbed, and adsorbed on the band tail, when the solute vaporizes. That would be so if the column could be operated adiabatically, but this is impossible, unless we consider either open tubular columns or huge preparative scale columns. In the first case, due to the extremely small thickness of the stationary phase layer (typically of the order of 1 pm), the stationary phase can be considered as isothermal, even when the column is overloaded. In the second case the radial heat transfer is too slow over the distance of the column radius, so the heat losses during the passage of the band are negligible. For packed columns, however, the heat signal generated can be quite significant (an HPLC detector has been based on this principle (20a)) as well as the radial heat losses. When an injection is made, radial and longitudinal heat signals propagate. When repetitive sequential injections are made, an equilibrium is achieved only after a very long time, because of the poor heat conductivity of the packing materials used in gas chromatography, which are very closely related in structure and nature to the very best materials used for thermal insulation. This effect is very difficult to account for quantitatively and no serious attempt has been made so far, to our knowledge. This would require the solution of a system of partial differential equations involving, in addition to the mass balance equations, an equation expressing the enthalpy balance (see Section I1 below). 7. Resistances to Mass Transfer The kinetics of mass transfer in gas chromatographic columns has been discussed in Chapter 4, together with its relationship to band broadening. Even in linear chromatography, at infinite dilution, it is not yet completely understood and a full, quantitative description of the relationship between mass transfer kinetics and the column HETP cannot be obtained without the introduction of empirical factors, to account for the extreme complexity of the geometrical structure of the packed beds. In the case of open tubular columns, however, an exact equation can be derived, in good agreement with an immense amount of experimental results (21). It becomes still more difficult to account for mass transfer kinetics when the solute concentration is not negligible. Diffusion coefficients and kinetic constants are functions of concentration (22). Some coefficients in the plate height equation are functions of the column capacity factor, which changes with increasing concentration. This variation is relatively slow, however. Furthermore, the variations of the diffusion coefficients with concentration are also slow. On the other hand, the References on p. 151.

134

maximum concentration in the gas phase achieved in experiments involving column overloading rarely exceeds a few percent. Considerable changes in band profiles are observed in that concentration range, due to the isotherm and sorption effects, but it seems very unlikely that the coefficients of the mass transfer kinetics change markedly (22). Accordingly it seems satisfactory to assume that the kinetics of mass transfer will proceed at the same rate whatever the concentration of sample involved. The practical solution to account for the kinetics of mass transfer will be to use an apparent diffusion coefficient, defined as follows (23). Let us assume that, if we introduce a narrow (Dirac 8 ) plug of sample of infinitely small size, the elution profile observed at column outlet is a Gaussian profile of standard deviation u. The band variance (in length units) is related to the column length, L, and HETP, H, by the following equation: u:

= HL

(1)

If we assume that the broadening of the injected plug is due only to diffusion, the apparent diffusion coefficient which would give the same Gaussian profile is given by the Einstein equation: 0:

= 2D0tR

Comparison between equations 1 and 2 gives the apparent diffusion coefficient:

The apparent diffusion coefficient is thus a function of the column HETP, the carrier gas average velocity and the column capacity factor. Note that the column HETP is a function of both u and k'. The use of Do permits an excellent approximation of the effects of the mass transfer kinetics on the broadening of the band profiles and on the relaxation of the very steep concentration gradients which would otherwise be generated by the thermodynamic effects during the migration of large concentration signals. 8. Column Flooding

If the partial pressure of some important component of the sample mixture is too close to its vapor pressure, the larger part of this solute dissolves in the stationary phase. The volume of solution made by dissolution of this solute in the stationary phase may locally exceed the internal porosity of the support. Then the solution oozes off the particles of support into the external porosity, i.e. the space between the particles, where the carrier gas flows (14). Interference between the solution and the gas stream results in the forced migration of this solution down the column. Eventually, when the solutes are eluted,

135

a significant part of the stationary phase has been moved along the column, towards its outlet. Repeated overflooding of the column results in a characteristic profile of the support coating ratio. Instead of being constant along the column as it was after column packing, the coating ratio becomes very low at column inlet, rises rapidly at some point inside the column, reaches some large value and finally returns to the constant value which it originally had. This is detrimental to proper column operation and to column performance. Such gross column overloading should be avoided by limiting the maximum vapor pressure of the most important components of the mixture analyzed, i.e. the sample size.

11. THE MASS BALANCE EQUATIONS

The general solution to the determination of the band profile at the exit of the column is obtained by writing the mass balance of solute in an infinitely narrow slice of column. As we have seen above, a constant flow rate cannot be assumed, since this is tantamount to neglecting the sorption effect, which is incorrect. Since the peak migration causes a local increase in the gas velocity it is necessary to write an explicit mass balance equation for the carrier gas. The mass balance equations for the solute and the carrier gas can be written in different ways, depending on the model assumed to represent the chromatographic process (1-12,15-26). Generally it is assumed that the gas phase is ideal, that the temperature effect is negligible and either that the pressure drop is neghgible, which is not quite realistic, or that the pressure profile remains constant during the elution of a large concentration band, which is a much better approximation. Since the column is usually operated at the same flow rate when the band profiles obtained for different sample sizes are compared, and the column capacity factor at zero sample size is usually measured without correcting for the second virial coefficient, the assumption of ideal behavior is really only the assumption that the isotherm effect can also take care of the variation of the equilibrium constant with the partial pressure in the gas phase, which is acceptable. Finally, it is usually assumed that the various sources of band broadening can be properly accounted for by the use of an apparent diffusion coefficient, as explained above (Section 1.7). This coefficient is a function of the flow velocity at which the experiment is performed. This approximation makes it possible to forget the kinetic equation which describes the resistances to mass transfer. As long as the kinetics of the exchanges between mobile and stationary phases are fast the assumption is excellent and supplies band profiles which cannot be distinguished from those obtained by the solution of the general system of equations. When the kinetics become slow the band profile becomes strongly unsymmetrical and may even assume the shape of a bimodal distribution (41). Fortunately such cases are rare in practice. In many cases the effect of finite concentration has been considered as a perturbation of normal, linear chromatography, which is a natural approach. It fails References on p. 151.

136

in this case, however, because the effects of diffusion and kinetics are second-order compared to the isotherm and the sorption effects, which are accounted for by the first-order terms of the mass balance equations. Writing the mass balances of the solute and the carrier gas in an infinitely thin slice of column permits the derivation of the following equations:

a(ux) a2x ax(,+ k’) + Da,2 at

=

aZ

(4)

and:

ax-

a[u(i-x)]

at

az

a2x

=

-7 at

If we assume the column capacity factor k’ to be constant, integration of this system leads to a Gaussian profile. In all other cases there is no analytical solution to the system of partial differential equations 4 and 5. Some simplifications are necessary. Houghton (24) has suggested one such simplification. If the sample vapor pressure is small, without being very small, it is possible to replace the isotherm by a two-term expansion, i.e. to replace the isotherm plot by a parabola having the same slope and the same curvature at the origin as the real isotherm, instead of replacing it by its tangent at the origin (See Figure 5.3, where the two typical isotherms are shown). Then, assuming the partial pressure of the solute to be small it is possible to eliminate the mass balance equation for the carrier gas, and to solve the resulting differential equation. This, however, is tantamount to neglecting the sorption effect. Ladurelli (17) and Jaulmes et al. (23) have shown that Houghton’s equation can be modified using results which enable one to take account of the sorption effect. This solution is further discussed in Section I11 below. Haarhof and Van der Linde (11)followed a similar approach, but kept the carrier gas mass balance equation. They also took into account the fact that when large sample sizes are introduced in a chromatographic column not only is the solute concentration large, but the volume occupied by the sample also is large. The complex set of reduced variables they used, however, makes the practical application of their solution much more complex. Conder and Purnell (19) have followed an entirely different approach. Starting from the same mass balance system, they have attempted to account for all the effects originating in the gas phase: gas compressibility, non-ideal behavior of the gas phase mixture, variation of velocity of the gas due to the sorption effect. They have been able to derive a relationship between the retention volume and the solute concentration. This, however, does not permit a simple derivation of the band profile. In the reports previously discussed, considerable importance was given to the phenomena responsible for band broadening and it was deemed important to account for them. Nevertheless the agreement between predicted and experimental

137

0

0.0002

Isotherm 2 Tangent 3 Parabola 1

0.0004

0.0006

aooi

0.0008

Partial pressure in gas phase

n

b

0.0025-

0

0.002-

.-

o

,

0.0002 0.0004 0.0006 0.0008 a001 0.0012 0.0014 0.0016 5

1 Isotherm 2 Tangent 3 Parabola

Partial

I

#

0.0018 a002

pressure of solute

Figure 5.3. Typical gas-liquid isotherms, their tangent at the

origin and the osculatory parabola. (A)

Langmuir isotherm. (B) ‘S-shape isotherm.

References on p. 151.

138

band profiles was not very good at large concentrations. Jacob, Valentin and Guiochon (20) have discussed the properties of the set of partial differential equations obtained by eliminating the apparent diffusion term. This is equivalent to considering a column of infinite efficiency, which is not realistic. The solution obtained has the advantage, however, of emphasizing the importance of the two major effects, the sorption and isotherm effects. This solution permits an excellent description of the propagation and change in profile of large concentration bands in a chromatographic column. The solution is applicable to preparative chromatography. It is not satisfactory for analytical applications, because the phenomena which are responsible for band broadening are similar in importance to the thermodynamic effects and must be treated accordingly. In the following we first discuss the solution derived by Houghton (24), which is of major importance for column overloading in analytical applications, since it describes how the band profile changes during the onset of overloading. Then we describe the most important features of the propagation of large concentration bands and we discuss how it is possible to calculate elution profiles. III. MODERATE SAMPLE SIZE COLUMN OVERLOADING When the sample size injected into a gas chromatographic column is progressively increased, the profiles of the peaks of the major components, usually Gaussian or quasi-Gaussian at first, become broader and unsymmetrical. One side of the peak, either its front or tail, becomes steeper and the peak maximum drifts in this direction, the other side of the profile changing relatively little or not at all. Usually the early eluting peaks acquire a steep front in the process, while the late eluting ones exhibit a sharp return to base line or tail, depending whether the sorption or the isotherm effect predominates. The change in profile may be less marked for compounds with intermediate retention, although the extent of the phenomenon depends a great deal on the temperature and the phase ratio, i.e. on the vapor pressure of the solutes at the column temperature. It is possible to derive an equation for the band profile. Although the derivation is not rigorous but involves some approximations, the result is highly satisfactory and accounts for the experimental observations, not only qualitatively but quantitatively in all cases where rigorous tests have been performed (27,28). This is because all the approximations rely on the sole assumption that the partial pressure of the solute is small. There is obviously some limit to the validity of this assumption. The derivation, the assumptions, the results and the limitations of the model are discussed here.

1. Derivation of the Overloaded Band Profile In most cases encountered in analytical applications the partial pressure of the solute at peak maximum is still rather small. The column is only slightly overloaded and the contribution to band broadening due to the sorption and isotherm effects is not very large compared to the classical band broadening contributions due to the

139

molecular diffusion and to the various resistances to mass transfer (see Chapter 4). So we cannot neglect here the apparent diffusion coefficient in equations 4 and 5 and set the RHS of these equations equal to 0, as did Jacob, Valentin and Guiochon (20). In order to take them into account and nevertheless achieve a tractable solution, Houghton (24) has made a number of simplifications. If we assume that the mole fraction of the solute in the gas phase is negligible compared to that of the carrier gas, the mass balance equation for the carrier gas can be omitted. We are then left with equation 4, now a partial differential equation. In order to solve it a certain number of modifications and approximations must be made. First the gas phase is compressible, the gas velocity increases regularly from column inlet to outlet (See Chapter 2, Section IV), and the velocity profile should be taken into account in the solution of equation 4. The exact calculation cannot be pursued to the final integration, however, which prevented Conder and Purnell (19) from deriving an equation for the band profile, leaving them only with a relationship between the retention volume and the solute concentration in the gas phase. To assume that the gas velocity is constant (i.e. that the pressure drop is negligible) and equal to the outlet gas velocity, would be too unrealistic. A satisfactory compromise is to assume with Dunckhorst and Houghton (27) that the gas velocity is constant and equal to the average velocity, u,. Then we replace the solute mole fraction by its concentration:

c=c,x

(6)

where C, is the average concentration (mole/mL) of the carrier gas (C, = p , / R T ) , and we rewrite equation 4 as follows: dC -(l+k')+u dt

dC -=D"dz

d2C

(7)

The derivation of equation 7 from equation 4 has been done (24) by considering that the gas velocity is constant, i.e. neglecting the sorption effect, which is the direct consequence of neglecting the mass balance of the carrier gas: this assumes that the velocity does not change when the band migrates. This is incorrect, however, because, in analytical gas chromatography, the partial pressure of the solute is often large enough to generate a sorption effect which is easily observed, such as in the elution of the solvent peak or of the earliest peaks on open tubular columns, in which case.very steep, almost vertical fronts and quasi-Gaussian tails are recorded. From mathematical consideration of the system of partial differential equations 4 and 5 reported by Haarhof and Van der Linde (ll),by Jacob et al. (12,20) and by Ladurelli (17), we have shown (23) that the average gas velocity should be replaced in equation 7 by the following relationship:

References on p. 151.

140

where k; is the column capacity factor at zero partial pressure of the solute. This modification permits a convenient reintroduction of the sorption effect, as a perturbation. This approach is acceptable since we are dealing with corrective terms, the solute concentration being assumed to be small throughout all this derivation. Finally, since we consider small solute concentrations, we may assume that the isotherm can be replaced by a two-term expansion: C, = K,C

+ K2C2

(9)

where C, is the concentration at equilibrium in the stationary phase (in gas-solid chromatography it is replaced by the surface concentration, n,/A), K , and K , are the slope and curvature of the isotherm at the origin (C = 0). Accordingly, k’,which is equal to the derivative of the isotherm multiplied by the phase ratio, is given by:

(

’y)

k ’ = k ; 1+-

Combination of equations 7, 8 and 10 gives the final differential equation (23). It may be solved, yielding the following equation for the peak profile:

In this equation the various parameters are defined as follows: - t R is the retention time of a zero concentration sample ( t R = (1+ kA)t,, with k; = K , v / V g , and q/V, is the phase ratio), corresponding to the slope of the isotherm at the origin. - a, is the standard deviation (time unit) of the zero concentration band, which results from the molecular diffusion and the resistances to mass transfer (see Section 1.7, above). - D‘ = D,/(l k;), where D, is the apparent diffusion coefficient (equation 2). - U = uJ(1 + k;), where u, is the average gas velocity. = 2(K2C,- K , ) / ( K , + V-/v,)G.

+

x

AU m -c”=zo‘s where m is the mass of solute injected (mole) and S is the cross section area of the column available to the gas phase. - C is the solute concentration at time t , at the outlet of the column. Equation 11 permits the prediction of the band profile, given a knowledge of the various parameters which control the band profile: the sample size, the coefficients

141

of the isotherm expansion, the apparent diffusion coefficient, the average gas velocity and the average column pressure. A discussion of the influence of these various parameters is now in order. 2. Discussion of the Characteristics of the Overloaded Band Profile

From equation 11 it is possible to derive a relationship between the retention of the peak maximum and the corresponding concentration, as well as to study the change in peak profile associated with changes in the experimental conditions. The influence of the various experimental parameters on the band profile and its change with increasing sample size is illustrated in Figures 5.4A-E. a. Retention Time of the Band Maximum A variation of the slope of the isotherm, i.e., of t R , has well known consequences (see Figure 5.4A). Differentiation of the elution profile (equation 11) with respect to time gives the coordinates of the band maximum (23). It can be shown that the retention time of the peak maximum, r,, and the corresponding maximum concentration, C,, are related by:

where t R is the retention time of a zero sample size peak (C, = 0), corresponding to k ; , or to the slope of the isotherm. A similar relationship was derived by Haarhoff and Van der Linde (11) and by Jousselin and Massot (29). A plot of t M versus maximum peak concentration is a hyperbola, starting at t =tR, C , = 0, with an initial slope equal to At,. It is important to emphasize here that the initial slope is not vertical, i.e. that when the sample size is increased, the retention time almost always varies with increasing sample size. At low concentrations, the variation of retention time is proportional to the sample size (see Figure 5.4B). For very small sample sizes the peak profile is nearly Gaussian and the maximum concentration of a Gaussian distribution also is proportional to the amount of sample. It is only because the proportionality coefficient h is small that the variation of the retention time with increasing sample sizes is moderate in most cases and, within a certain range of sample sizes, remains smaller than the error of measurement. Hence the conclusion, which is correct, that in that range the retention time does not vary significantly with the sample size, and the incorrect inference that the retention time is independent of the sample size in some range. It is only when h is zero, by compensation between the two terms, K,C,, and K,, that the retention remains constant when the sample size is increased (17,23). Since the first term of X is proportional to the average concentration of the carrier gas in the column ( P J R T ) , it is, at least in principle, possible to adjust the inlet pressure so that the coefficient X will be equal to zero, and the retention time remains References on p. 151.

142 80. Y ( t )

60

6

-

40.

20

-

0, 65

60

70

75

80

85

time (sec)

1

65

85 time (set)

75

I

65

70

75

80

85 time(5ec)

Figure 5.4. Influence of the four parameters on the band profile. See equation 11. (Reproduced from reference 23, with permission of the American Chemical Society). (A) Slope of the isotherm at the origin. (B) Sample size. (C) Curvature of the isotherm at the origin. (D) Isotherms corresponding to the profiles shown in (C). (E) Apparent diffusion coefficient.

constant up to rather large values of the sample size. In practice this is possible only as long as this corresponds to acceptable values of the average pressure, compatible with reasonable column performance. If an apparatus is available which permits adjustment of the outlet pressure, investigations can be made over a much larger range of the average carrier gas concentration (14).

143

b. Influence of the Sample Size on the Band Profile As long as the sample size is very small and coth(p/2) is much larger than unity, the peak profile is close to Gaussian and its size increases in proportion to the sample size since coth(x) is equivalent to l/x when x is small. Eventually, however, this term becomes of the order of unity. Then the denominator of equation 11 varies during the elution of the band and its variation contributes dramatically to the exact band profile (see Figure 5.4B). When the sample size continues to increase, the band profile changes and becomes more and more unsymmetrical. The peak maximum drifts towards either larger or lower retention times. The direction in which the peak becomes steeper and the retention time drifts depends on the sign of A. If X is positive the retention time of the peak maximum increases with increasing sample sizes and the peak tail becomes steeper and steeper. The opposite is true if X is negative. When the sample size becomes very large, the profile tends towards that of a slanted triangle. The peak apex locus is predicted to be a hyperbola (equation 12), at least up to a certain value.

c. Influence of the Isotherm Parameters

These two parameters are the slope and the curvature of the isotherm at the origin, i.e. the parameters K, and K, of the two-term expansion. The influence of K, is classical. It determines the retention time of the zero sample size pulse (see Figure 5.4A). In many analytical applications the sample size is too small (or the curvature of the isotherm is too small) for the variation of the retention time with increasing sample size to be significantly different from zero, because of the errors of measurements. In practice it is difficult to achieve a reproducibility of the retention time better than 0.5%. The change in peak profile, as well as the variation of retention time with increasing sample sizes is a result of the combination of the isotherm curvature and the average density of the carrier gas (see Figure 5.4C). The two parameters are combined in the calculation of the leaning coefficient A. Accordingly it is possible to adjust the value of A in some predetermined range, at least if the corresponding value of the average carrier gas pressure can be achieved in practice. Thus, with a given column, at a given temperature, it is possible to observe that the retention time of a certain compound increases with increasing sample size at some carrier gas flow rate, while at a different flow rate it will decrease. This phenomenon occurs quite readily in gas-liquid chromatography. It is far less frequent in gas-solid chromatography because the isotherm curvature is usually much stronger with adsorption isotherms than with partition ones. It should be emphasized that small deviations of the equilibrium isotherm from a linear behavior (see Figure 5.4D) result in important deviations of the band profile from a Gaussian one (23). References on p. 151.

144

d. Influence of the Apparent Diffusion Coefficient The apparent diffusion coefficient determines the band width and, accordingly, for a given sample size, the maximum concentration of the elution band. The smaller the apparent diffusion coefficient, the more efficient the column, the higher the peak and the stronger the non-linear effects. The peak apex remains on the same curve, independently of the column efficiency (cf. equation 12). Peaks with large values of D, are more nearly Gaussian while, on the other hand, peaks with small values of the apparent diffusion coefficient are more like slanted triangles whose non-vertical side is close to the peak apex locus (see Figure 5.4E). In principle, the apparent diffusion coefficient is independent of the sample size, i.e. of the peak height, since we have assumed the diffusion coefficients in the gas and stationary phases to be independent of the concentration.

e. Range of Validity of the Model The derivation of the differential equation 7 as well as its integration into the band profile, equation 11, requires that the maximum solute concentration in the gas phase be small (23,24). More precisely, the following condition must be fulfilled:

Ace 1

(13)

In practice the model gives predicted results which are in excellent agreement with the experimental data for values of the product XC not exceeding 0.05 to 0.10, which satisfies equation 13. . .

3. Experimental Results The predictions of the model have been verified in several different cases, by Dunckhorst and Houghton (27) and by Ladurelli (17) in gas-liquid chromatography, and by Jaulmes et al. (28) in gas-solid chromatography. The curvature of the isotherm at the origin can be derived from direct determinations of the equilibrium isotherm using one of the conventional methods or an independent chromatographic method, such as frontal analysis or the step and pulse method (also called elution on a plateau) (30,31). The curvature of the isotherm at the origin can also be derived from the variation of the retention time with increasing maximum peak concentration (equation 12), and the relationship between the curvature, K,, and the coefficient A. It can also be calculated from a least squares fit of the band profile on the profile equation 11, which affords values of the four parameters in this equation ( t R , A, p and 0,). An excellent agreement was found by Jaulmes et al. (28) between experimental values of the isotherm curvatures at 100 O C of benzene and n-hexane on graphitized carbon black obtained by the following methods or from the following sources: (i) quasi-linear variation of the retention time with maximum peak concentration, at least for small and moderate sample sizes (see Figure 5 . 9 , (ii) least squares fit of the

145

of the band maximum. See equation 13. (Reproduced from reference 28, with permission of the American Chemical Society.) n-Hexane (a) and benzene (b) on graphitized carbon black. Figure 5.5. Plot of the maximum peak height versus the retention time

peak profiles on equation 11, (iii) the step and pulse method, (iv) data from Avgul and Kiselev (32) and (v) data from Ross and Oliver (33). This confirms the validity of the method. Furthermore, it is worth noting that the value of the infinite dilution retention time, t,, and of the apparent diffusion coefficient derived from a least squares fit of the profiles recorded for a series of samples sizes, from 40 ng to 31 pg for n-hexane and from 58 ng to 23 pg for benzene, are constant (see Figures 5.6 and 5.7). This also confirms the validity of the model and of our assumption regarding the relationship between diffusion coefficients and concentration. This result demonstrates that band broadening at large concentration is due to thermodynamic effects (essentially the sorption and isotherm effects), not to a loss of column efficiency. Finally the model appears to be valid for values of the product XC up to cu 0.05 (28). In the case of benzene and n-hexane on graphitized carbon black this corresponds to maximum concentrations of 35 and 50 nmole/mL, respectively (i.e. about 0.1% v/v in the gas phase). References on p. 151.

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147

IV. LARGE SAMPLE SIZE STABILITY OF CONCENTRATION DISCONTINUITIES In the case of large concentration bands equation 13 is not verified and the Houghton model (24), as discussed above, is not applicable. Then one has to solve the system of partial differential equations as written above (equations 4 and 5), with a set of boundary conditions representing the injection band profile, for example a rectangular pulse. In practice the injection profile is more complex but this does not ease the fundamental difficulty of the problem. There are basically two approaches. First, one can neglect the contributions of the axial diffusion and resistances to mass transfer in the column and discuss the simplified system of partial differential equations obtained in this way (6,12,15-17,20,34-36). This is not a very realistic assumption, since it assumes a column of infinite efficiency, in which the axial diffusion coefficient is zero, while the radial diffusion coefficients are infinite (6,26), but this emphasizes the thermodynamic contributions and permits a good description of their origin, their onset and development and of their major effects (6,20). Furthermore, it is possible to reintroduce the column efficiency by way of an apparent diffusion when actual band profiles are calculated. This model of chromatography, which takes into account the non-linear behavior of the equilibrium isotherm but not the sources of band broadenings is called ideal, non-linear chromatography. A more profound discussion of the mathematical properties of the system of partial differential equations involved is possible (7). These results are beyond the scope of this book. The second approach is purely numerical (37,38). Since it is not possible to solve the system of partial differential equations and to obtain an analytical solution, i.e. a general band profile equation, similar to equation 11, a numerical solution is calculated. The result can be, in principle at least, very accurate. There are several difficult problems (35). First, the numerical solution of systems of non-linear partial differential equations is not straightforward and requires the solution of difficult problems of numerical analysis (38). Secondly, a large number of such numerical solutions is required for a good understanding of the relationship between the elution profile and the various experimental parameters. The first approach is described in this section, the second one in the last section of t h s chapter. The system of partial differential equations obtained when neglecting the second-order terms (diffusion and mass transfer) is quasi-linear. Among its important mathematical properties is the possibility of appearance and propagation of concentration discontinuities. A concentration discontinuity seems to be impossible since it would be associated with an infinitely fast mass transfer by diffusion, but we have just assumed that axial diffusion does not exist. As a matter of fact, a concentration discontinuity is physically similar to a shock wave or a rolling sea wave (16). A shock wave is a pressure discontinuity which propagates faster than sound; the local compression heats up the gas, so the waves which tend to propagate faster than the discontinuity enter a cold medium where their speed is lower, whereas those which would tend to propagate more slowly enter a region of space References on p. 151.

148

which is warmer and where they move faster. All join up with the shock wave, hence its stability. Mathematically, the conditions of stability of concentration discontinuities are similar to those of shock waves. The possibility of concentration discontinuities in ideal non-linear chromatography was described for the first time by De Vault (2). He recognized that there were conditions under which the equations describing the propagation of a continuous band profile lead to three values of the concentration at the same instant, at the same point. This is clearly impossible, as a real rolling wave would be. De Vault suggested an empirical solution, which is no longer useful since we have ways to handle this problem more rigorously. Helfferich and Klein ( 5 ) also recognized the existence and stability of the discontinuities, but did not use them. The detailed study of the properties of the system of ideal non-linear chromatography was made by Jacob et al. (6,12,20,34,35) who derived a general theory of the phenomenon. Simple considerations on the system of partial differential equations show that a rate of migration can be associated with each value of the solute concentration in the gas phase (6,11,20). A discontinuity arises when the speed of migration associated with the large concentrations around the band maximum is either markedly larger or smaller than the rate associated with the small concentrations. If it is larger, for example, the front of the profile becomes steeper and steeper, until the inflexion tangent becomes vertical. Then, since the band maximum cannot pass the inflexion point (which would give the three different values for the local concentration), the discontinuity builds up, at the expense of the continuous, adjacent parts of the profile. The discontinuity may disappear by the same process, if the rate-concentration relationship is reversed for some reason, or it may collapse entirely, depending on the experimental conditions. The maximum concentration of the peak decreases constantly, however, since chromatography is a dilution process. So, if the column is long enough, the shock disappears and the conditions of linear chromatography prevail eventually. Since we have neglected axial diffusion and assumed infinitely fast radial mass transfer in the model, however, it predicts a much slower dilution than the one which is actually taking place. As one may easily convince oneself by looking at chromatograms obtained in preparative gas chromatography (13,39), such shocks or discontinuities are not mere mathematical artefacts arising from the improper use of an incorrect model, as one would fear. They are the real consequences of some process actually taking place inside the column. Admittedly the band profiles are somewhat smoother than is predicted by the model, the concentration discontinuities being to some extent relaxed by the diffusion. The conditions of stability of discontinuities have been discussed in detail by Valentin and Guiochon (15). V. LARGE SAMPLE SIZE: PROPAGATION OF BANDS Using the knowledge gained from the study of the mathematical properties of the system of partial differential equations, Jacob wrote a program describing the

149

elution of large concentration bands, by combining continuous parts of the profile and discontinuities, whose behavior is described by a completely different set of equations. The result, although qualitatively correct, was still far from perfect, since the elution profile had between only 30% and 50% of the area of the injection profile (35). Such a loss is not acceptable in a numerical calculation and casts some doubt on the validity of the predictions of the model. Numerical integration of the chromatographic system of equations is a very long task requiring considerable computer time because a large number of intermediate profiles have to be calculated. The origin of the difficulties encountered in the previous work is related to the use of the characteristics method, which is very powerful in explaining what is actually happening to the band profile, but requires, for a numerical calculation, that the exact position of the shock be located on each intermediate profile. This considerably increases the rounding errors. A different approach was followed by Rouchon et al. (37) who wrote a program using the Godunov algorithm (38,40), which is a finite difference method. A further advantage of this approach is that it is possible to take account of the pressure profile of the carrier gas along the column, with the mere simplifying assumption that the presence of the solute vapor does not significantly perturb this profile. This is acceptable since the pressure gradient is involved in the system of equations only as a correcting term. On the other hand, the method takes full account of the sorption effect. At large values of the sample size there is a striking agreement (37) between the band profiles calculated from the adsorption isotherm measured on the same column, using the method of numerical integration just described and the same equation system as Jacob (6, 35). The agreement is not as good at intermediate sample sizes. For very small sample sizes, when the linear chromatography model would work acceptably and the profile is almost Gaussian, the calculation also gives a quasi-Gaussian profile, but the variance of the calculated profile is much smaller than that of the recorded peak. The reason is that this approach, like Jacob’s, belongs to the ideal chromatography model, i.e. the apparent diffusion term is dropped from the partial differential equations. The profile calculated for a very small sample plug is Gaussian, not rectangular, however, as should happen with an infinitely efficient column. This is the result of the accumulation of rounding errors arising in the millions of individual additions made to achieve the final numerical result (38). The ‘numerical diffusion’ thus introduced partially corrects for the simplifying assumption of infinite column efficiency. An adjustment of the parameters of the program, e.g. an optimization of the values of the time and space increments, probably could improve the agreement between the band profiles resulting from the calculation and those recorded. As the sample size increases, however, the band profile depends more and more on the thermodynamic effects, less and less on the kinetics of band broadening. The model accounts very well for the former, poorly for the latter. It is normal that the agreement becomes excellent at large sample sizes, the experimental profiles being just somewhat smoother than the calculated ones because of a larger column efficiency (37). References on p. 151.

150

The method also gives all the intermediate concentration profiles in the column during the elution of the band, which permits a study of its progressive changes (37). There is a last, fundamental problem, which has hardly been touched so far. In conditions of non-linear chromatography, when two compounds are partially resolved, there is an interaction between their respective concentration profiles: if the isotherm of a certain compound is not linear in the range of concentrations involved in its band profile, it is almost certain that the concentration at equilibrium in the stationary phase will be influenced by the presence of the other compound at a significant concentration (15). In other terms, the isotherm of compound A depends on the concentration of compound B present in the system. Since this concentration is constantly changing during the chromatographic elution process, a complex phenomenon of band profile interaction does take place (15). This is in agreement with many previous observations that the yield of pure compound in preparative chromatography is often much better than could be predicted by an analyst looking at the band profiles (13,39). The more strongly retained compound generally tends to displace the lesser retained compound in front of it, but the conditions of displacement chromatography are usually not met during the elution of large cancentration zones (39). Although there has been no study of this problem in gas chromatography, the slightly different problem encountered in liquid chromatography at finite concentration (no compressibility of the mobile phase, no sorption effect, but sorption of the mobile phase) has seen great progress recently, with the availability of a numerical solution of the multi-component problem (42). Most conclusions reached in liquid chromatography could be applied with few changes to the case of gas chromatography. GLOSSARY OF TERMS Concentration of the solute in the gas phase. Equation 6. Maximum concentration of a compound in its elution band. Equation 12. Concentration of the solute in the stationary phase at equilibrium. Equation 9. Average concentration of the gas phase in the column (mole/L). Equation 6. C,, D Diffusion coefficient in equation 4. Apparent diffusion coefficient. Equation 2. D, D’ Modified apparent diffusion coefficient. Equation 11. H Apparent column plate height. Equation 1. K , , K , Coefficients of the two term expansion of the isotherm. Equation 9. k’ Column capacity factor. Equation 3. Column capacity factor at infinite dilution of the solute. Equation 8. k; L Column length. Equation 1. rn Mass of the sample of a compound injected in the column. Equation l l b . Average gas pressure in the column. Equation 7. pN S Cross section area of the column available to the gas phase. Equation l l b . t Time. Equation 4. C C,,, C,

151 tM

Retention time of the maximum concentration of an overloaded band. Equation 12. Retention time of a compound at zero sample size. Equation 2. Apparent average velocity of a solute band. Equation 11. Carrier gas velocity. Equation 3. Average carrier gas velocity. Equation 7. Mole fraction of a compound in the mobile phase. Equation 4. Abscissa along the column. Equation 4. Leaning coefficient of an elution profile. Equation 11. Reduced sample size. Equation 11. Standard deviation of a Gaussian profile in length unit. Equation 2. Standard deviation in time unit. Equation 11.

LITERATURE CITED J.N. Wilson, J. Amer. Chem. Soc., 62, 1583 (1940). D. De Vault, J. Amer. Chem. Soc., 65, 532 (1943). E. Glueckauf, Proc. Roy. Soc., A186, 35 (1946). E. Glueckauf, Disc. Faraday Soc., 7 , 12 (1949). F. Helfferich and G. Klein, Multicomponenr Chromatography. Marcel Dekker. New York. NY. 1970. L. Jacob and G. Guiochon, Chromarogr. Reu., 14, 77 (1971). H.K. Rhee and N. Amundson, Trans. Roy. Soc., A267. 419 (1970). C. Bosanquet and G.D. Morgan, in Vapour Phase Chromatography, D.H. Desty Ed., Buttenvorths, London, UK, 1957. M.J.E. Golay, Nuture, 202, 490 (1964). D.L. Peterson and F . Helfferich, J. Phys. Chem., 69, 1283 (1965). P.C. Haarhof and H.J. van der Linde, Anal. Chem., 38, 573 (1966). L. Jacob and G. Guiochon, Bull. Soc. Chim. France, 1970. 1224. B. Roz, R. Bonmati, G. Hagenbach, P. Valentin and G. Guiochon, J. Chromarogr. Sci., 14. 367 ( 1974). P. Valentin, G. Hagenbach, B. Roz and G. Guiochon, in Gas Chromatography 1972. S.G. Perry and E.R. Adlard Eds., Applied Science Publ., Barking, UK. 1973, p. 157. P. Valentin and G. Guiochon, Separ. Sci., 10. 289 (1975). P. Valentin and G. Guiochon, Separ. Sci., 10, 245 (1975). A. Ladurelli, Thesis, Pierre & Marie Curie University. Paris, 1976. J.C. Giddings, S.L. Seager, L.R. Stucki and G.H. Stewart, Anal. Chem., 32, 867 (1 960). J.R. Conder and J.H. Purnell, Trans. Faraday Soc.. 64, 3100 (1968). L. Jacob, P. Valentin and G. Guiochon. J. Chim. Phys. Phys.-Chim. Biol.. 66. 1097 (1969). G . Claxton, J. Chromatogr.. 2, 136 (1959). M.J.E. Golay, in Gas Chromatography 1958. D.H. Desty Ed., Buttenvorths, London, UK, 1958, p. 35. R.B. Bird, W.E. Stewart and E.N. Lightfoot, Transport Phenomena. Wiley, New York, NY. 1960. A. Jaulmes, C. Vidal-Madjar, A. Ladurelli and G. Guiochon. J. Phys. Chem., 88, 5379 (1984). G. Houghton. J . Phys. Chem., 67. 84 (1963). V.V. Rachinskii, The General Theory of Sorption Dynamics and Chromatography, Consultants Bureau (English Transl.), New York, NY, 1965. J.F.K. Huber and R.E.Gerritse, J. Chromatogr., 58, 138 (1971). F. T. Dunckhorst and G. Houghton, Ind. Eng. Chem. Fund., 5, 93 (1966). A. Jaulmes. C. Vidal-Madjar, M. Gaspar and G. Guiochon, J . Phys. Chem., 88, 5385 (1984).

152 C. Jousselin and C. Massot, Chromatographie Isotopique, Ste Nationale des Petroles d'Aquitaine, Pau, France, 1968. P. Valentin and G. Guiochon, J. Chromatogr. Sci., 14, 56, 132 (1976). F. Dondi, M.F. Gonnord and G. Guiochon, J. Colloid Interface Sci., 62, 303, 316 (1977). N.N. Avgul and A.V. Kiselev, in Chernistty and Physics of Carbon, P.L. Walker Ed., Marcel Dekker, New York, NY, 1970, Vol. 6, p. 1. S. Ross and J.P. Oliver, On Physical Ahorpiion, Wiley, New York, NY, 1964. L. Jacob and G. Guiochon, J. Chirn. Phys. Phys.-Chim. Biol., 67, 185, 291 and 295 (1969). L. Jacob, P. Valentin and G. Guiochon, Chromatographia, 4 , 6 (1971). P. Valentin and G. Guiochon, Separ. Sci., 10, 271 (1975). P. Rouchon, M. Schoenauer, P. Valentin, C. Vidal-Madjar and G. Guiochon, J. Chim. Phys., 89, 2076 (1985). P. Rouchon, M. Schoenauer, P. Valentin and G. Guiochon, in The Science of Chromatography, F. Bruner Ed., Elsevier, Amsterdam, The Netherlands, 1985, p. 131. G. Chapelet-Letourneux, R. Bonmati and G. Guiochon, Separ. Sci., 19, 113 (1984). S.K.Godunov, Math. Sb. V, 47, 271 (1959). B.C. Lin, S. Golshan-Shirazi and G. Guiochon, Unpublished Data, 1987. G. Guiochon and S. Ghodbane, J. Phys. Chem., in press.

153

CHAPTER 6

METHODOLOGY Optimization of the Experimental Conditions of a Chromatographic Separation using Packed Columns TABLE OF CONTENTS .........................................................

The First Step: an Empirical Approach . .... ........................ 1. Nature of the Sample Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................. 2. Selection of the Stationary Phase and Support . . . ................. 3. Polarity of Stationary Phases . . . . . . . . . . . . . . . . 4. Selection of the Column Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Selection of the Temperatures of the Column, the Injection Port and the Detector . . . . . . 6. Selection of the Camer Gas Flow Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. How to Use the First Step Chromatograms . . . . . . . ............... 11. The Second Step: Optimization of the Main Experimental Parameters . . . . . . . . . . . . . . . . . 1. Optimization of the Column Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Optimization of the Column Temperature . . . . . . . . . . . . . . . . . . . . . . . . 3. Optimization of the Carrier Gas Flow Rate . . . . . . . . . . . . . . . . . . . . . 4. Combination of Stationary Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ill. Selection of Materials and Column Design . . . . . . . . . . . . . . . . . . . . . . . . . . ...... 1. Selection of the Phase Support . . . . . . . . . . . . . . . . ............... ............................... a. Treatment of the Phase Support . I.

3. Basic Sites

......................

.

153 155 156 156 158 160 161 162 162 164

181 181 183 189

...................

189

.............

192 193

c. Particle Shape. Fluidization . . . . . . . . . . . . . . . . . . . . . .

........................ c. Influence of the Column Diameter on its Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Selection of the Coating Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Selection of Phase Ratio . . . . . . . . . . . . . . . ..................... b. Procedure for Support Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Conventional Supports . . . . . . . . . . . . . .........................

195 196 196 201

.....................

.......................

Glossary of Terms . . . . . . . . . . . . . . . . . . ................................. Literature Cited . . . ...................... ......................

203 207 208

INTRODUCTION When a new analytical problem is defined, and one expects to solve it through gas chromatography, the first question the analyst must answer. - Which stationary phase should I use? - is the same today as it was thirty years ago when gas chromatography was in its infancy. References on p. 208.

154

The heart of the problem is our inability to predict with sufficient accuracy the activity coefficient of a solute of known physico-chemical properties on a given stationary phase. As discussed in Chapters 1 and 3, the retention time of a compound is related to its vapor pressure, the molecular weight of the stationary phase and the activity coefficient at infinite dilution (cf equation 7 in Chapter 3). In order to be able to calculate in advance the design and operation characteristics of the column required to perform a given separation, it would be sufficient to predict the value of each activity coefficient with an accuracy of about 10% but it is absolutely necessary to predict with a comparable accuracy the difference between the activity coefficients of any pair of compounds or the difference between the relative retention and unity, i.e., (a- 1). This requires predicting the relative retention within a fraction of one percent when it is below 1.1, within a few percent when it is below 1.5. In spite of the considerable progress made in the understanding of the underlying phenomena, the calculation of the extent of molecular interactions is still a difficult problem of physical chemistry, the solution of which requires years of painstaking measurements and tedious calculations. The derivation of the activity coefficient through the classical methods of statistical thermodynamics is a further chore. Although some notable success has been claimed in special cases (aromatic hydrocarbons and polychloro aromatics on graphitized carbon black, refs. 1-4), this is clearly not the approach to suggest to an industrial analyst. In spite of the advances made by chemical engineers in the development of empirical equations which can predict such data as vapor pressures and activity coefficients (9, it is not possible to expect the achievement of the precision required. Furthermore such equations usually require the determination of a number of physical or physico-chemical constants which are difficult and time-consuming to measure. It is scientifically useful to show relationships between retention volumes in gas chromatography and dipole moments, polarizabilities, refraction indices, etc., but it is not practical to have to determine all these constants to predict a retention volume which is easier and faster to measure directly, and often with much greater accuracy. In spite of the acquisition of an enormous data bank and of the progress made in chemometrics (6), in practice it is not possible to use an empirical approach to solve that prediction problem either. There are several reasons for this. First, retention data, relative retentions included, are difficult to reproduce from laboratory to laboratory. The reasons for that will be discussed when dealing with the selection of a proper support for the stationary phase, and also in Chapter 11. Secondly, there is a huge amount of data in the literature, but access to the information relevant to a specific problem is not easy, due to the lack of a useful data bank, which would require not only the collection of the tables of retention data published in thousands of papers, but a critical compilation of them, including all the pertinent information on the experimental conditions under which these data have been obtained. There are a few handbooks, none of them recent (7,8). Finally, there is no agreement on the selection of the factors which contribute to a significant extent to the amount of retention of a compound on a given stationary phase (9,lO). The remarkable work

155

done by McReynolds (ll),Rohrschneider (12) and a few others (13-16) has not been so useful and fruitful as was originally anticipated (see Subsection 3, below and Chapter 11). Accordingly, now, just as it was thirty years ago, common sense, experience, a good knowledge of physical chemistry and luck are the basic elements of a search for the best stationary phase. The determination of the other parameters which characterize a chromatographic analysis, i.e., the column length, the nature, particle size and coating ratio of the support, the column temperature, the nature of the carrier gas and its flow rate, the nature of the detector and its parameters, are easier to select since there are rational, rigorous methods to optimize them, based on theoretical considerations. In order to rapidly and economically achieve the design of a procedure for the chromatographic analysis of a new mixture, we suggest a two-step approach: - A first empirical step aims at determining the degree of complexity of the mixture, the difficulty of the separation and the potential ability of certain types of stationary phases to perform the separation. - A second step, based on theoretical considerations, permits the optimization of most of the experimental parameters. In practice these two steps will not be carried out exactly as they are described below and will often interact. In most cases it is not possible and it would not be economically feasible to carry out a rigorous, complete optimization of an analytical procedure. Besides, satisfactory results are frequently obtained during the course of the optimization step. The optimization of the experimental parameters is based on the following requirements, which are of critical importance for an industrial analysis: - All the compounds to be analyzed must be satisfactorily resolved, so that their quantitative analysis is possible with good accuracy, - the column life must be relatively long, so that analyses can be performed without significant change in the results, either retention times or response factors, for a period of at least months, preferably years, - the analysis times must be convenient, i.e. not too long. Very short analysis times are not necessary, nor even useful in many cases, because the response time of an industrial unit is often one to several hours. This is relatively long compared to the time required to perform a chromatographic analysis, which is often of the order oE ten minutes to half an hour. Only in rare cases will the reduction of analysis time be a requisite. The different steps of the selection of the stationary phase and the optimization of the experimental conditions of the chromatographic analysis will now be discussed in detail.

I. THE FIRST STEP AN EMPIRICAL APPROACH As described above, this first step is exploratory. Its main aim is to check out the information obtained from the production department requiring the analysis and References on p. 208.

156

some preliminary assumptions made by the analyst, regarding the complexity of the sample and the ability of certain phases suggested by past experience, by a necessarily cursory literature survey and by instinct.

1. Nature of the Sample Components It is rare in industry that the analyst has no specific information regarding the nature of the sample submitted for analysis, including its qualitative and sometimes semi-quantitative analysis. In fact there are two kinds of samples: those which come for the development of a routine analysis procedure are usually pretty well characterized, since the process which generates them has been carefully investigated at the research stage, and then developed and studied in detail at the pilot stage; those samples which come within the framework of an investigation regarding an error or an accident in production are more or less unknown and must be submitted to a combination of techniques of qualitative analysis (see Chapters 11 and 12). These techniques are also useful to identify the minor impurities of the samples of the first kind, especially when these impurities cannot be traced to those contained in the feedstock. In the present chapter we assume that the main component of the mixture and most of the components of some importance have been identified (otherwise, see Chapter 12). The main components of the mixture to be studied can be placed in the Kiselev (17) classification, based on the nature of their molecular interactions: - Group A: spherical molecules, molecules containing symmetrical sigma bonds, having no Lewis acid-base properties (i.e., no unshared doublets or empty electronic shell). Examples: noble gases, alkanes and related compounds (such as silanes). - Group B: molecules having local concentrations of electrons, pi bonds, unshared doublets. Examples: alkenes, alkynes, aromatic hydrocarbons, ethers, aldehydes and ketones, tertiary amines, nitriles, ma-arenes, thia-arenes, thiols and thioesters. - Group C: molecules having local concentrations of positive charges. Examples: organometallics. - Group D: molecules exhibiting both local concentrations of positive and negative charges. Examples: water, carboxylic acids, alcohols, primary and secondary amines, esters. The position of the main component of the analyzed mixture in this classification will help in the selection of the stationary phases for the first trial runs.

2. Selection of the Stationary Phase and Support In this first step of the optimization procedure, we want first to obtain a good idea of the actual complexity of the mixture we are dealing with and, second, to check the ability of the most commonly used stationary phases to perform the required separation. In fact we want to achieve chromatograms exhibiting the

157

largest possible number of peaks. Accordingly, the analyst will choose two widely different phases and record chromatograms of his new sample with the corresponding columns. One of these phases will be either non-polar or very similar in chemical composition to the main components of the sample. For example, if the sample is a hydrocarbon, squalane, Apiezon M or Silicone SE 30 or OV 101 will be used as stationary phase. If the sample is a mixture of chlorinated hydrocarbons, pentachlorodiphenyl will be preferred. For a mixture of esters, a polyester, such as polyglycolor poly(neopenty1 glycol) adipate or sebacate, could be an excellent choice. The reason for such a choice is that the activity coefficients, or at least, because of the difference in molecular weight between the stationary phase and the sample components, the thermal part of the activity coefficients, tend to be not far from unity and close to the same value for all the components belonging to the same famiIy. Therefore, the retention time and the elution order of these compounds are determined by their vapor pressures, i.e., to a great extent by their molecular weight and to a lesser extent by their shape. The selection of the second phase is made by trying to maximize the energy of the interactions which take place between the main components of the sample and the stationary phase. This depends on the nature and number of the functional groups carried by these molecules. Such a phase usually gives elution orders quite different from those observed on the neutral phase. Advantage can be taken of these reversals of the elution order in both qualitative and quantitative analysis. In the former case by giving information on the nature of the corresponding compounds, and in the latter by permitting the selection of an elution order which places the peaks of important components which have a small concentration far from the tail of major ones (cf Figures 1.6A-D, which illustrate the situation which should be avoided, e.g. chromatograms A-4 and C-5). In a number of cases several polar stationary phases will have to be investigated before one could be selected. There are several reasons why such a phase may give unsuitable results. These reasons are mainly related to a failure to meet the following requirements. The number of peaks separated must be comparable to the number of peaks obtained with the neutral column; authentic samples of the compounds known to be present in the mixture must be resolved either on one of the two columns or on a combination of both. The selection of the second phase cannot be made, however, without due consideration of the vapor pressure of the main components of the sample (see Section 1.4 below). Polar phases are much more sensitive to thermal degradation and to oxidative initiation of the thermal degradation than non-polar ones. As will be discussed later (see Chapter 9), it is important to reduce the amount of oxygen contained in the carrier gas as much as possible. The major requirement that the columns be stable over very long periods of time leads to the elimination, even at that stage, of stationary phases that cannot stand the required temperature (see Section 1.4). Depending on the formulation of the analytical problem, the stationary phase selected will be either the one which gives the larger number of peaks or the one References on p. 208.

158

which permits the achievement of the best resolution between the important components of the mixture. When designing a procedure for routine analysis of the effluent of a plant unit, it is often not necessary to separate all these compounds, fortunately, because many are not important enough and will not be quantitized later. For analysis carried out during this first step, a support of low specific surface area, such as Chromosorb P, with an average particle size between cu 100 and 150 pm will be selected. When polar compounds are analyzed, acid washed (AW), silanized (DMCS,dimethyldichlorosilane or HMDS, hexamethyldisilazane) Chromosorb P will be preferred. We always use a coating ratio of 20% (w/w), which combined with the good porosity and low specific surface area of Chromosorb P ensures that we are dealing with true partition, i.e., gas-liquid, chromatography (cf Chapter 3, Section A.X). This does not mean, however, that this mode should always be preferred. There are cases, as discussed in Chapter 7, where modified gas-solid chromatography gives markedly or even much better results. This latter mode of chromatography, however, is more difficult to deal with, requiring expertise and time for the successful development of an application. A preliminary, empirical approach using GLC is much faster to carry out and usually gives simple results in a short time. Tables 6.4, 6.5 and 6.8 list the inorganic supports and adsorbents (Table 6.4, pages 182-183), the organic supports and packing materials (Table 6.5, pages 184-185) and the liquid stationary phases (Table 6.8, page 206) which are most widely used in gas chromatography, respectively. 3. Polarity of Stationary Phases The number of stationary phases which have been used in gas chromatography is so vast that a classification is dearly needed (7-10). A large number of analysts have tried countless attempts to correlate retention times or volumes with various properties of the solutes and stationary phases, in the hope of devising a simple scheme for the prediction of the retention of a new compound, or of the relative retention of two compounds on a new phase (10-16). Because retention times depend strongly on the operational parameters of the column, it is useful to select, in this approach, derived retention data which depend very little on these parameters. The Kovats retention indices (18) seem the most practical to use (see Chapter 1, page 21). They are chosen by nearly everybody who is interested in retention data prediction. Retention indices vary, in principle, only with column temperature, by a few units for a temperature change of 10°C. Unfortunately they depend also on the nature of the support and the coating ratio, and their interlaboratory reproducibility has never been of the level required for the systematic use of tabulated data (19). While they were widely used 10 years ago, they are less favored now, because it has been recognized that data from the literature have to be remeasured on any new column. The first approach tried in the hope of predicting retention data was the derivation of a polarity scale for stationary phases (8,20). It was based on the

159

retention index increment (18), i.e., the difference between the indices measured for a compound on a stationary phase ( I p ) and on the reference phase (polarity = 0):

61=

I ~ - P

Squalane has traditionally been chosen as reference. It was recognized very early on (18) that it was not possible to predict the retention index of a compound merely from its molecular structure and physical properties, nor was it possible to relate simply the retention indices of a compound on different phases using one single parameter, characterizing the phase “polarity”. This concept is too simplistic. A more detailed discussion of the properties of the retention indices is presented in Chapter 11. There we especially discuss a sophisticated combinatory method which permits the calculation of the increment of a new compound from contributions due to the structure of the carbon skeleton, to the aromatic rings and to functional groups, as long as they are independent. Precision has to be traded for complexity, however, and satisfactory results are obtained only if a large data base permits the calculation of all the contributions, and if the functional groups are few and independent. The method does not give any data for compounds having polar groups which have not been previously studied, by measuring the retention indices of a number of different compounds bearing them. Kovats (18) has proposed relating the polarity of a stationary phase to the retention dispersion, i.e., the set of retention increments of long chain n-alkyl members of the main functions (n-alkyl benzene, - n-alkanol, n-alkanal, n,2-alkanone, n-alkyl acetate, methyl n-alkoxylate, n ,l-chloroalkane, n-alkylamine, n-alkyl dimethylamine, etc.). This is an attractive method for comparing a few phases, but {here is not much of a correlation between the changes of the retention increments of these compounds from one phase to another. A simpler method is required to compare the 3W-odd phases described in the literature (7,8). A more powerful approach has been suggested by Rohrschneider (21) and developed by McReynolds (22). It uses the retention increments of ten probe solutes, selected for their widely different molecular interactions with a solvent. They are: Benzene Pyridine Iodobutane 2-Octyne cis-Hydrindane

Butanol 2-Pentanone Nitropropane 2-Methyl-Zpentanol 1,4-Dioxane

This list is similar to the one of 5 probe solutes selected by Rohrschneider (21). It is possible to characterize each solute and each stationary phase by a set of 10 numbers such that:

81;

=aixS

+ b,yS + c i z S+ d,qS+ eirS+fiss + g i t S + h i u S+ iius + j , w s References on p. 208.

160

The number set ( a , b, etc., ...,j ) characterizes the solute i while the set ( x , y, etc, . ..,w ) characterizes the stationary phase. If we select ten probe compounds and measure their retention increments on one phase, there are 110 unknowns and 10 equations. Thus we can give each probe solute an arbitrary set of numbers and we shall take for each probe solute one number equal to 100 and the other nine equal to zero, which gives ten different sets. Then it is possible (by inversion of a 10 X 10 matrix) to calculate the set for the stationary phase. Once the set for each possible stationary phase has been derived (22), it is possible to calculate the retention increment of any new compound on one of these phases, knowing its number set, which may be derived from the determination of its retention increments on 10 different phases (hence 10 linear equations with 10 unknowns). The method has two drawbacks which prevented its widespread use. First, although equation 2 works reasonably well, the predictions are not very accurate. This is due in part to the modest accuracy of some determinations of the McReynolds constant of a number of phases, in part to the lack of reproducibility of phase systems. As explained in Chapter 3 (Section A.X), there are often mixed mechanisms operating in GC columns. The retention times depend not only on the nature of the stationary phase and its temperature, but also on the nature of the support and of the possible treatment(s) applied, on the coating ratio, on the nature of the carrier gas, etc.. Secondly, the amount of work required to obtain data which are scarcely precise enough for the useful prediction of the relative retention of two compounds is rather important. For each new compound, retention data on TEN different stationary phases have to be measured, assuming that the literature data on the phases are used. Although the abundant literature in this field can give good insights into possible retention mechanisms and guide the analyst in his quest for the selection of the best stationary phase, it is not generally advisable to try to apply the quantitative relationships. 4. Selection of the Column Length

We want this first step to give "good" chromatograms, i.e., to separate as many components of the mixture as possible, but we also absolutely want to elute all the components of the sample injected in the column within a reasonable time. Accordingly, for this empirical step it is advisable to select a relatively short column. The higher the boiling point of the main components of the sample, the larger the probability that the retention time of the heaviest component of the mixture is long. Using the most practical 4 mm inner diameter stainless steel tubings, the recommended column length is as follows: Boiling point of the main component between 0 and 5OOC: Recommended column length: 4 m. - Boiling point of the main component between 50 and 100O C: Recommended column length: 2 m.

-

161

Boiling point of the main component between 100 and 200°C: Recommended column length: 1 m. - Boiling point of the main component greater than 200 ” C: Recommended column length: 0.5 m. -

Longer columns should be avoided until the analyst is assured that all components of the mixture are being eluted.

5. Selection of the Temperatures of the Column, the Injection Port and the Detector We consider that the golden rule is the selection of a temperature 50 ” C higher than the boiling point of the main component of the mixture, or, if there are a few major components in this sample, a temperature 50°C higher than the highest boiling point of these compounds. Thus, for example, if the main component of a mixture has a 130°C boiling point, we use columns 1 m long, at 180°C. The temperatures of the injection port and the detector will be equal to the column temperature. The error most commonly made at that stage, even by seasoned analysts, is to use too long a column at too low a temperature, in the hope of acheving a decent separation, possibly the final one, right from the beginning. It is certain that a longer column, used at a lower temperature would give a much better resolution of the early eluted compounds than the column we recommend. Since retention times increase exponentially with decreasing temperature, however, high boiling compounds which are sometimes unexpected, would then have prohibitively long retention times, would give very broad peaks, easily mistaken for a base line drift, and would thus go unnoticed. The result of such an analysis is misleading and dangerous. For the same reason, and to increase yet further the probability that any component of significance in the mixture under study be eluted, we recommend carrying out an additional analytical run, using temperature programming up to the maximum temperature limit of each phase. It should not be forgotten that the aim of the first step is to: - obtain a good idea of the complexity of the mixture. This requires the elution of “heavy”, “slowly eluting”, “strongly retarded”, etc. compounds. - form an opinion regarding the ability of conventional phases to achieve the requested separation. It is an information-gathering step, and it does not aim at designing the final column. Long experience has taught us that time spent in carefully performing that step (usually a few hours to a day) is well and wisely invested and may prevent costly surprises whch may otherwise happen later. The use of short columns at high temperatures provides for fast analysis. In line with the main aim of this preliminary stage, it is advisable to let the elution proceed for a rather long time. Finally, it should be pointed out at that stage that if using a 1 m long column a resolution significantly greater than zero is not observed between two compounds which must be resolved, the resolution required for proper quantitation (1.0 to 2.5, References on p. 208.

162

depending on the relative concentration of these compounds, see Chapters 1 and 4) will be impossible to achieve with a packed column of any practical length. The unavoidable conclusion in such a case is that either the use of a capillary column must be investigated or a better stationary phase must be found. The reason ‘for this will be made clear below (see Section 11.1). 6. Selection of the Camer Gas Flow Rate The optimum flow rate of a 4 mm i.d. column packed with 100-150 pm particles of Chromosorb P with our packing method is typically 3 L/h of nitrogen, i.e., 50 mL/min. This is the flow rate uniformly used at that stage. It corresponds to a flow velocity of the carrier gas of 9.5 cm/s, assuming a total porosity of 0.70 for Chromosorb P. The carrier gas commonly used in industrial laboratories is nitrogen with a flame ionization detector and helium with a thermal conductivity detector. Helium is relatively expensive and is replaced by nitrogen whenever possible, in spite of the lower diffusion coefficient of the latter gas, resulting in a smaller optimum flow rate and a longer analysis time. From a theoretical standpoint (cf Chapter 2), hydrogen would be a much better carrier gas, because of its larger diffusion coefficient and much lower viscosity than nitrogen or helium. Because of safety regulations, however, the use of hydrogen is often very difficult, sometimes impossible. Our University laboratory has used hydrogen as a carrier gas for 25 years, however, with only one incident to report, when a student switched on the oven without fastening the column to the apparatus by tightening the corresponding Swagelock nuts. The ensuing explosion opened the chromatograph door without any further damage than slightly bending the door. Proper operation of a chromatograph requires a very small leakage of the camer gas stream, much lower than what would be required for its safe operation. This comment should certainly not be construed as a suggestion that safety regulations should not be followed to the letter, however. 7. How to Use the First Step Chromatograms

These chromatograms afford an image of the composition of the sample and of its complexity. They are the starting point of the optimization process. Basically three different situations are encountered. They are illustrated by Figure 6.1 drawn on the assumption of a “pure” industrial product, i.e., for a sample which contains one main component and a large number of different impurities. There can be a large number of minor components eluted before the main product and a very small number of them eluted after it (Figure 6.1A), a small number of minor components eluted before the main component and a large number of them eluted after it (Figure 6.1B), or both, a large number of components eluted before and after the main one (Figure 6.1C). The case when there are only very few minor components is also rarely encountered and does not deserve any special treatment because of its simplicity. In each case there is a series of

163

A

Figure 6.1. Chromatographic profiles of typical samples. (A)Many early peaks and few late ones. (B) Few early peaks and many late ones. (C) Many early peaks and many late ones.

complementary analyses to be performed in order to finish the first step of the optimization procedure, the collection of information on the analyzed mixture and the selection of the stationary phase. They are detailed in Table 6.1. Depending on the nature of the problem, the design of a routine analysis to be carried out on-line in the plant or off-line in the laboratory, the optimization may involve analyses carried out using temperature programming. On-line analysis cannot be achieved using temperature programming (see Chapter 17). On the other hand it is perfectly reasonable to use column switching in such a case. This technique, whlch lacks flexibility, is often neglected in research laboratories and is not a favorite for off-line routine analyses either, especially if the same chromatograph has to be used to carry out different analyses in the course of the same day. TABLE 6.1 The Use of the Chromatograms Obtained during the First Step Type of chromatogram

Configuration

Changes to make

A

Many peaks before; few peaks after the main component

Decrease temperature and/or increase column length

B

Few peaks before; many peaks after the main component

Increase temperature and/or decrease column length

C

Many peaks before: many peaks after the main component

Increase temperature and/or increase column length

In addition, try temperature programming to complete the first step. For on-line analyses use column switching. For off-line analyses use column switching and/or temperature programming. References on p. 208.

164

On the other hand, when an analysis has to be carried out any number of times per day, day in and day out, on a dedicated instrument, there is no objection to the use of the column switching method, which permits the elution of compounds of widely different polarities and vapor pressures in conditions suitable for their quantitation. However, routine analysis performed in the laboratory may use temperature programming. This is often the preferred solution, for the sake of simplicity. It must be pointed out, however, that quantitative analysis is often appreciably more accurate when carried out under isothermal conditions (see Chapter 16). Column switching, which can be achieved automatically, under the control of the instrument computer on modem gas chromatographs, should be investigated as an alternative to temperature programming as soon as the number of repetitive analyses to be made warrants its study. 11. THE SECOND STEP OPTIMIZATION OF THE MAIN EXPERIMENTAL PARAMETERS

The previous study shows whether it is possible to achieve the required separation on a column made with one of the stationary phases already studied. When the answer is positive, it is possible to move to the second step, the optimization proper. In the negative case, a more thorough search of the literature and a more detailed investigation of the numerous stationary phases available is warranted. If this search proves to be unsuccessful, the design of a mixed phase column, or the combination of two columns made with different stationary phases may be the solution. Assuming that a suitable stationary phase has been found, optimization of the column design and operation parameters can be carried out. Table 6.2 contains retention data of most chloroalkanes with 1 and 2 carbon atoms on pentachlorodiphenyl. These results will be used to illustrate the following discussion of the optimization of the column parameters. 1. Optimization of the Column Length

From either the chromatogram of the sample obtained on the selected stationary phase, using the column prepared for the preliminary step of the project, or the chromatograms obtained separately for pure, authentic samples of the compounds to be separated, the pair most difficult to separate can be identified and the resolution between these two compounds can be calculated. The previously derived relationships between the column efficiency or the resolution of a pair of compounds, the parameters of the column and the characteristics of the separation are summarized in Figure 6.2. Equation 6 on Figure 6.2 permits an easy derivation of the length of the column which will be necessary to achieve a resolution R, larger than the resolution R, observed with the original column of length L,. The new column length will be: n 2

A

L =L , y RI

(3)

165

For example, if the resolution observed on the 1 m long column is 0.70, it will be necessary to prepare a 2.04 m long column to achieve a resolution of 1.0, which is the absolute minimum for an acceptable quantitative analysis, and a 4.60 m long column to achieve a resolution of 1.5 which permits good quantitation of two TABLE 6.2A Relative Retention Times and Resolution of Chlorinated Hydrocarbons on Pentachlorodiphenyl

Nr 1

2 3 4 5

6 7 8 9 10 11 12 13 14 15 16 17 18 19

B.P. ("C) - 24 - 13 13 37 40 48 57 59 61 74 76 82 87 113 121 130 146 160 186

Formula

Name

CHJl C2H3Cl C,H,CI c 2 H2Clz CH 2C12 C2HZClZ

Methyl chloride Vinyl chloride Ethyl chloride Vinylidene chloride Methylene chloride truns-Dichloro-1,2-ethylene Dichloro-1,l-ethane cis-Dichloro-1,Zethylene Chloroform Trichloro-l,l,l-ethane Tetrachloromethane Dichloro-1,2-ethane Trichloroethylene Trichloro-1,1,Zethane Tetrachloroethylene Tetrachloro-l,1 ,1,2-ethane Tetrachloro-1,1,2,2-ethane Pentachloroethane Hexachloroethane

c2 H4C1 2

C2H2C12 CHCl, C2H3C13

CCI 4 CH4Cl2 C2 HCl3 CH3Cl3 c2c14

cZ H2C14 CZH2C14

C,HCI, C2Cb

TABLE 6.2B Relative Retention Times and Resolution of Chlorinated Hydrocarbons on Pentachlorodiphenyl Compound name

Column length = 4 m 30°C a

Methyl chloride Vinyl chloride Ethyl chloride Vinylidene chloride Methylenechloride . . rruns-Dichloro-l,2-ethylene Dichloro-1,l-ethane cis-Dichloro-l,2-ethylene Chloroform Trichloro-1,l.l-ethane Tetrachloromethane Dichloro-1,2-ethane Trichloroethylene

0.03 0.04 0.10 0.21 0.28 0.40 0.49 0.66 0.75 '.OO

50°C R

a

lLi7 4.38 5'18

0.04 0.06 0.11 0.25 0.32 0.44

2'37 3.40 1.73 3'07 lA5 2.71 1.62 1.47

1.91

0.52 0.68 0.75 "0° 1.15

80°C R

a

R

3.71 lS9

0.06 0.07

0.74 3,00

5'69 2'34 3'68 2'oo 3.40

0'14 0.30 0.36 0.48 0.55 o.71

3,38 1'37

0.78

5.76 2.03 3.26 1.84 3.50 1.40 3.12

1.88

l.O0 ''15 1.21 1.66

1.23 4.84

2.00 0.61 4.34

References on p. 208.

166 TABLE 6.2C Relative Retention Times and Resolution of Chlorinated Hydrocarbons on Pentachlorodiphenyl Compound name

Column length = 2 m 80°C

cis-Dichloro-1,2-ethylene Chloroform Trichloro-1,l,l-ethane Tetrachloromethane Dichloro-1.2-ethane Trichloroethylene Trichloro-l,1,2-ethane Tetrachloroethylene Tetrachloro-1,1,1,2-ethane Tetrachloro-l,1,2,2-ethane Pentachloroethane Hexachloroethane

120 O c

l00OC

a

R

0.20 0.22 0.28 0.32 0.34 0.46 1.00 1.26

0.90 2.44 1.54 0.55 2.98 5.99 2.57

140°c

a

R

a

R

0.22 0.24 0.31 0.36 0.37 0.49 1.00 1.25 1.82 3.12 5.05 9.68

0.75 2.00 1.26 0.26 2.30 5.84 2.38 3.84 5.13 4.83 6.41

0.24 0.26 0.33 0.40 0.40 0.52 1.00 1.24 1.73 2.83 4.50 8.28

0.60 1.87 1.22 0.04 2.17 4.38 1.98 3.22 4.84 4.55 6.16

a

R

0.44 0.56 1.oo 1.23 1.70 2.65 4.12 7.31

2.00 4.03 1.87 3.07 4.13 1.41 6.03

R , resolution between two successive compounds.

compounds if the ratio of their concentrations is not very different from unity. If this ratio is very large, which happens in the case of trace analysis, a resolution of 2.5 might be necessary (see Chapter 1, Figures 1.6A-D and Chapter 4), and a 12.8 m long column would then be required. Further numerical results are given in Table 6.3. To double the resolution between two compounds requires the use of a column that is four times longer. This is a very steep increase indeed, and this rule cannot be extrapolated very far. The carrier gas pressure drop increases in proportion to the resolution: the absolute inlet pressure is proportional to the square root of the column length, at least when the inlet pressure exceeds a few atmospheres (see Chapter 2, equations 3 and 16 and Section VI), while the resolution is also proportional to the square root of the column length (see equations 1.35 or 2.16). The inlet pressure may thus become prohibitively large. In the introduction to Chapter 8 we discuss the advantages and drawbacks of capillary columns versus packed columns. The situation in most cases of routine analysis is not so obviously in favor of capillary columns as it is for all research applications, but we are certainly of the opinion that whenever a packed column longer than 10-12 m is required, an open tubular column should be preferred. The use of equation 3 and of equations 4 and 6 in Figure 6.2 assumes that the column plate height is independent of the column length, which is generally considered to be true and supported by experimental results (29). This requires, however, that (i) the packing method used gives a column whose plate height is independent of the length, and (ii) that the column plate height be independent of the pressure drop. The former is true only within a “certain” range: for example certain packing methods require that the column be packed straight and coiled afterwards (see Section 111.4 below). When the column length exceeds a few meters

167

The number of theoretical plates for a certain compound is defined as: 2

N =16(

$)

where f R is the retention of a compound and w its peak width (see Chapter 1, equations 1 and 23). For a given column N may depend significantly on the specific compound considered, but most often N varies only slightly from one compound to another. For this reason, people often refer to the plate number of a column or the plate number generated by a given column. One should be careful about this generalization, especially when dealing with open tubular (capillary) columns, where the plate number depends on the column capacity factor and should not be quoted without mentioning the value of k’ for which it has been measured (cf equations 16, 21 and 22, Chapter 4). The height equivalent to a theoretical plate is defined as: H = -L N where L is the column length (cf equations 1.26, 4.16 and 4.17). The resolution between the peaks of two compounds is defined as the ratio of the distance between their maxima to half the sum of their widths:

It has been shown by Purnell(27) that the resolution is related to the characteristicsof the separation and of the column by:

where k’ is the column capacity factor for the second compound of the pair and a is the relative retention of the two compounds ( f A 2 / r A 1 ) . The resolution can thus be expressed as the product of two factors, fi/4, which depends essentially on the quality of the column (and a little on k’), and the specific resolution, which depends essentially on the nature of the two compounds and of the stationary phase (and a little on the phase ratio of the column). The specific resolution is: R =--a - 1 k’ (5) I a 1+k’ Solving equation 4 for the plate number gives:

Combination between equations 2 and 6 shows that the length of the column required to achieve a certain separation, characterized by a desired resolution between two compounds, increases as the square of R (see Section 11.1 for discussion). N given by equation 6 is often referred to as the necessary plate number for the achievement of a certain resolution between a given pair of compounds on a certain stationary phase. Figure 6.2. Summary of relationships between the characteristics of a separation and the column parameters (see Chapters 1 and 4).

the use of a scaffold or of the staircase of a high rise building may become necessary, neither of which is very practical. The latter assumption is not true (see Chapter 4, Section VII), although the column plate height varies only slowly with increasing pressure drop. Nevertheless, the use of equation 3 gives good results for columns up to 5 m long or so, and acceptable results up to 10 m. References on p. 208.

168

TABLE 6.3 Resolution and Column Length * Resolution on a 1 m long column

Length of a column giving a resolution equal to 1.0

1.5

2.0

2.5

0.1

100.0 25.0 11.1 6.2 4.0

225.0 56.3 25.0 14.1

400.0

0.2 0.3 0.4 0.5

9.0

100.0 44.4 25.0 16.0

625.0 156.3 69.4 39.1 25.0

0.6 0.7 0.8 0.9 1.o

2.8 2.0 1.6 1.2 1.o

6.2 4.6 3.5 2.8 2.3

11.1 8.2 6.2 4.9 4.0

17.4 12.8 9.8 7.7 6.3

1.2 1.4 1.6 1.8 2.0

0.7 0.5 0.4 0.3 0.3

1.6

2.8 2.0 1.6 1.2 1.o

4.3 3.2 2.4 1.9 1.6

0.8 0.7 0.6

1.3 1.1

2.2 2.4 2.6

1.1

0.9 0.7 0.6

0.9

See equations 3 and 4, Figure 6.2, page 167.

An estimate of the reliability of this approximation is given by comparing the data for the chloroalkanes # 8 to 13 in Tables 6.2B and 6.2C. The average ratio of the resolutions obtained for the successive pairs on the 2 m long and the 4 m long columns is 1.33 (theoretical value: 1.41); the relative standard deviation of this ratio is 125%.We would predict from these data that, in order to achieve a resolution of 1.0 for the separation of carbon tetrachloride ( # 11) from 1,2-dichloroethane ( # 12) at 80 O C, the required column length is 6.6 m (data on the 2 m long column) or 10.7 m (data on the 4 m long column). Since the data on the longer column tend to be more precise, the solution here is to try a 10.7 m long column and cut a section off if the resolution achieved exceeds the requirement. The efficiency of the column required for the separation of two components depends on their retention and their relative retention, through the classical equation:

N

a)’( -)’ k‘

= 16R2(

OL-1 l + k ’

(4)

When the relative retention becomes close to 1, the separation becomes very difficult. The column length required, the inlet pressure and the analysis time

169

Relative retention

Figure 6.3. Plot of the number of theoretical plates required to perform a certain separation as a function of the relative retention of the two compounds. k’ = 3. Resolution: 1.5.

increase rapidly and become prohibitively large. Figure 6.3 shows a graph of log N versus ct which illustrates the nature of the problem. For further discussions regarding the optimization of the resolution between two or more compounds readers are referred to the papers by Guiochon (30) and Scott (31) on this topic.

2. Optimization of the Column Temperature As discussed in Chapter 3, the retention of a solute is related to its physico-chemical properties and to the characteristics of the column by the following equation:

where k f is the column capacity factor. Other useful relationships between the retention time, the thermodynamics of the gas-stationary phase equilibrium and the column parameters are given on Figure 6.4. The only parameters in equation 5 which vary with temperature are the vapor pressure P o , T and the activity coefficient at infinite dilution. The product V,p is the mass of stationary phase in the column and Vm is the geometrical volume available to the gas phase inside the column, and dilatation of the column tube and packing particles is negligible. Although the activity coefficient varies with temperature, usually decreasing with increasing temperature, its variations are slow, so that the exponential increase of the vapor pressure with increasing temperature is the References on p. 208.

170 The retention time of a compound is given by: L rR = (1+ k’)U,”

where: - k’ is the column capacity factor - L is the column length - u, is the average carrier gas velocity. The column capacity factor is given by:

where: - V, is the volume of stationary phase in the column (V,p is the weight of liquid phase in the column), - V, is the volume available to the gas phase inside the column, - p is the density of the liquid phase, - M, is the molar weight of the stationary liquid phase, - R is the ideal gas constant, - T is the absolute temperature of the column, - P o is the vapor pressure of the analyte at the column temperature, - y is the activity coefficient of the solute in the solvent (liquid phase). Differentiation of equation 2 gives: dln(k’) SHS S H Y S H E (3) R R R d(l/T) d(l/T) d(l/T) A plot of In(k’) or of ln(tA) versus the inverse of the absolute temperature is a straight line if SHS remains constant. In fact it varies very slowly with temperature, because the heat capacity of the solute is different in the gas and the solution. A more detailed discussion of solution thermodynamics applied to chromatography and to the study of retention is given in Chapter 3. dln(r;) dln(V,) -=-=-=-=---

Figure 6.4. Summary of theoretical relationships between the retention data and solution thermodynamics (see Chapters 1 and 3).

dominant effect. Accordingly, retention times decrease rapidly with increasing temperature (see Chapter 3, Section A.VI). A plot of the logarithm of the corrected retention time of a solute (proportional to k’) or of the relative retention time of two solutes (equal to k i / k ; ) , versus the reverse of the absolute temperature gives a straight line. The slope of this line is equal to the dissolution entha€py of the solute in the former case (see equation 17 in Chapter 3), and to the difference between the dissolution enthalpies of the two solutes in the latter case. It should be pointed out at this stage that these plots of log t;P versus 1 / T are linear only to a first approximation, although this is usually an excellent one. Because the heat capacity of a solute is markedly different when in the gas or the solution state, the plot is slightly curved. This curvature can be observed only when very accurate measurements are carried out over a relatively large temperature range (32). These theoretical considerations are illustrated on Figures 6.5A and 5B, where

171 (A)

13

9 8

1/T

10 l9

ao -c

50

30

I

1 \ \

l7

I t

15 14

1 t

I .

l/T I

I

I

I

1

I

d

I

1

I

I

I

too 120 1-10~~ Figure 6.5. Plot of the logarithm of the relative retention time versus the reverse of the absolute temperature. Chlorinated hydrocarbons on pentachlorodiphenyl (see Tables 6.2A-C). (A) Compounds # 1 to 13; reference l,l,l-trichloroethane. (B) Compounds # 8 to 19; reference 1,1,2-trichloroethane. ao

the logarithm of the relative retention times of the chloroalkanes are plotted versus the inverse of the temperature (cf data of Tables 6.2A-C). The lines converge towards the higher temperatures, illustrating the well-documented fact that the relative retentions usually decrease with increasing temperatures, i.e. .that the lower References on p. 208.

172

the temperatures, the easier the separations tend to be. This is because the enthalpies of dissolution are related to the molecular weight and tend to increase (in absolute value, i.e. to decrease since they are negative, dissolution of a vapor being an exothermic process) with increasing molecular weight of the solute. There are some exceptions to this rule, however, as is illustrated by the behavior of carbon tetrachloride (# 11) and 1,2-dichloroethane( # 12) whose straight lines intersect for a temperature of ca 125O C. They will be very difficult to separate in the temperature range between 110 and 140OC. A large number of similar graphs have been published in the literature. Only a few references can be given (33). In practice only a few data points are required to draw plots such as those shown on Figures 6.5A and 5B. If accurate measurements are made, it may be sufficient to use the data obtained at the temperature at which the “profile chromatogram” of the mixture under study has been recorded (i.e. 50 O C above the boiling point of the main component of the mixture) and data obtained at a temperature either 30 O C lower or 30°C higher, depending on the compounds studied and their retention. It is only in the cases of compounds whose (log t; vs 1/T) lines intersect in this temperature range, or which are very close, that more data may become necessary. The selection of the column temperature is made from an analysis of the graph containing the log t; vs 1 / T plots corresponding to each compound of the sample. The optimum temperature should be such that: (i) a minimum resolution should be observed between each pair of successive compounds. (ii) the shortest analysis time possible is achieved. The first condition immediately excludes all temperature ranges around the temperatures at which an inversion between the elution order of two compounds takes place. When there is a large number of compounds and especially when several of them experience an inversion of their elution order, it may become very difficult and tedious to make the selection of an optimum temperature from the graph. As for the optimization of the composition of a mixed stationary phase, two methods can be used to achieve the selection of the optimum temperature, the band plot and the window diagram. Using the band plot method, the analyst measures, on chromatograms recorded at different temperatures, the times corresponding to the elution of the beginning and the end of each peak, i.e. at the intersection between the base line and the inflexion tangents of the peak. Then the corresponding plots of the logarithms of these two times versus the inverse of the absolute column temperature are added on the previous graph. Now each compound is represented by a band, centered on the previous line (log t; vs l/T), whose width corresponds to the peak width (cf Figure 6.6). In order to obtain a resolution of unity between the two compounds a column temperature must be selected which is outside the range where the two bands intersect. When all the temperature ranges in which such intersection occurs between the bands, corresponding to all possible pairs of compounds, have been eliminated, the temperature can be chosen in the remaining range(s). The optimum temperature is usually the lowest temperature among those which remain possible

173 a 14

4 5: 13

3-

;

10

2-

<

t

and which corresponds to a reasonable value of the coating ratio and of the analysis time (see Section 111.3). A graph corresponding to some of the chlorinated hydrocarbons chosen as example (# 8 to 13) is shown on Figure 6.6. A temperature between 80 and 100O C would permit an easy separation. A further discussion of the selection of an optimum temperature is presented at the end of this subsection. As we shall discuss in more detail (see Section 111.3 below), the retention time of a compound is a function of the phase ratio, i.e. of the coating ratio of the support. Thus, once the column temperature has been selected, the analysis time or the column capacity factor for the last compound can be adjusted to the desired value, at least in principle, by selecting the proper value of the phase ratio (cf equations 7 and 10 in Chapter 3). In practice this can be done only within a certain range of the phase ratio. The difficulty here is that, in the process, some early eluting compounds may become difficult to separate, not because their relative retention is small, but because their column capacity factor becomes too low when the phase ratio is reduced (cf equation 4, Figure 6.2). This phenomenon is often difficult to deal with when using the band plot method. The more refined window diagram method advocated by Purnell (27) involves calculating for each temperature the resolution of the pair of compounds which is the most difficult to resolve. This pair may be an early eluted one, because of a low value of k', or a highly retained one, because of a low value of a (cf Figure 6.2, equations 4 and 5). The most difficult pair to resolve usually changes with increasing temperature. Because we do not know at that stage what column efficiency will be required to perform the analysis, we calculate the specific resolution (cf equation 5 , Figure 6.2). The result is plotted versus the temperature and the optimum column temperature is selected among the values of the temperature for which the specific resolution is the greatest, so as to minimize the analysis time, i.e. the retention time of the last component of the mixture, on the shortest possible column. The column References on p. 208.

174

length can be calculated as described in Section 11.1 above, knowing the desired minimum resolution between two peaks and the plate height of the columns which can be packed. Figure 6.11 shows the window diagram applied to a different but similar problem, the selection of the phase composition. Since the separation of the chloroalkanes (see Table 6.2) is a relatively easy separation, the window diagram does not afford markedly better results than the band plot method. It may seem to be a complex and superfluous procedure, which is true in the present instance. On the other hand, for a complex mixture, with several pairs of compounds undergoing an inversion effect, it is very useful and practical. If the final analysis time is considered to be too long and it is not possible to use a higher temperature, there are two possible solutions: - the separation can be made on two different columns, using the method of column switching, and two isothermal columns at two different temperatures. The light compounds elute unresolved but very early from the first column; they are separated on the second column, while the late eluted compounds are resolved on the first column and do not travel along the second one. They exit to the detector through an empty narrow tube of permeability comparable to that of the second column (see details on column switching in Chapter 9). The selection of the stationary phases and of the column temperatures are made separately and independently for optimization of the separation of the two parts of the mixture, as explained above. The selection of the time delay for the operation of the switching valve permits successive recording of the two chromatograms without interference. - temperature programming can be preferred in routine laboratory analysis. This method is more flexible but gives quantitative results which are less accurate (see Chapter 9, Section V.2 and Chapter 16, Section IV). Finally, it should be pointed out that the inversion phenomenon can be used to select the most convenient elution order in the case of trace analysis: much better resolution and quantitative results are obtained when the trace compound is eluted before the main component of the sample rather than just after it.

3. Optimization of the Carrier Gas Flow Rate The influence of the carrier gas flow rate on the column efficiency has been discussed in Chapter 4. The column plate height decreases with increasing flow velocity at very low values of this velocity, goes through a minimum, then increases indefinitely with increasing flow velocity (see Figures 6.7 and 6.8). The plot of H (height equivalent to a theoretical plate) versus the outlet flow velocity, uo, is an hyperbola in a first approximation. The column efficiency is maximum for a certain value of the gas velocity. At that flow rate the resolution is the largest. In most cases we choose the corresponding flow rate to operate the column. It is often believed that the analysis time can be significantly reduced by operating the column at twice that flow rate, while the efficiency is decreased only slightly. This is true if a general purpose column is used, and its efficiency is too large for the separation studied. It can be shown, however, that if a dedicated column is designed for a specific application, the shortest possible analysis time is obtained by selecting the carrier

The height equivalent to a theoretical plate varies with the carrier gas flow rate (see Chapter 4 and Figure 6.8). It decreases with increasing flow velocity at very low values, goes through a minimum value and increases indefinitely. As a first approximation, around the minimum, the relationship between H and u is hyperbolic: B H = - + A + CU

This is the Van Deemter equation (36). Because of the very complex structure of the column and the complications due to the compressibility of the carrier gas, it has proven impossible to simply relate A, B and C to the design and operation parameters of the column. As a first approximation: B = 2Dg

(2)

A = 2Xd,

(3)

c = (C,+C/)U

(4)

with (36, 59, 70):

and:

cg=

1+6k’+llk’* di 96(1+ k‘)’

D.e

where: - Dg is the diffusion coefficient of the solute in the gas phase, - DIits diffusion coefficient in the liquid phase, - d , is the average thickness of the film of stationary liquid phase on the support, - d , the average particle size of the column packing. A more detailed discussion of these contributions to the plate height is found in Chapter 4. Figure 6.7. Summary of the relationships between the height equivalent to a theoretical plate and the column parameters (see Chapters 1 and 4).

gas flow velocity giving the largest efficiency and adjusting the column length so as to achieve the exact resolution desired (34). For a typical 4 mm i.d. column packed with 100-150 pm particles, the optimum flow rate is usually around 3 L/hour, i.e. 50 mL/min. The standard US column size is around 4.5 mm i.d.; this would correspond to a flow rate of 65 mL/min. On the other hand, with the 1 mm i.d. columns which are sometimes used, the optimum flow rate is only 0.2 L/hour, i.e. 3.3 mL/min. Whatever its diameter, the minimum plate height of a column packed with 100-150 pm particles is around 0.5 mm. It has been shown that the column efficiency is roughly proportional to the average particle size, while the optimum velocity is inversely proportional to this size (see Chapter 4, Sections IX.2 and X). Thus, a column packed with 100-150 pm particles‘ gives about 40% more theoretical plates than a column packed with 150-200 pm particles. On the other hand the permeability of the former column is about twice as small. Since the optimum flow rate will also be 40% greater for the former column, its pressure drop will be much higher than that of the latter column. References on p. 208.

176

L

* U

Figure 6.8. Plot of the height equivalent to a theoretical plate versus the carrier gas flow velocity.

This explains why most gas chromatography columns are packed with materials having an average particle size between 100 and 300 pm. Larger particles give columns which are highly permeable (very low inlet pressures), but moderately efficient, while smaller particles would give highly efficient columns with a very low permeability ( 3 9 , requiring very high inlet pressures (which may be difficult to handle in a routine laboratory and impossible to use in on-line process analysis). The minimum plate height varies very little with the nature of the carrier gas, unless the resistance to mass transfer in the stationary phase is important (cf Chapter 4, Section VII) while the optimum velocity is proportional to the diffusion coefficient of the solute in the carrier gas (see Chapter 4, Section XI.2). For this reason the gases commonly used as mobile phases in GC can be listed in the following order: hydrogen better than helium, better than nitrogen, better than argon or carbon dioxide. Unfortunately, hydrogen is dangerous and helium expensive, so for most of our routine work helium is selected when a thermal conductivity detector is used for maximum sensitivity (see Chapter 10, Section 111), and nitrogen is selected when the detector is a flame ionization detector. In the case of difficult analyses, however, a significant reduction in the analysis time can be achieved by replacing nitrogen by helium, or by hydrogen, which has the further advantage of enjoying a much lower viscosity. Thus, the James and Martin compressibility correction factor is much larger with H, than with He, and retention times are markedly smaller at the same outlet flow rate. Finally, the resistance to mass transfer in the liquid phase may become a significant contributor to column plate height at flow rates around or above the optimum. The corresponding term (cf Chapter 4, Section VIII) increases with increasing average thickness of the liquid layer, so it is advisable to use a moderate phase ratio. Chromosorb P has a rather small specific surface area, which favorably reduces the influence of adsorption on the retention of compounds, by limiting the extent of secondary mechanisms (see Chapter 3, Section A.X). It is possible to use

coating ratios up to 30% (w/w) without filling all the pores and experiencing major loss of column efficiency. It is better, however, not to exceed 15 to 20% above which value the column efficiency begins to decrease significantly. 4. Combination of Stationary Phases If it has been impossible to achieve the desired separation after repeated attempts using different stationary phases, at different temperatures and with long columns, the combination of two or several phases might be a solution (22). This method is particularly well suited to process control analysis, which must be carried out automatically, but can easily accommodate column switching. The combination of two different stationary phases has also been used successfully in temperature programming for routine analysis camed out in the laboratory. Combination of stationary phases is usually limited to two phases, but the same method can easily be extended to several phases if needed. In practice there are three different ways to achieve it: - by mixing the different stationary phases, at the required concentrations, in the same solution, prior to coating of the support, following the classical procedure (see Section III.3.b). - by mixing the coated supports before packing the column. Supports of identical particle size and size distribution must be used to ensure good packing homogeneity. The coated supports are thoroughly mixed, in suitable proportions, before column packing. - by placing on-line columns packed with support coated with the different stationary phases. It is often said in the literature that the results obtained by these three methods are identical (23-26), but this is true only to a first approximation and a few exceptions occur. When two coated supports are mixed the retention volumes are additive: VR = Vr + KlVI.l+ K2v,,2

(64

where q,l and K,2 are the volumes of the two solvents introduced in the column. This relationship is strictly valid as long as the two phases do not mix inside each particle, which may happen after a long time. When the two phases are mixed, molecular interactions take place between them, leading to an activity coefficient of the solute in the mixed phase which is different from the one we could expect if the two solvents behaved independently. It has been shown by Purnell(27), however, that in most cases, the retention volume on a mixed phase is the sum of the independent contributions due to each phase and which are calculated as if each phase were pure:

where mi is the mass of solvent i contained in the column and Vg,i the specific retention volume of the studied compound on pure phase i (a correction for column References on p. 208.

178

temperature must also be applied, see Chapter 1). Equations 6a and 6b are equivalent (see Chapters 1 and 3). Although some exceptions are probable, in the case of mixtures of solvents which give strong associations or complexation adducts, it is reasonable to expect the first two methods to give very similar results in most cases. The situation is different with on-line column coupling. Because of the compressibility of gases, the carrier gas velocity varies all along the column (see Chapter 2). If two columns are in series, the average gas velocity will be different in both, therefore the retention will be different if the order of the two columns is reversed. The retention time is not given by a linear relationship as previously, especially if the pressure drop of the column series is significant (28). This problem has been discussed in detail in Section XI of Chapter 2 which gives an equation to relate the apparent column capacity factor to the capacity factors measured on each pure solvent. In the cases when a linear relationship between the retention time on the mixed column and the composition of the stationary phase can be expected, i.e., when either a single mixed phase column is used or the pressure drops in the two columns are not too important, the graphic procedure derived by Rohrschneider (12) is used to calculate the optimum composition. A log k’ versus composition graph is drawn. Log rk can also be used, if the two columns have been used at the same flow rate, but the result might be less accurate. The corrected (or the relative) retention times of all solutes are reported on the vertical axis corresponding to the two pure stationary phases (see Figure 6.9). The two points corresponding to each solute are joined by straight lines. In simple cases, the composition for which the mixture is best resolved can easily be selected. For example, a graph using the relative retention times of four compounds, acetone, carbon tetrachloride, l,l,l-trichloroethane and benzene is shown in Figure 6.9. The stationary phases are Carbowax 20M, a polyethyleneglycol, and tris(cyanoethoxy)propane (TCEP). A composition of the stationary phase between 10 and 15% of Carbowax, or the use of two columns with the corresponding length ratio, would permit an easy separation. The chromatogram obtained with the two pure solvents (TCEP and Carbowax) and with a column combination (1 m Carbowax 20M, 4 m TCEP) are compared in Figure 6.10. An excellent resolution of the four-component sample is obtained. Because a series of two columns was used, the retention times are slightly different from the prediction of a linear model. For this relatively easy separation this does not matter much, however. In more complex cases it is advisable to use either the band plot or the window diagram method. The window diagram corresponding to the mixture studied above (see Figures 6.9 and 6.10) is shown in Figure 6.11. The improvement over the band plot method is negligible in this simple case, but the method is clearly much simpler and powerful for complex mixtures. In the simpler band plot method, the analyst measures on the chromatograms recorded with the two pure solvents the times corresponding to the elution of the beginning and the end of each peak, i.e. the times corresponding to the intersection between the base line and the inflexion tangents of the peak. These two points are also reported on the corresponding vertical axes, and the corresponding points are

179

100%Carbowax

0% TCEP

75

50

25

25

50

75

12.5%

0% 100%

Figure 6.9. Combination of stationary phases. Plot of the relative retention time ( r ; = 1 for CCl,) versus the percentage of TCEP in a Carbowax 20M / TCEP mixture. Compounds: 1 - Acetone; 2 - carbon tetrachloride; 3 - l,l,l-trichloroethane; 4 - benzene. - First column (A) (data on the left vertical axis). 15% (w/w) Carbowax 20M on 60-80 mesh Chromosorb P, at 80' C. Column length 2 m, i.d. 4 mm. - Second column (B) (data on the right vertical axis). 15%(w/w) TCEP on 60-80 mesh Chromosorb P at 80 C. Column length 4 m, i.d. 4 nun.

joined. Now each compound is represented by a band, centered on the previous line ( t ; versus composition), whose width corresponds to the peak width. In order to obtain a resolution of unity between the peaks of two compounds a stationary phase composition must be selected which is outside the range where the two bands intersect. Once all the composition ranges in which the bands corresponding to all possible pairs of compounds intersect have been eliminated, the composition can be chosen in the remaining range(s). This method can be used with complex mixtures if there are only few inversions (33). The more refined window diagram method advocated by Purnell (27) consists of calculating, for each composition, the resolution of the pair of compounds which is most difficult to resolve (see Figure 6.11). This pair may be an early eluted one, because of a low value of k', or a markedly retained one, because of a low value of a. The most difficult pair to resolve usually changes with changing composition. Because we do not know at that stage what the column efficiency required to perform the analysis will be, we calculate the specific resolution (see Figure 6.2, equation 9,which is the resolution achieved on a hypothetical column having 16 References on p. 208.

180

+

A

C

B +1

4

4

1

2

Figure 6.10. Combination of stationary phases. Comparison between the chromatograms obtained with the pure solvents and a mixed column. (A) Carbowax 20M column. Same as Column A, Figure 6.9, except temperature 82°C. (B) TCEP column. Same as column B, Figure 6.9, except temperature 82°C. (C) Mixed column. First section identical to column B (see Figure 6.9). Second section identical to column A (see Figure 6.9), except length: 1 m, temperature 82' C. Carrier gas: nitrogen, flow rate 3 L/hour. Flame ionization detector.

0

26

50

75

Figure 6.11. Window diagram. Determination of the window diagram for the separation of the mixture: (1) acetone, (2) carbon tetrachloride, (3) l,l,l-trichloroethane, (4) benzene (see Figures 6.9 and 6.10).

181

plates. Once the calculation is made, the specific resolution is plotted versus the solvent concentration and the optimum composition is selected among the values for which the specific resolution is maximum, so as to minimize the analysis time, i.e., the retention time of the last component of the mixture. The column length can be calculated as described in Section 11.1 above, knowing the desired minimum resolution between two peaks and the plate height of the columns which can be packed. When the stationary phase must be a mixture of several solvents the same method can be used. A simple computer program is now necessary, but since linear relationships are used, the optimum composition is very easy to derive. Finally, if a series of two or several columns is preferred to a mixture of stationary phases, the equations derived Chapter 2, Section XI can be used to calculate the exact retention time and resolution of the components of a mixture. The Rohrschneider diagram, with lines or bands, or the window diagram methods can be used to obtain a first approximation of the column lengths required. A simple iteration process permits an accurate prediction of the final chromatogram (27). 111. SELECTION OF MATERIALS AND COLUMN DESIGN

Once the stationary phase has been selected, the column length determined and the column temperature and carrier gas flow rate optimized, there is a number of choices to be made before preparing a column on which the analysis should be satisfactory. Failure to select the proper materials for the liquid phase support and the column tube, to treat them, to properly coat the support with the stationary phase or to pack the column well may result in serious troubles which may be avoided by careful attention to a number of critical details. 1. Selection of the Phase Support

It is not possible to carry out gas-liquid chromatography without immobilizing the stationary solvent. This requires the use of an inert support, the surface of which would ideally not interact with the analytes. On the other hand, however, the support must also offer a significant surface area so that the average film thickness of the solvent is small and diffusion of the solute molecules proceeds rapidly through it, in order to achieve a good column efficiency. Obviously these requirements are contradictory and we are still, after 30 years, seeking a really inert support. The support must also be wetted by the liquid solvent, another requirement to achieve a t h n film favorable to rapid mass transfer. Finally, it must be mechanically stable: during packing the particles should not penetrate each other, nor change shape (which would be detrimental to column permeability and result in excessive carrier gas pressure drop) nor lose their porosity; neither should they be readily crushed into fine powder, which would again be detrimental to the column permeability.

182

TABLE 6.4 Physical Characteristics of Inorganic Chromatographic Supports Used in Gas Chromatography

Commercial supports

Origin (manufacturer)

Nature

Carbopack A

Supelco

Carbopack B

Supelco

Carbopack C

Supelca

Carbosieve B

Supelco

Chromosorb P

Johns Manville

Chromosorb A

Johns Manville

Chromosorb W

Johns Manville

Chromosorb G

Johns Manville

Spherocarb

Analab

Spherosil XOA 075

Rhone Poulenc/ IBF Union Carbide Union Carbide Union Carbide Union Carbide

GraDhithd cardon black Graphitized carbon black Graphitized carbon black Molecular sieve carbon Diatomaceous earth or Kieselguhr Diatomaceous earth or Kieselguhr Diatomaceous earth or Kieselguhr Diatomaceous earth or Kieselguhr Carbon molecular sieve Porous silica beads

Molecular Sieves 3A Molecular Sieves 4A Molecular Sieves 5A Molecular Sieves 13X

Zeolites Zeolites Zeolites Zeolites

Specific surface area (m2/g)

Pore sue (A)

15

2250

100

310

9

2000

100 4

2.1

1 0.5 1200 50-100

15 300 3 4 5 10

In summary, the main characteristics of a chromatographic support which must be studied in connection with the design of a column for a new separation are: - its specific surface area; - the chemical nature and the activity of its surface; - its porosity and, to some extent, the average pore size and pore size distribution; - the average particle size and the size distribution; - the particle shape; - the mechanical properties. Most supports used in gas chromatography are inorganic materials derived from silica or from alumino-silicates. A few porous polymers, such as the Porapaks and Tenax, have also been used as supports of liquid phases, as has porous Teflon. The most popular supports are (see Tables 6.4 and 6.5, for the physical characteristics of the most common chromatographic packing materials): - diatomaceous earths, such as crushed firebrick C22 and the Chromosorbs P, A, W,G. They have a rather small specific surface area (a few square meters per gram) and a rather large porosity (except Chromosorb G); - silica gels, such as Spherosils;

183

Loose weight

Treatment

Liquid phase capacity (%)

Applications

0.66

30

0.84

25

Gas and light compounds belonging to Kiselev’s Groups I, 11, 111, IV Gas and light compounds belonging to Kiselev’s Groups I, 11. 111, IV

0.66

30 Gases

0.38

0.40 0.18 0.47

NAW-AW-AW/DMCS AW/DMCS-HMDS NAW NAW-AW AW/DMCS-HMDS NAW-AW-AW/DMCS

0.5 0.5

30

Kiselev’s groups I, I1

25

Kiselev’s groups I. I1

15

Kiselev’s groups 1, I1

5

1 to 25

0.75 0.72 0.69 0.64

Kiselev’sgroups I, 11,111 and IV Gases Kiselev’sgroups I, 11. Gases Gases Gases Gases

graphitized thermal carbon blacks, such as Carbopack; non-porous glass beads; porous polymers, such as Porapak, Tenax, Chromosorb Series 100, etc.; porous Teflon (Fluoropack). The silica gels and carbon blacks are used essentially with low coating ratios, leading to very t h n liquid films, a few molecular layers or less, in a mode of chromatography intermediate between gas-solid and gas-liquid chromatography, sometimes referred to as gas adsorption layer chromatography (see Chapter 7). Because all supports exhibit some kind of chemical activity, they must be treated before coating, to suppress or reduce to an acceptable level the effects of residual adsorption of the components of the mixture under investigation. -

a. Treatment of the Phase Support A chemical modification of the support surface may be necessary for one of two different reasons, which are not mutually exclusive: (i) the surface energy of the support may not be large enough, so the liquid stationary phase does not wet the References on p. 208.

184 TABLE 6.5 Physical Characteristics of Organic Chromatograhic Supports Used in GC Support

Manufacturer

Nature

Maximum temperature ("C)

Specific surface area (m*/g)

Chromosorb T

Johns Manville

250

7 to 8

Chromosorb 101

Johns Manville

275

< 50

Chromosorb 102

Johns Manville

250

300- 400

Chromosorb 103

Johns Manville

275

15 - 25

Chromosorb 104

Johns Manville

250

100- 200

Chromosorb 105 Chromosorb 106

Johns Manville Johns Manville

250 250

600- 700 700- 800

Chromosorb 107

Johns Manville

250

400-500

Chromosorb 108

Johns Manville

250

100- 200

Porapak P

Waters Assoc.

250

100- 200

Porapak Q

Waters Assoc.

250

500- 600

Porapak R Porapak S Porapak N Porapak T

Waters Assoc. Waters Assoc. Waters Assoc. Waters Assoc

250 250 190 190

450- 600 300- 450 225 - 350 250- 350

Tenax GC

Akzo

Polytetrafluoroethylene Teflon 6 Styrenedivinylbenzene Styrenedivinylbenzene Cross-linked polystyrene Acrylonitriledivinylbenzene Polyaromatic Cross-linked polystyrene Cross-linked acrylic esters Cross-linked acrylic esters Styrenedivinylbenzene Ethylvinylbenzene Divinylbenzene Vinylpyrrolidone Vinylpyridine Vinylpyrrolidone Ethylene glycol dimethylacrylate 2,6-Diphenylp-phenylene oxide

350

support; this results in the formation of large pools of liquid phase and in a poor column efficiency, because of slow mass transfer by diffusion, (ii) the surface of the support may bear some high energy sites which strongly adsorb one or several components of the sample, resulting in long retention and/or tailing peak(s). Some sensitive compounds may also undergo catalytic reactions (mainly isomerization or dehydration) during their elution. In all these cases a chemical treatment is necessary to deactivate the support surface. Various kinds of high energy sites can be found on the surface of the conventional supports, which are silica or silico-aluminate based materials: - silanol groups (37); - acidic sites other than silanols, especially Lewis acids; - basic sites, especially Lewis bases and oxides of the Group Ia and IIa metals P a , K,Mg, Ca);

185

Pore size (A)

Loose weight density (g/ml)

NB

Applications

0.42

t

Kiselev’s groups I, 11. 111, I V Polar compounds Kiselev’s groups I. 11. 111, I V Acids. aldehydes, ketones, alcohols Qselev’s groups 1. 11. 111, I V Polar compounds, water Kiselev’s groups I, 11. 111, I V Basic compounds. amines. etc.. Kiselev’s groups I, 11. 111. I V . H,S. NH, Nitriles. nitro-, sulphur-derivatives Kiselev’s groups I. 11, 111. I V Aqueous solutions, alcohols, acids Kiselev’s groups I, 11. 111. I V Fatty acids C, to C, Kiselev’s groups I, II Kiselev’s groups 1, 11, 111. I V Gas and light polar compounds Ktselev’s groups I. 11. 111, I V Weak polarity, carbonyls. glycols Kiselev’s groups I. 11. 111. I V Hydrocarbons, nitrogen oxide. aqueous sol. Weak polarity, esters, ethers etc Kiselev’s groups I. 11. 111. IV. alcohols CO,. NH2. H 2 0 . light hydrocarbons Kiselev’s groups I. 11, 111, I V Strong polarity Kiselev’s groups I. 11. 111. I V High boiling compounds such as alcohols. diols. phenols, amines, amides. aldehydes. ketones

3000 - 4000

0.30

85

0.30

3000 - 4000

0.32

600 - 800

0.32

400-600

0.34

50

0.28

90 235

0.30 0.30 0.27

PS

0.34

QS

0.30 0.35 0.38 0.43

NB.

Liquid phase loading capacity. 5%. PS, QS, silanized materials.

- oxides of transition metals (Al, Fe, Ti). The treatment selected depends on the nature of the high energy sites which exhlbit properties detrimental to the desired separation: we can attempt either to wash away the atoms or groups of atoms involved or to react them into inactive sites. The treatment will vary with the support used and the nature of the components of the sample studied.

I . Silanization Silanol groups and other groups having a reactive hydrogen moiety can be eliminated by reaction with a chlorosilane or an aminosilane (38). The main reagents used to carry out this treatment are: - dimethyldichlorosilane (DMDCS or DMCS), Sic1 2(CH3),; - trimethylchlorosilane (TMCS), SiC1(CH3),; References on p. 208.

186 - hexamethyldisilazane(HMDS), (CH,)@NHSi(CH,) 3; - vinyltrichlorosilane (VTS), SiC13CH=CH2.

All these compounds react with active hydrogen (i.e. with silanol groups) leading to the formation of a bond between the silicon atom of the reagent and the active group on the support surface. Hydrogen chloride (or ammonia in the case of HMDS) is evolved. The reaction can also take place with water, so the material to be silanized and the glassware used must be thoroughly dried before introducing the reagent. On the other hand, this property can be used to eliminate the excess reagent when the reaction is completed. Washing with methanol should be preferred, however, because with this solvent no polycondensation of the polychlorosilane reagent into silicon oil or grease is possible. Ammonia is a good catalyst of the silanization of silica (39). These reactions (see Figure 6.12) have been extensively studied in connection with the preparation of chemically bonded phases for liquid chromatography (39,40). Although at first dichloro- or trichlorosilanes were preferred in the illfounded hope that they would react with two or even three closely placed silanol groups, workers in this field have now come to the conclusion that the best result, i.e. the highest coverage of the surface, is obtained with monochlorosilanes. The umbrella provided over the surface surrounding the bound SiOSiRR’R” group of the support by the three akyl groups (in the trimethylsilyl-bonded supports) or the dimethyl functional silyl group is a better shield than the improbable disilyl ether (see Figure 6.12). Furthermore supports treated with di- and trichlorosilanes have to be further treated to eliminate the unreacted chlorine atoms, for example by washing thoroughly the silanized material with methanol. Polymerization of the reagent may take place, however, during the silanization reaction or the beginning of the washing step with traces of water adsorbed on the support surface or dissolved in the methanol. As a consequence, silicon chains may be bound to the surface, resulting in the coating of the support with a significant amount of an undesired, possibly undesirable, stationary phase. Thus monochloro, dimethyl, functional (methyl, akyl, cyanopropyl, vinyl, epoxide, ...) silanes should be preferred. Unfortunately in some cases only the trichloro, functional silane is available. Then one should be extra cautious with the drying steps. The sieved support and the glassware are dried normally at 150OC for 3 hours and kept in a desiccator if needed. When a di- or trichlorosilane is used, however, drying takes place at 200 O C for at least three hours and the reaction is carried out immediately, under a stream of dry nitrogen, obtained by passing the gas through a freshly activated Molecular Sieve column. DMCS and TMCS are used as 5% solutions (w/w) in toluene or carbon tetrachloride. The dry support is poured into the solution, which is agitated for 10 minutes. The suspension is then filtered, washed with pure solvent and (in the case of DMCS only) treated several times with excess methanol. The support is then dried at 100°C for 2 hours before coating with the stationary phase. HMDS being much less reactive, the suspension of support in a 5% solution in petroleum ether is refluxed for 3 hours. The support is then washed and dried as for silanization with TMCS.

187

, ,-:

Dimethylchlorosilane DMDCS o r ~ M C s,)

p

Si-OH

h

- GI

Y

Si-CH,

CI

CI

after washina with methanol

I

CH3 1

/

?

Trimethylchlorosilone

TMCS

Vinyltrichlorosilane

I CH3

Hexamethyldisilazane

HMDS

t NH~’

Figure 6.12. Reactions of common silanization reagents with the silanol groups at the surface of the

support. References on p. 208.

188

Figure 6.13. Silanization of glass beads or porous support with a polychlorosilane. 1 - Nitrogen flow rate controller; 2 - drying cartridge (Molecular Sieve or alumina); 3 - flow meter; 4 solution of vinyltrichlorosilane (3.5% w/w) in carbon tetrachloride; 5 - carbon tetrachloride; 6 - glass beads: 7 - stirrer.

VTS is used to deactivate the support, by reacting the SiOH groups, to enhance the wettability of the support by the stationary phase or to permit the graft of stationary phase. This considerably increases the stability and the useful life time of the column (41). The procedure is very similar to the one described previously for reaction with DMCS, but it is more critical and should be strictly adhered to (41). The glassware and the support or glass beads are dried at 200 O C for 3 hours. The so1,ution of VTS in carbon tetrachloride (3.5% w/w) is dried for 24 hours on Molecular Sieve. The reactor is closed and swept by a steady stream of dry nitrogen (dried on Molecular Sieve). The VTS solution is poured progressively onto the support (see Figure 6.13) which is slowly agitated for 2 hours. The support or glass beads are then decanted and washed with methanol, to react the chlorine atoms on the bound SiCl,CH=CH, groups into OCH, groups and destroy the excess of unreacted VTS.Finally, the material is dried at 120O C for 2 hours and is ready for coating (e.g. 0.25% w/w, of polypropylene glycol (Niax 1025) on the glass beads). Silanization can also be carried out in the gas phase. A stream of dry nitrogen bubbles through a flask containing the silanization reagent and percolates through a tube packed with the support to be treated. A flow rate controller keeps the nitrogen flow rate constant and the reagent flask is maintained at constant temperature. This permits the achievement of a constant mass flow rate of reagent to the support. The support is usually heated at 200 O C for satisfactory deactivation. After a few hours of this treatment, the support is washed with methanol to eliminate the sorbed, unreacted reagent and dried as described above. Engewald and co-workers (42) have shown, however, that excellent results are obtained in the silanization of the wall of glass open tubular columns if the reaction is carried out at a much higher temperature, 420 to 450°C. Although, to our knowledge, nobody has yet reported on the results of this high temperature treatment for the silanization of packing

189

support, this may be worth trying for the preparation of inert support for some difficult analyses. It has been shown also that deactivation can be carried out, if needed, on the final column, after coating of the support and packing (43). The same procedure can be used to regenerate certain columns. The gas phase treatment just described can be used, but it is also possible merely to inject large samples of silanizing reagent into the heated column. This is not a highly popular nor a strongly recommended procedure, however, because it is difficult to control, it is not very reproducible, very often the column cannot be heated to a temperature high enough to achieve a satisfactory yield and it can be done only with stationary phases which have no reactive hydrogen atoms. 2. Acidic Sites An alkaline treatment may be very efficient on this kind of support. It has to be carried out prior to a possible silanization. The support is treated in a boiling alcoholic solution of sodium hydroxide (10% w/w), then rinsed with a large excess of water and with acetone to eliminate the water. The treated support is dried at 150O C for 3 hours before coating. 3. Basic Sites An acidic treatment is performed. The support is refluxed in a 2 N aqueous solution of hydrogen chloride for 30 minutes. It is then rinsed with excess water until the water is neutral, then with acetone and dried at 150 O C for 3 hours. Zlatkis et al. (44) recommend a treatment with boiling aqua regia which dissolves undesirable metal oxides and salts. 4. Metal Oxides These can be eliminated or their influence can be drastically reduced by an acidic treatment or by coating the support with modifying agents. Strong acids extract a large part of the metals as oxides or salts. Aqua regia (44) does the same. Depending on the nature of the analytes, it may be useful to carry out an impregnation with a non-volatile acid (phosphoric acid), a base (potassium hydroxide) or a more selective organic or inorganic compound. These modifying agents also improve the wettability of the support surface by the liquid stationary phase, saturate strong adsorption sites and may play a role in the retention of the analytes, contributing appreciably to the selectivity in some instances.

b. Particle Size and Size Distribution of the Support

These are important parameters which are difficult to assess properly but which must be considered very carefully because they control the permeability of the column and the kinetics of mass transfer in the mobile phase, and hence the column efficiency. It is difficult properly to assess the influence of the particle size and size distribution on the column performance because it is nearly impossible to define and measure the diameter of non-spherical particles. Particle sizes can be measured References on p. 208.

190

using a wide variety of methods, the most important ones being optical (measurement of the size of optical or electronic images of the particles contained in a small sample), fluidic (measurement of the permeability of a packed tube or column) or electrical (measurement of the size of pulses proportional to the particle volume). All these methods give the result of two averaging processes: for each particle they average its dimensions in all directions, deriving the diameter of an “equivalent” sphere; then they determine the average of this “size” for all the particles in a batch of support and their size distribution. The first averaging process greatly depends on the principle of the method used. Optical methods permit the calculation of the average of all the dimensions of any visible particles in all the directions which are perpendicular to the optical axis of the instrument. If the particles have one dimension which is noticeably or much smaller than the other two, the chances are that most of them will lie perpendicular to this axis and we shall systematically obtain too large a result. Fluidic methods measure the total surface area of all the particles along which the mobile phase drags, i.e. they afford an average of the square of the particle diameter. But they give no information at all on the size distribution and they overemphasize the contribution of the fine particles, which plug flow channels between particles of average size. The Coulter counter gives pulses whose total charge is proportional to the volume of the particles. As with optical methods, a figure is also obtained for the size distribution. The basic difficulty arises from the fact that for irregularly shaped particles, the cube root of the average of d; is not equal to the square root of the average of d;, which is not equal to the average of d,; hence methods based on the determination of the average particle size, (tip), e.g., optical or electron microscopy, do not give the same result as those based on the determination of the average of the square of the particle diameter, ( d i ) , e.g. hydrodynamic methods, or on the determination of the average of the cube of the particle diameter, ( d i ) , e.g. methods measuring the average particle weight or volume. Failure to understand the complexity of this situation has led to a great deal of confusion in the literature, some authors reporting a strong dependence of certain properties of columns on the particle shape or on the extent of the width of the size distribution, without backing such sweeping statements by sufficient experimental results. The situation is further complicated by the way certain column characteristics depend on the particle size. For example, the HETP seems to be proportional to d,, and therefore the reduced plate height, independent of the particle size. In fact, a more careful analysis of the nature of the height equivalent to a theoretical plate reveals that h is proportional to the ratio of the average of the square of the particle diameter to the square of the average particle diameter, ( d i ) / ( d , ) 2 ) . This ratio is equal to 1 for monodisperse particles and it increases with increasing width of the size distribution *. The unconvinced reader is invited to list the integers from 1 to 11 in a column and to write their squares in a second column. The average and standard deviations are respectively 6 and 3.16 for the numbers in the first column, and 46 and 39 for those in the second column. This is, admittedly. an extreme example, but it proves the point.

191 TABLE 6.6 Influence of Particle Size on Chromatographic Data Average particle size (am)

40-50

50-80

80-100

100-160

160-200

40-100

100-200

Retention time of tetrachloroethylene (sec)

470

413

320

235

145

375

210

Carrier gas pressure drop (atm)

8.4

6.6

4.6

3.0

1.8

5.7

2.5

Number of plates per meter

1325

1590

2570

1320

1050

1325

1100

Ratio of column diameter to particle size

0.045

0.06

0.09

0.13

0.18

0.07

0.15

Reduced velocity Reduced plate height

11.2 16.8

16.2 9.7

22.5 4.3

32.5 5.8

45 5.3

17.5 10.8

37.5 6.1

Based on average particle size. The reduced velocity is calculated on the basis of an outlet velocity of 25 cm/sec (porosity = 0.70). Column length: 3 m; id.: 1 mm; flow rate: 0.5 L/hour in all cases. Temperature 100 O C; Spherosil 75 m2/g, coated with 5% (w/w)Carbowax 2OM.

The comparison of data obtained with columns packed with particles of different average size is difficult because a change in the particle diameter results in both a reduction of the minimum value of the plate height and an increase in the optimum velocity. The combination of these two effects makes the comparison complex, unless one uses the reduced plate height and the reduced velocity (cf Chapter 4, Section X). The data in Table 6.6 illustrate this problem. With the caution imposed by the consequences of the previous discussion, we can say at this stage that: - the column permeability is approximately proportional to the square of the particle size. It decreases with increasing width of the size distribution (at constant (d,)) and with increasing amount of small particles. It seems that the permeability is larger to some extent for spherical particles than for irregular ones (see next section and Chapter 7). - the minimum value of the height equivalent to a theoretical plate is approximately proportional to the particle size, at least for materials with narrow size distribution. The packing homogeneity tends to be better (smaller A term in the Knox equation, Chapter 4, Section X, equation 32), or a good quality packing is easier to acheve with spherical particles. A good support for gas chromatography will have a narrow size distribution, an average particle size between 100 and 300 pm (below 100 pm the pressure drop of a column having the necessary efficiency becomes too large, while above 300 pm the analysis time becomes excessively long). The support must be strong enough to withstand pressure during operation of the column, without experiencing increased compactness and decreased permeability. It must also resist abrasion and erosion and not generate a significant amount of fine particles during the operations of References on p. 208.

192

coating and packing. The fragmentation of particles which may occur during these stages has two detrimental effects, a decrease of the column permeability and the appearance of fresh support surface, which has not been treated and may be highly active, resulting in poor chromatographic performance.

c. Particle Shape. Fluidization It has been our observation that GC columns packed with spherical particles tend to have a somewhat larger efficiency (up to ca 20%) and larger permeability. Accordingly, we treat raw support material, before any chemical treatment, in order to improve the particle shape by self abrasion of the particles in a fluidized bed. We use a device similar to the one used for the attrition test of catalysts. The apparatus (see Figure 6.14) is a glass or metal cylinder, with two conical end sections. At the bottom of the cylindrical part a 10 pm metal frit is soldered. 250 to 500 g of support is placed in the apparatus, the bottom cone of which is connected to a source of dry gas. The upper cone is connected to a trap (where a fraction of the fine particles are collected) and vent. The gas flow rate is adjusted so that the particle bed is fluidized. The bed expands and boils gently. The operation lasts about 3 hours. During the process particles erode each other, become much smoother and their shape tends towards that of eggs. A significant amount of fine particles is formed. Part is vented, part is collected in the trap. The rest is eliminated by elutriation of the material obtained when the operation is finished. The support is washed with methylene chloride then poured in a graduated cylinder filled with methylene chloride. The “good” support particles fall rapidly and are recovered. The fine suspension is decanted, filtered and the solvent recovered; the fine particles are

Figure 6.14. Fluidization of support particles. Schematic of the apparatus used to erode the raw support particles and give them a smooth semi-spherical shape.

193

discarded. This operation is carried out at least three times. Methylene chloride is used rather than water because of the secondary effects of residual water on the stability of certain stationary phases. After drying at 150O C the support is ready for chemical treatment (usually acid washing and silanization). 2. Selection of Column Tubing

Figure 6.15 shows the cross section of the most popular column types used in gas chromatography. The major distinction is between the packed columns, which are entirely packed with stationary phase particles and the open tubular columns which have an empty channel at their center. The problems associated with the use of open tubular columns of the various kinds are discussed in Chapter 8. The introduction to that chapter also contains a discussion regarding the advantages of both types of columns for quantitative routine analysis. Packed columns of a wide range of diameters have been used. We merely quote here, for the sake of completeness, the preparation and use of columns of 40 cm i.d., for preparative applications (44). Analytical applications are usually carried out

Figure 6.15. Cross-sections at the same scale of columns of different types used in gas chromatography. A - Conventional packed column. i.d. 4 mm. B - Narrow bore packed column. i.d. 1 mm. C - Support coated open tubular column (SCOT)or porous layer open tubular column (PLOT). i.d. 0.5

mm. D - Wall coated open tubular column (WCOT) or open tubular column (OTC) or capillary column. i.d. 0.25 mm. References on p. 208.

194

with 1 to 4 mm i.d. columns, but columns with diameters down to 0.3 to 0.5 mm have been prepared and used successfully (46-50). The major distinction is made between Conventional Packed columns (CP) which have an inner diameter greater than 5 to 10 times the average particle size of the packing material, and the Packed Capillary columns (PC) which have an inner diameter less than 5 times the diameter of the particles used (51). In practice, only packed columns and open tubular columns are widely used in routine analysis. The advantages of PC columns (large permeability) are more than offset by their difficult preparation, especially with polar liquid phases. Because of the special requirements of on-line process control analysis (sampling, injection, column switching, detection), OTC are still excluded from this field, in spite of some promising experiments. It seems probable, however, that this fact has now as much to do with the extreme conservatism of the field of process control analysis, where so much is at stake, than with the real advantages of CP columns. On the other hand, OTC are extremely valuable for routine analysis in the laboratory. For this reason Chapter 8 is devoted to them. The selection of the nature and size of the column tubing depends on the nature of the components of the sample, the requirements regarding sample size and the influence of the column diameter on the column efficiency. a. Nature of the Metal Tubing

The column tubing must be totally inert towards the components of the mixture analyzed. Some metals may catalyze a variety of reactions in the gas phase, causing changes in the qualitative and quantitative composition of analyzed samples. More frequently, analytes may adsorb on the metal or oxide surface of the column walls resulting in unsymmetrical peaks which are difficult to quantitize accurately. Compounds of Groups A and B (see Section 1.1, above), can be analyzed with nearly all kind of materials: stainless steel, copper, nickel, glasses, silica, or Teflon. With the polar compounds belonging to Groups C and D, glass, silica or Teflon columns will be preferred. Similarly, silanized metal columns yield good results. b. Relationship between Sample Size and Column Diameter

The automatic sampling systems used in on-line or laboratory chromatographs cannot easily handle the small samples which are normally used in research laboratories. Furthermore, small samples may be more easily contaminated or spoiled than larger ones, or may undergo a change in composition for a variety of reasons. Accordingly, sample sizes tend to be rather large in routine analysis. Since the amount of sample which can be injected into a column without causing marked overloading is proportional to its cross-section area, i.e. to the square of its diameter (see Chapter 5), the column diameter will be selected accordingly. For these reasons the conventional column inner diameter of 4 mm is often very convenient, ind narrower columns will be used only rarely. Such a 4 mm i.d. column accepts usually a 1pL liquid sample or a 1 mL gas sample.

195

c. Influence of the Column Diameter on its Efficiency As discussed above, it has been shown that the efficiency of a packed column increases when its diameter decreases until the internal diameter of the column becomes about 10 to 5 times larger than the average particle size (51,52). The optimum was stated by Halasz and Heine to be for a ratio of 5 (51). It seems, however, that the maximum increase in efficiency is rather limited (53,54), which is illustrated by the data in Table 6.7, pertaining to a material with spherical particles (55). In t h s last case, the maximum efficiency is attained with a coiumn-to-particle diameter ratio of cu 10 (55) instead of 5 (51) observed with irregular particles. With 80-100 pm particles and a narrow size distribution, using a narrow diameter column (i.d. cu 1 mm), an efficiency of cu 2,500 plates per meter is achieved, corresponding to a value of the reduced plate height of 4.0.Much smaller reduced plate heights are obtained in HPLC where packing is much tighter, due to the high viscosity and density of liquids. There are several possible explanations for this improvement. They deal essentially with an increase in the degree of radial homogeneity of the column with decreasing column diameter. First, the difference in average speed of the various gas channels is reduced; eventually, with a column to particle diameter ratio of 5 there is only one channel, Secondly, radial concentration gradients can be relaxed almost exclusively by molecular diffusion, since there is almost no radial convection; when the column diameter decreases, the time constant of this process decreases as the square of the diameter. Similar results have been obtained in liquid chromatography (56). TABLE 6.7 Influence of the Column Diameter on Chromatographic Data Reprinted from Anulyticul Chemistry, 43, 2015 (1971) Column diameter (mm)

4

3

2

Particle size (pm)

100-200

100-200

100-200

180-200

100-200

Carrier gas velocity at column outlet (cm/sec)

6.65

6.65

6.65

6.65

6.65

Carrier gas flow rate (L/hour)

3.0

1.70

0.80

0.80

0.20

Retention time (sec) (tetrachloroethylene)

380

360

375

Column efficiency (plates per meter)

1450

1510

1580

2500

1545

Column diameter to particle size ratio

0.037

0.05

0.075

0.095

0.15

4.6

4.4

4.2

2.1

4.3

Reduced plate height

**

1

450

All data in this table are the average of three different results. * C, and C, chloroalkanes analyzed at 100* C, on Spherosil 27 m2/g, coated with 28 (w/w)Carbowax 20M. Column length: 4 m. ** Based on average particle size.

References on p. 208.

196

The method of column packing used has a considerable influence on the homogeneity of the packing and on the column efficiency (see Section 111.4, below).

3. Selection of the Coating Ratio a. Selection of Phase Ratio

Traditionally, chromatographers give the amount of stationary liquid phase in the column as the weight of solvent for 100 g of support. This is, unfortunately, a very poor unit, because the actual amount of solvent, hence the retention volume or time of a solute depends to a large extent on the density of the support, its porosity and its specific surface area, which determine the amount of solvent inside the column and the average film thickness, respectively. The average film thickness is given by:

where: - m , is the weight of solvent, - p its density, - S the specific surface area of the support, - m, the weight of the support. For example, Chromosorbs G, P and W are the most often-used supports in gas-liquid chromatography. The same average film thickness would be obtained with the following coating ratios: - 20% on Chromosorb P, - 2.5% on Chromosorb G, - 5% on Chromosorb W. A coating ratio of 20% on Chromosorb P usually gives excellent results, but this is not a rule. Depending on the temperature selected, the coating ratio often has to be adjusted to increase or reduce the analysis time, since the resolution depends both on the relative retention (a)and on the absolute retention (k’,hence the coating ratio, see equation 7 or 10 in Chapter 3). Figure 6.16 shows that, for a support with a small specific surface area, the retention times increase linearly with the phase ratio. The resolution between the pairs of compounds which have a small retention increases markedly at first, although the efficiency decreases slowly, and tends towards a limit. The thicker the liquid phase film, the larger the retention time, the slower the mass transfer (the efficiency decreases when the film thickness becomes significant, cf equation 14 in Chapter 4), and the larger the resolution, at least if k’ is smaller than about 3. As a consequence of the trend illustrated in Figure 6.16, we can conclude that compounds having a large vapor pressure at or near ambient temperature will be analyzed with heavily coated supports (otherwise they would not be retained and no resolution could be observed), while lightly loaded supports will be preferred for the analysis of compounds with low vapor pressure. Thus, the selection of the coating ratio cannot be made without some consideration of the column temperature.

197 I

Figure 6.16. Chromatograms of a mixture obtained with different coating ratios on the same support. 1 - Air; 2 - n-hexane; 3 - methylene chloride; 4 - toluene. Chromosorb P, 60-80 mesh. Carbowax 20M. Coating ratios: 1, 5,10,20 and 30% (w/w).Same weight of packing material in each column (hence different lengths). The retention time of each compound increases linearly with the coating ratio. Temperature: 80 'C. Carrier gas: helium, 3 L/hour.

There are upper and lower limits to the values of the coating ratio which can be selected, however. There is a maximum value of the coating ratio, determined by the support porosity: when most of the pores are filled, the plate height increases rapidly and the solvent may start to flow in the interparticle space and interfere with the gas stream. With Chromosorb P this upper limit is around 30%. There is also a minimum value of the coating ratio, depending on the surface area of the support. When the amount of solvent coated on the support becomes too small, the References on p. 208.

198

film of stationary phase, which does not always completely wet the surface, leaves an excessive amount of the support surface exposed to the gas phase. Some active sites can interact directly with the solute, resulting in strong adsorption and possibly tailing. From a theoretical standpoint, it has been shown that the fastest analyses are obtained by a combination of low coating ratios and low temperatures, where the relative retentions tend to be larger, except around the inversion points (30,57). These conclusions have been confirmed by a large number of studies made in many different conditions, by Scott (31,58), Golay (59), Duffield and Rogers (60), Kirkland (61) and Hishta et al (62). In practice, however, these conditions promote adsorption both at the gas-liquid and at the gas-solid interfaces, with possible adverse consequences. When polar compounds are analyzed on a non-polar liquid phase or, conversely, non-polar compounds on a polar stationary phase, the solubility of the solutes is low, the activity coefficient large, and the compounds tend to become adsorbed at the gas-liquid interface (cf Chapter 3, Section A.X). Since the extent of the liquid surface area varies greatly with the coating ratio, the small pores filling first, the

I

40 0 \

E

>” 30-

-

20

/ @

0

Figure 6.170. Specific retention volume of 4 solutes versus the film thickness of the stationary phase. 1 - Diethyl ether; 2 - acetone; 3 - methyl ethyl ketone (2-butanone); 4 - methyl isobutyl ketone (3.3-dimethyl-2-butanone). Columns: 1 m long, packed with Spherosil64 m2/g (200-250 pm). coated with 3,3’-oxydipropionitrile(2, 5, 10,20 and 30%.w/w). Temperature: 110’ C. Carrier gas: nitrogen, 3 L/hour. Reprinted from Analytical Chemistry, 43, 2015 (1971).

199

I I

I I 1

/

Amount o f stationary phase

Figure 6.176. Plot of the retention time of an analyte on an adsorbent coated with a liquid stationary phase, versus the coating ratio.

retention of such compounds decreases with increasing coating ratios at low values, goes through a minimum and increases at large values of the coating ratio. This phenomenon may be used to separate some compounds from a mixture of other ones with very different polarity (55,63).It may also play havoc with optimization schemes, especially if it is unknown or unrecognized. The support solid surface may also play a considerable role in retention. No support is really inert. The solid surface is often only partly wetted by the liquid. The naked surface may adsorb the solute. Furthermore, the solid surface orients the liquid phase molecules lying on its surface, which may change their interaction energy with solute molecules sufficiently to modify the partition coefficient. Residual silanol groups, metal ions or metal oxides (especially Fe, Al, Mg) have a significant effect on the retention of some compounds. For these reasons, there is a complete spectrum of packing materials for gas chromatography going from 30% loaded Chromosorb P, which exhibits an almost pure partition mechanism, to high specific surface area adsorbents, such as silica, exhibiting pure adsorption. Intermediate products are lightly loaded supports and modified adsorbents on which liquid films of various thicknesses, from one hundred angstrom down to a fraction of a monolayer, are coated (64,65).Depending on the situation, one may wish to modify the properties of the adsorbent (64)or those of the stationary solvent (65). References on p. 208.

200

Figure 6.17a shows the variation of the specific retention volume of four compounds: diethyl ether, acetone, butanone (methyl ethyl ketone) and 3,3-dimethyl-2-butanone (methyl isobutyl ketone) versus the thickness of a film of 3,3'-oxydipropionitrile on a silica gel (specific surface area 64 m2/g). Figure 6.18 shows chromatograms obtained with the different packing materials investigated. For concentrations of 2 and 5 % the film thickness (equation 7) is smaller than the molecular size. The liquid phase is most probably dispersed over the surface of the support as a pattern of tiny droplets and patches of monomolecular film. Adsorption contributes considerably to the retention, the peaks tail strongly. At the minimum of the specific retention volume the film thickness is only 17 A, corresponding to twice the thickness of a monomolecular layer. Both gas-liquid and liquid-solid adsorptions certainly contribute greatly to the retention mechanism. For high coating ratios, the specific retention volume seems to tend towards a limit, but at 30% the film thickness is still equivalent to 6.5 monolayers, much too thin to eliminate the influence of adsorption at these interfaces. There is little gas-solid adsorption and the peaks are nearly symmetrical. Similar variations of the retention

d

0

20x

\

N

E

f

ul

5%

40

35

30

25

20

15

10

5 min

'

Figure 6.Z8.Chromatograms of a mixture obtained with different coating ratios on the same support. a - Diethyl ether; b - acetone; c - methyl ethyl ketone (2-butanone) peak in black; d - methyl isobutyl ketone (3,3-dimethyl-2-butaone). Same columns and conditions as for Figure 6.17a. Reprinted from Analytical Chemistry, 43, 2015 (1971).

201

volume take place on more conventional supports, which have a much smaller specific surface area, but in this case the modification of the solid surface properties is replaced by the variation of the specific surface area of the liquid as the basic phenomenon. In both cases the relative retention of some compounds may change dramatically, which may be used to achieve spectacular separations. When the coating ratio of an adsorbent, or even of a normal support, is increased progressively, a plot of the retention time or volume versus the coating ratio follows a characteristic curve which exhibits a minimum, as shown on Figure 6.17b. At low values of the coating ratio, ,the retention time decreases rapidly with increasing coating ratio. This is the realm of modified gas-solid chromatography (see Chapter 7, Section I). The surface energy decreases by saturation of the active sites by the liquid phase. In the same time the retention by the bulk liquid increases with increasing coating ratio. So there is a minimum retention (see Figure 6.17b). Below this minimum we may consider that we have a modified gas-solid retention mechanism, while above the minimum, it becomes partition. At any rate, it is a typical situation of mixed mechanism (see Chapter 3). Figure 6.19 provides a comparison between the separation of a mixture of three compounds, vinylidene chloride (b.p. 37 O C), 2-methylpentane (b.p. 60 O C) and cyclohexane (b.p. 81' C), using the same solvent: 3,3'-oxydipropionitrile coated on two different supports. The theoretical film thicknesses are 20 and 250 angstrom, respectively. The elution order is completely different. With the thin film the stationary phase behaves much more like a non-polar liquid phase (cf chromatogram Figure 1.5, obtained on Apiezon) than with a conventional thick film. The systematic use of supports of large specific surface area with moderate coating ratios, i.e. of adsorbents modified by a thin layer of liquid, may provide exceptionally good results. The performance, properties, methods, advantages and drawbacks of this approach are discussed in detail in Chapter 7. b. Procedure for Support Coating

Almost all packing materials, whether adsorbents or supports, are coated using the same method, except for Teflon powder, which is very delicate and deserves special treatment. 1. Conventional Supports The aim of a coating procedure is to prepare a support, or adsorbent, homogeneously coated with the desired solvent, with minimum pollution or erosion of the treated support, which will give stable columns. Most methods used are similar. They require the use of a rotary evaporator, with an inclined flask, in which the various steps of the coating procedure are carried out. The rotation must be slow, in order to prevent erosion of the particles and the formation of fine powder. Without rotation or with too slow a rotation, particles may agglomerate, so the proper compromise must be found. The following steps are then performed: - The support is dried under vacuum, supplied by the water ejector, at 150 O C for 3 hours. This step is critical for supports with large specific surface area. It is less References on p. 208.

202

A

2

f

sE 2

K

U

1

\

z a a

0

m 0

. 9

3

3

01

0

9

\

m

R

t Figure 6.19. Comparison between the separations of a mixture by gas-adsorption layer chromatography (A) and by gas-liquid chromatography (B). 1 - Vinylidene chloride; 2 - 2-methylpentane; 3 - cyclohexane. 3,3'-OxydipropioNtrile at 55 O C. Column length: 2 m. i.d.: 1 mm. Carrier gas: nitrogen, 0.2 L/hour. Column A: 5.5% solvent (w/w) on Spherosil (90-100 pm). 28 m2/g. Elution order: 1, 2, 3. Column B: 20%solvent (w/w) on Chromosorb P (60-80 mesh). Elution order: 2, 3, 1.

important for conventional supports. Drying may be performed for a shorter period or altogether forgotten with supports having a specific surface area less than 4 m2/g. - After cooling, but still under vacuum, the support is flooded with an excess amount of pure, dry solvent. The level of solvent in the flask is about 1/4 inch above the support level. The same solvent as the one used to dissolve the stationary liquid phase should be used. The slurry is rotated slowly for about 10 minutes. - The required amount of stationary liquid phase is added, in solution in the same solvent. Slow rotation of the flask containing the support, the liquid phase and the solvent is performed for about 30 minutes. - The slow evaporation of the solvent is performed, under moderate vacuum, at a temperature equal to about half the boiling point of the solvent (in O C), while slow rotation proceeds. It should take about 2 to 3 hours. - When the material looks like a wet cake, the temperature is increased to the boiling point of the solvent, and drying performed until the material flows like a dry powder.

203

- The coated support is permitted to dry overnight in an oven, at the boiling point of the solvent. - The coated support is sieved, to eliminate the fine powder and the agglomerates which are formed, but this operation should be limited, and should be performed rapidly to minimize the erosion of the particles. - The packing material is ready. The coating of organic supports, such as Porapak, requires basically the same procedure, although the drying step can be eliminated, and the wetting of the support by the solvent, prior to coating, requires a shorter time. Sieving, on the other hand, is more critical. Agglomerates tend to form easily and must be eliminated carefully, as they reduce the efficiency of the final column. The coating of adsorbents with a large specific surface area requires a few additional steps (see Chapter 7). 2. Teflon Powder This is an excellent support for the separation of highly polar compounds or of very aggressive chemicals. Unfortunately this material is very sensitive to pressure or mechanical compression. Columns with an extremely poor efficiency. are easily obtained, and a special procedure must be carefully followed in order to obtain good columns (66-68). The material must be handled very gently at every step. The commercial product (also found as Chromosorb T, Fluoropack or Teflon 6) is a powder of wide particle size distribution (250-550 pm). Sieving this powder is difficult, so this operation is better performed only once, after coating, prior to column packing. - The Teflon powder is mixed with dry sodium chloride powder in the proportion 85% NaCl, 15% Teflon (w/w) (68). The sodium chloride has been previously sieved and the 300-500 pm fraction is used for this purpose. The mixture is heated at 32OOC for 6 hours. After cooling the product is washed with water, until the sodium chloride is completely dissolved and extracted. - The Teflon powder is washed with acetone and dried at 100°C. - Coating proceeds as described in the previous subsection. Coating ratios larger than 15% must be avoided. - Sieving and packing are carried out at O°C, the packing material being previously cooled to the same temperature (66,67). Teflon undergoes a vitreous transition slightly below ambient temperature, so at 0 O C it is much more resistant to mechanical compression and much easier to handle (67). Efficienciesas high as 800 theoretical plates per meter can be obtained when this procedure is carefully followed (liquid phase: GE SF 96, on Chromosorb T). 4. Column Packing

This is a tedious procedure, but it is very important since it contributes considerably to the efficiency of the column, and the analyst must pay great attention and care to the procedure. References on p. 208.

204

The column end is closed by a glass or silica wool plug, kept in place by a small coil of metal sieve (see Figure 6.20). This plug must be carefully placed to retain all the packing material inside the column but it should have a large permeability. In the preparation of columns for the analysis of many polar compounds it may be necessary to silanize the glass wool, to eliminate a sometimes pernicious source of adsorption. This end of the column is connected to a water ejector, to create a gas stream which helps in carrying the stream of packing particles to the top of the rising bed during packing. The other end of the column is connected by a rubber tubing to a small funnel. The packing material is slowly poured into the funnel, while the column is vibrated with a mechanical vibrator, or tapped with a piece of rubber hose or soft wood (see Figure 6.21). This aims at preventing the particles to form plugs inside the column, upstream from the top of the rising bed, as does the slow pouring of the particles in the funnel (the material should never fill the entire bottom tube of the funnel). Vibrations should be gentle, to avoid excessive rebounce of the larger particles during packing and the formation of stratas of large and small particles, or the formation of small particles by breaking the large ones. The column can be packed straight or coiled. The controversy between the supporters of both methods has never really been settled. Our experience is that similar results are obtained, and the choice is more a matter of convenience. It is easier to homogeneously pack a straight column, but coiling it after packing might crush particles and form regions of low and high packing density. Coiling after

Figure 6.20. Schematic of the column ends. A. Column inlet. a, Glass or quartz wool. B. Column outlet. a, Glass or quartz wool. b, roll of metal sieve.

205

Figure 6.21. Packing of chromatographic columns.

a - Funnel, filled with packing material, b - Column, c - Connection to a water ejector, d - Rotating rod. Note the cross section. with a flat surface, e - Mechanical or ultrasonic vibrator.

packing should be done only with relatively large coil diameters. On the other hand packing a coiled column must be carried out with the column axis vertical, and the coils horizontal, to avoid the formation of empty sections, whch do not contribute to separation and scarcely to retention but certainly contribute to band broadening. For this reason too, packing must be carried out with persistence, until the column is full. The total weight of packing material introduced into the column must be measured as accurately as possible. This permits the calculation of the packing density, knowing the inner volume of the column. Comparison between the packing density achieved and the apparent density of the packing material prepared gives an estimate of the quality of the column packed. If the packing density is too low, there are probably empty sections inside the column and it may have to be emptied and repacked. The packing material may not be reused in this case, as the packing and unpacking procedures may break too many particles, exposing too large an area of untreated support. The actual quality of a column, however, is best determined from its chromatographic performance: resolution between critical pairs of solutes and total analysis time. Packing a section of glass tubing, every now and then, and aging it in an oven is a useful, instructive exercise, which should be reserved, however, for the none-tooanxious analysts: “what the eye does not see does not bother the mind” (69). References on p. 208.

206 TABLE 6.8 Most Often Used Stationary Phases Phases

Polarity

Applications

**

Max.temp.

Solvent

***

(“C) Apiezon M Arochlor 1254 Carbowax 2OM Carbowax 1500 Dexsil300 Dexsil400 Dibutyl phthalate Diethylene glycol adipate (DEGA) (LAC 1 R 2%) Diethylene glycol sebacate (DEGSB) Diethylene glycol succinate (DEGS) (LAC 3 R 728) Dinonyl phthalate FFAP Fluorosilicone QF1 Poly neapmtylglycol adipate OV 1 (methyl silicone) OV 17 (Me, Ph silicone) O V 25 (Me, Ph silicone) O V 101 (Methyl silicone) O V 105 (cyanopropyl, methyl silicone) O V 210 (trifluoropropyl, methyl silicone) O V 225 (cyanopropylmethyl phenyl. methyl silicone) P.P’-Oxydipropionitrile Polyphenyl ether (5-rings) Polyphenyl ether (6-rings) Polypropylene glycol Polyvinyl pyrrolidone Silicone G E SF 96 Silicone GE XE 60 (Nitrile gum) Silicone G E XF 1150 (50% nitrile) Silicone SE 30 SE 52 phenyl Squalane Tetrahydroxyethylethylene diamine (THEED) 1.2.3,4-Tetrakis-(2-cyanoethoxyhexane) P,P’-Thiodipropionitrile Tricresyl phosphate (TCP) 1,2,3-Tris-(2-cyanoethoxy)propane (TCEP)

N I P P I I I

I, 11, 111, IV I, I1 I, 11, 111, IV 11, 111, IV I, 11, Ill 1. 11, Ill I, 11

100

B, C. D C, D C, D A. C, D C C C, D

275 125 250 200 400 400

P

11, Ill

200

C, D

P

11, I11

200

C, D

P I P I

11, Ill I, 11, Ill I, 11, Ill I, 11, Ill

200 175 275 250

C, D C, D C, D A

I

N

11, Ill I, 11, Ill I, 11, Ill I, 11, Ill I, 11, Ill

240 350 375 350 350

A, C, D C, T C, T C, T C, T

P

I, 11, I11

275

C, T

I

I, 11, 111

275

C

I

275

I I I P N

I, 11, 111 11, Ill I1,III. IV 11. 111, IV 11, Ill Ill I, I1

200 300 150 225 300

A, C C, D A, C,D A, C, D M, C, D M T, C , D

I

I, 11, Ill

275

C, D

11, Ill

200 300 300 100

A

A

N I I

P

1

80

N

I, I1

I N

I, 11, 111

P

11, I11

135

C, D

P P I

11, 111. IV 11. Ill

180 100 125

C. D C. D C, D

180

C, D

P

I, I1

I, I1 11. Ill

C, D C, D

Polarity: N: non-polar; 1: intermediate; P: polar. tt Applications: Kiselev’s groups of compounds. ttt Solvents: A: acetone; B: benzene; C: chloroform; D: dichloromethane; E: ethyl acetate; M: methanol; T: toluene; W:water; X: xylene.

201

GLOSSARY OF TERMS Coefficient of the plate height equation. Equation 1 in Figure 6.7. Coefficient of the plate height equation. Equation 1 in Figure 6.7. Coefficient of the plate height equation. Equation 1 in Figure 6.7. Coefficient of the resistance to mass transfer in the mobile phase. Equation 4 in Figure 6.7. Coefficient of the resistance to mass transfer in the stationary phase. Equation 4 in Figure 6.7. Diffusion coefficient of the analyte in the mobile phase. Equation 2 in Figure 6.7. Diffusion coefficient of the analyte in the stationary phase. Equation 5 in Figure 6.7. Average thickness of the film of liquid phase (supposed to be uniform) coated on the support. Equation 5 in Figure 6.7. average particle size. Equation 3 in Figure 6.7. Height equivalent to a theoretical plate. Equation 2 in Figure 6.2. Retention index of a compound on a polar stationary phase. Equation l. Retention index of a compound on squalane. Equation 1. Partition coefficients of a solute on two different liquid phases used to make one column. Equation 6a. Column capacity factor. Equation 4. Column length. Equation 3. Length of the initial column (used in the first step of optimization). Equation 3. Molecular weight of the stationary phase. Equation 5. Masses of each stationary phase contained in a mixed column. Equation 6b. Mass of stationary liquid phase contained in the column. Equation 7. Mass of support contained in the column. Equation 7. Column plate number for a given analyte. Equation 1 in Figure 6.2. Vapor pressure of the analyte at the column temperature. Equation 5. Resolution required between the peaks of two analytes. Equation 3. Ideal gas constant. Equation 5 . Initial resolution observed between the peaks of two analytes. Equation 3. Specific resolution. Equation 5 in Figure 6.2. Specific surface area of the support. Equation 7. Absolute temperature of the column. Equation 5 . Retention time. Equation 1 in Figure 6.2. Retention times of two solutes. Equation 3 in Figure 6.2. Corrected retention time. Equation 3 in Figure 6.4.

208

Carrier gas velocity. Equation 1 in Figure 6.7. Average carrier gas velocity. Equation 1 in Figure 6.4. Vg,,,Vg+2,Vg,3Specific retention volumes of a solute on the different stationary phases contained in a mixed column. Equation 6b. Volume of liquid phase contained in a column. Equation 5. K,llV,,2 Volumes of the two liquid phases contained in a mixed column. Equation 6a. vm Gas hold-up of a GC column. Equation 5 . VR Retention volume of an analyte. Equation 6a. W Band width (Chapter 1, Section VI). Equation 1 in Figure 6.2. WI9W2 Band widths of two solutes. Equation 3 in Figure 6.2. a Relative retention of two solutes. Equation 4 in Figure 6.2. P Density of the stationary phase. Equation 5. Y Activity coefficient of the analyte in the stationary phase. Equation 5. AH^ Excess enthalpy of mixing of the analyte with the stationary phase (Chapter 3, Section A.VI). Equation 3 in Figure 6.4. AH^ Vaporization enthalpy of the analyte from the solution in the stationary phase (Chapter 3, Section A.VI). Equation 3 in Figure 6.4. Vaporization enthalpy of the pure analyte (Chapter 3, Section A.VI). AH^ Equation 3 in Figure 6.4. Retention index increment of compound i between stationary phase SI? S and squalane. x Coefficient in equation 3 in Figure 6.7.

U

u a"

v

LITERATURE CITED (1) C. Vidal-Madjar, L. Jacob and G. Guiochon, Bull. SOC.Chim. Fr., 1971, 3105, 3110. (2) C. Vidal-Madjar, M.F. Gonnord and G. Guiochon, J. Chromatogr. Sci., 12, 839 (1974). (3) C. Vidal-Madjar, M.F. Gonnord and G. Guiochon, in Aduances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1975,Vol. 13,p. 177. (4) C. Vidal-Madjar, F. Dondi and G. Guiochon, J. Chromatogr., 291, 1 (1984). (5) J.M. Prauznitz, C.A. Eckert, R.V. Orye and J.P. OConnell, Computer Calculations for Multicomponent Vapor- liquid Equilibria, Prentice-Hall, Englewood Cliffs, NJ, 1967. (6) D.L. Massart, B.G.M. Vandeginste, S.N.Deming, Y. Michotte and L. Kaufman, Chemometrics: A Textbook, Elsevier, Amsterdam, NL, 1988. (7) O.E. Schupp 111 and J.S. Lewis, Compilation of Gas Chromatographic Retention Data, ASTM, Committee E 19, Philadelphia, PA, 1967. (8) W.O. McReynolds, Gas Chromatographic Retention Data, Preston Technical Abstracts Co., Evanston, IL, 1966. (9) P.H. Weiner, H.L. Liao and B.L. Karger, Anal. Chem., 46, 2182 (1974). (10) D.L. Massart, P. Lenders and M. Lauwereys, J. Chromatogr. Sci., 12, 617 (1974). (11) W.O. McReynolds, J. Chromatogr. Sci.. 8, 685 (1970). (12) L. Rohrschneider, J. Gas Chromatogr., 6 , 5 (1968).

209 (13) R.A. Keller and L.R. Snyder, in Gas Chromatography 1970, R. Stock Ed., The Institute of Petroleum, London, UK, 1971. (14) B.L. Karger, L.R. Snyder and C. Eon, J. Chromatogr., 125, 71 (1976). (15) R.A. Keller, B.L. Karger and L.R. Snyder, in Gas Chromatography 1970, R. Stock Ed., The Institute of Petroleum, London, UK, 1971, p. 125. (16) L.R. Snyder, J. Chromatogr., 92, 223 (1974). (17) A.V. Kiselev and Y.I. Yashin, in Gas Adsorption Chromatography, Plenum Press, New York, NY, 1969, also in La Chromatographie Gus Solide, Masson, Paris, France, 1970. (18) E. sz Kovats, in Advances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1965, Vol. 1, p. 229. (19) Anon., in Gus Chromatography 1964, A. Goldup Ed., Butterworths, London, UK, 1964, p. 348. (20) L. Rohrschneider, Z. Anal. Chem., 170, 256 (1959). (21) L. Rohrschneider, in Advances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1967, Vol. 4, p. 333. (22) W.O. McReynolds, J. Chromatogr. Sci., 8, 685 (1970). (23) G.R. Primavesi, Nature, 184, 2010 (1959). (24) W.H. McFadden, Anal. Chem., 30,479 (1958). (25) H.J. Maier and O.C. Karpathy, J. Chromatogr., 8, 308 (1962). (26) P. Chovin, Bull. SOC.Chim. Fr., 1964, 104. (27) J.H. Purnell, J. Chem. Soc., 1268 (1960). (28) G. Guiochon and J. Gutierrez, J. Chromatogr., 406, 3 (1987). (29) D.H. Desty and A. Goldup, in Gas Chromatography 1960, R.P.W. Scott Ed., Butterworths, London, UK, 1960, p. 162. (30) G. Guiochon, in Advances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY. 1969, Vol. 8, p. 179. (31) R.P.W. Scott, in Advances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1970, Vol. 9, p. 193. (32) C. Vidal-Madjar, M. Gonnord, M. Goedert and G. Guiochon, J. Phys. Chem., 79, 732 (1975). (33) J. Krupcik, J.M. Schmitter and G. Guiochon, J. Chromatogr., 213, 189 (1981). (34) M. Martin, C. Eon and G. Guiochon, J. Chromutogr., 99, 357 (1974). (35) H.H. Lauer, H. Poppe and J.F.K. Huber, J. Chromatogr, 132, 1 (1977). (36) J.J. van Deemter, F.J. Zuyderweg and A. Klinkenberg, Chem. Eng. Sci.,5, 271 (1956). (37) L.R. Snyder, in Principles of Adsorption Chromatography, M. Dekker, New York, NY, 1968. (38) A.E. Pierce, Silylation of Organic Compounds. A Techniquefor Gas Phase Analysis, Pierce Chemical Co., Rockford, IL, 1968. (39) J.-F. Erard and E. sz Kovats, Anal. Chem., 54, 193 (1982). (40) H. Colin and G. Guiochon, J. Chromatogr., 141, 289 (1977). (41) C.L. Guillemin, Anal. Chim. Acta, 27, 213 (1962). (42) T. Welsch, W. Engewald and E. Kowasch, Chromatographia, 10, 22 (1977). (43) E.P. Atkinson and G.A.P. Tuey, Nature, 199, 482 (1963). (44) A. Zlatkis, S. Ling and H.R. Kaufman, Anal. Chem., 31, 845 (1959). (45) R. Bonmati, G. Chapelet and G. Guiochon, Sep. Sci., 19, 113 (1984). (46) I. Halasz and E. Heine, Anal. Chem., 37, 495 (1965). (47) C. Landault and G. Guiochon, Chromatographiu, I, 119, 277 (1968). (48) M.S. Vigdergauz and L.V. Andrejev, J. Chromatogr., 18, 226 (1965). (49) C.B. Herrin, J. Gus Chromatogr., 6, 470 (1968). (50) C.A. Cramers, J. Rijks and P. Bocek, J . Chromatogr., 65, 29 (1972). (51) I. Halasz and E. Heine. in Advances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1967, Vol. 4, p. 207. (52) M.S. .Vigdergauz and L.V. Andrejev, in Gas Chromatography 1964, A. Goldup Ed., The Institute of Petroleum, London, UK, 1965, p. 1. (53) J.C. Sternberg and R.E. Poulson, Anal. Chem., 36, 1492 (1964). (54) J.H. Knox and M.J. Salem, J. Chromatogr. Sci., 7, 745 (1969). (55) C.L. Guillemin, M. Deleuil, S. Cirendini and J. Vermont, Anal. Chem., 43, 2015 (1971).

210 (56) G. Guiochon, J. Chromarogr., 185, 3 (1980). (57) J.C. Giddings, And. Chem., 34, 314 (1962). (58) R.P.W. Scott, in Gas Chromurogruphy 1958, D.H. Desty Ed., Butterworths, London, UK, 1958, p. 189. (59) M.J.E. Golay, in Gas Chromurogruphy, V.J. Coates, H.J. Noebels and I.S. Fagerson Eds., Academic Press, New York, NY, 1958, p. 1. (60) J.J. Dufficld and L.B. Rogers, Anal. Chem., 32, 340 (1960). (61) J.J. Kirkland, Anal. Chem., 37, 1458 (1965). (62) C. Hishta, J. Bomstein and W.D. Cooke, in Aduances in Chromurography, J.C. Giddings and R.A. Keller Eds., M.Dekker, New York, NY, 1970, Vol. 9, p. 215. (63) R.L.Martin, Anal. Chem.. 33, 347 (1961). (64) A. Di Corcia, A. Liberti, C. Sambucini and R. Samperi, J. Chromurogr., 152, 63 (1978). (65) C. Vidal-Madjar,S. Bekassy, M.F.Gonnord, P. Arpino and G. Guiochon, Anal. Chem., 49, 768 (1977). (66) C. Landault and G. Guiochon, J. Chromurogr.. 9, 133 (1962). (67) J.J. Kirkland, Anal. Chem., 35, 2003 (1963). (68) A. Saint-Yrieix and C. Lesimple, Bull. Soc. Chim Fr., 1967, 4365. (69) H. Eyring, Anal. Chem., 20, 98 (1948). (70) J.C. Giddings, Dynamics of Chromurography, M.Dekker, New York, NY, 1965, Chapter 4.

211

CHAPTER 7

METHODOLOGY Advanced Packed Columns TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......... I. Modified Gas-Solid Chromatography . . . . . . . ............................ 1. SilicaGels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Physical Chemistry of Silica Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Selection of the Silica Gel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. General Procedures for Chromatographic Applications ........................ 4. Applications to Fast Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Specific Advantages for Industrial Analysis . . . . . . . . . . . . . . . . . . . . a. Column Stability . . . . . . . . . . . . . ................................. b. Sample Volume ............................. ................. c. Use of Steam in the Carrier Gas . . . . . . . . . . . . . . . . . d. Accuracy in Quantitative Analysis .................... 6. Procedure for the Preparation of Modified Silica Gels . . . . . . . . a. Preparation of the Adsorbent . . . . . . . . . . . . . . . . . . . . . . . b. Drying the Adsorbent . . . . . . . . . .......................... c. Coating of the Adsorbent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Thermal Treatment . . . . .................................. 2. Graphitized Carbon Black . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Porous Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Steam as Carrier Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Production of a Suitable Camer Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. General Procedure for the Use of Steam in the Carrier Gas ....................... 3. Optimization of the Experimental Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Selection of the Adsorbent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Influence of the Specific Surface Area of the Adsorbent ....................... 3. Influence of the Water Content of the Carrier Gas ........................... 4. Influence of the Column Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Application to the Analysis of Aqueous Solutions . . . . . . . . . . . . . . . . . . . . Literature Cited .............................................

211 213 214 215 217 218 219 225 226

227 228 230

233 234 236 237 237 238 240 241 244

INTRODUCTION During the early 'eighties, following the surge of investments made in this area by many well-established companies and the appearance of several successful, dedicated new ones which was triggered by the expiry of the original patent on open tubular columns (l),the development by Hewlett-Packard of the use of quartz tubing for the preparation of these columns (1) and the publication of various successful recipes for the coating of the open tubular column walls (l), it seemed that gas chromatography was going to become carried out entirely with OTC. We are of the opinion, however, that in spite of the considerable advantages (1) offered References on p. 244.

212

by OTC's over conventional packed columns (CPC), the latter will continue to be used in routine and process control analysis for a long time. In the introduction to this chapter we present a summary of the case for advanced packed columns; in the introduction to Chapter 8, a more detailed discussion of the relative advantages and drawbacks of OTC's and CPC's is given. There is a number of important analyses and analytical applications which can be solved only with the use of packed columns. The analysis of permanent gases, and the analysis of many samples originating in the production of industrial chemicals either cannot be performed with open tubular columns or just do not require their use. Neither the resolution power of very efficient columns, nor the rapidity of OTC are usually required for these separations. Furthermore, for the analysis of many industrial products, the analyst rightly prefers the use of rather large samples, which are more difficult to pollute and easier to handle, and which have a larger probability of being representative of the composition of the feedstocks or products of the plant. The industrial analyst always looks for accurate analyses. These require the injection of the whole sample on the column; sample splitting has been proven to be the source of serious bias. Until quite recently, on-column injection was impossible with OTC's. The situation is now changing, but the new techniques are not yet fully developed, let alone accepted (1).Finally a very large number of these analyses has been performed satisfactorily for 20 years or more with packed columns and few objections have yet been made to the performance of this analytical tool. So, for many practical applications in the industrial laboratory, there is little incentive to change and adopt the OTC, as there is little reason to fix what is not broken. There is already a number of instances of on-line analyses, as well as off-line laboratory analyses, where it has become difficult to perform the required separations, and where still the use of OTC's appears to be unacceptable. Serious doubts are still voiced in a large segment of this rather conservative world regarding the long-term stability of OTC's, a problem which has only recently become seriously addressed by the manufacturers. The solution of many difficult analytical problems of practical importance in industry can be achieved with CPC's by using some approaches which have not been discussed much in the scientific literature but have proven useful during these last ten to fifteen years. They permit the progressive adjustment of column selectivity and the successful elution of the most polar compounds. Both methods discussed here are derived from gas-solid chromatography. The first method is gas-adsorption layer chromatography, where the stationary phase is a regular adsorbent, the surface of which has been modified by adsorption of a certain amount of a non-volatile product, whose presence greatly modifies the properties of the surface, and hence the adsorption energy and the selectivity. The second method uses steam as carrier gas or as a major component of the mobile phase. The presence of a large partial vapor pressure of water in the mobile phase has several important effects. It permits the injection of large samples of water, i.e., the chromatographic system is ideal for the analysis of small amounts of organic pollutants in water or water-rich products. It also permits the suppression of tailing,

21 3

with considerable improvement of band profiles and quantitative results in the case of the analysis of polar or very polar materials. These techniques have permitted the development of extremely selective and rapid methods of analysis using packed columns, resulting in analyses which are often as fast and more accurate and reliable than those based on the use of open tubular columns.

I. MODIFIED GAS-SOLID CHROMATOGRAPHY Modified gas-solid chromatography, also called gas-adsorption layer chromatography by Halasz (2), is a retention mechanism which uses an adsorbent covered by a stable layer of an organic or inorganic compound, whose presence modifies the chemical composition of the adsorbent surface, hence the nature and intensity of the molecular interactions taking place with the different analytes contained in the studied mixture. As a result the adsorption energy of each component of the mixture is usually much decreased, permitting the use of the sorbent material at a much lower temperature. At the same time, the selectivity of the stationary phase is much greater than that of any solvent and especially that of the solvent used to prepare the layer covering the adsorbent surface. Finally, by changing the nature of the modifying solvent and its surface concentration, it is possible to adjust absolute and relative retentions over a wide range. The advantages of this method over classical gas-solid or gas-liquid chromatography are of major importance. It permits a considerable reduction in the analysis times, a much larger flexibility in the adjustment of the selectivity of the stationary phase to the requirements of a new problem and the achievement of much greater column efficiencies at high carrier gas velocities. Modified gas-solid chromatography (mGSC) has been studied by numerous scientists, especially Halasz and Heine (2), Halasz and Horvath (3), C.G. Scott (4), Vidal-Madjar and Guiochon (5,6), Kiselev et al. (7), Di Corcia and Liberti (8). In fact, as will become obvious in the following, mGSC is the systematic use of a phenomenon which very often plagues the uninformed analyst: when a non-volatile solvent is spread on a solid of significant specific surface area, the properties of the stationary phase obtained are rarely those which could be predicted from the thermodynamical properties of the bulk solvent and the relationships derived in Chapter 3 from solution thermodynamics. The reason is due to the very small thickness of the liquid film formed at the surface of the solid and to the modifications of the properties of the solvent by the presence of a high-energy underlying solid, which modifies the structure of the liquid in the thin film (9). We have shown in the previous chapter (Chapter 6, Section III.3.a, Selection of Phase Ratio) that when the relationship between retention volume and coating ratio (in theory a strictly proportional relationship) is studied. experimentally, it is observed in most cases that the specific retention volume is a minimum for a certain value of the coating ratio (cf Figures 6.17a and 6.17b). Modified gas-solid chromatography is carried out with a solid of specific surface area greater than that of a References on p. 244.

214

regular support for GLC, at coating ratios lower than the one corresponding to that minimum, but not much smaller (see Figure 6.17b). Mixed retention mechanisms may take place in this range, but it has been recognized that, because the liquid film is very thin, most often close to a monomolecular layer or even less, the phenomenon is essentially adsorption on a modified surface. Modified gas-solid chromatography requires the combination of a solid adsorbent and a liquid solvent. Three types of adsorbents have been used extensively in the applications of the method: - inorganic, heterogeneous, polar adsorbents, such as silicagels (especially Spherosils), - non-polar, homogeneous adsorbents such as graphitized carbon blacks (especially Carbopacks). - organic adsorbents, such as porous polymers (especially Porapaks and Chromosorb 100). Solvents are mostly the very polar stationary phases of GLC, polyglycols, 3,3’-oxydipropionitrile, polyimines, etc. The properties of the stationary phases obtained by coating an adsorbent with small amounts of different solvents may be very different from the classical chromatographic properties of the pure materials. For example, the association of a very polar adsorbent such as silica and a very polar solvent, such as 3,3’-oxydipropionitrilemay be surprisingly non-polar (2). The properties of the new stationary phase depend on the nature of the reagents involved, on the surface energy of the adsorbent, on its specific surface area, etc. (10). We present here the conclusions of systematic studies carried out essentially with one kind of adsorbent, Spherosil, a silica gel available with a wide range of characteristics. The extension of these results to other adsorbents is also discussed. 1. Silica Gels

Silica gel is a generic name for an adsorbent made of silicon oxide. There is a huge number of different silica gels, about as many as there are different batches of the product prepared. They come in families, of which there are as many as there are commercial brands. They are characterized by their specific surface area (from 5 to 800 m2/g), their pore volume or porosity (from 0.3 to 1 mL/g), the average pore diameter (10 to 200 nm) and pore size distribution, the particle shape (spherical, ovoid or irregular), size (from about 1 pm to 500 pm) and size distribution and the surface chemistry (11-13). As an example, Figure 7.1 shows a plot of the pore diameter versus the specific surface area for Spherosil silica gels. Silica gels have been the basis for many stationary phases in gas and liquid chromatography, because of their excellent mechanical properties. They can be packed with minimum attrition and can withstand considerable pressures. They resist all chemicals used in gas chromatography, and especially oxygen and easily withstand temperatures up to 600 O C without change in their structure. The surface chemistry changes however, by heating under a stream of dry gas. Most of the work reported here was done in Guillemin’s laboratory, using Spherosil (Prolabo, Paris, France), a brand of silica gel manufactured by Rhone-

21 5

Spherosil

Figure 7.1. Plot of the average pore diameter of Spherosil silica gels (Angstrom) versus the specific

surface area (rn*/g).

Poulenc. It comes in a variety of specific surface areas and pore size distributions. Results obtained have shown that this product is reproducible and stable. I . Physical Chemistry of Silica Gels

In Chapter 3 we have shown that in gas-liquid chromatography, the corrected retention time is proportional to the amount of liquid phase (solvent) contained in the column, while in gas-solid chromatography it is proportional to the total surface area of the solid surface of adsorbent contained in the column, i.e. to its mass and its specific surface area. In gas-adsorption layer chromatography, the retention time, t,, is given by (lOJ4):

where L is the column length, ii the average carrier gas velocity, K , the equilibrium constant between the two phases, S the specific surface area of the adsorbent, p the weight of stationary phase contained in the column, d , the film thickness, and V, the volume available to the gas phase. If a series of adsorbents of similar chemical nature is prepared without special care, however, the true retention time is not going to be strictly proportional to the specific surface area of these products (10,15,16). The retention time depends rather on the adsorption (Henry’s) constant, which is also a function of the chemical nature of the surface and may vary greatly with the method of preparation and even References on p. 244.

216

H

I

"\Si /O

/\ Geminal

I

H I

0"

#*H\

I

H

I

0

I

Si

Si

A A Bound reactive

0

I

/O\

Si

Si

Si

m

A m

Free

Siloxane

Figure 7.2. Structure of the surface of silica gel (after Snyder, ref. 17).

with some minor changes in the experimental conditions of a specific method (15). The energy of adsorption depends on the number of silanol groups per unit surface area, on the activity of these groups, and hence on the nature of the chemical treatments applied to the product during its manufacture. The density of silanol groups on the surface of silica gels after careful drying under partial vacuum at 150-2Oo0C is approximately 5 groups per 100 A', i.e., an average of about 1 free silanol per silicon atom on the surface (12,15). There are four main categories of silanol groups, coexisting in various proportions on any silica surface (cf Figure 7.2): free silanols, geminal silanols, bound reactive silanols and siloxane groups (11,12,15,17). If the column capacity factor is determined for

-

1

GC

-I LC - GPC

Figure 7.3. Plot of the column capacity factor for an arbitrary compound versus the specific surface area of Spherosil silica gels. The range of useful applications for GC is from 10 to 400 m2/g. For liquid chromatography and size exclusion chromatography it ranges from 50 to 800 m2/g.

217

materials of the same origin, with increasing specific surface area, up to 400 m2/g in gas-solid chromatography, 800 m2/g in LC, two changes of the surface energy are observed. One takes place between 30 and 50 m2/g, in agreement with Kiselev’s data (15), the other between 600 and 800 m2/g (see Figure 7.3). This latter change has no application in gas-solid chromatography. Lower specific surface area Spherosil particles are prepared by a hydrothermal treatment of the original 400 m2/g product. Progressive dehydration takes place, first reversibly, then irreversibly. It causes parallel changes in the surface chemical composition and adsorption energy. The nature and density of the silanol groups change. The geminal and free groups disappear, and the density of siloxane bridges increases at the same time. Since the solid surface is highly heterogeneous, so is the liquid phase layer sorbed on the solid surface. The structure of the liquid film, usually a fraction of a monolayer thick, is very different whether it is close to highly active silanols or over the siloxane groups; it is very different from the structure of the bulk liquid, due to the orientation of the solvent molecules by the strong electrical forces near the silica surface. Selective adsorption of the solvent molecules is compounded by the Kelvin effect which changes the density of the liquid distribution, especially inside small pores, a capillary condensed liquid coexisting with the partial monolayer film. This complex structure has been discussed by Giddings (18) and Serpinet (19). The nature of the silica surface is further discussed by Kiselev and Yashin (15), Snyder (17), Unger (11) and Serpinet (19). 2. Selection of the Silica Gel The rules to be followed for the selection of the adsorbent, the adsorbate (or modifier) and the coating ratio depend on the conclusions of the previous discussion. As the problem is extremely complex, a few simplifying assumptions are made. These assumptions lead to approximate results. When the parameters describing a separation are critical, it may be useful to check whether some modifications of the experimental conditions thus derived would result in improved performance. The assumptions made are as follows: - We consider only adsorbents with specific surface areas not exceeding 200 m2/g. - The surface will be considered to be homogeneous, i.e. the retention time is assumed to be proportional to the specific surface area. - The layer of adsorbate will also be considered to be homogeneous; its thickness is supposed to be constant. The selection of the adsorbent is based on the properties of the compounds to be separated. The following rules are applied: - The higher the boiling point of the components of the mixture, the smaller the specific surface area of the support adsorbent used. - The higher the polarity of the analytes, the smaller the specific surface area of the adsorbent selected. - Depending on the position of the analytes in the Kiselev (12,15) classification (cf Chapter 6, Section I.l), molecules of the groups A and B are separated on an References on p. 244.

218

adsorbent which has a large or moderate specific surface area (depending on the two parameters just discussed); molecules of the groups C and D are analyzed on a small or moderate specific surface area adsorbent. 3. General Procedures for Chromatographic Applications (20)

Retention times in modified gas-solid chromatography depend on the specific surface area of the adsorbent used, at constant film thickness of the modifying solvent, and on the column length. Accordingly, analyses are first carried out on a series of columns packed with an intermediate grade of silica gel coated with the same solvent at different film thicknesses. The retention times of a few compounds selected for their importance or their relevance to the analysis under study are determined and the plots of the corrected retention times, ti, versus the film thickness, d , , are drawn. The film thickness at which the retention times are a minimum is usually selected (cf Figure 6.16). If different grades of Spherosils are used *, we have observed that when the coating ratio is adjusted to keep the film thickness constant, the selectivities of the stationary phases obtained are the same. Only the corrected retention times change, not their ratio. These corrected retention times are proportional to the product of the specific surface area of the adsorbent, S, by the column length, L (the column diameter is constant, so the product SL is itself proportional to the total surface area of adsorbent in the column). In practice, if the film thickness were kept constant, the retention time would depend only on the product SL and the column temperature. A 2 m long column packed with a 400 m2/g adsorbent gives the same corrected retention time as a 4 m long column packed with a 200 m2/g adsorbent. This is illustrated in Figure 7.4, which shows the chromatograms obtained for a mixture of aromatic hydrocarbons at the same temperature, with three columns packed with particles of three different grades of silica gels, coated so as to keep the film thickness constant (cu 9 Angstrom). The column length is inversely proportional to the specific surface area of the adsorbent. The carrier gas flow velocities have been adjusted to achieve the same corrected retention times for each compound on the three columns, which is possible only because the relative retentions of the different components of the test mixture are the same on all columns. Another advantage of the columns packed with modified adsorbents is the very rapid mass transfer between the mobile and the stationary phase. This results in a very flat Van Deemter curve (cf Figure 7.5). The thinner the film of liquid phase on the adsorbent surface, the better the efficiency, at least so long as all active sites of the adsorbent surface are deactivated by the liquid phase. As a consequence, the optimum velocity is larger and there is a smaller loss of efficiency associated with the selection of a gas velocity larger than the optimum value. Combined with the The same should be true for other brands of silica gels, but does not apply to products of different brands.

219

I

GC

1

0 5: 28 rn2/g

L : 5rn

+ Corbowax 2 0 M

B)

L: 1.50m t

t

5 9 6 rn2/ g

Carbowox 2 0 M

L: 0.70 m

2gllOOg

6.7Og/lOOg

5:200 rn2/g

Carbowox 2 0 M

14g/lOOg

Figure 7.4. Chromatograms of a given mixture on three different columns, in gas-adsorption layer chromatography, with constant product SL (L, column length, S, specific surface area of the Spherosil) (10). 1, Methane; 2, benzene; 3, toluene; 4, ethylbenzene; 5, styrene. Columns: 1 nun id., packed with Spherosil coated with Carbowax 20M. Temperature 130 C. Carrier gas nitrogen. (A) Column length: 5 m. Specific surface area: 28 m2/g. Particle size: 160-180 pm. Flow rate: 0.85 L/h. (B) Column length: 1.5 m. Specific surface area: 96 m2/g. Particle size: 80-100 pm. Flow rate: 0.58 L/h. (C) Column length: 0.70 m. Specific surface area: 200 m2/g. Particle size: 80-90 pm. Flow rate: 0.26 L/h. Flow rates have been adjusted to show that if the corrected retention times of one compound on the three columns are equal, this is valid for all other compounds. Reprinted with permission of Journal of Chromarography, 158, 21 (1978).

other characteristics of modified silica gels, this makes the achievement of very rapid analyses possible, as we show in the next section. 4. Applications to Fast Analysis

As illustrated in this section, the systematic use of simple rules makes it possible References on p. 244.

220

5

0

10

-

U cm/sec

Figure 7.5. Plot of column plate height versus the flow velocity (Van Deernter plot). (A) Partition chromatography. Fluidized Chromosorb P (see Section III.1.3), specific surface area 4 m2/g, particle size 125-150 pg, coated with 20%(w/w) Carbowax 2OM. (B) Modified gas-solid chromatography. Spherosil, specific surface area 200 m2/g, particle size 100-106 pm, coated with 14%(w/w) Carbowax 20M.

to achieve a considerable reduction of the analysis time. Compared to the performance usually obtained with conventional gas-liquid chromatography, a reduction of the analysis time by a factor of about 30, while keeping the resolution constant, is typical (21). We have developed a four-step procedure to optimize the experimental conditions of an industrial analysis. These steps are described here, with the application to the development of the separation of a mixture of chlorohydrocarbons (vinylidene chloride, CH =CCl , methylene chloride, CH ,C1 ,, carbon tetrachloride, CC14 r 1,2-dichloroethane, CH,Cl-CH,Cl, 1,1,2-trichloroethane, CHCl ,-CH,Cl, vinyl chloride, CH,=CHCl) and benzene, as an example (cf Figures 7.6A to 7.6E). Figure 7.6A shows the chromatogram obtained with a conventional gas-liquid chromatography column (20%Carbowax 20M on Chromosorb P, 145-175 pm). The film thickness of Carbowax 20M is about 300 Angstrom, which is conventional. The column efficiency is good: H = 0.5 mm, reduced plate height (cf Chapter 4) cu 3, but the flow velocity, 6.6 cm/sec, is rather slow and the analysis time long, about 23 min, which may be too long for an on-line analyzer placed in a closed loop control in a chemical plant. To accelerate the analysis, the first step is to replace the support by a silica gel adsorbent. The use of Spherosil 28 m2/g, combined with a decreased liquid phase loading (24%only, corresponding to a film thickness reduced from 300 to about 17 Angstrom), permits the achievement of a greater efficiency and of a very large reduction in the analysis time, which is now only 5 minutes (see Figure 7.6B). The resolution of all components is excellent, since the recorder trace returns to base line between the peaks. The relative retentions have changed, however, due to the difference in selectivity observed between gas-liquid and gas-adsorption layer

,

,

'

,

221 7

I,. 0

7

1

! J

Figure 7.6. Optimization of the experimental conditions for an analysis using modified gas-solid chromatography. 1, Vinyl chloride; 2, vinylidene chloride; 3, methylene chloride; 4, carbon tetrachloride; 5, benzene; 6, 1.2-dichloroethane; 7, 1.1.2-trichloroethane. Temperature: 130 C. Carrier gas: nitrogen. (A) Conventional GLC. Column: 4 mm id., 4 rn long. Support: Chromosorb P (particle size: 145-175 pm). 20% Carbowax 20M. Inlet pressure: 1.8 atm. Flow rate: 3 L/h. Sample size: 1 pL. (B) Modified GSC. Column: 4 mm i.d.. 4 m long. Support: Spherosil 28 m2/g (particle size: 125-200 pm). 2% Carbowax 20M. Inlet pressure: 2.5 atm. Flow rate: 3 L/h. Sample size: 1 pL. (C) Modified GSC. Column: 1 mm i.d.. 5 m long. Support: Spherosil 28 m2/g (particle size: 125-200 pm). 2% Carbowax 20M. Inlet pressure: 5.0 atm. Flow rate: 0.9 L/h. Sample size: 0.1 pL. (D) Modified GSC. Column: 1 mm i.d.. 0.70 m long. Support: Spherosil 200 m2/g (particle size: 100-110 am). 14% Carbowax 2OM. Inlet pressure: 2.7 atm. Flow rate: 0.63 L/h. Sample size: 0.05 pL. (E) Modified GSC. Column: 1 mm i.d.. 0.70 m long. Support: Spherosil 200 m2/g (particle size: 100-110 pm). 14% Carbowax 20M. Inlet pressure: 5.0 atm. Flow rate: 1.6 L/h. Sample size: 0.1 pL. References on p. 244.

222

chromatography. A similar reduction in analysis time would be observed with the use of 5% Carbowax 20M on Chromosorb P, but the resolution of the early eluted peaks would have been very poor. Since the resistance to mass transfer in the stationary phase is considerably reduced and the plot of column plate height versus carrier gas velocity is very flat, the column can be operated at a much greater velocity than for Figure 7.6B, without experiencing a serious loss of efficiency. Because most detectors do not operate well at high carrier gas flow rates, this requires the use of a narrower column. On Figure 7.6C the result of the second step can be seen. The flow velocity has been multiplied by 4.8 (the flow rate has been multiplied by 0.3, but the column diameter has been divided by 4 and its cross section by 16) and it is now 32 cm/sec. Because the column is 1 m longer and the pressure drop is greater than on the previous column (cf Chapter 2, Compressibility Factor), the retention time is divided only by 2. In the third step, we increase the specific surface area of the support used, which permits a proportional reduction of the column length, and keep the corrected retention times constant (cf Figure 7.6D). This is done at constant film thickness, to keep the selectivity of the stationary phase and the relative retentions constant. A reduction of the analysis time by a factor of 2 results from the considerable reduction in the pressure drop and the consequent increase of the value of the compressibility factor j . The gas hold-up time is also reduced. A reduction of the particle size, from about 160 pm to 105 pm permits the achievement of a greater efficiency, with a plate height of 0.5 mm in spite of the rather high flow velocity. As a consequence, a base-line resolution is still observed in Figure 7.6D. Finally, the carrier gas flow velocity can still be increased, by raising the inlet pressure to the maximum we can afford within the constraints of our equipment and those of the working conditions in an industrial laboratory carrying out routine analysis, i.e., 5 atm. This is the final or fourth step. The chromatogram is shown on Figure 7.6E. The flow velocity has been raised to 57 cm/sec, and the retention time has been reduced to 36 sec, admittedly with quite a significant loss of resolution this time. A better result could probably have been achieved by a reduction of the column length rather than by an increase in the carrier gas flow rate. This approach is illustrated by the chromatograms on Figure 7.7. Two very short columns, 4 and 8 cm long, respectively, packed with 25-40 pm particles have been used. They provide excellent separations of the mixture components except the first two compounds (CH,=CHCl and CH,=CC12), because the column capacity factor for the second of them is too small (cf. Chapter 1, equation 35). The carrier gas velocities are relatively close to the optimum values. Velocities of 7.8 and 23.4 cm/sec, respectively, have been used with these two columns, corresponding to reduced velocities of approximately 3.2 and 10. The second chromatogram (Figure 7.7B) shows an HETP of about 0.1 mm for the last peak, a reduced efficiency of about 3, similar to the value achieved with most columns we have operated in GC. Huber et al. have investigated the use of very narrow particles in gas chromatography and have shown that very small HETP can be achieved (22). The results shown on Figure 7.7 are in agreement with the conclusions of their work. Unless very short columns can be used, however, the advantages of these columns are offset

223

2

2

@ L

4 5 scc

Figure 7.7. Fast analysis by gas-adsorption layer chromatography, using very short columns. 1, Vinyl chloride; 2, vinylidene chloride; 3, carbon tetrachloride; 4, benzene; 5, 1,2-&chloroethane; 6, 1,1,2-trichloroethane. Spherosil 200 m2/g, coated with 14.5% 3,3'-oxydipropionitrile. Particle size: 25-40 pm. Column temperature: 85 C. Carrier gas: nitrogen. Column diameter: 1 mm. (A) Column length: 8 cm. Flow rate: 0.66 L/h. Inlet pressure: 1.9 atm. Sample sue: 0.05 pL. (B) Column length: 4 cm. Flow rate: 0.22 L/h. Inlet pressure: 0.75 atm. Sample size: 0.02 pL. Reproduced with permission of the Journal of Chromatography, 139, 259 (1977).

by the requirement of a very large inlet pressure, often prohibitively large in practice. This illustrates the theoretical findings that, in chromatography generally and especially in GC, easy separations can be carried out very rapidly, using very small particles or very narrow open tubular columns (23). Because of excessive pressure requirements, however, difficult separations have to be carried out with much coarser packing material, at the cost of a considerable increase in analysis time. In the analysis of mixtures of light chlorohydrocarbons discussed here, as in the case of many important analyses in the heavy chemical industry, separations are usually not very difficult and very fine particles can be used to achieve very fast analysis when needed. As shown on Figures 7.7A and 7.7B, the pressure requirement to achieve a reasonable reduced velocity of 10 is well within the range of capability of current commercial equipment (1.9 atm). The quality of the separation would be improved, however, if an apparatus designed to be used with capillary columns were to have been used: the dead volumes and the response time of the chromatograph used to carry out the chromatograms shown on Figure 7.6 are,too large and contribute quite significantly to the band width.

224

With these very short, efficient columns, extremely small sample sizes must be used. This also pushes the capability of the instrument to the limit. Figure 17.27 shows an application of fast GC analysis to the control of pollutants in the atmosphere of a workshop. The chromatogram has been obtained with a process control gas chromatograph. Other similar analyses have been described in the literature (21,24). Such short columns, operated at room temperature, are also used in the portable chromatographs utilized for air pollution monitoring. 5. Specific Advantages for Industrial Analysis

In the previous sections we have explained the meaning of modified gas-solid chromatography, how it is carried out with silica gels and what kind of results can be obtained with some of the most classical and useful adsorption layers prepared by coating silica gels with polar solvents. In this section we discuss the major

m2/g

+ 5%

2Omln

PEG 400

15

10

5

0

Figure 7.8. Quantitative analysis of trace impurities in 1,2-dichloroethane.

1. Methylene chloride; 2, 1,l-dichloroethane; 3, benzene; 4, trichloroethylene. Column: 4 mm id., 4 m long. Spherosil 83 m*/g, coated with 5 % Polyethyleneglycol 400. Carrier gas, nitrogen. Flow rate 3 L/hour. Quantitative analysis (response factors have been determined using the gas density balance, as explained in Chapter 14): results are given in Table 7.1.

TABLE 7.1 Quantitative Analysis in Modified GSC

CH2CI2 CH 3 -CHCI2 C6H6

CHCl= CCl, Cf. Figure 7.8.

Concentration (ppm) Standard

Found

Difference

66 102 41 94

71 101 int. std. 89

(%I +7 -1 -5

225

advantages of the technique over classical gas-liquid chromatography. For a discussion on the weaknesses and difficulties of application of gas-solid chromatography in the analysis of all mixtures, except gases, see Chapter 3, Section B.VI. The main advantages we have found are the following: (i) the long term stability of the columns, (ii) the flexibility in the adjustment of relative retention times by changing the coating ratio (film thickness), (iii) the large sample volumes which can be injected without overloading or flooding the column and (iv) the possibility of using steam as a component of the mobile phase. Finally, we show that this technique permits the achievement of quantitative analyses which are as accurate as those obtained by other retention mechanisms (see Figure 7.8 and Table 7.1). a. Column Stability We have observed over the years that the stability of the performance of modified gas-solid chromatography columns is excellent. It much exceeds that of conventional columns prepared with the same stationary phase and operated at the

1.5 pi

i I

J

Figure 7.9. Application of modified GSC to process control analysis. Analysis of trace impurities in

1.2-dichloroethane. 1, Trichloroethylene; 2, benzene; 3, 1,2-dichloroethane; 4, 1,1,2-trichloroethane; 5, 1,1,2,2-tetrachloroethane. Column 1 mm i.d., 2.50 m long. Spherosil 55 m*/g, coated with 9% hexakiscyanoethoxyhexane. Carrier gas: nitrogen, 0.36 L/h. Temperature: 108OC. Sample sizes: 1 pL (right) and 1.5 pL (left). Since the last component ( # 5 ) would have a very long retention time, a column switching valve permits the elution of components 1-4 on the entire column,while component 5 is eluted only on a short (ca 50 cm) section (cutting procedure). The valve is actuated at B (see Figures). For details on column switching see Chapters 9 and 17. References on p. 244.

226

same temperature. The organic solvent sorbed on the silica gel surface has a vapor pressure at a given temperature which is much less than that of the same solvent in bulk. This is due to the strong adsorption energy of a polar solvent on a polar adsorbent. As a result the upper temperature limit of the column is quite a lot higher in gas-adsorption layer chromatography than it is in gas-liquid chromatography. For example, 3,3'-oxydipropionitrile coated on Spherosil can be used routinely at 70°C, without noticeable base-line shift, but with a column lifetime of several months. b. Sample Volume The sample volume depends on the curvature of the equilibrium isotherm (cf Chapter 5) and the total surface area of adsorbed layer contained in the column (in modified GSC) or the total volume of solvent (in GLC). This total surface area or volume is of course proportional to the surface area of the column cross-section. Silica gels are available in a large range of specific surface areas. Packing material used can be selected to afford the required loading capacity. The sample size is sometimes determined by the detector's detection limits, but often by the fact that automatic sample valves used in process control analyzers are unable to properly deliver sample volumes smaller than 0.5 pL. This might be one of the most stringent reasons why open tubular columns are not used in process control chromatographs (stream splitting is not compatible with the achievement of precise quantitative analyses). The chromatograms on Figure 7.9 show that 1 mm i.d. conventional columns packed with coated Spherosil perform well with samples of 1 and 1.5 pL. This would correspond to a 16 or 24 pL sample, respectively, on a 4 mm i.d. packed column. The column is somewhat overloaded for the major component, but the resolution of the trace impurities (100 ppm level) is still very good, provided the first compound eluted after the major component is well resolved from it. c. Use of Steam in the Carrier Gas We have already mentioned the increased stability of the modified GSC columns compared to conventional columns where the same solvent is coated on a low specific surface area support. We have observed this phenomenon to be especially important when steam is incorporated in the carrier gas (cf Section I1 of this chapter), so much so that we consider the use of steam to be nearly impossible with most conventional gas-liquid chromatography stationary phases.

d. Accuracy in Quantitative Analysis Modified GSC gives quantitative results as precise as those of GLC. As an example, the data in Table 7.1, corresponding to the chromatogram shown on Figure 7.8, show that the accuracy of the quantitative analysis carried out with a modified GSC column is the same as that obtained by conventional GLC. The response factors used for the analysis have been determined using a conventional GLC column and the gas density detector (cf Chapters 10 and 14). The results obtained show that there is no loss of sample component by strong adsorption.

227

6. Procedure for the Preparation of Modified Silica Gels The preparation of a good packing material for modified gas-solid chromatography requires that several steps - washing, drying, coating and thermal treatment of the material - be thoroughly performed. Strict adherence to the following procedure should result in a satisfactory stationary phase. Although most of the results discussed above have been obtained with Spherosil, we are of the opinion that similar results could be obtained with other silica gels, provided they are chosen among those which have similar physical and physicochemical properties. This statement is supported by the results obtained by Lin, Pfaffenberger and Horning (25), who have prepared open tubular columns with a wall coated by a layer of Silanox, impregnated with various amounts of non-polar solvents, such as silicone oils. Excellent analytical results were obtained. The use of polar phases was less successful, however (26). Further discussion of results obtained with modified GSC open tubular columns is presented in Chapter 8. a. Preparation of the Adsorbent The adsorbent must first be washed very carefully to eliminate traces of inorganic materials, especially sodium, contained in the silica and of organics adsorbed on its surface. The adsorbent is washed with concentrated (68%) nitric acid for 8 hours, in a rotary evaporator, at room temperature (slow rotation on, no vacuum or gas stream). The product is then washed with distilled, sodium free water until a p H of 7 is achieved. It is then dried in an oven. The comparison between the two chromatograms on Figure 7.10 illustrates the extreme importance of a thorough nitric acid wash. On Figure 7.10A the alcohols give terribly tailing peaks and the material is certainly unsuitable for any analysis involving alcohols. After careful washing the same material gives an excellent chromatogram for the same mixture. b. Drying the Adsorbent T h s is another step of major importance. Failure to use a carefully dried silica gel for the coating step invariably results in a stationary phase which exhibits poor performance, low efficiency and tailing peaks. It seems that the reason for this behavior is related to the explosive vaporization of the microdroplets of water condensed in the bottom of pores in the silica gel by the Kelvin effect. This brutal phenomenon which takes place at a temperature somewhat higher than 100 O C (Kelvin effect) results in the bursting of the film of solvent coated on the adsorbent surface, releasing unprotected active sites on the surface of the silica. The result is a stationary phase offering mixed retention mechanisms, with adsorption on a free silica surface, which invariably leads to unsymmetrical, strongly tailing peaks (cf Chapter 3, Section A.IX and Figure 7.10). The drying aims at eliminating all the water which is physically sorbed. It does not change the nature and density of the silanol groups on the silica surface. It is carried out at 15OoC, for 2 hours, under vacuum. For this operation, the silica gel References on p. 244.

228

Figure 7.10. Influence of the nitric acid washing of Spherosil on the performance of a packing material. 1, Ethanol; 2, 2-propanol; 3, I-propanol; 4, 2-butanol; 5, 2-methyl-1-propanol; 6, I-butanol; 7, 2-methyl-1-butanol;8, 3-methyl-1-butanol. Columns: 1 mm i.d., 2 m long. Spherosil18 m2/g coated with 1.3%Carbowax 20M. Carrier gas: nitrogen, flow rate: 0.25 L/h. Temperature 100 C. (A) Unwashed Spherosil. (B) Spherosil washed as described in text.

should be placed in the same vessel used to coat it in the next step. After the adsorbent is dried, it is brought to atmospheric pressure by introduction of dry nitrogen, and then cooled to room temperature. c. Coating of the Adsorbent

Any classical liquid phase used for gas-liquid chromatography may be coated on Spherosil. The coating of a non-polar phase is much more difficult, however, than the coating of a polar solvent. It is rarely attempted and the operation is tricky. The washing and drying of the adsorbent must be performed with care. Preferred liquid phases are: - Carbowax 20M, - 3,3'-oxydipropionitrile, - Squalane. The coating ratio can be chosen using the nomogram in Figure 7.11. This graph permits the calculation of the coating ratio (amount of stationary phase for 100 g of adsorbent), as a function of the specific surface area of the support and the desired film thickness. It is necessary to know the density of the solvent used.

229

S

1

m2/g 100

90 80

70 60

50 40 30 20 10

2

*

df 8,

*

'.5

Figure 7.11. Nomogram for the calculation of the coating ratio. Abscissa: film thickness (Angstrom). Ordinates: right, specific surface area, left, coating ratio. p : density of coated liquid. w = 100 dJp To obtain a 15 Angstrom thick film on a 30 m2/g silica, with a liquid of density 1.5, the analyst draws the line 00 on the upper part of the graph, then the vertical from the intersection point between the horizontal at p = 1.5 and the slanted line corresponding to df = 15. The intersection of this vertical and the line 00 is at c, which corresponds to the coating ratio 6.8%.

The dried adsorbent is mixed with pure methylene chloride in a rotary evaporator. The solvent is gradually drawn into the slowly rotating flask, until the silica gel is covered by a solvent layer of about 1 cm. The flask is kept rotating for another 30 minutes. After that a solution of the desired amount of stationary liquid in an excess of methylene chloride is slowly added to the flask. The mixture is slowly rotated for one hour before vacuum and/or heat is applied to vaporize the solvent. References on p. 244,

230

It is very important, again, to use extremely dry methylene chloride and stationary liquid. The methylene chloride is dried as follows. Molecular Sieve 13X is dried at 300 O C for 3 hours under a stream of dry nitrogen, then cooled under dry nitrogen. The methylene chloride is kept for 48 hours in a carefully closed glass bottle in contact with a large amount of this Molecular Sieve. The rotating flask is slowly heated to vaporize the methylene chloride. This operation should proceed slowly and take at least three hours. d. Thermal Treatment This treatment improves the thermal stability of the stationary phase. Several phenomena are involved and their relative importance is still unknown. - mechanical effect: the viscosity of the liquid phase decreases considerably at high temperature. This favorizes an even spreading and the filling of the smallest pores. - physico-chemical effect: the liquid phase molecules migrate on the surface to the sites of highest adsorption energy. - chemical effects. It seems that certain phases, such as Carbowax may react with chemical groups on the surface, silanols or siloxane bridges, and become bound to it. The thermal treatment is carried out at the following temperatures: - 3,3’-oxydipropionitrile at 90 O C for 3 hours, - squalane at 150O C for 10 hours, - Carbowax 20M at 200 O C for 3 hours. The thermal treatment can be carried out either on the bulk material prepared, in an oven, or on the packed column, under a stream of nitrogen, immediately before use. 2. Graphitized Carbon Black

Graphitized carbon black (GCB) is one of the most reproducible adsorbents known (12). Its surface is highly homogeneous. It is prepared by the treatment of thermal carbon blacks at 2,700-3,000 O C, under an inert atmosphere (graphitization). In spite of this treatment active groups exist on the surface. Also the surface is reactive enough to capture oxygen above 300 O C, resulting in the appearance of a variety of selective adsorption sites: free radicals, phenols, ketones, quinones, and carboxylic groups. When the GCB is freshly prepared and has been exposed only to low temperatures, the free radicals, which seem to be the most abundant active sites on the surface of this adsorbent, can be reacted by soaking the powder for a week in a concentrated solution of styrene. Oligostyrene chains grow on the surface, permitting the easy dispersion of the powder in organic solvents, by reducing the strong interactions between the 001 graphite facets of different polyhedron particles which constitute graphitized thermal carbon black. Although impressive results have been obtained with this material used in pure GSC (8,12,15, 27-37), the practical applications have been limited. The very high surface energy of graphite results in high adsorption energies and very large

231

r 1.3

0.0-

-c-

- -- - -- I . l I 1

I

- - - - - - - - - - - - _- -_ - _ I

,

I

, I , /

I

I , I , I , I , I ,

Figure 7.12. Relative retention of some free acids on FFAP modified graphitized carbon black Sterling FT-G (60-80 mesh). (After Di Corcia, ref. 38). Squares: p/m-methylbenzoic acids. Open triangles: 3/2-methylbutyric acids. Solid triangles: m /o-chlorobenzoic acids. Reverse triangles: m /o-chlorobenzoic acids. The dashed lines indicate the values obtained with FFAP in pure gas-liquid chromatography. A, p/m-methylbenzoic acids; B, p/m-chlorobenzoic acids; C, m /o-chlorobenzoic acids. Reproduced with permission of Analytical Chemistry, 45, 492 (1973).

retention volumes for most solutes, except those (like pinenes, borneol, adamantane) whch have a structure preventing their molecules from lying on the flat 001 surfaces (28). Most other compounds cannot stand the temperatures which would permit their elution without experiencing some thermal degradation, in spite of the inertness of the graphitized carbon black (35). The few selective adsorption sites may also result in tailing peaks for polar compounds. Because of their stability, inertness, large surface energy and relative surface homogeneity, graphitized thermal carbon blacks are very suitable adsorbents for modified GSC. Carbopack B and C have been studied extensively by Liberti, Di Corcia and Bruner (33,34). Their specific surface areas are 100 and 10 m2/g, respectively. Carbopack products have been treated under hydrogen at 1,000 to 1,20OoC to eliminate a large fraction of the heteroatoms still present in the graphitized carbon black. Total hydrogenation is not possible, unfortunately. The general behavior of graphitized carbon blacks in modified GSC is similar to the one observed with silicagels as previously described. For example, the retention times of several organic acids on Sterling FT (specific surface area: 12 m2/g), coated with FFAP, decreases constantly with increasing film thickness, or coating ratio, in the range studied (0.2 to 2.5%), as shown on Figure 7.12. A monomolecular layer is not yet reached for a 2.5% coating ratio, which explains why in this case a minimum is not observed. The decrease in retention time is ascribed first to the decrease in the References on p. 244.

232

density of selective adsorption sites with increasing coating ratio (especially the rapid decrease in the range 0.3-0.9%, Figure 7.12), and then, to the increasing degree of microheterogeneity of the adsorbent surface brought about by the polymer chains occupying an increasing part of the carbon surface and preventing analyte molecules from lying flat on the carbon surface (28). The selectivity is a function of the coating ratio (38). Excellent analytical results have been reported by Vidal-Madjar et al., using Sterling FTG (Cabot, Boston, MA, U.S.A.), coated with various amounts of Carbowax 20M, Free Fatty Acid Phase (FFAP) and Polyphenyl ether sulfone (ASL). The material has the same ability as pure Sterling FTG to separate geometrical isomers, but carbazole and azaarenes are eluted with very symmetrical peaks (36). The large column loadability permits the identification of trace compounds by GC-MS at concentration levels much below that possible to achieve with conventional columns (37). Graphitized carbon blacks and especially Carbopacks are remarkably useful for the analysis of very polar analytes which exhibit differences in their geometrical structure and their polarizability. Cis-trans double bond isomers and positional isomers of multisubstituted aromatic (homo- or heteronuclear) compounds are often easily resolved. Analysis of free, underivatized carboxylic acids, alcohols, amines, nitrosamines, thiols can be carried out successfully on modified Carbopacks. A review contains many examples of separation (30). The coating of graphitized carbon blacks is relatively easy and carried out much like the coating of classical supports for GLC. Since graphitized carbon black does not absorb water, there is no need for a careful drying of the material. 3. Porous Polymers A number of polymers have been used in gas chromatography. It is possible to prepare small particles with reticulated polymers, in the size range required for successful gas chromatographic applications. The only popular materials at present are Porapaks and Chromosorb loo's (Johns Manville). Both commercial products come in a number of grades among which the analyst choses depending on the particular application. Most of these products are copolymers of styrene, ethylvinylbenzene and divinylbenzene. Some of them contain vinylpyrrolidone or other vinylic monomers. The specific surface areas of these products range from 15 m2/g for Chromosorb 103 to 600 m2/g for Porapak Q. The original and pioneering work of Hollis (39,40), who demonstrated the amazing properties of these non-polar materials, included separations of wet gases with the water eluting first. In most applications these adsorbents are used pure, as in classical GSC. It is always possible, however, to add some small amounts of liquid phases to adjust the selectivity of the stationary phase (39,40). The underlying polymer always seems to contribute to some extent to the retention, maybe because it would be very difficult with most products to achieve coating ratios large enough to really bury the surface. Furthermore, coating a reticulated polymer with a liquid layer is not like coating silica or graphitized carbon black. Some swelling or '

233

dissolution of the coating solvent in the porous polymer is likely to take place. Used at small coating ratios a number of additives, called modifiers or tailing reducers, permit a profound improvement of the band profile of some polar compounds (e.g. the use of polyimines results in symmetrical amine bands (40)). This phenomenon has been illustrated by Baumann and Gill (41). One of the most important applications of the porous polymers in routine analysis is the analysis of traces of water (42). Water is eluted very early with most materials. For example on Porapak Q, water elutes just after ethylene, totally resolved from this compound. With a good thermal conductivity detector (Chapter lo), the detection limit is about 10 ppm. On the other hand, columns packed with porous polymers can be used for the analysis of organic pollutants in water, since water is much less retained than light pollutants. Systematic investigations of this application have been made by Supina and Rose (43) and by Dave (44),among others. Compounds studied include: alcohols, glycols, ethers, aldehydes, ketones, acids, esters, chloroalkanes, amines, aromatic amines, diamines, nitriles, aromatic hydrocarbons, etc. As a general rule, all compounds belonging to any of the four classes distinguished by Kiselev (cf. Chapter 6, Section 1.1) can be separated on some porous polymer phase, provided their vapor pressure is rather large. High boiling compounds cannot be eluted in a reasonable time. For example chlorinated hydrocarbons with one or two carbon atoms are eluted in prohibitively long times when their boiling point exceeds 70-80 O C. The coating of porous polymers by a modifier is carried out like the coating of graphitized carbon black or of classical gas-liquid supports, without a careful drying prior to the coating procedure.

11. STEAM AS CARRIER GAS

Water can be used in gas chromatography either as a stationary or as a mobile phase. In 1957 Pollard and Hardy (45) demonstrated the potentiality of water as a stationary phase and used it for the separation of the chloromethanes. The vapor pressure of water proved too high, however, for a successful application in routine analysis. In the early 'sixties Wilkens (now Varian) offered a steam generator for use as a carrier gas or carrier gas component with any chromatograph (46,47). Used with conventional liquid phases in GLC, this system was not very successful either. Most stationary phases are steam distilled out of the column, which generates a variety of troubles: progressive decrease in the retention times and in the resolution, sometimes also large changes in the relative retention, base-line drift and excessive noise due to the response of the detector to the stationary phase, fouling of the detector, etc. The device was rapidly forgotten. More recently, several authors have reflected that a steam-rich gas stream could be an excellent carrier gas for gas-solid chromatography (2,16,48-50). A variety of References on p. 244.

234

applications have been described, including the analysis of heavy organics dissolved in water (51,52). Gradually, it has been demonstrated that the use of steam as a component of the carrier gas is much more than a fancy topic of academic interest (53). It may be developed into a highly reliable and very powerful method for routine analysis, in the laboratory or on-line, in combination with classical or modified gas-solid chromatography. In this case, water is both a component of the mobile phase and a constituent of the stationary phase, since a more or less important film of water is sorbed on the surface of the adsorbent. The situation is somewhat reminiscent of the retention mechanism in reversed phase liquid chromatography, where the exact composition of the adsorbent layer depends on the concentration of the organic solvent and organic modifier in the mobile phase (54). There is one important difference, however. The competition aspect between the analyte and the components of the mobile phase for adsorption on the surface of the adsorbent or within the chemically bonded groups there, so important in reversed phase HPLC,does not have any equivalent in normal gas chromatography, where the carrier gas is practically not adsorbed at all on the surface of the adsorbent or of the support, nor dissolved in the liquid stationary phase. In the present case on the contrary, the water molecules are sorbed on the adsorbent surface and interact with the surface modifier molecules. The analyte molecules can be either sorbed on the silica surface, at a gas-solid interface, on the silica surface at a liquid-solid interface or on the layer of sorbed water, at the gas-liquid interface. Multilayer adsorption is definitely a possibility in gas-solid adsorption equilibria (55). The interaction free energy is quite different in the three cases, however, and the retention volumes will depend on the nature and partial pressure of the carrier gas additive (see Chapter 3, Section V). Karger et al. have studied the adsorption of vapors at the gas-liquid water interface, using thin films of water sorbed on silica (60). Be that as it may, the use of a phase system composed of a steam-inert gas mixture as mobile phase and of an adsorbent covered by a film of a water-organic solvent mixture is a very powerful tool, offering the possibility of fine tuning the selectivity by adjusting the water content of both phases. 1. Production of a Suitable Camer

Gas

Several systems have been described in the literature, permitting either the production of steam as the only component of the mobile phase (45,46,51), or of mixtures of steam and a more conventional camer gas, with an adjustable composition (49,50,53). The latter permits a more flexible use of steam, and this is the method we choose. The principle is to bubble a stream of nitrogen or helium through a mass of water contained in a pressurized container and maintained at a carefully controlled temperature (cf Figure 7.13). The installation of such a system on a commercial gas chromatograph is easy. The camer gas line starts at the pressure controller, 1, on the inlet of the inert gas stream. The flow controller is eliminated and replaced by a pressure controller, for reasons discussed in Section 11.3.5 below, to prevent the effects on the detector

235

Figure 7.13. Schematic of the camer gas line of a gas chromatograph using steam as a carrier gas component. 1, Pressure controller on the inert gas. 2, Safeguard tank for the water in 4. 3, Stop valve. 4, Water tank. 5, Pressure gauge. 6, Sampling port. 7, Column. 8, Detector.

base-line of the surge of vapor following the injection of a large water sample. The carrier gas bubbles into the water contained in the water tank, 4, and goes to the sampling port, 6 , and the column, 7 (cf Figure 7.13). The water tank 4, tested to 10 atm, is placed in a temperature-controlled oven, separated from the column oven, but immediately next to it. There should be no cold spot, i.e. no place where the gas stream temperature becomes lower than the temperature of the water in the tank. Otherwise water would condense in these parts, then, when the amount of condensed water is large enough to interfere with the gas stream, liquid droplets would burst and be projected into hot parts of the apparatus where they would vaporize very rapidly, creating flow rate instabilities, resulting in an unsteady base-line and a very noisy detector signal. Similarly, noise resulting from the formation of bubbles in the water tank 4 can be considerably reduced by use of a metal frit with a 10 to 20 pm porosity. The critical sections of the carrier gas line are the connecting tubes between the water tank 4 and the sampling port 6 and between the column exit and the detector, 8, as well as the detector itself. The sampling port, the column and the detector should always be operated at a temperature higher than that of the water tank. An empty tank, 2, and a valve, 3, immediately upstream the water tank 4, permit the protection of the inert gas line against backflow of water in case of pressure surges in the line when the chromatograph is being started or stopped. The setting of the inert gas and the steam flow rates is done by adjusting the inlet pressure of the inert gas and the temperature of the water tank. These operations are independent and do not interact. First, the water tank being at room temperature, the inert gas flow rate is set by adjusting the inlet pressure. This flow rate is measured downstream from the detector using a conventional soap bubble flowmeter. The inlet pressure is adjusted to provide a flow rate of e.g. 2 L/hour for a 4 mm i.d. column. The inlet pressure References on p. 244.

236

corresponding to the total flow rate desired (inert gas+ steam) should also be determined at that stage. Then the temperature of the water tank is raised, so that the inlet pressure gauge, 5 (Figure 7.13) reads the pressure required to achieve the total flow rate desired (usually equal to 3 L/h, the flow rate which typically corresponds to the maximum column efficiency with the columns we use). This assumes that the viscosity of the inert gas-steam mixture is the same as that of the inert gas. This is only an approximation since the viscosity of steam is low, intermediate between that of nitrogen and hydrogen (cf Chapter 2, Table 2.1). So the actual flow rate achieved is somewhat greater than calculated, but for analytical applications, the consequences are negligible, as long as the flow rate and the composition of the carrier gas are reproducible, which they are. As a first approximation, the partial pressure of steam at the column inlet is the difference between the initial inlet pressure (inert gas alone) and the final inlet pressure (inert gas plus steam). Both partial pressures, that of steam and that of the inert gas, decrease along the column, although their ratio remains constant. Accordingly, the amount of water adsorbed per unit surface area of the adsorbent decreases along the column. In most analyses performed by this method the detector is a flame ionization detector. The hydrogen flow rate to the detector must be slightly higher than for conventional analyses, to keep the flame hot enough, permit a good ionization yield of the analytes, and keep a satisfactory response factor. The hydrogen flow rate is typically 3 L/h in these applications, while the air flow rate is 15 L/h. A large excess of air is required to avoid condensation of water in the detector. 2. General Procedure for the Use of Steam in the Carrier Gas

These rules are similar to those used for the selection of the adsorbent in gas-adsorption layer chromatography (cf Section I above): - The higher the boiling point of the analytes, the lower the specific surface area of the adsorbent selected and the higher the steam concentration in the carrier gas. - The higher the polarity of the analytes, the lower the specific surface area of the adsorbent selected and the higher the steam concentration in the carrier gas. Furthermore, referring to the Kiselev classification of compounds (Chapter 6, Section 1.1): - For molecules of groups A and B: - the specific surface area will be moderate to large, - the carrier gas composition will be 25 to 50% steam. - For molecules of groups C and D: - the specific surface area will be small to moderate, - the carrier gas composition will be 50 to 75% steam. These figures are orders of magnitude, to be adjusted as required for each application. Water molecules from the mobile phase are adsorbed on the silica surface and form a film of variable thickness. Sites of the highest energy are saturated with water molecules, so the silica surface is transformed essentially into a water surface,

\

231

which is much more homogeneous than the original silica surface, but retains some of its properties. The thickness of the water layer essentially depends on the column temperature and the partial pressure of water in the mobile phase, or more exactly on the ratio of the partial pressure to the vapor pressure. Since the vapor pressure of water decreases continuously from the column inlet to the outlet, the average film thickness of the water layer also decreases regularly from the column inlet to the outlet. The retention or column capacity factor, as well as the selectivity of the stationary phase, increases continuously from the inlet to the outlet of the column. This may result in difficulties in the elution of some heavy, polar compounds, which may be strongly retained and whose profiles may acquire tailing on the end of the column. There are two ways to attempt to correct this effect: - either by increasing the water content of the mobile phase, and hence that of the stationary phase, i.e. by decreasing the column temperature or by increasing the water concentration of the mobile phase, or both, - or by decreasing the activity of the adsorbent and selecting a silicagel with a lower specific surface area. The use of steam as a component of the mobile phase may permit a moderate increase of the solubility of the analytes in the mobile phase, because of favorable molecular interactions in the vapor phase, which is strongly analogous with liquid chromatography.

3. Optimization of the Experimental Conditions The main parameters to adjust are the nature of the adsorbent and its specific surface area, the column temperature and the water content of the mobile phase. It should be emphasized at this point that other suitable polar vapors or gas can be added to the carrier gas, the only major requirement being that this compound has a very low response factor with the flame ionization detector. Ammonia, formaldehyde, formamide, formic acid, could make excellent choices for the solution of a variety of analytical problems. Major corrosion problems may be encountered in certain cases. 1. Selection of the Adsorbent

There is a large variety of adsorbents among which to choose. Silica gels, silica gels coated with pyrocarbon (56,57), aluminas, activated carbons or charcoals, porous polymers, etc. Since the retention properties of the stationary phase depend on the composition of the mobile phase, rather important changes in selectivity, including inversions in the elution order of some compounds will result from adjustments in this composition. They will be used for the solution of specific problems. Figure 7.14 illustrates the influence of the nature of the adsorbent. With approximately 45% water, the elution orders are: - on silica: (1) 3-methylpentane, (2) cyclohexane, (3) n-heptane, (4) 1,2-dichloroethane, (5) acetone and ( 6 ) methyl ethyl ketone, References on p. 244.

238

.3

-2 B

A 4,

6

n

5

6

7min

L I

I

I

Figure 7.14. Separation of a test mixture on silica and pyrocarbon-coated silica, with steam as a component of the carrier gas (59). 1, 3-Methylpentane; 2, cyclohexane; 3, n-heptane; 4, 1,2-dichloroethane; 5, acetone; 6, methyl ethyl

ketone. (A) Column: 4 nun i.d., 2 m long. Spherosil32 mz/g, particle size: 150-200 pm. Temperature: 105" C. Carrier gas:nitrogen 5 2 1 , steam 48%.Flow rate: 2.9 L/h. (B)Column: 4 mm i.d., 1 m long. Spherosil50 m2/g, particle size: 150-200 pm, coated with pyrocarbon. Temperature: 150 O C. Carrier gas: nitrogen 56%, steam 44%. Flow rate: 3.06 L/h. Reprodud with permission of Journul of Chromurogruphy, 301, 11 (1984).

- on pyrocarbon coated silica: (3) n-heptane, (2) cyclohexane, (1) 3-methylpentane, ( 5 ) acetone, (6) methyl ethyl ketone, (4) 1,2-dichloroethane. Whereas, on silica, the retention order is mainly controlled by the polarity of the molecule (first, hydrocarbons, then chlorinated hydrocarbons, ketones last), on pyrocarbon-coated silica the size of the molecule is much more important (57). This property has been used in the analysis of acetaldehyde in drinking water at the 10 ppb level: on pyrocarbon-coated silica this compound is eluted before acetone and well resolved from it. In the literature there are examples of the use of a large variety of adsorbents with steam as a mobile phase (52). 2. Influence of the Specific Surface Area of the Ahorbent (58) Retention volumes are a function of the specific surface area of the adsorbent used. Of course the specific surface area of a silica gel used with steam as a

239

Figure 7.15. Plot of the logarithm of the column capacity factor versus the specific surface area of the adsorbent used (59). 1, 3-Methylpentane; 2, cyclohexane; 3, n-heptane; 4, 1,2-dichloroethane; 5, acetone; 6, methyl ethyl ketone. Column: 4 m m i.d., 2 m long. Temperature 115OC. Flow rate: 3 L/h. Carrier gas: nitrogen 42%, steam 58%. Spherosils 32, 53, 108, 230 and 367 m2/g, particle size: 150-200 pm. Reproduced with permission of Journal of Chromatography, 301, 11 (1984).

component of the carrier gas will depend not only on the specific surface area of the initial (unmodified) silica gel, but also on its average pore size and pore distribution. When a pore is filled with water, condensed by capillarity or by the Kelvin effect, the surface of the water layer available for adsorption is independent of the total inner area of the pore, and is much smaller. This phenomenon is illustrated in Figure 7.15, a plot of the column capacity factors determined for the same mixture of test solutes as separated on the chromatograms in Figure 7.14, as a function of the specific surface area of the silica gel used. From this figure we can make the following observations: - the column capacity factors increase almost linearly with increasing specific surface area. - the resolution between compounds which have similar adsorption energies requires the use of large specific surface area adsorbents, e.g., the separation of 3-methylpentane and cyclohexane. - the retention of polar compounds on large surface area adsorbents may be prohibitively long. References on p. 244.

240

L

5-

-

4- 1:

a5 -

4-3 1*2

:

I

,

I

I

1

,

I

,

I

Figure 7.16. Plot of the logarithm of the column capacity factor versus the water content of the mobile phase (59). 1, 3-Methylpentane; 2, cyclohexane; 3, n-heptane; 4, 1,2-dichloroethane; 5, acetone; 6, methyl ethyl ketone. Column: 4 mm i.d., 2 m long. Spherosil 32 m2/g, particle size: 150-200 pm. Temperature 115 O C. Flow rate: 3 L/h. Carrier gas: nitrogen and steam 33, 52 and 66%. Reproduced with permission of Journal of Chromrography, 30I, 11 (1984).

These results also illustrate the rules given in the previous section regarding the selection of the adsorbent. Finally, we want to emphasize that the method is most useful to enhance the resolution between some of the important components of a sample, rather than to improve the separation of a complex mixture.

3. Znfruence of the Water Content of the Carrier Gas (58,59) The increase in water content of the carrier gas results in a decrease in the surface activity, since the surface becomes increasingly water-like and homogeneous. Experimental results are in agreement with this prediction, as is illustrated by the data in Figure 7.16. The column capacity factor decreases exponentially with increasing water content. The decay constant of the exponential increases with the polarity of the analytes (compare acetone and cyclohexane in Figure 7.16). This observation also confirms our analysis of the retention mechanism in GSC with steam as a component of the mobile phase since, in modified GS.C, the retention time also decreases with increasing surface coverage of the adsorbent, at least as long as the film of organic modifier is thin (cf. Chapter 6, Figure 6.17).

241

The use of plots such as the one shown in Figure 7.16 permits the selection of the optimum steam content of the mobile phase. In difficult cases it is conceivable to program the steam content, for example to permit the separation of light, weakly polar compounds on an active adsorbent, followed by the separation and elution with symmetrical peaks of the heavy, polar components of the mixture. This procedure would be identical to the gradient elution programming of liquid chromatography, an analytical procedure which as far as we know has not yet been carried out in gas chromatography. 4. Influence of the Column Temperature (59)

A change in the column temperature has several effects. First, the vapor pressure of water is changed. Accordingly, at constant water concentration the amount of water sorbed and the average film thickness increase with decreasing temperature. On the other hand, since adsorption is an exothermic process, the retention volume of analytes increases with decreasing temperature. The combination of the two effects may result in considerable variations of the relative retention of some pairs of analytes with changes in the column temperature.

4

50 -

\

10 -

5-

I

I

150

200

250 ‘C

,

Figure 7.17. Plot of the logarithm of the corrected retention time versus the reverse of the column temperature (59). 1, 3-Methylpentane; 2, cyclohexane; 3, n-heptane; 4, 1,2-dichloroethane; 5, acetone; 6, methyl ethyl ketone. Column: 4 mm i.d., 1 m long. Spherosil 50 m’/g, coated with pyrocarbon, particle size: 150-200 pm. Flow rate: 3.06 L/h. Carrier gas: nitrogen 56%, steam 44%.Temperatures: 150 C, 170 C, 216 O C and 260 O C. Reproduced with permission of Journal of Chromarogruphy, 301, 11 (1984).

References on p. 244.

242

Some conventional plots of the logarithm of the retention time versus the inverse of the absolute column temperature are shown in Figure 7.17. The same test compounds have been used as for the previous figures. Care should be taken to acquire data only at constant water concentration in the mobile phase, or at a constant value of the ratio of the water partial pressure to the vapor pressure. In this latter case most of the effect of changing the temperature on the amount of water sorbed and on the average film thickness is cancelled. The dramatic variation of the relative retentions of l,Zdichloroethane, acetone and methyl ethyl ketone in Figure 7.17 illustrates the consequences of the phenomena just described and the potentialities offered to the analyst for the optimization of a separation. 5. Application to the Analysis of Aqueous Solutions

The most important field of application of this technique is obviously in the analysis of organic pollutants in water samples. Such samples are difficult to analyze due to a number of problems associated with the injection of a large amount of water in the chromatograph, when operating under classical conditions, i.e., with a very dry carrier gas. A very large injection is required for trace analysis. The migration of a large water band creates drastic but temporary changes in the properties of the support (especially the degree of activation of the support, whether a silica gel or a diatomaceous material), and hence in retention and resolution, alters the working conditions of the detector (i.e. changes the response factors), and makes quantitative analysis less accurate and less reliable. The conventional alternative,

Figure 7.18. Application of the use of steam in the camer gas to the analysis of water pollutants. Detection of 20 ppb of vinyl chloride in water. Sample sue: 200 pL. Column: 4 mm i.d., 2 m long. Spherosil 360 mz/g, particle size 100-200 pm. Column temperature: 128OC. Carrier gas, nitrogen (728) and steam (288), flow rate 3.35 L/hour. FID, hydrogen flow rate 4 L/hour, air flow rate 9 L/hour. Reproduced by permission of Journal of Chromatographk Science, 17, 677 (1979).

243

extraction with a solvent or with a non-polar adsorbent (Tenax, Amberlite, chemically bonded C18 silica, etc.), is cumbersome and introduces a whole new set of problems and sources of error. The injection of large amounts of water samples (20, 50, 100, 200 pL) results in the production of a large volume of mobile phase (25, 62, 125, 250 mL NTP, respectively), an effect which takes place with all solvents, but is especially important with water, due to its low molecular weight. This is a major perturbation for a column and a detector operating at 3 L/h or 50 mL/min. To avoid spurious detector signals and base-line drifts which might hide the peaks of trace compo-

1 7min

Figure 7.19. Detection limits of organic compounds in water samples. Column: 4 mm i.d., 2 m long. Spherosil32 m2/g, particle size 150-200 pm. Column temperature 160O C. Carrier gas, nitrogen (35%) and steam (65%), flow rate 3 L/hour. FID, hydrogen flow rate 4 L/hour, air flow rate 20 L/hour. Sample size 25 pL. (After Guillemin et al., ref. 59). Reproduced with permission of Journal of Chromarogruphy, 301, 11 (1984).

References on p. 244.

244

nents, or erratic detector response which might lead to major quantitation errors, the flow-rate controller on the inert carrier gas line is replaced by a pressure controller, operating at the pressure required for maintaining the desired flow rate through the column. A one-way valve, placed between the sampling port and the pressure controller, prevents back flow of steam with subsequent flooding of the upstream gas line. Thus, when the large water sample is injected and vaporized abruptly, giving rise to a strong pressure surge in the sampling port, the inert gas flow rate is reduced and the total flow rate through the detector is kept nearly constant. The migration of the large band of steam-enriched carrier gas does not seem to create serious enough changes in the retention pattern to result in significant errors on either the determination of the retention times (qualitative analysis) or the peak area (quantitative analysis). The chromatogram obtained for the analysis of a 200 pL sample of polluted water with a Spherosil column and a flame ionization detector is shown on Figure 7.18. The base line is quite acceptable at that level of sensitivity, permitting the detection of 20 ppb of vinyl chloride, thus demonstrating the validity of the method. Figure 7.19 shows another example of the detection of trace amounts of organic compounds in aqueous samples.

LITERATURE CITED (1) See Chapter 8, Open Tubular Columns. for details and references. (2) I. Halasz and E. Heine, in Advances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1967, Vol. 4, p. 207. (3) I. Halasz and C. Horvath, Anal. Chem., 36, 2226 (1964). (4) C.G. Scott, in Gas Chromatography 1962, M. Van Swaay Ed., Butterworths, London, UK, 1962, p. 36. (5) C. Vidal-Madjar and G. Guiochon, Separ. Sci., 2, 155 (1967). (6) C. Vidal-Madjar and G. Guiochon, Bull. Soc. Chim. Fr., 1096 (1966). (7) A.V. Kiselev, N.V. Kovaleva and Yu.S. Nikitin, J. Chromatogr., 58, 19 (1971). (8) A. Di Corcia and A. Liberti, in Aduances in Chromatography, J.C. Giddings, E. Grushka, J. Cazes and P.R. Brown Us., M. Dekker, New York, NY, 1976, Vol. 14, p. 305. (9) J.C. H e w e r . Reus. Modern Physics, 21, 322 (1949). (10) C.L. Guillemin, J. Chromntogr., 158, 21 (1978). (11) K.K. Unger, Porous Silica. Its Properties and Use as Support in Column Liquid Chromatography, Elsevier, Amsterdam, NL, 1979. (12) A.V. Kiselev and Ya.1. Yashin, Gas Adsorption Chromatography, Plenum Press, New York, NY, 1969. (13) H. Engelhardt, B. Dreyer and H.Schmidt, Chromatographiu, 16, 11 (1982). (14) L.S. Ettre, J. Chromatogr., 4, 166 (1960). (15) A.V. Kiselev, in Aduances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York,NY, 1967, Vol. 4, p. 113. (16) C.L. Guillemin, M. Le Page and A.J. De Vries, J. Chromatogr. Sci., 9 , 470 (1971). (17) L.R. Snyder, Principles of Adsorption Chromatography, M. Dekker, New York, NY, 1968. (18) J.C. Giddings, Anal. Chem., 34, 458 (1962). (19) J. Serpinet, PhD Thesis, Universite Claude Bernard, Lyon, France, 1974. (20) C.L. Guillemin, M. Deleuil, S. Cirendini and J. Vermont, Anal. Chem., 43, 2015 (1971). (21) C.L. Guillemin and F. Martinez, J. Chromatogr., 139, 259 (1977). (22) J.F.K. Huber, H.H. Lauer and H. Poppe, J . Chromatogr., 112, 377 (1975).

245 (23) G. Guiochon, in Column Chromatography, E. sz Kovats Ed., Sauerlander, Aarau, Switzerland, 1970, p. 250. (24) S. Cirendini, J. Vermont, J.C. Gressin and C.L. Guillemin, J. Chromatogr., 84, 21 (1973). (25) S.N. Lin, C.D. Pfaffenberger and E.C. Homing, J. Chromatogr., 104, 319 (1975). (26) A.L. German and E.C. Homing, J. Chromatogr. Sci., f l , 76 (1973). (27) I. Halasz and C. Horvath, Nature, 197, 71 (1963). (28) A.V. Kiselev, in Gas Chromatography 1964, A. Goldup Ed., Institute of Petroleum, London, UK, 1965, p. 238. (29) C. Vidal-Madjar and G. Guiochon, Bull. SOC.Chim. Fr., 3105 (1971). (30) C. Vidal-Madjar and G. Guiochon, in Separation and Purification Methods, E.S. Perry and C.J. Van Oss Eds., M. Dekker. New York, NY, 1973. Vol. 2, pp. 1-125. (31) A. Di Corcia and F. Bruner, Anal. Chem., 43, 1634 (1971). (32) A. Di Corcia, P. Ciccioli and F. Bruner, J. Chromarogr., 62, 128 (1971). (33) A. Di Corcia and F. Bruner, J. Chromatogr., 62, 462 (1971). (34) F. Bruner, A. Liberti and M. Possanzine, Anal. Chem., 44, 2070 (1972). (35) C. Vidal-Madjar, J. Ganansia and G. Guiochon, in Gas Chromatography 1970, R. Stock Ed., Institute of Petroleum, London, UK, 1971, p. 20. (36) C. Vidal-Madjar, S. Bekassy, M.F. Gonnord, P. Arpino and G. Guiochon, Anal. Chem., 49, 768 (1977). (37) P. Arpino, C. Vidal-Madjar, G. Guiochon and S . Bekassy, J. Chromatogr., 138, 173 (1973). (38) A. Di Corcia, Anal. Chem., 45, 492 (1973). (39) O.L. Hollis, Anal. Chem., 38, 309 (1966). (40) O.L. Hollis, J. Chromatogr. Sci., 11, 335 (1973). (41) F. Baumann and J.M. Gill, Aerograph Research Notes, 1966. (42) O.L. Hollis and W.V. Hayes, J . Gas Chromatogr., 4 , 235 (1966). (43) W.R. Supina and L.P. Rose, J. Chromarogr. Sci., 7, 192 (1969). (44) S.B. Dave, J . Chromatogr. Sci., 7, 389 (1969). (45) F.H. Pollard and C.J. Hardy, in Vapour Phase Chromatography 1958, D.H. Desty Ed., Butterworths, London, UK, 1957, p. 115. (46) Anon., Aerograph Research Notes, Wilkens Instruments and Research, Walnut Creek, CA, 1961. (47) Anon., Chem. Eng. News, 40, 50 (1962). (48) L.H. Phifer and H.K. Plummer, Anal. Chem., 38, 1652 (1966). (49) B.L. Karger and A. Hartkopf, Anal. Chem., 40, 215 (1968). (50) B.L. Karger, A. Hartkopf and H. Posmanter, J. Chromatogr. Sci., 7, 315 (1969). (51) A. Nonaka, Anal. Chem., 44, 271 (1972). (52) A. Nonaka, in Advances in Chromatography, J.C. Giddings, E. Grushka, R. Keller and J. Cazes Eds., M. Dekker, New York, NY, 1975, Vol. 12, p. 223. (53) C.L. Guillemin, F. Martinez and S. Thiault, J. Chromatogr. Sci., f 7 , 677 (1979). (54) W.R. Melander and C. Horvath, in High Performance Liquid Chromatography. Advances and Perspectives, C . Horvath Ed., Academic Press, New York, NY, 1980, p. 114. (55) L.R. Snyder and H. Poppe, J . Chromatogr., 184, 363 (1980). (56) H. Colin and G. Guiochon, J. Chromatogr., 126, 42 (1976). (57) Hr Colin and G. Guiochon, J . Chromatogr., 158, 183 (1978). (58) E. Hamon and C.L. Guillemin, unpublished data, 1986. (59) C.L. Guillemin, J.L. Millet and E. Hamon, J . Chromatogr., 301, 11 (1984). (60) B.L. Karger, R.C. Castells, P.A. Sewell and A. Hartkopf, J. Phys. Chem., 75, 3870 (1971) and J . Colloid Interface Sci., 35, 328 (1971).

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241

CHAPTER 8

METHODOLOGY Open Tubular Columns

TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Classification of Open Tubular Columns 1. Wall Coated Open Tubular Columns ( ............................... 2. Porous Layer Open Tubular Columns (PLOT) 3. Packed Capillary Columns (PC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Pr n Tubular Columns . . . . . 1. ...................................................... 2. ubing Used . . . . . . . a. Glass Tubings . . . . . . . . . . . . . . b. SilicaTubings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Surface Treatment of Glass Tubings a. Geometrical Modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

................... ................... 4. Whisker Growing 5. Other Treatments

251 252 253

259 260 260 261 262

.........

................................................

1. Leachng with HCl 2. Reaction with Polyg

.......................... ..........................

d. Surfactant Coating .......................................... e. Silicon Deposit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... 4. SilicaTubings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Coating Procedures for Wall Coated Open Tubular Columns . . . . . . . . . . . . . . . . . . . . . a. Dynamiccoating.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Static Coating . . . . . . . . . . . ...................... c. Immobilization of the Stationa ............................. 1. Free Radical Reactions . . . . . . . . . . . . . . . . . . .

................................... d. Preparation of Thick Layer Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . e. Wide Bore Open Tubular Columns ....................... 6. Coating Procedures for Porous Layer 0 a. Porous Layers of Adsorbents (PLOT .......................... b. Porous Layer of Coated Support (SC .......................... 7. Preparation of Packed Capillary Columns .................. 1. 2. 3. 4.

248

Analytical Test . . . . . . . . . . . . . . . . Permeability . . . . . Height Equivalent to Phase Ratio . . . . . .

264 265 265 266 266

267 268 211 212 215 275 211 278 219 219

............ ...............................

280 281

.................... ...........................

284

248

.

5. Separation Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Otherparameters .................................................... IV. Open Tubular Column Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Injection Techniques on Open Tubular Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. SplittingSysterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Split-Splitless Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. TbeRosInjector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. On-Column Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . e. The Programmed Temperature Vaporizers (prv) . . . . . . . . . . . . . . . . . . . . . . . . . . f. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Column Switching Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Guidelines for the Use of Open Tubular Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Improving Peak Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Reducing Analysis Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Thickness of the Stationary Phase Layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Selection of the Carrier Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. SamplingandSampleSi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Detector Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GlossaryofTerms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . .

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284 285 286 286 288 291 293 295 298 300 300 304 305 305 305 306 306 307 308 310 311

INTRODUCTION Open tubular columns (OTC) are the most powerful separation tool available to the analyst. As will be illustrated later in this Chapter, they permit the achievement of the resolution of compounds which have a relative retention very close to 1.0, in a reasonably short time. The relationship between analysis time, resolution and the difficulty of the separation contemplated has been derived in Chapter 4, where a discussion regarding the comparison between the performance of conventional packed colums and of open tubular columns can be found. At this stage it is important to underline the two concepts discussed together in this Chapter, which are often not clearly distinguished. The confusion is illustrated by the loose use of the two names, “open tubular columns” and “capillary” columns, often considered to be synonymous. Truly, in principle, these two names do not cover the same thing although, in practice, the large bulk of columns used in analytical applications deserve both names. Capillary columns are made with a capillary tube, i.e., have a very small inner diameter. This diameter is usually between 0.1 and 0.3 mm, although columns as narrow as 30 pm or as wide as 1 mm have been used for the solution of special problems. A capillary column can be empty or packed. A packed capillary column is merely a conventional packed column made with capillary tubing. Because of the small inner diameter, however, there are some interesting properties, which are discussed in Sections 1.3 and 11.7 below. Traditionally, capillary columns are used empty, their inner wall being covered with a layer of stationary phase. An open tubular column is an empty tube, whose center is available for an almost unrestricted flow of mobile phase, and whose

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wall can be covered with a layer of stationary phase. It is the emptiness of the tube which gives the column the important properties and the major advantages described first by Golay (1,2). At least in theory there is no restriction on the diameter of the tube used to make the column. A proposal has been made to use the Maine-Texas pipeline as an OTC (3); although this is not very attractive from an economical point of view, the column would have the same kind of properties as other OTC‘s, when due allowance is made for the different size. The idea of “capillary columns” dates back to 1956, when A.J.P. Martin suggested: “we shall have columns only two tenths of a millimeter in diameter, and these will carry, I believe, advantages of their own that I have no time to go into” (4). From the context, there is no doubt that he was referring to some form of packed capillary column (PCC) or micropacked column. The invention of the open tubular column occurred in the same year (1957), when Golay began to analyze the detail of the chromatographic process in a packed column. He remarked that a packed column (PC) was, from the fluid dynamic point of view, like a bundle of interconnecting squeezed tubes. He then wondered about the properties of a single, cylindrical tube, through which the stream of mobile phase could flow unhindered (1). A complete, detailed analysis of the chromatographic process in an OTC led him to the derivation of a plate height equation wluch is rigorous, at the difference of the similar equations proposed for packed columns (5). It results directly from the integration of the mass balance equation, properly taking the kinetics of mass transfer into account (see Chapter 4, Sections IV, V and VI). OTC‘s were thus born from theory (1). Reducing them to practice was a difficult exercise. Initial attempts resulted in strongly tailing peaks, due to the too large dead volume of the thermal conductivity detector used (2). Improvements to the TCD permitted the recording of chromatograms showing a dramatic increase in performance compared to Pc‘s, but still quite inferior to those predicted by theory (See Figures 8.1 and 8.2). The final solution appeared soon thereafter, with the development of the flame ionization detector, whose small dead volume, short time constant and high sensitivity is ideally suited to the characteristics of OTC’s which accept. only very small sample sizes and deliver very narrow bands (6). A long series of papers, too numerous to be exhaustively listed, let alone discussed separately, demonstrated the validity of the concept and the amazing separation power of open tubular columns (7-21). A short time later, chapters and whole books dedicated to the discussion of the technical problems related to the use of OTC’s in chromatographic analysis began to appear (22-31). In spite of the conviction of the experts regarding the attractive character of OTC’s for the solution of most analytical problems amenable to GC, it took almost 20 years before these columns began to enjoy their deserved popularity. This is due in part to the very serious technological difficulties which had to be solved to bring them to practice, requiring skilful manipulations, often beyond the capability of most analysts. The fundamental reason, however, was the rigid position adopted by the owner of the rights of the Golay patent (32), which essentially froze development work by third parties until the end of the protection period, in 1977, which was the start of an impressive boom (33). Technological advances, such as the deactivation of the wall References on p. 31 1.

250

+-

I8.8min Figure 8.1. First separation performed on an open tubular column. Golay (2). Column: 150 ft long, 0.25 mm id.. Temperature 40O C. Carrier gas: helium, 0.96 mL/min. Inlet pressure: 20 psi. Stationary phase: didecyl phthalate. Sample: aliphatic hydrocarbons (hexane isomers). Reprinted from Gas Chromatography 1958, D.H. Desty Ed., Butterworths, London, UK, 1958.

surface, the manufacturing of special silica tubings, the liquid phase immobilization, the split-splitless injection, the aluminum clad silica tubings, etc., fueled an expansion facilitated by the development of a new generation of gas chromatographs designed to fulfill the special requirements of OTC's. Despite the definite advantages of OTC's in separation power and analysis time, there remain some practical difficulties in the sample injection, due to the two drastic requirements of OTC's for a very small sample size and a very small injector

6ol 50

20 10

SEPARATION

+51.8rnin -+iH P-XYLENEq

- +4.8min--I

ETHYLBENZENE

-

M , P - X Y L E N E = 80%

M-XYLENE

n 0-XYLENE

START

0

4

1

I

Figure 8.2. Separation of aromatic hydrocarbons. Golay (2). Same column as for Figure 8.1. Temperature: 70 C. Carrier gas: helium, 0.48 mL/min. Inlet pressure: 10 psi. Sample: xylene isomers and ethylbenzene. Reprinted from Gas Chromatography 1958, D.H. Desty Ed., Butterworths, London, UK, 1958.

25 1

volume. The technical solutions proposed are not entirely satisfactory and some doubts have been cast on the validity of quantitative results supplied by splitter injectors. The precision obtained with a careful use of packed columns has been consistently better than the one achieved with OTC‘s. Recent advances in the art of injecting samples into OTC‘s, together with the use of macrocapillary tubes (i.d. cu 0.5 mm) now permit the achievement of a comparable precision. Thus it is probable that OTC’s will soon invade the last field held securely by packed columns, industrial routine control analysis and on-line analysis. Finally, we point out that the solution to the problems of the selection of the stationary phase, the temperature and the carrier gas flow velocity are obtained in much the same way as for conventional packed columns. These problems have been discussed in Chapter 6, Sections 1.2, 11.2 and 11.3, respectively. The main difference is that in most cases it will be easier to find out conditions permitting the achievement of the required analysis in a reasonable time. Unless very complex mixtures are analyzed, the optimum experimental conditions would result in analysis times whch are too short to be practical. A better compromise is achieved by accepting a resolution larger than would be necessary, thus permitting an improvement in the precision. The preparation and evaluation of open tubular columns are the main topics of the present chapter.

I. CLASSIFICATION OF OPEN TUBULAR COLUMNS The original concept of an open tubular column (1)has led to the development of a variety of column designs, involving all kinds of physical and chemical modifications of the column wall (34). Since the column inner diameter must be small for the solution of most analytical problems, the development of OTC‘s and of the instrumentation required for their use has been part of the historical trend towards miniaturization of analytical tools. The two approaches have been closely mixed at times. The most important classes of columns considered at present are the wall coated open tubular columns, the porous layer open tubular columns and the packed capillary columns (See Figure 6.15).

1. Wall Coated Open Tubular Columns (WCOT) These are the classical open tubular columns, sometimes referred to under that name (COT), or the name of Golay columns. Their inner diameter is typically 0.2 to 0.5 mm. When the tubing inner diameter is less than 0.2 mm the column is called “small bore”. As soon as the market for them picks up, somebody will call them “microbore”. Columns as narrow as 30 to 50 pm have been used for successful separations (35). When the inner diameter is larger than 0.5 mm, they are called “wide bore”, “wide bore capillary” (36) or even “megabore columns”. They vary in length from about 30 cm (35) to 1 mile (37). Columns having well in excess of one million theoretical plates have been made and studied (38). References on p. 311.

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The inner wall has been submitted to various kind of physicochemical or chemical treatment (see Section 11.3), in order to reduce the strength and selectivity of the adsorption on this wall as much as possible and to promote the adhesion of the film of stationary phase, two requirements which are somewhat contradictory. 2. Porous Layer Open Tubular Columns (PLOT) One of the drawbacks of conventional open tubular columns is the low phase ratio which can be achieved while obtaining a high efficiency (small value of the HETP). The thickness of the liquid film coated on the inside wall of the column must be thin, a few tenths of a micrometer at most, otherwise the resistance to mass transfer in the liquid phase, i.e., the time required for diffusion through the film, will be too large and the efficiency low. In the case of conventional packed columns, the amount of liquid phase coated on the support may be large without resulting in similar difficulties because the support is porous, has a significant specific surface area (a few m2 per gram) and the liquid film remains thin even at rather large phase ratios. Hence the idea of coating the inner wall of an empty tubing with a thin layer of fine support powder, impregnated with the suitable liquid phase (39,40). Such columns are called porous layer open tubular columns (PLOT) or support coated open tubular columns (SCOT). The center of the column remains free, although close examination of such columns reveals that the support layer caves in, in places. The layer thickness is usually a few micrometers, but thicker layers have been tried. Phase ratios comparable to those of lightly loaded conventional packed columns may easily be obtained, thus permitting the analysis of low boiling compounds, the retention volume of which would be too small on a WCOT to resolve them. In order to combine the advantages of open tubular columns and those resulting from the extremely large selectivity afforded by adsorption, the same technology has been applied to the preparation of columns where a layer of fine adsorbent powder is coated along the inner wall of the column (41,42). The inner diameter of the tubing used for the preparation of PLOT or SCOT columns tends to be larger than that of WCOT columns.

3. Packed Capillary Columns (PC) It is possible to pack a narrow tube but it is easier to draw a narrow glass tube from a larger one, previously loosely packed with the proper support (43). When the packing density is lower than for conventional packed columns and the inner diameter of the tubing is not more than 6 to 8 times the average particle diameter of the packing material used, the column has properties which are intermediate between those of a PLOT column and a conventional packed column (CP). The permeability is larger, the efficiency better than for a CP column and the phase ratio larger than for a PLOT or SCOT column. PC columns have been studied by Halasz (43,44) and others (45). They have been largely ignored, because their advantages over classical open tubular columns are

253

quite limited, except in the case of gas-solid chromatography. PC’s made with alumina or silica gel have extremely attractive properties for the separation of very complex mixtures of light hydrocarbons (46). Pc‘s should not be mistaken for micropacked columns, which are 0.5 to 1 mm i.d. packed columns, packed with fine, but otherwise conventional, coated supports. They are regular, miniaturized packed columns, and nothing in this chapter applies to them, except that which deals with the careful use of instruments with low dead volumes.

11. PREPARATION OF OPEN TUBULAR COLUMNS

The explosive development of open tubular columns which has led them from a research curiosity in the middle seventies to a dominant position in the early eighties, has had profound effects on the technique itself. It is certainly possible to prepare excellent columns in the laboratory. Some dedicated equipment is required, as well as much time and very careful attention. One of the drawbacks of preparing your own columns is that very skilful, hence expensive, personnel is required for a task which is rarely original anymore. The numerous details which must be carefully attended to make it impossible to entrust the preparation of good OTC’s to technicians, unless they are specialized and closely supervised in the workshops of column manufacturers. Only those who have special requirements, because of the nature of their research or of the samples they want to analyze, should now devote time to the preparation of WCOT’s. Research on molecular interactions and retention processes, research involving the synthesis of new stationary phases or development of new analytical procedures for very complex nixtures of polar compounds certainly requires the ability to prepare one own’s columns. Routine applications do not. Unless one is very skilled and willing to invest the time and the equipment money, the columns prepared will probably not compare favorably to those which can be purchased from some reputable manufacturers. It is nevertheless worthwhile reviewing the present state of the art of column preparation and some of the major advances which have laid the ground for the modern columns. 1. Problems

The first analytical application of high efficiency OTC‘s was in the analysis of light hydrocarbons and gasoline (8-12,38). Spectacular results were rather easily achieved, generating very optimistic hopes regarding the application of the new method to the analysis of all kinds of complex samples. Soon afterwards, when more polar petrochemicals were studied, it turned out that the results were much less impressive than expected. Broad bands and tailing peaks were obtained. Compounds were lost, not eluted, unless the column was grossly overloaded. Columns were not stable for a long time. It was then realized that the preparation of OTC’s References on p. 31 1.

254

for the analysis of polar compounds was going to be a task of major complexity. It took almost 20 years to reach the present state when columns with performances close to those predicted by the theory can be prepared with a large majority of the potentially interesting phases to be used for the analysis of just about all kinds of volatile samples. Although the same column could not be used to achieve an excellent analysis of free acids and free amines, for example, the versatility of these columns is amazing. The success of this considerable endeavour is due to the accumulation of contributions by many analysts and chemists too numerous to be cited here. It seems appropriate, however, to acknowledge the Grob family for its pioneering work (48). In order to achieve the column performance predicted by the Golay theory we must be able to produce columns which are as similar as possible to the model on which the Golay equation is based. First, the column must be a cylindrical straight tube, In practice, we must use coiled tubes, but it can be shown that with a ratio of the coil to the tube diameter exceeding several hundred (e.g., column i.d. 0.25 mm, coil radius 10 cm, ratio 400), the column performs like a straight tube (47). This ensures that the first two terms of the Golay equation correctly represent the contributions of the axial molecular diffusion and of the resistance to mass transfer in the gas phase (see Chapter 4, Sections 111 and IV). Secondly, the stationary liquid phase must constitute an homogeneous thin film on the inner surface of the column wall. Then the resistance to mass transfer in the stationary phase will be small (because the film is thin) and its contribution to the HETP will be properly predicted by the third term of the Golay equation (because the liquid makes a film of constant thickness). The essential problems to be solved are thus the preparation of a column wall which is well wetted by the stationary liquid phase (contact angle zero) and the coating of this wall by a stable liquid film. Furthermore, the wall should not carry any active adsorption site, the presence of which would result either in irreversible adsorption, hence losses, of the most polar analytes, or in band broadening and tailing of these peaks, in somewhat more favorable cases. Obviously the wall, too, should not carry sites having any catalytic activity which might enhance the decomposition of some analytes, thus affecting the quantitative results and possibly creating peaks which do not correspond to components of the original sample. The specific surface area of the inner wall of an OTC is very small. A typical column has an inner diameter of 0.25 mm. The geometrical specific surface area is 0.008 m2/mL, which is extremely small. A glass or silica surface is very smooth and the real surface area is probably not larger than 0.02 m2/mL. Since the impurities of the tubing material tend to concentrate on the surface, its chemical composition may be very different from that of the bulk, the difference being still more important than for large surface area adsorbents. The preparation of a “good” inner wall surface is not sufficient. The liquid phase film must wet it and be stable. Because the inner diameter of the tubing cannot be expected to be constant, but fluctuates by at least a fraction of 1%along the column, the film, supposed to be homogeneous initially, is not stable, but will slowly accumulate in the areas where the tubing is narrower (49). To prevent this effect,

255

Solid

Figure 8.3. Surface tension and interfacial tension between a liquid droplet and a solid surface. 8 , contact

angle.

Grob and Grob have suggested the use of polymer greases rather than polymer fluids (50). In the early days it was frequent to see columns, which had excellent performance when freshly prepared, degrade rapidly during prolonged heating, hence the popularity of temperature programming analyses which do not call for the same long exposure to high temperatures as isothermal analysis. The formation of a continuous film on the column wall is possible only if the liquid phase wets it. Spreading of a liquid on a solid surface occurs if the contact angle is zero. Otherwise the liquid tends to form scattered droplets on the surface. The contact angle of the liquid depends on the surface free energy of the solid and the liquid and can, in theory, be derived from the surface tensions at the gas-liquid, liquid-solid and solid-gas interfaces, but these tensions are generally not known (see Figure 8.3). Theoretical and experimental work due to Shafrin and Zisman (51) has shown that a liquid will wet a solid surface if the surface tension of the liquid is less than a certain value, characteristic of the solid surface and called its critical tension. Thus it is, in principle, possible to prepare an efficient, stable OTC with all stationary phases which have a surface tension lower than the critical tension of the material used for the tubing (52). Data are given in Table 8.1. Caution is required in the application of these data, as the critical surface tension of a polymer depends on the mechanical stress applied to the product during extrusion of the material when manufacturing the tubing. The data in Table 8.1 explain the origin of the difficulties encountered in trying to prepare glass capillary columns with most polar liquid phases. Several authors have also stressed the importance of the wettability of the column wall by the liquid phase (5435). Accordingly, the role of the surface treatment of the tubing is to: - increase the wettability of the surface by the stationary phase, to permit the formation of a thin film (instead of a network of droplets, through which mass transfer by diffusion will be much slower), - eliminate, reduce or modify the active sites on the column wall, to prevent selective adsorption and catalysis. Gradual realization that the first objective was doomed to failure, although this had been predicted clearly as early as 1962 (52), led to its replacement by a more realistic, and maybe more effective one: References on p. 311.

256

TABLE 8.1 Surface Tension of Some Solid Materials and Some Stationary Phases (52) Solid Surface

Critical Surface Tension (dyne/cm)

Stainless Steel Aluminum Copper Pyrex Glass Polytetrafluoroethylene Polyethylene Polyethyleneglycoltereph thalate Polyamide 6-6

24.0 f 0.5 27.4 f 0.5 27.0 f 0.5 28.0 f 0.5 19*1 33f2 4Qf2 41*2

Liquid Phases ov-101 Squalane Phenyl silicone oil DC-704 Carbowax 400

Tris(cyanoethoxy)propane

Surface Tension (dyne/cm) 19.5 29.7 36.5 46.7 52.4

Contact Angle 0.0 5.3 10.6 20.0 32.0

Critical Surface Tension after Zisman (53). Reprinted with permission from Nature, 196, 63 (1962). - immobilize the film of stationary phase on the wall surface by chemical bonding and weak cross-linking. We now survey the methods tried and used to perform these tasks.

2. Nature of the Tubing Used

Criteria for the selection of the material used for the small bore tubings necessary to the preparation of OTC's have been reviewed by Ettre (56). The most important ones are the following: - Possibility to obtain long tubings (up to at least 50 m), in various diameters (at least 0.2 to 0.5 mm). - For a given piece of tubing the inner diameter should be constant over the entire length. There seems to be a feeling that 1%is satisfactory, but no hard data to prove that 2% would not be good enough nor that 0.5% would result in an excellent column. With immobilized stationary phase films this constraint could be relaxed somewhat, although the film should be stable at least during the time required for the bonding reaction to proceed. -The inner tubing surface should be uniform and devoid of fine cracks or micropores, traditionally held to be responsible for selective adsorption of polar compounds, There should be no or very few pores, unless the tubing is used to make a PLOT column. Then the pores should be rather large and homogeneous in their size distribution. The surface does not have to be very smooth, however. Some surface roughness is favorable to anchoring the film and preventing it slipping to places where the inner diameter is minimum.

251

- The tubing material should present no chemical reactivity with any component of the sample. It should not give rise to selective adsorption which could result in either quasi-irreversible adsorption (i.e., the retention time on the liquid phase is short compared to the desorption kinetics, the area measured for the peak, as detected, does not correspond to the amount of material present in the sample) or peak tailing. The material should not be able to catalyze reactions of the components of the sample, such as dehydration, isomerization or hydrogenation, when the carrier gas is hydrogen (Schomburg has shown that this does not take place in GC-MS coupling, when a platinum tubing connects the column to the MS source, hydrogen is the carrier gas and various alkenes are analyzed.) - The tubing must be wetted by the stationary phase and allow the formation of a stable, thin liquid film. - The tubing should be mechanically strong enough to be handled, coiled, etc., and should not be too brittle. A large variety of materials, some conventional such as polymers, copper, stainles steel, glass, and other more esoteric, such as gold, have been tried. Stainless steel and copper were used in the very first attempts (6-14,17-19,38). They have now been abandoned because their inner surface is too irregular, presents fine cracks and oxide patches favoring strong analyte adsorption or even catalytic reactions. Some brilliant results were obtained with various polymers, especially with nylon catheters (57). Polymeric tubings were rapidly abandoned, however, due to their lack of regularity over long sections and the poor thermal behavior at even moderate temperatures. In the late 'sixties and the 'seventies, glass became practically the only material to be used. Silica became very popular in the early 'eighties and now only silica and, to a lesser extent glass, are in widespread use. Although they do not have all the properties demanded, their wall surface can be modified to a sufficient degree in order to achieve a compromise which is satisfactory in most cases. a. Glass Tubings

The ability to draw very long glass tubes having a small inner diameter was recognized very early by Desty (58). These tubes meet the requirements discussed above, Section 11.1, except for the surface inertness and the mechanical strength. Glass tubes are brittle and difficult to handle. Their inner surface is not inert. It is covered with various metal ions, depending on the nature of the glass and its impurities. The surface concentration of some ions may be much larger than their bulk concentration. Also present are silanol and siloxane groups, aluminate and borate ions, AlOH groups, in various concentrations depending on the nature of the glass as well as on the previous history of the particular tube used. Various treatments, before drawing, during the drawing process itself (such as filling the original, large tube with NH,), and after drawing, will be designed to change the surface composition and decrease the concentration of strongly acidic or basic sites. The difficulties encountered in carrying out these treatments as well as the fragility of the glass tubings have led to their progressive replacement by silica tubings which do not suffer these drawbacks. References on p. 311.

258

Figure 8.4. Photograph of a glass drawing machine built according to drawings by Desty et al. (58).

I

~

~

_

_

Figure 8.5. Schematic of the glass drawing machine (58). a.b Feeding rollers, c,d rubber traction rollers, e, glass tube support, f. low voltage furnace, g, glass tube, h. glass capillary tube, j. coiled stainless fube, k. running stack stem.

~

___

~

_

_ ____

259

Figure 8.4 shows a photograph of the first glass tube drawing machine built by Desty (58). Several other machines have been described, very similar to the one on Figure 8.4. The principle of a drawing machine is illustrated on Figure 8.5. The original glass tube (ca 2 mm i.d.) is slowly pushed into a furnace by a pair of rubber rollers. The furnace heats the tube to about 700°C and the glass softens. Another pair of rollers, turning about 50 times faster, pulls the tube out of the furnace. Since the glass mass is conserved, in steady state conditions the inner and outer diameters of the final tube are about 7 times smaller than those of the tube fed to the machine and the length of tubing prepared is 50 times larger than the length of the original tube used. The rollers push the narrow tube into a stainless steel tube coiled over a 90-degree angle, at the proper coil diameter, and heated by a low voltage, high intensity electrical current to about 600 " C. By adjusting the ratio of the rotation speeds of the two rollers and the inner diameter of the starting tube, it is possible to draw capillary tubes of any diameter from 0.05 to 0.5 mm. The proper adjustment of the temperatures of the drawing furnace and the coiling tube needs some experience, but the really difficult part is to weld another starting tube to the first one when very long columns are necessary. The diameter of the final tube is reasonably constant, and in excellent agreement with the value calculated from the rollers velocity ratio and the diameter of the starting tube (59). All kinds of glasses, in a variety of diameters have been drawn in our research groups, to prepare WCOT, PLOT and SCOT columns with no major problem. b. Silica Tubings

The use of silica tubings was first developed and advocated by Dandeneau (60,61) and by Lipsky (62). Although the silica drawing machines are similar in principle to the glass drawing machines, they are much more complex and expensive. Silica melts at a much higher temperature and in a much narrower temperature range than such glasses as Pyrex, which makes the machme much more difficult to drive. Furthermore, the silica tube must be externally coated with a thin layer of polyimide or other material in order to prevent the formation of surface cracks, making t h s material very brittle, whereas, once treated, it is exceptionally strong. These operations need professional attention. When the tube is drawn, it is so resilient that it not necessary to heat it again to coil it. It can be coiled at room temperature on a spool, more easily than a thin piece of copper wire. The external coating is heated in air, by contrast with the inside wall coating, which is heated in an atmosphere containing a very small concentration of oxygen. In spite of the exceptionally good thermal stability of polyimides in these conditions, the organic coating limits the upper temperature at which a silica column may be used to about 350°C.This is, paradoxically, 250°C lower than the temperature at whch a glass open tubular column has been used (42). There are stationary phases of polymeric origin which can stand temperatures as high as 400 to 450 " C. Recently Lipsky has suggested the use of aluminum clad columns, which are as References on p. 31 1 .

260

strong as regular polyimide coated silica tubing, somewhat stiffer, but can stand a temperature up to ca 600 O C (63). Silica capillary tubes are available from several vendors, in a large range of inner diameters. They can be used to prepare all kinds of GC columns, but it is better to let the specialists draw the tubing. A large variety of chemical reactions can be very easily performed inside the columns, permitting the analyst to experiment with surface deactivation, surface tension modification, chemical bonding and cross-linking as described in the following sections. 3. Surface Treatment of Glass Tubings The inner surface of a freshly drawn glass tube is not suitable for the preparation of a good OTC. It is too smooth, too dehydrated and too active. A series of chemical treatments must be applied to correct this situation: - A first treatment will increase the roughness of the surface, either by coating microparticles of an inert material or by corrosion of the surface. Some procedures even result in a porous layer, up to 1 pm thick or more. The main aim of this stage, however, is to create a rough surface to which the thin film of stationary phase can anchor, or on which it can spread into a network of tiny droplets with an average diameter not exceeding 1 to 2 pm. A low resistance to mass transfer in the mobile phase is thus obtained. - The second type of chemical treatments aims at fully hydrating the silica surface, to lower its surface energy and make it much more homogeneous. At the same time the metal cations which are on the glass surface are leached, in an attempt to generate an almost pure highly hydrated silica surface. - The third and last treatment deactivates the surface and eliminates active adsorption sites, by reaction with the surface silanols prepared during the second stage treatment. These three successive stages, as well as the main alternative available at each stage, are illustrated in Figure 8.6. It appears to be difficult to classify many of these treatments into well defined categories, such as geometrical, physical, physico-chemical and chemical treatments, as suggested by Grob (48). As pointed out by Verzele (34), many treatments have a complex effect and, depending on the exact experimental conditions can have a mixed effect or reveal a variety of changes of the glass surface which belong to all the classes listed above. Accordingly, the following classification has some fuzzy border lines, and this should be kept in mind in order to avoid merely semantic discussions. a. Geometrical Modifications

The main aim of these treatments is an increase of the surface area of the inner tube wall, in order to improve the stability of the film of stationary phase and permit an easier spreading of this phase during coating. Most of these treatments involve the formation of a network of tiny crystals on the glass surface, which helps to anchor the film by the simple play of surface

261 G L A S S TUBING

c

ETCHING

-*

LEACHING

(activation)

*

DEACTIVATION

COATING

A

0

Figure 8.6. Schematic of the effects on the wall surface of the various treatments performed: - Etching: A, Gaseous HCl, NaCl or BaC03. B, Pyrolysis of a fluoro ester or ammonium fluoride. C, HF or caustic soda. - Leaching: Solution of HCl. - Deactivation: Silanization or treatment with Carbowax 20M. - Coating: with stationary phase. Static or dynamic procedure.

tension forces. This cannot occur without also modifying the surface energy of the wall and its chemical composition, however.

I . Etching with HCl Tesarik and Novotny (64) and Alexander and Rutten (65) have proposed a static treatment by gaseous HCI. The gas reacts with the sodium ions on the surface of the glass to form a layer of tiny crystals embedded in this surface. Silanol groups and water are also formed during the process. Several attractive procedures have been described (66-68). Satisfactory coatings have been obtained with polar phases which are difficult to coat because of their high surface tension (69). The wettability of the wall is improved, or rather the stability of the liquid phase coating, whether it is a film or a network of fine droplets. The useful column lifetime and its efficiency are much improved. Efficiencies up to 2,000 plates per meter for 0.25 mm i d . columns have been reported, corresponding to reduced plate heights of 2 or to coating efficiencies of about 40%. References on p. 311.

262

2. Deposit of NaCI Since the formation of a wall deposit of sodium chloride appears to be such a good solution, it might be better to make it directly, without relying on the availability of sodium ions on the glass surface. Diffusion of sodium ions from the glass bulk appears to be necessary for the formation of the amount of NaCl observed on the wall of columns treated by gaseous HC1, and this may explain the high temperature and long reaction times required, as well as the variability in performance reported. Watanabe and Tomita (70,71) have reported excellent results, similar to those obtained with the gaseous HC1 treatment, by coating the column wall with sodium chloride. Other procedures have been described (72-75). Excellent columns have been obtained, with reported efficiencies up to 3,400 plates per meter for 0.25 mm i.d. columns. This corresponds to reduced plate heights of about 1.2 and coating efficiencies of about 80%. The hygroscopicity of the sodium chloride remains the major drawback of the method. It compells the use of very dry reagents during the following steps of the column preparation, of a very dry carrier gas and of dry solvents and samples during the whole course of the analytical work, thus drastically reducing the flexibility of chromatographic analysis and the useful life of the columns prepared in this way. 3. Deposit of BaCO, Since most of the difficulties encountered in the use of NaCl coated capillary columns are ascribed to the hygroscopicity of this salt, it was natural to try other salts that would be stable in the presence of water. Grob et al. suggested the deposit of a layer of barium carbonate crystals (76) and described a successful procedure (77,78) and excellent results (79). The main advantages of this procedure are as follows: - The column efficiency is markedly improved. - It is easy to carry out and gives successful results, even when applied by unskilled people. - The results are highly reproducible. - The results are independent of the nature and quality of the glass tube used. - The thermal stability of the stationary phases used is markedly enhanced, due to a much decreased catalytic activity of the surface. - The procedure can also be applied to smooth or etched surfaces. - The properties of the column wall surface obtained are insensitive to water exposure following preparation of the barium carbonate crystal layer. - The procedure is compatible with just about any prior or subsequent treatment of the wall surface. Despite these impressive qualities, the procedure has met with scant popularity because, although it is robust, it is also lengthy and tedious, especially if it has to be repeated three times to achieve excellent surface quality (see Figure 8.7). 4. Whisker Growing

In an attempt to duplicate a chemical treatment described by Tesarik and

263

Figure 8.7. Results of an activity test performed on a capillary column treated to grow whiskers and deactivated with barium carbonate. (After Schieke et al., ref. 80). Injection of n-butanol. a, after a single barium carbonate treatment. b, after the procedure is repeated three times. Reprinted with permission of Journal of Chromatography, 112, 97 (1975).

Figure 8.8. Photograph made with a scanning electron microscope of an open tubular column treated to grow whiskers on the surface. (After Schieke and Pretorius, ref. 82). Reprinted with permission of Journal of Chromatography, 132, 223 (1977).

References on p. 311.

264

Novotny (64), Pretorius observed the formation of very fine needles or whiskers of silica in the glass tube (80). The procedure involves filling the tube with nitrogen methyl ether, sealing the column at both saturated with 1,1,2-trifluoro-2-chloroethyl ends and heating at 400 O C. HF is formed and attacks the glass surface, giving SiF,, which rapidly oxidizes and gives fine silica needles (see Figure 8.8). the carbon deposit formed during the pyrolysis of the haloether is eliminated by heating at 450 O C under a stream of oxygen. Further publications refined the procedure (67,8143) and described variants (84-86). According to Sandra et al. (87), the advantages of this procedure are as follows: - The whiskers greatly facilitate the coating of any stationary phase. There is no formation of liquid phase pool and the columns are very stable. - The large increase in the wall surface amounts to the formation of a layer of inert support and permits a significant increase in the stationary phase loading. This, in turn, allows the use of rather large amounts of samples. - The thermal stability of the stationary phase is improved. - The preparation of the column is not difficult. There is no critical step and the procedure is robust. - Columns are easily regenerated by heating to 45OOC under a stream of air, to bum out the stationary phase, and then recoating. Unfortunately, the drawbacks are not minor. For instance: - The whiskers generate a very active silica surface, which has to be very carefully deactivated. This treatment may be more difficult than the growing of whiskers (see Figure 8.7). - The excessive roughness due to the whisker layer results in a significant decrease of the column efficiency about 20%. - The carbon deposit is difficult to eliminate completely. - The column preparation is very long and tedious.

5. Other Treatments A number of different etching treatments have been suggested, described or studied. It is impossible to mention all of them. It is not without some measure or arbitrariness that we quote the following. HF. The etching of the glass by hydrofluoric acid was first proposed by Tesarik and Novotny (64). The process was improved by Onuska and Comba (88), by Schieke and Pretorius (79,81) and by Schomburg et al. (89-91). This study eventually led these last two groups of authors to the development of the whisker procedure. NH,OH. Mohnke and Saffert (92) have prepared a porous silica layer on the wall surface of a glass tube by filling the column with a 17%NH,OH solution, sealing at both ends and treating at 17OOC for seventy hours. According to Traitler and Prevot (93), this treatment leads to a very uniform surface, well suited for deactivation by silanization. NuOH. Liberti et al. (94) and Bruner and Cartoni (95) obtained similarly a PLOT column by treating the glass tube with a 10%solution of NaOH at 100°C for nine hours.

265

b. Chemical Modifications

The aim of these treatments is to prepare an homogeneous surface with low, uniform adsorption energy, which will coat with the film of stationary phase but will not give strong adsorption of polar solutes, resulting in tailing of their bands, or in extreme cases in the lack of an elution peak for some components of the mixture analyzed. These procedures combine a first leaching treatment to fully hydrolyze the silica surface exposed during the previous treatments with a chemical reaction, similar to the one described for the preparation of conventional supports. 1. Leaching with HCI

This leaching has an aim which is quite different from the one of the physical treatment with gaseous HCl. It is carried out with HCl solutions. The goal is both: - to open as many as possible siloxane bridges (Si-0-Si) on the silica surface and turn them into vicinal silanol groups (Si-OH), in order to obtain a surface of highly uniform energy, similar to that of hydroxylated silica. This both decreases the density of active sites on the surface and renders it easier to further deactivate by chemical reaction. - to eliminate the metal cations which are on the glass surface and may be responsible for the formation of active adsorption sites or catalytic centers which may promote either reactions of sensitive sample components or thermal decomposition of the stationary phase (96). Several procedures have been described (96-98). 2. Reaction with Polyglycols The deactivation of the column wall with Carbowax 20M, which is the most popular of these treatments, is not specific to OTC's. It was developed originally for the deactivation of conventional supports by Aue et al. (99,100) and Guillemin et al. (101) (see Chapter 7, Section I.6.c). Cronin (102) has applied this procedure to capillary columns. The procedure has been found to give a very thorough deactivation of the wall surface by Blomberg (103,104) and by Dandeneau and Zerenner (105), for all kinds of glasses. A similar procedure was described by Ives and Giuffrida (106) and modified by Franken et al. (107,108). Variants have been described by Verzele (34), Grob and Grob (76,109) and Novotny et al. (110). c. Silanization Procedures

Silanization is the most widely used procedure for the deactivation of chromatographic supports or column walls. The reaction replaces a vast majority of the silanol groups on the surface by Si-0-Si(CH,), groups which are non-polar and shield an area around them. It destroys the most active adsorption sites. Silanization was first applied to capillary columns by Novotny and Tesarik (111) and Novotny and Zlatkis (112). These authors recommend the following procedure: References on p. 311.

266

- In the case of a non-polar stationary phase or a weakly polar one (e.g. poly(methylphenylsiloxane)), treatment with phenyltrichlorosilane, - In the case of a polar stationary phase, treatment with allyltrichlorosilane. At present, monochlorodimethylsilanesare preferred to trichlorosilanes, although they are less reactive, more difficult to prepare and more expensive. But only one of the chlorine atoms may react in practice with a silanol, and only a monochlorosilane may result in a complete deactivation of the silica surface. Mixtures of hexamethyldisilazane and diphenyltetramethyldisilazane have also been used successfully (97). A wide variety of silanizing reagents has been tried. It is impossible to quote them all, or to discuss the huge literature dealing with the results of these studies. Only a few references can be included (93,97,111-121). The literature has been summarized in reviews and books, to which the reader is referred for detail (28-31). In this literature, persilylation refers to silanization procedures where the reaction is carried out using polar silyl reagents and where it is attempted to drive it to completion. d. Surfactant Coating Surfactants have been used for the deactivation of glass columns as they have been for the deactivation of metal columns. Rutten and Luyten (113) have studied a number of cationic or anionic reagents: - Cationic surfactants: Gas Quat L (trioctadecylmethylammonium bromide), BTPPC (benzyltriphenylphosphoniumchloride), - Anionic surfactants: Kalignost (sodium tetraphenylborate). The deactivation of the column wall surface is effective only as long as the column is not heated to such a temperature that the surfactant is vaporized or pyrolyzed. e. Silicon Deposit

Pretorius et al. (122-124) have obtained a very high degree of deactivation by cracking silane inside the column, giving a silicon deposit. The advantages of this method are as follows: - The surface tension of silicon is very high, allowing a facile coating by the most polar stationary phases. - The thermal stability of the column depends only on the thermal stability of the stationary phase. - The coating does not react with organic compounds. There are important drawbacks, however, which have prevented this method from becoming widely used: - Silane is a very dangerous gas, which burns spontaneously on contact with air. Safe handling is difficult. - Silicon oxidizes readily in the presence of air or water. Accordingly, aqueous samples or gas blends containing oxygen cannot be analyzed on these columns.

261

f; Selection of a Deactivation Procedure As should be obvious from the huge amount of literature on this important topic and from the many contradictions and controversies encountered in this review, there is no ideal procedure. Although considerable progress has been made during the last ten years and excellent columns can be readily prepared, there is no universal method. The best procedure depends largely on the nature of the stationary phase whch is to be used and on the samples to be analyzed. For example, Ignatiadis et al. (97) have shown that the optimum procedure is quite different for the preparation of columns with non-polar, medium polar and very polar stationary phases. This illustrates very well the present state of the art. Excellent columns can be prepared to analyze just about any kind of mixture, provided they do not contain components with too widely differing properties, such as strong acids and bases, such as may coexist in trace amounts. The development of the proper column may take a few months for an experienced analyst. Buying the columns may be preferred, and this seems to be the right solution as long as the analysis can be achieved satisfactorily with an available, ready made column. Otherwise, there is no substitute for the hard work. 4. Silica Tubings Silica tubings are much more difficult to etch than glass tubes. Accordingly, it has been difficult to prepare polar columns with this material. This is due to the great inertness of silica. Besides, when attacked, silica dissolves regularly, without giving rise to an etched, rough surface. On the other hand, the inner wall surface of silica tubes is much more homogeneous than that of glass columns and there is practically no metal cation there. The difficulties come from the very low degree of hydratation of this surface and its extremely smooth nature. Most successful precoating treatments seem to have evolved from hydration at high temperature, followed by chemical bonding of some silanizing reagent and weak cross-linking of the stationary phase, involving the bonded groups as well as the liquid phase itself. Since it is practically impossible for an analyst to draw his own silica tubes, there have been relatively few studies carried out so far on the pretreatments and treatments of silica columns. The availability of untreated quartz tubes has not always been widespread. Studies on the preparation of efficient columns for a variety of applications should probably begin to appear, because the material is extremely promising, although much more difficult to work with than glass, while finished silica columns are much easier to handle than their glass counterparts.

5. Coating Procedures for Wall Coated Open Tubular Columns Ths is the last step in the preparation of an OTC. Two kinds of method are used; static and dynamic. To enhance the stability of the finished column, the stationary phase is more and more often treated with reagents to cross link it. Considerable progress in this area has resulted in columns which are much more practical to use than they were a few years ago. References on p. 311.

268

a. Dynamic Coating

This method was used by Golay to prepare the first OTC (2). It has been described in detail by Dijkstra and De Goey (8) and by Novotny and Zlatkis (72). A plug of a solution of the stationary phase is forced through the column under gas pressure. The concentration of the solution depends on the thickness of the liquid film which is desired. Typically, it is around 10%. A schematic of the equipment required is given in Figure 8.9. The solvent must wet the column wall well. It must have a low surface tension, be pure, especially be free of polar impurities which could modify the retention data, and be free of dust. Filtration of the solution of stationary phase before coating is important to avoid plugging the column during this operation. Methylene chloride and n-pentane are the most popular solvents. The thickness and the uniformity of the liquid film depend on the concentration of the solution, its viscosity (which may be much larger than that of the pure solvent used to dissolve the liquid phase), on the temperature, on the velocity of the plug of solution and on the nature of the surface of the coated tube. The relationship between the film thickness and these various parameters has been studied by various authors, especially by Desty et al. (38), Scott and Hazeldean (18) and Kaiser (22). Various empirical equations have been suggested, some in

Figure 8.9. Schematic of the apparatus used for dynamic coating of WCOT columns. The solution of stationary phase is forced through the column under pressure. a, Reservoir of stationary phase solution. b, Stationary phase solution. c. Column.

269

excellent agreement, others contradictory. Kaiser has proposed the following expression for the film thickness (pm):

d,=

+

C 0.265U 0.25 r

200

where C is the concentration of the solution (v/v), r is the inner radius of the column, U is the linear velocity of the solution plug. The finite limit of the film thickness at zero velocity and the reverse dependence on the column radius are surprising. Novotny et al. (110,125), after the work of Fairbrother and Stubbs (126) consider that the following equation better fits the experimental results:

d I--o- ;r

(y2

where q is the viscosity of the solution, u is the surface tension of the solution. From theoretical considerations developed by Levich (127), Guiochon (128) has shown that the Concus (129) relationship is in agreement with hydrodynamics and fits the data as well as the empirical equation of Novotny:

Within the velocity limits recommended by Desty et al. (38) and Scott and Hazeldean (18), the film thickness vanes between 0.2 and 1 pm for a 10% solution concentration. Whatever the method used and the result obtained, however, there is no easy way to find out whether the liquid film thickness is constant along the

,// I

Figure 8.10. Schematic of the mercury drop coating procedure. (After Schomburg and Husmann, ref. 130). The mercury plug migrates under pressure of the gas, pushes the stationary phase solution, and laminates the film formed against the wall. After the solvent is vaporized, a thin, homogeneous film is obtained. a, solution of stationary phase. b, mercury plug. c, air and film of solution against the wall. Reprinted with permission of Tetrahedron. 44, 3935 (1976).

References on p. 311.

270 TABLE 8.2 Resolution of Different Couples of Hydrocarbons on two Columns of Different Lengths col. 1

Col. 2

Ratio

4.9

6.5

1.32

2-methylpentane 2,2-dimethylbutane

12.0

16.8

1.40

n-hexane n-heptane

34.1

56.0

1.59

2-methylhexane 3-meth ylhexane

3.3

5.1

1.53

2,rl-dimethylhexane 2,Sdimethylhexane

1.3

1.9

1.46

2,2,5-trimethylhexane 3-methylheptane

1.8

2.6

1.44

n-heptane n-octane

44.3

62.9

1.42

n-nonane n-decane

41.6

55.5

1.34

cyclopentane methylcyclopentane

17.0

23.8

1.40

1-cis-4-dimethylcyclohexane 1-cis-2-dimethylcyclohexane

10.2

15.0

1.47

rnethylcyclohexane cycloheptane

28.5

40.5

1.42

cumene propylbenzene

11.8

16.1

1.37

sec-butylbenzene rert-butylbenzene

6.6

8.7

1.32

ethyltoluene pseudo-cumene

8.4

12.9

1.53

Couples n-pentane isopentane

Average Relative Standard Deviation

1.43 5.78

Stationary Phase: Squalane (59).

column, nor within which limits. Merle d’Aubigne et al. (59) checked the reproducibility of the dynamic coating method by measuring the amount of phase contained in different columns. For example, columns of 20 and 60 m long having the same inner diameter were coated with 6.8 and 21.6 mg squalane, respectively. Data in Table 8.2 show that the ratio of the resolutions of 14 pairs of hydrocarbons on the two columns were constant and equal to the cube root of the ratio of the column lengths (see Chapter 4).

271

In order to remedy the main difficulty encountered with the dynamic method, the formation of bubbles behind the receding meniscus of the solution by draining of the film and capillary condensation, Schomburg and Husmann (130) have developed the mercury drop technique. The coating solution is twice as concentrated as before (ca 20%), and a plug is forced under gas pressure inside the column, occupying about 10% of its length. Immediately after, a mercury plug, about 3 to 10 cm long is inserted into the column, immediately followed by the gas stream (see Figure 8.10). The plug train moves along the column at about 0.5 cm/sec. The mercury plug laminates the film of solution and leaves behind a thin film of constant thickness, eliminating the possibility of accumulation of solution or the formation of droplets and resulting in a much greater homogeneity of the liquid film, with far less trouble and care, and more rapidly than with the classical method. The procedure ends by drying the column under a stream of inert gas. b. Static Coating

This method was first used by Golay to obtain the original open tubular columns (1,2). Later Bouche and Verzele (131) developed a different approach to static

coating. The Golay method consists in filling the tube with a dilute solution of stationary phase, sealing one end of the column and slowly drawing the other end into an oven and coiling it, in such a way that the solvent vaporizes when the solution enters the oven and exits as a vapor through the open end. To maintain the vapor stream, the pressure rises slowly at the level of the meniscus and it moves into the oven. The column velocity must be slow enough to permit the vaporization process to take place at the inlet into the oven. The Bouche and Verzele method (131) consists of filling the column with a dilute solution (ca 1%)of stationary phase in a volatile solvent, sealing the other end hermetically and connecting the other end to a vacuum pump. The solvent slowly vaporizes until the receding meniscus reaches the other end of the column. Careful degassing of the solvent and a leakproof seal are critical (59,131-136). An extremely constant temperature is required for the achievement of a uniform coating thickness (59,137).

The film thickness can be easily calculated from the concentration of the solution used, since all the stationary phase introduced in the column remains on the wall after vaporization of the solution. The film thickness is given by: W

d -I- 2 m r ~ p

(4)

where w is the weight of stationary phase introduced in the column, with the solution, r is the column inner radius, L is the column length, p is the specific weight of the stationary phase. Table 8.3 gives the specific weights of the main stationary phases used in gas chromatography, after Rutten and Rijks (138). References on p. 311.

272

TABLE 8.3 Density of Some Stationary Phases (138) Liquid Phase

Density

Liquid Phase

Density

AN 600 DC 200 DC 510 DC 550 DC 710 DEGS 0s 124 ov-1 OV-3 OV-7 ov-1 1 OV-17 ov-22 OV-25 OV-61

1.08 0.97 1.00 1.068 1.10 1.26 1.21 0.98 0.997 1.021 1.057 1.092 1.127 1.15 1.09

ov-101 OV-105 ov-210 OV-225 OV-275 PEG 400 QF 1 SE 30 SE 54 SF 96-200 SF 96-2000 SILAR 5 CP SILAR 10 C SP 2401 Squalane XE 60

0.975 0.99 1.32 1.086 1.16 1.125 1.32 0.960 0.P8 0.972 0.974 1.125 1.116 1.30 0.83 1.08

It is also possible to calculate the film thickness by observing that the concentration (v/v) of the stationary phase in the solution is also equal to the ratio of the volumes of the stationary and mobile phases in the column. Hence:

L

This method can be used with all stationary phases, regardless of the nature of the tubing used. The main drawbacks are the time required to prepare the column, which increases as the square of its length (59), and the skill required to achieve the tight seal at the column's end. c. Immobilization of the Stationary Liquid Phase

One of the major sources of problems in practical applications of OTC's is the long-term stability of the liquid film. Also, because the phase ratio is much smaller than for conventional packed columns and the carrier gas flow rate is large compared to the weight of stationary phase, the vapor pressure of this phase must be much smaller than with conventional packed columns. Finally, it is not possible in practice to prepare and operate columns with thick liquid films, not mainly because of the relative loss in efficiency, which one could accept in some applications requiring the use of large sample sizes, but because of their lack of stability, due to the surface tension forces. A solution to these problems could be obtained by immobilizing the stationary phase immediately after coating. The idea was first suggested by Novotny (139) and Jonsson et al. (140) as early as 1972. The stationary phase would be bound together as a weakly cross linked polymer, possibly with some bonds to the support.

273 TABLE 8.4 Comparison between Retention Indices of Steroids and Prostaglandins on OV-101 and Polymethylsiloxane (141) Compounds

Retention Index PMS ov-101

Difference OV-101- PMS

PGF2L3 PGF,p 13,14-dihydro-PGF2, 15-epi-PGFl, 15-keto-PGF2, 15-epi-PGF2, 11-epi-PGF,, PGF3, PGFIa PGFh Andros terone Etiocholanolone Dehydroepiandrosterone 11-ketoandrosterone 11-ketoetiocholanolone 11-hydroxyandrosterone 11-hydroxyetiocholanolone Pregnanediol Pregnanetriol Tetrahydrocortisone Tetrahydrocortisol Allo-tetrahydrocortisol

2655 2678 2713 2734 2754 2691 2693 2718 2803 2745 2500 2520 2561 2600 2613 2698 2715 2756 2789 2969 3029 3034

5 5 3 1 -4 4 6 -8 5 -3 1 2 2 0 -3 -5 -3 2 91 -9 -6 2

2660 2683 2716 2735 2750 2701 2699 2710 2808 2742 2501 2522 2563 2600 2610 2693 2712 2758 2880 2960 3023 3036

Except for pregnanetriol, the difference is negligible. Reprinted with permission of Tetruhedrun, 44, 3935 (1976).

A

C.BU

9

I

Figure 8.11. Chromatogram of a urine sample. (After Rigaud et al., ref. 141). Sample: steroids, as methyloxime ether, trimethylsilyl ethers. A, androsterone. E, etiocholanolone. 1, dehydroepiandrosterone. 2, 11-ketoandrosterone. 3, 1l-hydroxyandrosterone. 4, 11-hydroxyetiocholanolone.5, pregnanediol. 6, tetrahydrocortisone. 7, tetrahydrocortisol. 8, allotetrahydrocortisol. 9, /3-cortolone. CBu, cholesteryl butyrate (internal standard). Reprinted with permission of Tetrahedron, 44,3935 (1976).

References on p. 311.

214

The first successful procedure to achieve a cross linked stationary phase was described by Rigaud et al. (141) and Madani et al. (142-145), using in situ polymerization of polysiloxanes. This is achieved by carrying out hydrolysis of alkylhalo silanes into reactive polysiloxane polymers which react with silanol groups at the glass surface. The column efficiency exceeds 2,000 plates per meter for a 0.25 mm i.d. column. The polarity of the polymethylsiloxane obtained is very similar to that of OV-101 or SE-30, as illustrated in Table 8.4, where we compare the retention indices of methyloxime ether trimethylsilyl derivatives (MO-TMS) of steroids and of methyl ester trimethylsilyl derivatives of prostaglandins (141). Figure 8.1 1 shows a urine profile of steroid metabolites as MO-TMS derivatives, performed on a polysiloxane capillary column, under temperature programming. Blomberg et al. (146-148), following the procedure just described, prepared immobilized polyphenylsiloxane stationary phases whose polarity is similar to that of OV-17. The authors emphasized the increased thermal stability and column lifetime under temperature programming compared to conventional wall-coated columns. According to Grob (149), the improvement in column lifetime is due to the enormous viscosity of the film, a large fraction of the molecules of which are bonded to the wall. An increase of the temperature does not result in a marked decrease of the liquid phase viscosity, while most polymeric phases become fluid at high temperature. Their film breaks and tears into a network of droplets, and the column efficiency falls catastrophically. Similarly, the use of these immobilized stationary phases permits the preparation of films several micrometers thick. Modifications of the procedure described by Rigaud have been suggested by Sandra et al. (150), Blomberg et al. (151), Grob and Grob (152,153) and Moseley and P e W (154). More recently two general procedures, applicable to any stationary phase, have been described. They involve cross linking by free radicals and by high energy irradiation. Both methods are classical for cross linking polymers. In the present case, however, the aim is to prepare very weakly cross linked films. The bonded chains are subject to very low shear forces in gas chromatography, except maybe when the column is rinsed with a solvent to regenerate it. So the chains do not have to be held very tightly. On the other hand, the cross linking should leave the chains free to oscillate, to let the diffusion coefficients of the analytes remain large enough to keep the resistance to mass transfer in the stationary phase small. 1. Free Radical Reactions Peroxides have been used as a source of free radicals by Grob et al. (155), Sandra et al. (150) and Blomberg et al. (151). They are benzoyl, dichlorobenzoyl and cumenyl peroxides. The peroxide is dissolved in the stationary phase solution, prior to coating, which is performed by one of the usual methods. Cross linking proceeds when the column is heated to 100-150 O C for several hours. The volatile intermediates formed as side products of the cross linking reaction are eliminated by heating the column under gas flow.

215

An excess of peroxide increases the column polarity, while an insufficient amount of peroxide results in lack of thermal stability, mechanical stability and a reduced column life time. Wright et al. (156) have recommended the use of 2,2'-azobutane as a source of free radicals, to reduce these drawbacks. 2. Radiation Cross Linking Bertsch et al. (157), Schomburg et al. (158), followed by Hubball et al. (159,160) and Vigh and Etler (161-163) have pioneered this cross linking technique. After proper coating, the OTC is submitted to y irradiation by a cobalt 60 source. No significant amount of secondary compounds is generated during this treatment and the characteristics of the stationary phase remain unchanged, except for the consequences of the cross linking.

The general properties of these cross linked columns make them extremely attractive for routine analysis as well as for process control applications. The possibility for preparing rather thick films, as well as their three-dimensional structure, permits the use of large samples, eliminating the need of a splitting system, the major obstacle to applications to quantitative analysis. Overloading the column grossly and systematically does not result in a rapid loss of performance. The column can be washed with a solvent and cleaned from non-volatile material introduced slowly, after many repetitive injections. The availability of such columns opens new possibilities to the industrial analyst who has little time to prepare classical OTC's and little opportunity to use them with the tender loving care they need. d. Preparation of Thick Layer Columns

Grob and Grob (164) have distinguished three categories of OTC's, depending on the average thickness of the stationary phase film: - Regular or conventional columns: d , smaller than 0.3 pm. - Thick film columns: d , between 0.3 and 1.0 pm. - Very thick film columns: d, larger than 1 pm. They have also underlined the potential advantages of columns with thick films of liquid phases (165). The preparation and practical operation of such columns was not possible, however, before the development of procedures permitting the immobilization in situ, by cross linking of the liquid film. Now that this is possible, we begin to see a diversification of the characteristics of OTC used for different applications. The trend at present is towards rather wider and shorter columns than were used in the past, with thicker films of stationary phase. This corresponds to a decrease in the efficiency required, as more and more simple analyses, previously performed with conventional packed columns, are now carried out on OTC's, but still require a rather modest efficiency. The increase in the film thickness results in a larger phase ratio, an increase in the retention volume observed at a given temperature and an easier separation, especially for light compounds. Accordingly a shorter, less efficient column is required References on p. 311.

276

to achieve the separation. The analysis of complex mixtures will always require long columns and those are better made with narrow diameter tubing (to achieve a higher efficiency,see ref. 35) and thin liquid phase films (again to increase the efficiency, by reducing the resistance to mass transfer in the stationary phase and to reduce the retention time). Whereas 50 to 80 m long columns, 0.20 to 0.25 mm id., with films 0.1 to 0.3 pm thick were the standard in the late ’seventies and early ’eighties, most commercial columns sold now are 10 to 25 m long, 0.3 mm i.d., with film thickness around 1 pm. Columns with films as thick as 5 to 8 pm have been used successfully. They permit large phase ratios and the injection of large sample sizes. Hence they are very suitable for trace analysis, as has recently been demonstrated by Lipsky (63). As an example, Johansen et al. (166,167) have shown that separation of low boiling compounds is more efficient on short columns with 1pm thick films than on longer columns with 0.25 pm thick films. This observation has been discussed by Ettre (168-170) who has clearly described the criteria by which the optimum column characteristics should be chosen for the different types of analysis. The reasons for the selection of a thin film of stationary phase are as follows: - The resistance to mass transfer increases as the square of the average thickness of this film. Thin film columns are more efficient. They can achieve a “coating efficiency” in excess of 80% (see Chapter 4, Sections VII and IX). - The analysis time is proportional to the amount of stationary phase contained in the column, and hence to the film thickness. Clearly a minimum amount of liquid phase is required (without retention there is no possible separation), but thin film columns permits a much faster analysis. The advantages of thick film columns appear in the following areas: - The resolution between two components depends on the retention, i.e. on the column capacity factor. It is proportional to the term k’/(l k’), while k’ is proportional to the film thickness. Hence, if k’ is large, a reduction in the film thickness wiLl result in a decrease in the retention time, while, if k’ is small, a reduction in the film thickness will actually result in an increase in the analysis time, because a much longer column will be required for the increase of column efficiency to compensate for the decrease in retention. This problem was discussed very early on by Purnell(l71). While the conclusion of this author was somewhat too rigid, the point remains valid. The selection of the optimum value of k’, and hence of the phase ratio, has been discussed in detail (172-174). - The amount of solute injected is a function of the amount of stationary phase in the column. The local concentration of the analyte at band maximum is proportional to the square root of the plate number and inversely proportional to the retention volume (see Chapter 1, Section XI.l). It should not exceed the value at which it is not possible to consider the partition isotherm as linear. Hence, for a column of a given efficiency, the sample size is proportional to the amount of stationary phase contained in the column. As a first approximation, we can consider it as being proportional to the film thickness. Grob and Grob (165) have shown that the injection of an amount as large as 1.6 pL could be carried out on a thick film OTC without overloading the column too much.

+

211

- Finally, the thicker the liquid film, the less likely it is that some residual adsorption of the analyte on the column wall may contribute appreciably to its retention or to its elution profile. A thick film column usually gives more symmetrical peaks (175). Ettre (168-170) and Grob and Grob (164,165) have concluded that the main applications of thick film columns are to be found in the following three areas: trace analysis, when the number of components of the mixture is not very large, and the rapid analysis of gases and vapors.

e. Wide Bore Open Tubular Columns Also named macrobore or megabore columns in a world which has too little use for balanced opinions, these columns have an early origin but became popular very late in the development of OTC's. The use of 0.5 to 1 mm i.d. OTC has been reported as early as 1959 by R.P.W.Scott (17) and several other authors (176,177). Several major difficulties impeded their early development. The pioneers were more interested in high speed analysis or in extremely efficient analysis. In both cases narrow bore columns are required. Furthermore, wide bore columns suffer from two major disadvantages. Glass tubes are brittle. Narrow, thin dass tubes still have some flexibility. Wide bore columns tend to break when looked at too hard. The preparation of thick liquid phase films was impossible without the technology of cross linking. Thus, with a constant maximum film thickness around 0.3 pm, the phase ratio would decrease with increasing column diameter (as 2 d J d , ) , resulting in a loss of sensitivity. One major advantage of wide bore columns, however, would be their compatibility with all instruments designed and built for use with conventional packed columns. The column volume, carrier gas flow rate and velocity, column efficiency and loadability become of the same order of magnitude as they are for packed columns. The development of quartz tubes and immobilized thick liquid phase films has permitted a fruitful revisit of this area of column technology. Quartz columns as wide as 0.5 to 0.6 mm i.d. are available. They may be less flexible than the narrow ones but they are as strong and can be handled with little caution. Film thicknesses up to 5 or even 10 pm could be or have been prepared (63). Thus the theoretical advantages of this type of column for certain applications can be put to use. They are as follows: - The permeability of the column increases as the square of the diameter, while the HETP increases as the column diameter. Thus much more efficient columns can be prepared. Conversely, the analysis time will be much longer. Compared to packed columns of a similar efficiency, the pressure drop of wide bore OTC's is almost negligible. The James and Martin compressibility correction factor (see Chapter 2, Section V) is practically equal to 1, and the gas hold-up time is shorter for a given column length. -The phase ratio is smaller than for comparable packed columns, thus the retention time can be much smaller. Combined with a somewhat better efficiency References on p. 311.

278

this property may offset the smaller loadability and result in a comparable or better maximum concentration of the analyte at column outlet, and hence qualify these columns for trace analysis. - The thermal stability of the stationary phase is definitely better. This results from the much more inert surface of the support, pure glassy silica versus diatomaceous earth or silica gel. Cross linked packings also seem to be more stable than coated ones (but there does not seem to be any reason why cross linking should not be attempted successfully with coated supports). The result is a larger signal to noise ratio with wide bore OTC's than with packed columns. - On-column injection is definitely possible with wide bore columns. This is a critical advantage over conventional OTC's, the use of which is limited in routine analysis, because of the understandable reluctance of analysts to trust splitting devices. Some progress on the injection devices, especially the automatic syringe systems and autosamplers has been made, however. The amounts typically handled by these devices is too large for wide bore columns by 2 to 5 times. The loadability of wide bore columns has been estimated by Ettre (170) to be about one order of magnitude smaller than that of conventional packed columns, in spite of some optimistic claims. On-line automatic sample valves cannot repeatably deliver sample amounts below cu 0.1 pL. The margin is now narrow and it is quite likely that this roadblock will not survive very long. We are of the opinion that wide bore open tubular columns will become very popular in routine analytical laboratories and in process control within the next few years. They will permit major advances in the precision, accuracy, speed and sensitivity of analysis. This progress will be triggered by the development of new injection devices, maybe related to the pulse injection valve (178) or to fluid logic injection systems (179,180). 6. Coating Procedures for Porous Layer Open Tubular Columns PLOT and SCOT columns are open tubular columns, the walls of which are coated with a layer of particles of an adsorbent or a support impregnated with a liquid phase. Although it was not so originally, the name of PLOT now seems to be used for columns having an adsorbent layer, while SCOT means columns having a layer of coated support. a. Porous Layers of Adsorbents (PLOT Columns)

The layer of adsorbent can be prepared either by properly attacking or etching the column wall, or by coating it with a layer of thin particles. The first principle was used by Mohnke and Saffert (92) and then Bruner and Cartoni (94) to prepare silica columns and by Petitjean and Leftault (181) to prepare alumina columns. Very interesting results were obtained by Schwartz et al. (182), Schneider et al. (183), De Nijs (184) and Vidal-Madjar et al. (185,186). Porous layers of modified adsorbents, similar to the adsorbents used in gas-modified adsorption layer chromatography (see Chapter 7, first part), could be used with open tubular columns. In fact, extremely large selectivities and spectacular sep-

279

arations could be obtained by this method, which has been almost completely neglected so far. The potentialities of the combination of open tubular columns, modified adsorbents and the use of steam as a component of the mobile phase have not been unraveled yet. The work of Halasz and Horvath (39), German and Horning (187-189) and Vidal-Madjar et al. (185,186) has merely scratched the surface. The question is whether there will be some applications requiring the great flexibility of this method, or will it remain ignored? b. Porous Layer of Coated Support (SCOT Columns)

Halasz and Horvath (39) have shown excellent separations of light hydrocarbons using metal or glass columns coated with ferric oxide or Sterchamol (a diatomaceous support for packed columns, originating from Germany), both coated with squalane. Preparation is carried out in one stage, by filling the column with a suspension of the particles in a solution of the stationary phase, and using the static method (see Section II.5.b above). Successful separations of alkanes, alkenes, aromatic hydrocarbons, fatty acid esters and alcohols were achieved (190-193). A number of variants for the preparation of these columns have been described (194-203). Excellent analytical results have been described, demonstrating enhanced thermal stability of the stationary phase, very good column efficiency and flexibility in manipulating the selectivity (187,198-200,202).

7. Preparation of Packed Capillary Columns These columns are characterized by a very low ratio of the column to the average particle diameters. This ratio is smaller than 5 to 7 with packed capillary columns, while it is typically 10 to 40 with normal packed columns. The small column diameter and the anastomosis of the flow pattern ensure very fast radial mass transfer. Thus, these columns may be less densely packed than conventional columns without experiencing the adverse consequences of channeling on the column efficiency. The preparation of packed capillaries is achieved by drawing a glass tube previously loosely packed with the support of adsorbent desired. Adsorbents such as silica or alumina are activated in the process. Molecular sieves should be dried carefully before and after packing, before drawing the column. The supports are coated using the dynamic method and a dilute solution of liquid phase. Further details are to be found in the relevant literature (43-46). 111. EVALUATION OF OPEN TUBULAR COLUMNS There are several different parameters which characterize the performance of OTC’s and which should be checked separately. Some depend on the particular column used, others on the combination of this column and the instrument. A skilled analyst developing a column for a particular application will have different requirements from a beginner experimenting with his first column. References on p. 31 1.

280

The most important factor to evaluate is the suitability of the column for the components contained in the mixtures which it will analyze. There should be no significant amount of adsorption: at worst adsorption may hold the complete amount of one or several components in the column for such a long time that their elution band will be too small to be detected. At best adsorption results in tailing peaks, which creates interferences and makes the detection of the peak end by the integrator more difficult, decreasing the accuracy of the analysis. A small degree of adsorption, as well as the quality of the column coating, may be conveniently tested by measuring the column efficiency for the analytes of interest, their column capacity factors, and the peak asymmetry. This is all that the skilled analyst wants to know, assuming he is not working with a new instrument. In addition, it may be useful to measure the column permeability, which offers a convenient check of its true diameter, and, in some cases, to measure the quality of the instrument used, by determining the efficiency of an empty tube. 1. Analytical Test

Two mixtures should be run on each new column, the classical Grob test mixture (204) and a dedicated mixture containing the analytes of importance in the

laboratory, for the analysis of which the column under consideration will be used. The determination of the composition of this second mixture is specific to each laboratory. It should be representative, but not too complex, so that each compound can be identified from its relative peak size, since the relative retention will change from column to column. It is good practice to inject it several times, varying the amount in a rather large ratio, since adsorption may be a problem only at low concentrations. The composition of the Grob test mixture is given in Table 8.5. It is important to prepare this mixture carefully, so as to be able to compare quantitative results obtained on different columns. Sometimes a certain amount of an analyte is lost TABLE 8.5 Composition of the Grob Test Mixture (204) Compound Methyl laurate Methyl undecanoate Methyl caprylate n-Decane n-Undecane 1-Octanol Nonanal 2.3-Butanediol 2,6-Dimethylaniline 2,6-Dimethylphenol Dicyclohexylamine 2-Ethylhexanoic acid

Concentration (mg/L) 41.3 41.9 42.3 28.3 28.7 35.5

40.0 53.0 32.0 32.0 31.3 38.0

281

while its peak remains symmetrical. A cursory glance to the chromatogram would not reveal the problem, which may have nasty consequences. The use of the relative response factors (see Chapter 14) will be helpful in ascertaining that the entire amount of sample of the test mixture injected is eluted. Among the components of the test mixture some are more critical than others. Some of these polar compounds may disappear entirely from the chromatogram on certain columns, whde the others give symmetrical peaks and no detectable loss of peak area. Conclusions regarding the quality of the deactivation may be derived directly from these analyses (97). 2. Permeability The permeability, k , of a straight, cylindrical empty tube of diameter d , is given by :

k='

d2 32

The permeability of a column is easy to calculate from either the variation of the flow rate or the gas hold-up time ( 2 , ) with increasing inlet pressure (see Chapter 1, TABLE 8.6 Properties of the Main Column Types (205) Column Type

Conventional Packed Columns (CP) (w/Porous Particles) Conventional Packed Columns (w/Glass Beads) Conventional Packed Columns (w/Porous Layer Beads) Packed Capillary Columns (PC) Conventional Open Tube Columns (COT) Porous Layer Open Tube Columns (PLOT)

Permeability (v2)

Phase Ratio

(v,/V,)

Minimum Plate Height (mm)

Optimum Gas Flow Velocity (cm/sec)

Sample Size (pg)

10-

100

4- 200

0.5-2

5- 20

10-1000

15-

150

50- 500

1-3

10- 20

I- 100

15-

150

50- 400

0.5-2

20- 60

1- 100

50-

400

10- 300

0.5-2

10- 40

1-

50

500- 8000

100-1000

0.3-2

10-100

0.1-

50

2000-10000

20- 300

0.6-2

20-160

1-

50

NB. I t will always be possible to prepare a column of any type having at least the value of one parameter outside the range indicated here. More than 901%of the columns in use, however, fall within these ranges. Reprinted with permission from Aduances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1969, Vol. 8, p. 179. References on p. 311.

282

Section VII and Chapter 2, Section 11). For example:

where L is the column length, p , is the outlet pressure, P is the inlet to outlet pressure ratio, 11 is the carrier gas viscosity (see Chapter 2). In practice the measured permeability is about 10 to 30% lower than the one calculated from the column diameter. The difference can be attributed to the non-linearity of the column, to fluctuations of the diameter, to local flattening, especially with metal tubes, and to the roughness of the wall (59). Typical values of the column permeability are reported in Table 8.6. OTC's are ten to a hundred-fold more permeable than packed columns and for this reason very long columns can be used (205).

3. Height Equivalent to a Theoretical Plate As has been shown by Golay (1,2,5)and demonstrated by the results of hundreds of reports, the HETP of OTC's is given by the following equations, discussed in more detail in Chapter 4:

H

=

K+ 1 +

- Cguo f C,ju,

where:

B=2Dg

(9)

c, = 1 + 6k' +

d: -

96(1+ k')2

c,= f=

2k'

Dg

d:

6(1+ k')2

9( P4 - 1)(P 2 - 1) 8( P3 - 1)2

B represents the contribution due to axial diffusion, C, and C, the contributions of the resistances to mass transfer in the mobile and stationary phases, respectively, and f is a compressibility coefficient. D, and D, are the diffusion coefficients of the analyte in the mobile and stationary phases, respectively.

283

Equation 8 approximately represents an hyperbola, if the variation of the compressibility factor, f , with the inlet pressure can be neglected. The coordinates of the minimum of the hyperbola are:

Compared to packed columns, the HETP equation of OTC‘s exhibits the following differences (206): - The coefficients are related to the experimental parameters by rigorous relationships, without the “fudge” factors which mar the kinetic theory of packed columns. - There is no constant, or A , term. - The C, term is very similar for packed columns and OTC’s. There is no coupling term, however, and the HETP increases rapidly at large flow velocities. - The C, term is smaller than for packed columns, and at large phase ratios can be neglected compared to the C, term. Then the minimum HETP becomes:

H,,

= d,

1

+ 6k’ + Ilk’’ 12(1 + k’)’

- The column efficiency is proportional to the column diameter. It is also strongly dependent on the column capacity ratio for values of k’ below 3 or 4. When comparing the efficiencies of different columns, it is important to do so for the same value of the reduced velocity ( v = ud,/D,, see Chapter 4), and for similar values of the phase ratio. Otherwise the comparison could be meaningless. Failure to understand the complex relationships between column efficiency, resolution, column capacity factors, column diameter and carrier gas velocity has led to the development of a variety of yardsticks to compare column performance, most of them being useless when they are not severely biased or simply wrong. As an example of the difficulties encountered by analysts in understanding the meaning of their experimental results, Figure 8.12 shows a plot of the plate number of a column versus the column capacity factor. This number decreases sharply with increasing retention. Nevertheless, the number of effective theoretical plates, as described in Chapter 1, which is proportional to the square of the resolution between two components, increases steadily: at constant relative retention, it is easier to separate compounds which are well retained than those which are weakly sorbed. References on p. 311.

284

v

c 160 VI

140

5

Number of theoretical plates ( n )

u

2

120

*J P,

1 i2

B 0 100 B 100 0

$ 5

60

5

40

1

L

2s z

2 ber of effective plates (N) 2 0o l f k m umber [

I

I

2

1

1 4 4

I

I

I

I

6 8 Partition ratio

I

I

l

l

10

(k)

Figure 8.12. Plots of the number of theoretical plates (n) and the number of effective theoretical plates versus the column capacity factor. Theoretical curve (equation 8) and experimental results (After Ettre, ref. 23).

The optimum velocity decreases with increasing retention, which means that the column efficiency can be a maximum during any given run for one compound only. Less retained compounds will be analyzed at a velocity lower than their optimum, while more retained compounds will be eluted at a larger velocity.

4. Phase Ratio This is the ratio of the volume available to the mobile (gas) phase to the volume available to the stationary (liquid) phase. For a true OTC we have: d fi=L 4dJ

For OTC‘s the phase ratio is much larger than for packed columns, due to the ease with which a thin liquid phase coating can be prepared and the difficulty of making a thick one. Phase ratios of 100 to 1,000 are readily accessible. This permits the achievement of analysis at temperatures much lower than those required by packed columns, for which phase ratios are typically between 5 and 100. 5. Separation Number

The separation number has been introduced in 1962 by Kaiser under the name

285

“Trennzahl” (207) and by Hurrel and Perry under the name “Effective Peak Number” (208). Their definitions are nevertheless very similar: T Z = S N = d z + 1) - d z ) - 1 f ( Z + 1) l ( z )

+

+

where t,(z 1) and t R ( z )are the retention times of the n-alkanes with z + 1 and z carbon atoms, respectively, l(z 1) and f ( z )the widths at half height of their bands and w ( z 1) and w ( z ) the base widths of their peaks. In practice the separation number is preferred to the EPN because band widths at half height are more accurately measured than base widths, which require the drawing of the inflexion tangents, a very inaccurate operation. Ettre (209) has shown that:

+

+

EPN = 1.177 T Z

+ 0.177

(19)

It should be emphasized, however, that the separation number is not a well-defined characteristic of a column: it depends rather strongly on the temperature, as was conclusively shown by Krupcik et al. (210).

6. Other Parameters Part of the performance of a capillary column may be lost because the chromatograph contributes excessively to the band spreading. This arises essentially from excessive volumes of the connecting tubes, injection systems and detectors, and sometimes from the detector response time. The easiest control is in the determination of the efficiency of a non-retained peak on a non-coated tubing (59). Equation 15 gives for k’ = 0:

H,, = 0.29dc

This is a very small value, which is observed at a very large flow velocity:

4

U, = 13.9-

d C

Accordingly, it is better to carry out this test first with a tube wider and longer than the column used. If the result is satisfactory, tubes with dimensions closer to those of the columns used will be tried (59). An attempt at formalizing a test for the equipment contribution has been made by Kaiser and Rieder (211). Based on the classical observation that, for OTC‘s, the peak width at half height increases approximately as a linear function of the References on p. 311.

286

retention time in an homologous series (212,213), they have developed the "AbT concept". Unfortunately, it has been proven that the entire scheme is based on fallacies (213) and that the numbers obtained in practice, being severely tainted by experimental errors, are meaningless (214). Cram et al. (215) have calculated 29 parameters which can be used for the quality control of OTC's. They are not all independent of each other. The authors conclude that the most useful parameters are the separation number, the number of plates per unit length (i.e. the HETP), the baseline drift in temperature programming, the relative retention of 2,6-dimethylphenol and 2,4-dimethylaniline, which characterizes the acidity (or basicity) of the column, and the third moment of the 1-octanol peak, which characterizes the symmetry of that peak and the extent of adsorption undergone by the compound. Finally, the most practical and less controversial parameter which has been derived is probably the coating efficiency (23,27). It is the ratio of the theoretical efficiency, as predicted by the Golay equation when the contribution of the resistance to mass transfer in the stationary phase is neglected, to the actual plate height, measured for a mobile phase velocity around the optimum: CE =

B/u

+ C,u

He

where B and C, are given by equations 9 and 10, respectively, u is the velocity of the carrier gas at which the plate height has been measured and He is the value obtained. Coating efficiencies in the range 75 to 908 are easily achieved at present, except for very polar compounds. Lower values obtained with very long columns or very narrow ones have been ascribed to the fact that the compressibility factor, f, has been neglected in equation 22.

IV. OPEN TUBULAR COLUMN TECHNOLOGY The proper operation of OTC's requires the use of a special, dedicated gas chromatograph, or at the very least some special adaptation, to ensure that the contribution of the injection system and the detector to band broadening is small compared to that of the phenomena taking place inside the column itself, and that the minute sample which has to be supplied to the column is metered, vaporized, transferred and detected correctly. The most serious problems are found with the injection system and with certain detectors which their principle makes difficult to miniaturize. By an exceptional stroke of luck, the flame ionization detector is, on the other hand, ideally suited to the strict requirements of OTC's (6). 1. Injection Techniques on Open Tubular Columns

For a very long time, up until these last few years, OTC's were been mainly used as research tools, for qualitative analysis or for very important and rather excep-

287

tional quantitative analysis, when the use of complex, expensive equipment, operated by very skilled scientists was justified. Quantitative routine analysis was almost ruled out by the conjunction of two major roadblocks, which are just beginning to give way: - The direct injection of the amount of sample required was nearly impossible, - The early eluted peaks were too narrow and too fast to be recorded and quantitized accurately. The second problem has now been completely solved with the development of computer-based data acquisition systems (see Chapter 15), which can acquire data at 20 to 100 Hz,fast enough to determine the area of 1 sec-wide peaks with the required accuracy. The design and construction by chromatographic instrument manufacturers of detector electronics and amplifiers with a low noise level in the 10 to 50 Hz frequency range and with the proper level of mains frequency rejection was a major contribution. The first problem still subsists, in spite of several major advances made to permit direct on-column injection, improve the performance of on-column injection methods, and increase the sample size acceptable by an OTC. The injection problem stems from the extreme difficulties met in taking the proper sample aliquot, vaporizing it, and transferring it with neither loss nor dilution nor discrimination into the column in the small time allocated. The maximum concentration of the analyte in the elution profile, assumed to be nearly Gaussian, is given by the equation:

where m is the amount of sample, V, its retention volume, and N the column efficiency (see Chapter 1, equation 39). The maximum concentration must not exceed the value for which the equilibrium isotherm of the solute between the mobile and the stationary phase deviates from linear behavior, resulting in unsymmetrical peaks (see Chapter 5). According to Littlewood (216), the concentration should be less than about 10 pg of component per mL of gas (i.e., for a compound with a molecular weight of 100, a concentration of 0.2% v/v), thus, approximately: m < 0.02

(1

+k')v, fi

where m is in milligram and V, in mL. The gas hold-up volume of a 0.25 mm i.d. OTC is 1 mL per 20 m. The efficiency is about 40,000 plates for 20 m. For a compound with a column capacity factor of 4, the maximum sample size would thus be 0.5 pg, which is very difficult to handle. A comparison between different column types, based on the maximum sample size, has been made by Choubey and Mitra (217) and is summarized in Table 8.7. In fact, the figure selected by Littlewood, References on p. 31 1 .

288

TABLE 8.7 Maximum Sample S i z e allowed for Different Types of C o l u k s (217) Column Type

Phase Ratio

Inner Diameter

Minimum

HETP (mm)

(mm) CP CP SCOT WCOT

10 10 30 100

4.0 2.0 0.5 0.25

1.5-2 0.75-1 0.6-0.8 0.4-0.7

Maximum Sample S i z e for One Compound

Note

2-2.5 0.25-0.3 0.01-0.02 0.0001-0.0002

(1) (1) (2) (3)

Calculated according to equation 2, in pL. (1) Syringe injection. (2) Splitter injection, with small splitting ratio. (3) Splitter injection, with large splitting ratio.

although giving a correct order of magnitude, is arbitrary. It depends on the thickness of the stationary phase layer, on the nature of the compound, etc. (59). The duration of the injection must be short, about ten times smaller than the width of the narrowest band of interest in the chromatogram. Typically, it means that injection should be carried out in 0.1 to 0.5 sec, if the analysis is carried out at constant temperature. The injection port must be swept rapidly by the carrier gas. This constraint is more drastic than for packed columns which give wider peaks. Accordingly, the sampling ports for OTC's must be an order of magnitude smaller than those used with conventional gas chromatographs designed for PC columns, except in the case of wide bore OTC's. For this reason it is practically impossible to efficiently use OTC's on equipment designed for PC's, and vice versa. If the analysis is performed in temperature programming mode, the injection can take a much longer time, without resulting in any significant band broadening (218), which is one of the major advantages of temperature programming. In summary, a good injection device for OTC's must be very small, must be able to vaporize the sample very rapidly and must do so with a high degree of repeatability, without giving any significant fractionation of the sample components, nor destroying the sample by pyrolysis or catalytic reactions. a. Splitting Systems

Conventional syringes cannot deliver the 0.1 to 10 nL sample volume required. The reproducibility becomes poor below 50 nL. Accordindy, the first procedure used was indirect injection of a much larger sample than required, in a gas stream of large flow rate, followed by vaporization of the sample and splitting of an aliquot of the gas mixture obtained to the column (2,10,219-221). Typically a 0.5 pL sample is injected in a 500 mL/min gas stream, and 0.1 to 0.5% of the gas is diverted to the column, the rest of the stream being vented. The flow of the gas in the by-pass is adjustable with a needle valve (see Figure 8.13). Because of the very large difference between the flow rates in the column and in the vent, serious doubts exist regarding the repeatability and the linearity of the

289

Figure 8.13. Schematic of a splitter injector with septum purge (After Grob and Grob, ref. 229).

flow rate ratio. Obvious precautions should be taken to ensure the constancy of the splitting ratio, such as temperature control of the needle valve and its protection against plugging or condensation by disposing a filter and a plug of glass wool or a short charcoal column just upstream, to prevent the accumulation of sample material in this valve. A number of studies have investigated the linearity of the splitting devices and compared the performance achieved with a number of different designs, especially with respect to the accuracy and precision in quantitative analysis. As an example, Figure 8.14 shows the different devices investigated by Schomburg et al. (222). It is important to achieve rapid vaporization of the sample and good mixing of its vapor with the carrier gas, to make an homogeneous gas mixture prior to splitting (223). Systematic determination of the standard deviation of the peak area ratios obtained with the different designs for the couple methanol (b.p. 65 O C) and ethyl-Zhexanol (b.p. 185 O C) shows that the best results are obtained with the design “d” on Figure 8.14, a tube filled tightly with a long wool plug. Problems with the splitting systems arise independently of those resulting from the use of a syringe (224), and in addition to them (see Chapter 10, Section III.2.a). References on p. 311.

-1

-5

-10

1 25

25


2.1

2.0

% standard deviation

Figure 8.14. Study of vaporization liners for the homogenization of the mixture of carrier gas and sample vapors in a splitter injection (After Schomburg et al., ref. 222). a, empty tube. b, short glass wool plug close to the splitting region. c, short glass wool plug in the injection region. d, long and tight glass wool plug. e, Jennings tube. f, tube with irregular cross section. g, tube packed with chromatographic support. The number below each tube is the standard deviation for a series of injections. Reprinted with permission of Journal of Chromatography, 142, 87 (1977).

The splitter may behave as a distillation column with a few theoretical plates, but nevertheless act as a separator. Fractionation takes place when there is a large difference in vapor pressure or polarity between components of the mixture analyzed. Thus Muller and Oreans (225) reported excellent results using a splitting device in process-control gas chromatography,with an automatic sampling valve, but the feed was a mixture of the xylene isomers and ethylbenzene. An excellent repeatability was obtained over a time of several months, but the analysis of n-decane and squalane in solution in n-pentane demonstrates a non-linear behavior. At high injection block temperature, and high detector sensitivity, a number of artefacts have been observed and reported. Especially important in temperature programming (226-228), the appearance of ghost peaks is due to the pollution of the carrier gas, mainly by plasticizers exuding from the septum or the membranes of pressure and flow rate controllers (229). Grob and Grob (229) suggested an injector with a purge leak placed close to the septum, permitting a flush of these vapors. To avoid discrimination between the components of the sample, Langlais et al. (230) advised the closing of this septum purge during injection. Purcell, Downs and Ettre (231) recommend the addition of a packed trap upstream of the injector, to sorb the vapors coming from the membranes of the controllers, the use of controllers with stainless steel membranes and the use of a rotatory device permitting the closing of the injection port by a steel plate when injection is not performed (232). In summary, the advantages of the splitting systems are: - Sample sizes are compatible with the loading capacity of OTC's. - Analyses of normal mixtures are possible. - The devices are very simple.

291

The drawbacks are important, however: - Discrimination cannot be avoided for mixtures containing components of widely different vapor pressure and polarity. - Most of the sample is vented and lost. - The injection of samples diluted in a volatile solvent is impractical.

b. Split- Split less Systems The device used is very similar to the splitter just described. The injection technique is different. The sample is trapped at the top of the column. This method has been used early on by several authors, notably by Rushneck (233), Lewins and Ikada (234) and Merritt et al. (235), and then improved and adapted to OTC’s by Grob and Grob (236,237). The method used is as follows (see Figure 8.15): - First step: the sample is injected in the vaporization chamber. An aliquot of the vapor mixture (solvent and analyte) enters the top of the column, maintained at room temperature, where it is trapped as a narrow plug (Figure 8.15a).

-

Figure 8.15. Schematic of a splitless injector. a, condensation of solute and solvent in the column top. b, backpurging of the vaporization chamber. c, the purge is closed and the programmed temperature analysis started.

References on p. 31 1 .

292

- Second step: the excess of sample is removed from the vaporization chamber by opening the split vent valve (Figure 8.15b). - Third step: the analysis is performed under temperature programming. A detailed analytical protocol has been described, with application to the analysis of a steroid mixture (236). The phenomena which take place during the first step, referred to as “the solvent effect”, have been discussed by Grob and Grob (238,239), taking into account earlier work by Deans (240) and Harris (241) and modeled by Pretorius et al. (242-245). It seems that a condensed solvent zone forms at the top of the column, which is at room temperature, and plays the role of an additional stationary phase, retaining the solutes. Assuming that the solvent homogeneously coats the first 30 cm of the column, a solvent film thickness of 12 pm is calculated by Pretorius (against a film thickness of 0.12 pm for the stationary phase). Solutes are strongly retained until the programmed temperature analysis is well on its way and the solvent has all gone. The most important parameters of the split-splitless technique are: - the temperature of the column top, which should be above the freezing point of the solvent and 30 O C below its boiling point, - the carrier gas flow rate in the OTC, - the volume of sample injected, - the relative volatility of the solvent and the main components of the sample, including the less retained component. The proper implementation of the split-splitless technique requires exact timing of the different steps. Although automation is not required, the use of timers is a considerable help and markedly improves the repeatability of the results. Following Grob and Grob (237), the advantages and drawbacks of this technique may be summarized as follows: Advantages: - Reduction of the possible quantitative errors due to discrimination of the splitting techniques, - Reduction of the sample losses, owing to the solvent effect. Up to 90%of the amount injected can be channelled into the OTC. - Possibility of injecting very dilute samples, without a need to concentrate them prior to analysis, - Absence of oxidation of the analytes due to the large amount of air in head space samples, because oxygen is swept off when the column is still cold, - No adsorption can take place in the vaporization chamber, which can be kept much cleaner. Drawbacks: - The repeatability of the retention times is affected by the solvent effect, and is not very good, - It is difficult to analyse volatile compounds which have a vapor pressure close to that of the solvent, - The technique is limited to the use of volatile, light solvents. The method can be used only in connection with programmed temperature gas

293

chromatography, and for the analysis of relatively dilute solutions, in a light solvent. Under these conditions it gives excellent results. Another splitless injection technique was developed by Evrard and Guiochon (246), who applied it to the analysis of traces of heavy organics. The sample is injected on a short, narrow-bore, cold-packed column. The solvent is eluted. Then the packed solumn is temperature programmed to 250 O C and all its effluent sent to an open tubular column. This transfer permits a concentration of the injected band. A high degree of concentration is achieved, permitting the achievement of extremely low detection limits. The method is tedious and cumbersome and has not been widely applied. c. The Ros Injector

Also called “dry sampling” or “moving needle method”, the use of the injector designed by Ros (247) and improved by Van den Berg and Cox (248) is especially suitable for the analysis of dilute samples of high boiling compounds. The principle of the method is to coat a small fibre with the analyte solution, evaporate the solvent and transfer the fiber into a heated area where the sample components are vaporized and carried to the column. A glass stem (see Figure 8.16) is fixed to a steel plunger at one end, and to a thin glass, quartz or metal fiber or small solid needle at the other end. A magnet moves the stem in a vertical glass tube. The stem has two positions. A side, suitable injection port with a septum is placed at the level of the needle when the stem is in the “high” position. The carrier gas enters on the side of the glass tube and splits into two parts. The larger flow rate goes upwards, the smaller part goes to the OTC. The injection is performed in two steps: - In the first step, the glass stem is in the “high” position, in the cold area (room temperature). The analyst places, with a syringe, a droplet of solution on the fiber (ca 1pL). The carrier gas upper stream vaporizes the solvent vapor and carries them to vent, via a capillary restriction. The sample is dried in a few minutes. This step can be repeated as needed, to inject a large sample. - In the second step, the glass stem is moved down with the magnet, into the hot zone of a small but conventional injection block, a few millimeters away from the column tip. The analytes are rapidly vaporized and their vapors carried to the column. After a few seconds the glass stem is brought back to its upper position and, after cooling, its tip is ready to be coated again. It takes 3 seconds to inject totally a sample of octacosane (n-C,,H,,) at 250 O C (247). The advantages of the method are as follows: - The Ros injector is a low cost device, easy to build for a glassblower, and can be adapted to nearly any gas chromatograph. - Contact between the sample and a material part is very limited. The fiber is easy to clean in a flame or to replace. - Analysis of very dilute samples can be performed without preconcentration. - There is no solvent tail, hardly even a solvent peak, with the advantages of easy resolution and detection of early peaks. References on p. 311.

294

c a -

I I

Figure 8.16. Schematic of the Ros injector (After Ros, ref. 247). a, carrier gas inlet. b, open tubular column. c, septum and injection port. d, syringe for sample introduction. e, Ros needle. f, magnet. g, purge valve.

The main drawbacks are: - Possible loss of compounds of high or intermediate volatility during the first step, when the solvent is vaporized. - The Ros injector is simple but there are many sources of leaks, which must be plugged before starting operation. The system is brittle. - The system is manually operated, very difficult to automate. - Although it is in principle possible to carry out isothermal analysis, the position of the needle during sample vaporization is then very critical. The injector is better used with programmed temperature analysis, which minimizes the injection volume contribution to band broadening.

295

d. On-Column Injection All injection devices or methods described so far require the use of a splitting device, which makes quantitative analyses difficult and results in packed columns giving more accurate and more precise results than OTC‘s, which does not have to be the case. This has been acknowledged by many scientists, such as Zlatkis and Walker (249), Ettre et al. (250), Willis and Engelbrecht (251,252) and Verzele et al. (253). The suppression of the splitter would be a major improvement, opening the door wide for the widespread adoption of OTC’s in routine and process control laboratories. On-column injection has been pioneered by Grob and Grob (254,255), who wrote: “Injection has been the major, if not the only, respect in which packed columns have been superior to capillary columns. On-column injection completely eliminates all the above drawbacks, thus favouring the analysis of heat-sensitive material and exact quantitative work.”

t

=plastic glass

Figure 8.17. Schematic of the on-column injector from Carlo Erba (After Galli et al., ref. 224). 1, open tubular column. 2, carrier gas inlet. 3, inlet cone to the column. 4, stop valve. 5, needle guide. 6 , spring. 7, stream of cooling air. 8, thermal insulation. Reprinted with permission of Journal of High Resolution Chromatography and Chromatography Communications, 2 , 366 (1979). References on p. 311.

296 TABLE 8.8 Standard Deviation of the Measure of the Response Factors of Fatty Acid Methyl Esters (286) Compound

RSD (%)

Methyl heptadecanoate Methyl stearate Methyl oleate Methyl linoleate

1.6 3.9 4.2 4.0

TABLE 8.8a Discrimination Observed on a Test Mixture of Hydrocarbons in Different Conditions (224) Solvent: n-Pentane (b.p. 36 " C) Oven Temperature

50°C

Secondary cooling

OFF Ratio

C-18 c-20 C-24 C-30 c-34 C-38

100°C

ON RSDS

Ratio

0.97 9.6 0.98 0.98 6.0 0.97 Internal Standard = 1.00 0.99 2.6 0.99 1.05 5.5 1.02 0.93 3.1 0.97

ON

OFF RSDW

Ratio

RSD%

Ratio

RSD%

0.9 1.7

1.71 1.30

39.4 27.0

1.02 1.01

2.4 3.4

1.6 1.6 1.6

0.77 0.73 0.71

19.1 16.5 11.5

1.00 1.03 0.99

2.0 3.0 3.3

TABLE 8.8b Discrimination Observed on a Test Mixture of Hydrocarbons in Different Conditions (224) Solvent: n-Hexane (b.p. 68°C) Oven Temperature

100°C

Secondary cooling

OFF Ratio

C-18 c-20 C-24 C-30 c-34 C-38

150°C ON RSD%

Ratio

7.8 1.02 4.9 1.02 Internal Standard = 1.00 0.96 1.9 1.02 0.99 3.3 0.99 0.97 5.0 0.97 1.20

1.08

OFF

ON

RSDX

Ratio

RSD%

Ratio

RSD'R,

2.1 1.2

2.38 1.56

58.9 39.7

1.03 1.02

2.5 1.7

1.3 2.1 1.9

0.89 0.86 0.83

6.1 12.7 14.0

1.02 0.98 0.91

1.6 2.6 2.7

Reprinted with pemhsion of Journal of High Resolution Chromatography and Chromatography Communications, 2, 366 (1979).

On-column injection is permitted by the considerable improvements in column technology made during the late 'seventies and early 'eighties, especially by the development of immobilized films of stationary phases (see Section 11.5.~'above). On-column injectors are very much like conventional injection ports for packed columns, but with one major difference. The septum has to be replaced by a stop

297

TABLE 8 . 8 ~ Discrimination Observed on a Test Mixture of Hydrocarbons in Different Conditions (224) Solvent: n-Heptane (b.p. 98'C) Oven Temperature

l00'C

Secondary Cooling

OFF Ratio

C-18 c-20 C-24 C-30 c-34 C-38

150'C

OFF

ON RSDS

Ratio

1.01 1.5 1.00 1.02 1.3 1.01 Internal Standard = 1.00 0.99 1.6 0.98 0.98 1.7 0.99 0.99 1.8 0.99

ON

RSDS

Ratio

RSDS

Ratio

RSDS

1.3 1.5

1.93 1.53

48.0 30.5

1.02 1.02

1.0 1.3

1.6 1.7 1.7

0.68 0.60 0.59

18.9 17.6 20.1

0.98 0.97 0.99

1.5 1.5 2.2

valve (see Figure 8.17). The thin, long needle required to place the sample inside the capillary column cannot be inserted through a septum. Thus the chromatographic system is not completely leak free, and during injection some amount of air

11

10

II 3

Figure 8.18. Schematic of the on-colurnn injector by Schomburg (222). 1, Carrier gas inlet. 2, Carrier gas outlet. 3, Open tubular column. 4, Graphite or vespel ferrule. 5, Sampling device. 6, Sliding valve. 7, Thermal insulation. 8, Sampler handle. 9, Device for handling very small samples. 10, Micropipette. 11, Silicone seal. Reprinted with permission of Journal of Chromatography, 142, 87 (1977).

References on p. 311.

298

penetrates inside the column, which is very detrimental to the column lifetime, although the analysis, here again, is usually carried out in programmed temperature GC. Otherwise, injection is carried out as with packed columns. The thin long syringe needle, guided by the co~$calaperture, is inserted into the OTC. After the cold sample is placed inside the'column, the needle is withdrawn, the stop-valve closed and the column purged &%h carrier gas. -The temperature progriyn is started. To keep the column top below the boiling point of the solvent, a stream of cold air flows around the injector body (224,254). Galli et al. (224) have illustrated the importance of the injector temperature during injection of a hydrocarbon mixture (see Table 8.8). The repeatability of the peak area is assured only if the solvent is kept from boiling. To overcome the inconvenience and drawbacks of stopping the carrier gas flow during the injection, Schomburg et al. (222) have proposed a more complex injection device, using a dedicated micropipette (see Figure 8.18). In order to avoid air leak into the column, however, this system should also include a lock. The advantages of the direct, on-column injection are as follows: - Better quantitative results are achieved. Sample discrimination is limited to the same extent as encountered with packed columns, and is due to differential vaporization inside the syringe needle. - Decomposition of temperature sensitive compounds is limited, since they are analyzed in temperature programming, and are not flash vaporized for injection. - Analytes do not see any other surface than the (treated) column wall. - There is no septum, fewer ghost peaks and fewer leaks. - The sample volume can be larger, if the column loadability is sufficient. - The column efficiency is not affected by the use of large dead volume injection systems. - There is no serious effect on the column lifetime, provided air is purged before heating the column. There are a few drawbacks, however: - The method is not suitable for pure samples: in most cases, the column loadability is insufficient. Dilute solutions must be used. - The column is slowly polluted by the non-volatile impurities contained in the samples: the quality of the samples analyzed must be carefully watched. - This is a manual method, difficult to automate. Automatic sampling valves are difficult to adapt to the requirements of on-column injection devices. - Special syringes, with special, long, fragile needles are required. e. The Programmed Temperature Vaporizers (PTV)

This injection method designed by Poy et al. (256-269) is a remarkable improvement to the splitless injection method of Grob (see Figure 8.19). Since, except with on-column injection methods, it is impossible to avoid component discrimination, i.e., faster vaporization of the compounds with larger vapor pressure, it might be better to try to master the phenomenon and use it to good effect. The principle of the PTV is based on the injection of the sample on a glass wool plug placed in a cold tube, just upstream the column. All the liquid contained in the syringe is transferred onto the glass wool and the syringe withdrawn. Then the temperature of

299

r‘ r i e r

Air

Figure 8.19. Schematic of the Program Temperature Vaporizer (prv) from Dani (After Poy, ref. 256). 1, Vaporizer block. 2, Glass liner. 3, Graphite seal. 4, Open tubular column. 5, Septum. 6, Septum cap. 7, Internal fitting. 8, Split needle valve. 9, Silanized quartz wool. 10, Temperature probe. 11, Solenoid valve. 12, Microfdter. 13, Heating element. 14,Flow switch. 15, Solenoid valve. Reprinted with permission of Cupillmy Chromutogruphy I K Huethig, Heidelberg, 1981

the tube is rapidly raised to a set value and the vapors transfered to the column. The injection block contains a glass insert, connected at its lower end to the OTC, which penetrates a few millimeters inside the liner and to the vent, and at its upper end to the carrier gas line. The wool plug is placed in the lower part of this glass tube. The main feature of the PTV is the speed at which the injector is heated, with a fast air stream, and the reproducibility of the temperature reached. The operation of the system, including the temperature program and the actuation of the valves, can be performed automatically, which permits a much better repeatability of the results than manual operation. Five different modes of injection can be carried out with the PTV: - Splitless injection, with cold injection of the sample, followed by vaporization with all the gas going to the OTC. The analysis must be performed with temperature programming, to avoid band broadening due to the large volume of the injector. References on p. 311.

300

- Solvent split injection, similar to the previous mode, but the split is open during the first part of the heating period, allowing splitting of the solvent vapor and venting of most of it. - Split injection, with the vaporizer cold at injection (followed by temperature program) or hot (conventional split injection). - Precolumn concentration, by injecting the sample on the glass wool, vaporizing the solvent only, and repeating the operation any number of times, before eventually vaporizing the whole analyte onto the column. - Total injection in microbore capillary columns. The advantages ensuing from the use of the PTV in practice are as follows: - The injection is carried out with standard syringes into wide bore glass inserts which can be easily cleaned or replaced. - OTC‘s of any inside diameter can be used. - The solvent can be easily separated from the sample and vented. - Precolumn enrichment can readily be used, in place of the injection port. - The device is easy to automate and can be used in routine laboratory analysis with minimum difficulty. The PTV is an excellent system to use. It meets most of the requirements of OTC sample injection. Poy et al. (256-260) have illustrated the superior results obtained with the PTV introduction system over traditional hot splitting injection, by analyzing mixtures of n-decane to n-octacosane. The standard deviation of the total area of the chromatogram, which is a measure of the total amount of hydrocarbon introduced, is 5.0% for direct introduction, 5.1% with the FTV and 15% for the splitting system with a hot vaporizer. Hinshaw and Seferovic (261)have shown that the results obtained with the PTV for the quantitative analysis of a synthetic mixture of triglycerides are comparable to those obtained by cold on-column injection and much better than those given by the hot split technique, which gives strong discrimination and even decomposition of some components. Schomburg et al. have proposed a so-called “cold needle” injection method to avoid possible discrimination of some light components during the end of the solvent split operation (262). f: Conclusion

The PTV seems to be the most practical approach for quantitative analysis, particularly because it can be entirely automated. Comparable results are obtained with on-column injection but this method is more difficult to implement and requires skilled analysts. 2. Column Switching Techniques

Multidimensional chromatography is the name given, somewhat improperly, to the systematic application of the column switching techniques developed and widely used by process control engineers as early as 1957 (see Chapter 9,Section IV). The backflush technique was used with OTC by McEven (263)in 1964. At that time packed and capillary columns were successfully coupled for the analysis of

301

6

Figure 8.20. Dual column system set up with Deans pneumatic device for flow switching (After Schomburg et al., ref. 273). 1, Injector. 2, Column (conventional packed or OTC). 3, Switching device. 4, Auxiliary carrier gas inlet. 5, Valve. 6, Cold trap. 7, Main column (usually OTC). 8, Detector. Reprinted with permission of Journal of Chromatography, 112, 205 (1975).

light hydrocarbon mixtures (264). Many other examples of such couplings have been described in the early literature (265-271). The systematic development of multi-dimensional chromatography started, however, with the pioneering work of Schomburg et al. (66,130,272-274), based on the use of the pneumatic switching technique designed by Deans (275), which avoids the use of valves on the carrier gas lines, and eliminates the problems created by their dead volumes, fittings, leaky “0”-rings, baked solenoids, etc. Although special valves have been designed and produced for use with OTC‘s (269-271), it seems that the Deans switching method is much more practical and more popular (276-278). This method is described in detail in Chapter 9, Section IV.2. It permits both backpurging and heartcutting. An attractive coupling device has been described by Schomburg et al. (273) for trace enrichment. The system uses an intermediate trapping stage, between a precolumn and a column connected by a Deans interface (see Figure 8.20). The precolumn may be either a packed column or an OTC. After elimination of the solvent peak by means of the heartcutting device, and of the undesirable heavy components by the backpurging function, the trace impurities are trapped and then re-injected into the OTC. Intermediate trapping for band focusing gives excellent chromatograms and makes quantitation easier, more precise and the detection limits lower. The cooling and heating of the trap are carried out by air streams, the References on p. 311.

302

{ented

I

trapped-

I Figure 8.21. Trace analysis of 2-nitronaphthalene (26 ppm) in 1-nitronaphthalene.(After Schomburg et al., ref. 222). Procedure using Deans heartcutting method and an intermediate trapping of the trace component. I, Heartcutting. 11, Analysis of the trapped material. Reprinted with permission of Journal of Chromatography, 142, 87 (1977).

temperature of which can be controlled easily. The whole system can readily be automated for routine analysis. The incorporation of a second detector, located between the precolumn and the column, permits a more accurate 'timing for the switching operations. An illustration of the usefulness of the method is given by the analysis published by Schomburg et al. (222) of 26 ppm of 2-nitronaphthalene in 1-nitronaphthalene (see Figure 8.21). The first chromatogram on this figure is obtained with the intermediate detector. The end of the peak of the main component and the trace components are collected by actuating the valve 5 and cooling the trap 6 (see Figure 8.20) with liquid nitrogen. The second chromatogram gives the final analysis. Separation of the trace component from the fraction of the main one which has been collected in the trap is easy, and the detection limit is much lower than necessary. The addition of an internal standard which could be collected with the trace component and can be eluted close to it would easily improve the precision of the determination to a considerable extent. This method can be extended to the analysis of very dilute traces by cumulative trace trapping. A special coupling device designed by Oreans and Muller (279,280) makes the use of the Deans technique much more simple (see Figure 8.22). The device is made of two crosses set against each other. Each cross has a branch for carrier gas input and one for carrier gas output. The two OTC's are connected one at each end of the double cross (see Figure 8.22). By adjusting the pressure difference between the two circuits it is possible to let the carrier gas flow in one or the other direction, thus permitting heartcutting and backpurging when desired. The system is easy to

303

Figure 8.22. Schematic of the double chromatograph by Siemens (After Muller and Oreans, ref. 279), performing multi-dimensional analysis, using the Deans switching method. A, Stand-by position. B, Heartcutting. C, Backpurging. Reprinted with permission of Siemens.

automate. The main positions of the device are: - Stand-by (Fig. 8.22A). The main carrier gas stream (white on Fig. 8.22A) flows successively through the injector (J),the column 1, the coupling device, the column 2 and the main detector. The differential pressure between points b and b’ of the coupling device is such that most of the gas feeding the auxiliary detector (exit at c) comes from this main circuit (i.e., from point a). A small stream enters at b and then at b’ to join this main gas stream and flow to the main detector through column 2, while the rest of the gas stream entering the coupling device at b’ exits through c’ and goes directly, as scavenger gas, to the main detector. - Heart cutting (Fig. 8.22B). The differential pressure between b and b’ is inverted, by raising the pressure at b’. The flow direction in the central capillary is reverted. The main gas stream now flows through the injector, the column 1 and the auxiliary detector. It is joined in this detector by the stream entering at point b and by a small fraction of the gas entering at point b’ and flowing through the central capillary. The gas entering at b’ flows mainly through column 2 to the main detector. The two columns are isolated. - Backpurging (Fig. 8.22C). The pressure is dropped at the main carrier gas inlet and gas flows from point b through the auxiliary detector, but also through the column 1 and the injector, backflushing the column 1. Gas entering at b also joins gas entering at b’ to flow through column 2 to the main detector. References on p. 311.

304

These features permit the ready implementation of complex separation schemes, involving the combination of separations on two different columns, intermediate trappings and enrichments and column backflushing. V. GUIDELINES FOR THE USE OF OPEN TUBULAR COLUMNS

The selection of the stationary phase is performed in the same way as is used for conventional packed columns. The main difference is that OTC's offer a much greater efficiency for comparable analysis times. The most important consequence in routine analysis, when the samples are not very complex, is that the liquid phase selection is much less critical with OTC's than with PC's. The price paid in choosing a conventional stationary phase instead of one which would give a much better resolution of the analyte component is often rather inconsequent, unless a rapid analysis is required. For most exploratory work, when data are collected on the different components of the mixture analyzed and on various possible stationary phases, it is strongly recommended to use wide bore OTC's, because they offer fast separations, which means that most or all components, including strongly-retained ones, have a good chance to be eluted in a decent time. Wide bore silica capillary columns, coated with a layer of immobilized stationary phase, are probably going to replace conventional packed columns in most of their applications in routine analysis and in a number of cases, even in process control analyses. This is because they accept samples which can be delivered by automatic sampling valves, require flow rates large enough to be compatible with the use of conventional flow controllers and offer a large efficiency, lower than more conventional, small bore OTC's, but more than enough to facilitate the separation of most mixtures analyzed in routine laboratories. Furthermore, the very inert silica wall surface gives rise to very little analyte adsorption, a precious quality for the analysis of strongly polar compounds. One present limitation is the small number of immobilized liquid phases offered by vendors, and the near impossibility for an analytical laboratory to start manufacturing its own columns. A list of the phases available today (March 1987) is given in Table 8.9. The first step in the development of an analytical methodology for a new sample would thus be its analysis on short, wide-bore silica columns, CQ 10 to 15 m long, which allow analysis at low temperatures and which offer short analysis times. Several columns, coated with layers of stationary phases of different polarities, will TABLE 8.9 List of Immobilized Stationary Phases Available in Fused Silica Open Tubular Columns Poly(methylsiloxane) Poly(phenylmethylsiloxane) Poly(cyanopropylmethy1siloxane) Poly(trifluoropropylmethylsiloxane) Poly(ethyleneglycol)

305

be used. Further optimization work depends on the aim of the work, requiring either faster analysis or better resolution.

1. Improving Peak Resolution When more resolution is needed, the first step is to operate the wide bore column at the optimum flow velocity, which usually corresponds to a flow rate of about 2 to 5 mL/min. If this is not sufficient, a longer column may be used. Up to lengths of several hundred meters, the column back pressure is going to remain low and will not create additional problems. The analysis time will become very long, however. If a still larger efficiency is required for some reason, and the separation cannot be improved by using a more selective stationary phase, the use of a narrower bore OTC becomes mandatory. Injection will then become difficult, because of the small sample size such columns may handle without being overloaded, and because of the high inlet pressure (25,206,281).

2. Reducing Analysis Time Analysis time can be drastically reduced when a wide bore OTC is used and the resolution achieved exceeds the one needed for good quantitative analysis. The first possibility is to operate the column at a larger flow rate. Values of up to 30 or 50 mL/min can be achieved without raising the inlet pressure excessively. Alternately the column can be cut. In both cases, the band width becomes narrow and problems may arise if the detector is unable to respond fast enough to the rapidly changing analyte concentration in the carrier gas (see Chapters 10 and 13).

3. Thickness of the Stationary Phase Layer The thickness of the stationary phase film is a very important parameter. It controls the phase ratio and thus determines the retention times, the amount of sample which can be injected in the column and the range of temperatures where the elution of the analytes is possible in a reasonable time. Vendors offer OTC's with various liquid film thicknesses, from 0.1 pm to 5 pm and more. In practice the choice should be governed by the following remarks: - Choose a thick film column if: the sample size has to be increased, light components have to be separated. - Choose a thin film column if: high boiling compounds have to be analyzed, the sample contains temperature sensitive molecules, a faster analysis is required, a higher column efficiency is required. We recommend starting the investigation of a new analytical problem by using a wide bore silica column, 0.5 to 0.6 mm i.d., coated with a lilm of immobilized liquid phase 1 pm thick. Optimization of the column design parameters will be carried out later, depending on the first set of results obtained, as suggested by Ettre (282). References on p. 311.

306

Computer programs are now available to determine the optimum column length and diameter, film thickness and flow velocity, starting from a first set of data (283). 4. Selection of the Carrier Gas

It has been demonstrated that the best carrier gas for gas chromatography is hydrogen, because this gas is both the one with the lowest viscosity and the one with the largest diffusion coefficient. Thus, the optimum velocity is larger than with any other gas. Mehran (284), for example, has shown that for 0.53 mm i.d. OTC’s the optimum carrier gas flow rates were 1.5, 3.2 and 4.2 mL/min for nitrogen, helium and hydrogen, respectively. Because the viscosity of hydrogen is 2.5 times lower than that of helium, the compressibility factor is much closer to unity for hydrogen than for helium, which also contributes to reducing the analysis time, although this advantage is not extremely important when wide bore, short OTC‘s are used, because their permeability is large anyway. For safety reasons, however, helium is often preferred. The analysis time is typically 30% longer with wide bore columns, 50 to 60% longer with narrow bore columns than with hydrogen. It is still twice as fast as with nitrogen. The wide bore columns often accept a flow rate large enough to permit the use of most detectors without additional scavenger or “make-up” gas, which is a significant advantage, increasing the simplicity of the operation of the chromatograph.

5. Sampling and Sample Size Any sampling system developed for the use with OTC’s can be used with wide bore columns, but on-column injection, which is practical only with wide bore, thick film columns is a method of choice for quantitative analyses, because it avoids all the pitfalls associated with the use of splitting devices with very large splitting ratios. Although some technical literature claims that wide bore columns admit sample sizes similar to conventional packed columns, this statement is somewhat meaningless, because there is a wide variety of packed columns accepting sample sizes between 0.1 and 10 pL (not counting preparative columns), and because for OTC‘s the loadability or the maximum sample size depends on several parameters, mainly: - the film thickness of the stationary phase, - the complexity of the mixture, - the concentration of the solutes analyzed, main components or traces, and their resolution from the most important components. In practice, a wide bore silica OTC, 0.53 mm i.d., coated with a 1 pm thick liquid film should accept samples 30 to 300 ng per component. If a sample divider or splitter has to be used with a wide bore column, the splitting ratio should not exceed 10/1 to 25/1, which is easier to manage than the split ratio of several hundreds to 1,OOO or more required by conventional narrow bore OTC‘s (see Chapter 14, section on response factors). Wide bore OTC‘s cannot yet be used in process on-line analysis, because they cannot accept the 0.5 pL samples, which is the smallest that automatic valves can

307

B

A

C

!

/ Y f 5

L

M z Figure 8.23. Analytical results obtained by coupling a pulsed injection valve with a wide bore open tubular column. Column: 10 m long, i.d. 0.53 mm. Stationary phase: immobilized methylsilicone. Camer gas: helium. Flow rate: 0.2 L/h. Temperature: A: 150 O C:B, C: 120 C. Pressure pulsed injection: 0.4 atm. Injection time: 0.5 sec. Detector: A, B: thermal conductivity detector. C: flame ionization detector. Sample size: 0.2 pL. A: undiluted mixture. B: same as for A, but diluted at 10%in n-hexane. C: same as for A, but diluted at 1%in n-hexane.

repeatably inject. The pulse injection system (see Chapter 9, Section III.2.d) has been tried, however, in connection with wide bore OTC's. The excellent results obtained (see Figure 8.23) suggest that this combination may be the key to opening up the last area where OTC's could not be widely used (178). A 0.2 pL sample of a four hydrocarbon blend (n-heptane, n-nonane, n-decane, n-undecane in equal concentrations) has been injected with the pulse injection system. Three series of experiments were performed, with the pure mixture or with solutions in n-hexane, diluted 10 and 1%.The column temperature was uniformly 120O C except for the first run. The column is overloaded by the first sample. The second and third samples give excellent, similar peak profile and column efficiencies. 6. Detector Selection

There is no restriction on the selection of detectors. In practice, wide bore OTC's can work with all detectors designed for operation with conventional OTC's or with References on p. 311.

308

packed columns. In this last case, when they are operated close to their optimum flow rate for maximum efficiency, it may be necessary to add a stream of “make-up” gas at column exit, before the column effluent enters the detector. 7. Conclusion

Thirty or twenty years ago, the analyst had to pay much more attention to the selection of the proper stationary phase than to the column packing and to its efficiency. This was so because it was extremely difficult to markedly increase the efficiency of a packed column. Columns more than 5 m long were a rarity. Columns more than 10 m long were monsters. Only the selection of the stationary phase

D

0

5

10

I>

mi n

Figure 8.24. Separation of high molecular weight reference aza-arenes. Column inner diameter, 0.3 mm; length 30 m. Stationary phase, silicon grease SE 52. Film thickness: 0.15 pm; temperature 280 C. Reprinted with permission of Journal of Chromatography, 246, 23 (1982).

309

permitted the achievement of the required separation. This was a long procedure, requiring tedious, systematic experiments, and good insights into molecular interactions. It resulted in the use of more than 300 different phases.

0

0

cu

BI

0 0 d

0

0

cr)

OV-73

I

90

10

2p

30

40

50

60

70

110

130

150

170

190

210

230

0

0 *

I

SP-2340

4p

50

134

156

178

-

rnin

60

c

1

112

'C

0

z

90

.

rnin*

200

222

L isoth.. 'c

Figure 8.25. Effect of alkyl substitution on the separation of petroleum ma-arenes (crude oil sample from Congo). First column inner diameter, 0.3 mm, 55 m long; stationary phase, OV-73 (apolar). Film thickness: 0.18 pm. Second column, column inner diameter 0.3 mm; length, 55 m; stationary phase, SP-2340 (strongly polar). The film thickness is 0.15 pm. Reprinted with permission of Journal of Chromatography, 246, 23 (1982). References on p. 311.

310

Nowadays the situation is reversed. Silica open tubular columns, wide or narrow bore, coated with films of immobilized liquid phases most often offer a much larger efficiency than needed. The analyst can rapidly select a suitable column to perform his separation and the problem is more how to trade the excess resolution for more sensitivity or for a shorter analysis time. Implementing a new separation with OTC‘s is usually fast and optimization is superfluous. Wide bore silica columns, coated with films of immobilized liquid open a new era in industrial control analysis and possibly in process control and automation, as emphasized by Van Straten (285) and by Mehram (284). Large diameter open tubular silica columns, coated with immobilized films of stationary phase and operated at large flow rates provide the analyst with a simple route to higher resolution, faster analysis and more sensitive detection than is possible with packed columns, in most cases, while keeping the advantage of favorable sampling conditions. Analysts should really change their minds about “capillary chromatography”. Figures 8.24 and 8.25 illustrate the potential advantages of open tubular columns, still very much unleashed, in the separation of heavy mixtures of highly polar compounds, such as ma-arenes, in a complex matrix like crude oil.

GLOSSARY OF TERMS Coefficient of the first term of the Golay equation. Equation 8. Concentration of the liquid phase in the coating solution (v/v). Equation 1. C, Coefficient of the resistance to mass transfer in the mobile phase in the Golay equation. Equation 8. C, Coefficient of the resistance to mass transfer in the stationary phase in the Golay equation. Equation 8. CE Coating efficiency. Equation 22. C,,, Maximum concentration of the analyte in the elution band. Equation 23. D, Diffusion coefficient of the analyte in the mobile phase. Equation 9. D, Diffusion coefficient of the analyte in the stationary phase. Equation 11. d, Column inner diameter. Equation 6. d, Thickness of the film of stationary phase. Equation 1. EPN Effective peak number. Equation 18. f Correction factor of the HETP for the compressibility of the mobile phase. Equation 8. H Column plate height. Equation 8. He Experimental value of the plate height. Equation 22. Hmin Minimum value of the plate height. Equation 13. k Column permeability. Equation 6. k’ Column capacity factor. Equation 10. L Column length. Equation 4. I Width of a peak at half height. Equation 17. m Weight of analyte introduced in the column. Equation 23. N Number of theoretical plates of the column. Equation 23. P Inlet to outlet pressure ratio. Equation 7. B C

31 1

W(Z)

w

/3 7

p u

Outlet column pressure. Equation 7. Inner radius of the column. Equation 1. Separation number. Equation 17. Trennzahl or separation number. Equation 17. Gas hold-up of the column. Equation 7. Uncorrected retention time of an analyte. Equation 17. Linear velocity of the coating solution plug. Equation 1. Carrier gas velocity at column outlet. Equation 8. Optimum carrier gas velocity, at column outlet. Equation 14. Specific retention volume. Equation 24. Retention volume. Equation 24. Base-line width of the peak z. Equation 18. Weight of stationary phase introduced in the column. Equation 4. Phase ratio. Equation 16. Viscosity of the coating solution. Equation 2. Density of the liquid phase. Equation 4. Surface tension of the coating solution. Equation 2.

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319

CHAPTER 9

METHODOLOGY Gas Chromatographic Instrumentation

TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I . Description of a Gas Chromatograph . .................................. I1. Pneumatic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Serial Flow . . . . . . . . . . . . . . . . . . . .................

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3. Pressure Controller . . . . . . . . . . .................................. 4. Flow Rate Controller . . . . . . . . . .................................. 5 . Operation of the Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Sampling Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. GasSamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Membranevalves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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..

...

........... d . Piston Valves . . . . . . . . . . . . . 2. Liquidsamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a . Syringes and Vaporization Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................. b . Automatic Piston Sampling Valves c. Rotary and Sliding Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d . Pulsed Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Comparison between the Repeatability of the Different Injection Systems . . . . . . . . . . . . a . Gas Sampling Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... b . Liquid Sampling Valves IV . ColumnSwitching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................ 1. Valve Switching . . . . . . . . . . . . . . a . Backpurging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b . Backflushing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Heartcutting . . . . ................ .. d . Intermediate Storin ............................................ ................. 1. Dynamic Method or Cutting 2. Static Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....................... e. Column Reversing . . . . . f . Combination of Switching Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Intermediate Pressure Control (Deans Method) ............................... a. Backpurging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b . Heartcutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Advantages of this Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Determination of Switching Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a . First Problem: Calculation of the Length of Intermediate Column Segments . . . . . b . Second Problem: Calculation of the Transit Time on an Intermediate Column Segment c. Third Problem: Calculation of the Retention Time on a Column having an Outlet Pressure above Atmospheric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d . Examples of Application . . . . ................

320 320 321 321 322 323 326 321 321 321 328 329 330 331 331 332 333 336 336 339 339 339 340 341 341 345 346 347 341 349 349 350 351 353 355 360 362 365 313 313 380

320 1. Determination of the Length of an Intermediate Column Segment . . . . . . . . . . . . . 2. Determination of the Switching Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Ancillary Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Oven and Temperature Control . . . . . .................................. 2. Temperature Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........... a. Isothermal Analysis ..................... b. Temperature Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Design of a Modem Gas Chromatograph for Temperature Programming. . . . . . . . . . . d. Other Parameters in Programmed Temperature Gas Chromatography . . . . . . . . . . . . . e. The Future of Temperature Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Flow Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

380 380 384 384 385 386 386 387 388 389 389 390

INTRODUCTION A dedicated instrument is required to carry out analyses or separations by gas chromatography. Although the emphasis placed at meetings, in University as well as professional courses, in the instrumentation industry as well as among the users, is on the electronic equipment used by the gas chromatograph, we are of the opinion that none is really required to properly operate a gas chromatograph. As illustrated by the apparatus described by Jan& (1) or more recently by Annino et al. (2), a chromatograph may operate very well without a source of electricity. As a matter of fact, Rayleigh could have separated and detected the rare gases using a gas chromatograph made with parts available at the time. On the other hand, the contribution of electronics to the reliability, flexibility and accuracy of the gas chromatograph is obvious. It is essential in the detector compartment, where the signal delivered by a sensor measuring a physical property of the column eluent is transformed into a voltage, the only property easy to record. The contribution of the electronics is also major in the area of the controls of the experimental parameters, notably the temperature, and to a lesser degree the pressure or flow rate. The problems arising in connection with the chromatographic equipment are discussed in two chapters. The present one deals with the plumbing systems and the temperature control of the column, while the next chapter (Chapter 10) is devoted to the ’detection problem.

I. DESCRIPTION OF A GAS CHROMATOGRAPH The structure of the gas chromatograph results from the simple definition of the process used. “Chromatography is the separation process resulting from the differential elution of the components of a mixture undergoing partition or adsorption equilibria between a stationary phase and a mobile phase which percolates across the stationary phase” (3). In the case of gas chromatography, the instrument incorporates: . - a system delivering a stream of constant flow of carrier gas to the column. This system includes pressure and/or flow rate controllers,

321

a sampling system, a chromatographic column, with a temperature control system, a detector, with its system of data acquisition and handling, - possibly, in the case of preparative applications, a fraction collector and a carrier gas recycling unit. Various classification procedures can be used, such as between series and parallel gas lines, depending whether the chromatograph uses one or two columns. Chromatographs can also be classified after the detector used. The pneumatic circuit of an equipment is more complex if it uses a flame ionization detector than if it uses a thermal conductivity detector. -

11. PNEUMATIC SYSTEM

Although it is not a part of the gas chromatograph, the carrier gas cylinder is an essential element of the gas line. Through a one or two-step pressure controller, it provides a convenient source of pure, pressurized gas and is a cost-effective replacement of the pump used in liquid or supercritical chromatography. The gases contained in cylinders are usually very pure. Care should be taken to avoid pollution of the carrier gas by oxygen or vapors contained in the laboratory atmosphere, which can diffuse into the carrier gas line, through the membranes of pressure and flow rate controllers, through injection septa, or through the vent. For applications requiring extreme purity of the carrier gas, the use of steel membranes and a protection of the septum between injections are recommended. Sometimes traces of organic solvents used to wash metal parts can contaminate the carrier gas for a long time (4). The gas cylinder should be treated carefully and attached in a stable position during all experiments. Because the heat content of gases is small and their thermal conductivity sufficient to permit rapid heating or cooling, the carrier gas does not have to be preheated at the column temperature and the cylinder is always kept at ambient temperature. The carrier gas plays an important role in chromatographic analyses. A good stability of the carrier gas flow rate is a requisite of major importance for the achievement of good performance and reliable analytical results. Accordingly, the analyst must know the details of the design of the pneumatic circuits of gas chromatographs and the principles of the various devices used. 1. Serial Flow

As shown on Figure 9.l.a, the carrier gas flows through a pressure controller and/or a needle valve (a) used to fine-tune the flow rate, the reference cell of the detector (g, usually a thermal conductivity detector with this schematic), the sampling system (d, syringe injector or sampling valve), the column (f) and finally the measure cell of the detector (g). A manometer (c) is connected to the gas line just before the sampling system. When a flame ionization detector is used, there is no reference cell and the detector is also fed by streams of hydrogen and air or oxygen. References on p. 390.

322

Figure 9.1. Schematic of the Gas Streams. a - Serial Stream. b - Parallel Streams.

With this schematic, the sampling system, column and detector are usually placed in the same oven, at the same temperature, 8 , and the column is operated isothermally. 2. Parallel Flow

In this case two columns are connected in parallel, to the same gas cylinder. Both have a pressure or a differential pressure (i.e., flow rate) controller (b), a side manometer (c), a sampling system (d), a column (f) and a detector (g, see Figure 9.1.b). If a thermal conductivity detector is used it is connected so as to use one gas stream as reference and the other as eluent. Sometimes one pressure controller is placed upstream of a Y or T connector and both lines have their own flow rate controller. Both columns are usually placed in the same oven, while both detectors are in a second oven, contiguous to the column oven, but with an independent temperature controller. This design permits the use of temperature program analysis (5). This technique is widely used in laboratory analysis, because it permits a considerable reduction in the analysis time, while keeping a good resolution of compounds with a high vapor pressure, which are eluted early, and of compounds with a low vapor pressure, which are eluted later, when the temperature has become sufficiently high.

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This method is used for the analysis of mixtures of compounds with a large range of boiling points. A proper use of the method requires that the detector be in a separate oven, kept at constant temperature, while the column temperature is programmed, to avoid base line drift and change in the response factors. Temperature programmed gas chromatography is not used in process control analysis, because retention times, which are the basis for qualitative analysis, i.e. peak identification in routine analysis, are too difficult to reproduce, because the column lifetime is much reduced and because the results of quantitative analysis are less reproducible. In a dual column chromatograph, either column may be used for analysis. If the two columns are nearly identical, as is most often the case, and if the two detectors are arranged so that the data system records the difference between their output signals-a certain compensation for various drifts may take place. This permits an important increase in base line stability. Drifts due to the change in carrier gas flow rate, because the gas viscosity increases with increasing temperature (see Chapter 2), or to the loss of stationary phase, because its vapor pressure or rate of decomposition increases with increasing temperature, can be easily compensated by the use of a differential detector. Serial flow instruments are simpler and are used for most tasks of routine analyses. This design is selected for most process control analyzers as well. Analyses are performed isothermally. In sophisticated instruments, secondary sources of carrier gas, at controllable flow rates, are available to flush the detector reference cell, to backflush the column or for other tasks. Parallel flow instruments are used for more complex tasks, research applications, analysis development or analyses requiring the use of temperature programming.

3. Pressure Controller This is used to lower the pressure of the gas stream, while keeping the downstream pressure constant, in spite of possible changes in flow rate or flow resistance, such as a variation of the column temperature, resulting in a change in the carrier gas viscosity. The pressure is controlled by a variable flow restriction which is controlled by the movement of a needle inside a narrow conical hole (see Figure 9.2). The needle moves up or down under the combination of the stresses resulting from the compression of a spring and from the pressure acting on a flexible membrane. If the downstream pressure increases, the needle moves so as to reduce the gas flow, thus reducing the pressure. A manometer placed downstream of the pressure controller permits the adjustment of the inlet pressure to the gas chromatograph. This adjustment is made by more or less compressing the spring which acts on the membrane (see Figure 9.2). The pressure controller is closed when the spring is loose. Progressive compression of the spring by rotation of a screw raises the set pressure, while increasingly opening the valve a. The equilibrium position is reached when the sum of the spring stress and the pressure stress acting on the membrane is zero:

References on p. 390.

324

Figure 9.2. Schematic of the Pressure Controller. PI - Pressure of the incoming Gas,from the Cylinder. P2 - Controlled downstream Pressure.

f - Stress applied by the loading Spring. a - Needle.

where: - f is the spring stress, - PI and P2 are the carrier gas pressures on both sides of the membrane (see Figure 9.2), - Pa,, is the atmospheric pressure, - S, is the cross section area of the opening of the needle valve, - S2 is the cross section area of the membrane. Because PI is usually much larger than P2,we may write:

The relationship is linear only as a first approximation, because S, varies with the controlled pressure P2.S, decreases with increasing source pressure PI. The carrier gas flow rate will be a function of the controlled pressure. As explained in Chapter 2, the outlet carrier gas velocity, u,, which is the important parameter in gas chromatography, since it directly determines the column efficiency and the analysis time, is related to the experimental parameters by the following relationship:

where: - k is the column specific permeability, depending only (and slightly) on the packing method used, - d , is the average particle size of the packing material, - pi and po are the inlet and outlet column pressures, - q is the carrier gas viscosity, - L is the column length. From the design of the pressure controller, it is obvious that the pressure P2

325

depends on the atmospheric pressure. In fact if the atmospheric pressure varies, the controlled pressure varies too. Its variations copy those of the atmospheric pressure. If both Pz,practically equal to pi since the pressure drop of the sampling system is negligible, and the atmospheric pressure remain constant, the outlet carrier gas velocity remains constant, provided that the gas viscosity does not change. This requires that the column temperature remains constant. The viscosity increases with increasing temperature, proportionally to the 0.8 power of the absolute temperature (see Chapter 2), and so in temperature programming the outlet velocity decreases. Because gases are compressible, there is a certain lag in the effect, the outlet velocity at a certain time during the program, being larger than the steady state velocity corresponding to the viscosity at this temperature (6). Since the diffusion coefficients also increase with increasing temperature, the optimum carrier gas velocity, corresponding to the maximum column efficiency, increases with increasing temperature. Unless the column is operated well above the optimum flow velocity at the beginning of the analysis, the analyst runs the risk of having part of the analysis carried out under conditions where the efficiency is lower and the analysis time longer than possible. To avoid this problem flow rate controllers are used in temperature programming. The stability of the pressure controller has been studied with great detail and care by Goedert and Guiochon (7). They have shown that the exact value of the controlled pressure greatly depends on the temperature of the controller. The controlled pressure exactly follows the variation of the outlet pressure. The controlled pressure depends also on the stability of the inlet pressure. Thus, by operating a Negretti and Zambra pressure controller by reference to vacuum ( po ca 0.05 torr), in a temperature-controlled oil bath where temperature was stable within 0.1"C and with a source pressure fluctuating by 10 mbar they were able to control the outlet pressure within 0.3 mbar. Pressure (and flow rate) controllers use membranes which are usually in elastomeric materials, such as neoprene. They are rarely made of metal. These last membranes should be preferred whenever possible. Oxygen diffuses slowly across organic membranes, but not across metal membranes. Although the diffusion of air is very slow, it is sufficient to raise the oxygen concentration in the carrier gas much above its level in the cylinder. Measurements of the oxygen concentration at the outlet of a GC column give shocking figures, often exceeding 20 to 30 ppm (8). This is more than enough to give a considerable decrease in the thermal stability of the stationary phase. These organic polymers decompose thermally by free radical processes. Oxidation is a very efficient initiation process for these reactions. The use of a metal membrane pressure or flow rate controller and of a metal port-hole to protect the sampling port between injections and limit oxygen access to the outside of the septum permits a large increase of the average column life time. The general ignorance of this problem, together with the variety of designs of controllers, sampling systems, etc., resulting in some being by chance more favorable than others, explains the very conflicting results found in the literature on column life time, maximum temperature at which stationary phases may be used, influence of oxygen, etc. References on p. 390.

326

4. Flow Rate Controller

The flow rate controller is a differential pressure controller, which maintains constant the pressure difference between the two ends of a flow restriction, e.g., a needle valve. As far as the temperature of this valve is constant, the mass flow rate of carrier gas will remain constant. The performance of many commercial instruments may be considerably improved by merely controlling the temperature of the needle valve and of the controller itself (see previous section). Some of the best instruments incorporate a temperature controlled flow rate controller. A schematic of the flow rate controller is shown on Figure 9.3. The needle can move vertically inside a conical hole, permitting a gas stream with variable flow rate, depending on the position of the needle. This position depends on the pressure differential (P2- P3), pushing the membrane down, and on the tension of the spring, pushing the membrane and the needle up. When the spring tension is set, a decrease in flow rate results in a lower pressure drop in valve V, a larger pressure P3, the pressure differential decreases and the needle rises with the membrane, opening the hole for a larger flow rate. The device can thus control flow rate. The external command of the flow rate controller changes the spring tension, permitting an adjustment of the controlled flow rate. An equilibrium is reached between the pressures acting on the membranes and the spring tension when:

f = ( 4- p 2 P

(4)

Proper operation of a flow rate controller requires a stable inlet pressure. The flow rate is kept constant, at the flow rate controller temperature. Hence, if the column temperature changes, the volume flow rate will change, following the classical law of ideal gases: PV = nRT

(5)

The outlet column gas velocity increases as the column absolute temperature.

P2 P4

Figure 9.3. Schematic of the Flow Rate Controller. P2 - Pressure of the incoming Gas, from the Pressure Controller. P3 - Differential Pressure, determined by Valve V. P4 - Chromatographic Column Inlet Pressure. f - Stress applied by the loading Spring.

321

This is somewhat faster than the optimum carrier gas velocity (6), but at least the loss of column efficiency is traded for a decrease in the analysis time. 5. Operation of the Controllers

It is important to be able to recognize rapidly what kind of pneumatic design is used on a gas chromatograph one is not familiar with. This is easy if one observes that an increase of the column flow rate is obtained by rotating the command knob of a pressure controller clockwise, but by rotating the command knob of a flow rate controller counterclockwise. Setting up the flow rate, flow velocity or inlet pressure on a gas chromatograph for an isothermal analysis is straightforward. This operation is more complex on a sophisticated gas chromatograph having both a flow rate controller and a pressure controller used for programmed temperature analyses. The setting is carried out at the maximum temperature reached during the temperature program. Then a simple procedure is followed: - the needle valve of the flow rate controller is open fully, - the flow rate is set to the desired value by adjusting the pressure with the pressure controller. The corresponding pressure P2 is noted, - the set pressure of the pressure controller is increased by 1atm, to Pz 1. Since the needle valve of the flow rate controller is open fully, P2 1 is equal to the pressure P3 read on the manometer at the inlet of the sampling system. - the needle valve of the flow rate controller is then closed until the inlet pressure is back again to P2.The flow rate is measured carefully with a soap bubble flow meter and adjusted if needed. Since the flow resistance decreases with decreasing temperature, the inlet pressure will remain sufficiently below the set pressure of the pressure controller to permit correct operation of the flow rate controller during the entire analysis.

+

+

111. SAMPLING SYSTEMS

All column chromatography instruments must provide a sampling system which is used to meter the sample injected and to raise its pressure from atmospheric to the column inlet pressure. Dedicated systems are used for gas, liquid and solid samples. 1. Gas Samples

A syringe is sometimes used for rapid transfer of large samples, mainly for qualitative or semi-quantitative analysis. This method is applicable only if pollution of the sample by small amounts of air is inconsequential. Some details about the recommended procedure are given in Chapter 13. Mostly, sampling valves are used. We do not describe here glass valves or sampling systems using systems of glass taps, which were used in gas chromatograReferences on p. 390.

328

phy in the 'fifties or early 'sixties. They have been extensively reviewed (9). Their present interest is mainly historical. The valves used are membrane valves, rotary valves, piston valves and sliding valves. They can be actuated automatically, and can withstand rather high temperatures. Some implementations, using special materials, may be used with highly corrosive gases. Six-port valves are all that is needed to carry out a gas sample injection. 8-port or 10-port commutation valves are sometimes used. Only 6-port sampling valves are described here. Commutation valves are very similar in design. Only their use will be discussed.

a. Membrane Valves These valves use as their basic design element a socket, closed by a flexible membrane, and connected to two narrow tubes placed on the same side of the membrane (see Figure 9.4). If no pressure is applied to the membrane, the pneumatic switch is open. If a pressure higher than the one in the socket is applied to the other side of the membrane, the switch closes (see Figure 9.4). The valve is made of two cylindrical metal blocks, separated by a flexible, plastic membrane. The lower block contains the control system. Two independent channels carry compressed air to holes placed at the level of each one of 6, 8 or 10 sockets, a

Figure 9.4. Schematic of the Membrane Valve. a - Inlet and Outlet Ports of the Valve. b - Flexible Membrane. c - Solenoid Valve, directing compressed Air to one Line and putting the other Line under atmospheric Pressure.

329

A

B

Figure 9.5. Schematic of the Use of 6-Port Membrane Valves for Gas Injection. closed; 0: open. S + : Sample; G -B : Carrier Gas. (A) Filling the Sample Valve Loop with the Sample. The sample enters in 2 and goes through 1 to the loop and to 4 and 3. The carrier gas enters in 6 and goes through 5 to the column. (B) Injection of the Sample S in the Carrier Gas Stream. The carrier gas flows from 6 through 1 to the loop, which it sweeps, and then through 4 and 5 to the column. 0:

machine-tooled in the upper block. The holes are alternately connected to one of the two air channels (See Figure 9.4). The upper block contains the sockets. Each socket is connected to its two neighbors through two “Y” shaped channels. Depending on the state of the control solenoid valve, one or the other of the two control air channels is pressurized, and the gas entering each of the even numbered channels of the upper block exits through one or the other of its neighbor odd numbered channel (see Figure 9.4). Accordingly, changing the state of the control valve, C, shifts the exits of all gas streams, at the same time, clockwise or counterclockwise. The operation of a 6-port valve is shown on Figure 9.5. The sample loop is first swept and filled (Figure 9.5.A). Then its content is injected in the column (Figure 9.5.B). The membrane must be flexible and resistant to tearing caused by a very large number of switchings. It must also resist corrosion by the sample or its most aggressive components. It must not adsorb any component of the sample nor be permeable to them. Neoprene and Viton are the most popular. Mylar and Teflon are not flexible enough and tend to leak. The most serious drawback of this type of valve is the memory effects due to adsorption of sample components; these are especially serious in trace analysis. During commutation of the control pressurized air, some pressure shock may be generated in the membrane valve and may propagate to the detector, resulting in a base line perturbation or a spurious signal. b. Rotary Valves

These valves are made of two cylindrical metal blocks having a common axis, which are strongly pressed against each other by a spring. The faces in contact are carefully polished and slide smoothly against each other during rotation. The upper block has six (or 8 or 10) equally spaced holes connected to as many inlet tubes. The lower block has three (or 4 or 5 ) grooves, in the shape of circular arcs, just long enough to connect two neighboring holes (see Figure 9.6). References on p. 390.

330

G

6

A

Figure 9.6.Schematic of the Use of 6-Port Rotative Valves for Gas Injection. S + : Sample; G + : Carrier Gas. (A) Filling the Sample Valve Loop with the Sample. (B) Injection of

the Sample S in the Carrier Gas Stream.

Rotary valves can be actuated manually or automatically, with an electric or a pneumatic command. This last mode is preferred since it permits a much better reproducibility of the injection band profiles. Figures 9.6.A and 9.6.B show the two positions of the valve, for sample filling or injection. The materials used are selected depending on the nature of the analytes. Stainless steels, Hastelloy B or C, Teflon, filled Teflon, Vespel, etc., are commonly used. Adsorption and memory effects are considerably lower than with membrane valves. Spurious signals on the actuation of the valves, due to the propagation of a shock wave to the detector, are less important, but still significant, especially for trace analysis. The Deans technique (see below, Section IV.2), which manipulates pressures in various sections of the gas stream, is more flexible and does not suffer from this drawback. c.

Sliding Valves

A rectangular cross-section piston, usually of Teflon or filled Teflon, can move back and forth between two metal blocks strongly pressed against it (see Figure 9.7). The piston has grooves which can connect the holes in the metal blocks and the tubings to which they are connected in different patterns, depending on the position of the piston. These valves can be manually or automatically operated. G

S

G

S

I

I,

A B Figure 9.7. Schematic of the Use of CPort Sliding Valves for Gas Injection. S : Sample; G + : Carrier Gas. (A) Filling the Sample Valve Loop with the Sample. (B) Injection of the Sample S in the Carrier Gas Stream.

-.

331

B

of 6-Port Piston Valves for Gas Injection. S + : Sample; G -+ : Carrier Gas. (A) Filling the Sample Valve Loop with the Sample. (B) Injection of the Sample S in the Carrier Gas Stream. Figure 9.8. Schematic of the Use

The same materials are used as for rotary valves. The advantages and drawbacks are similar. d. Piston Valves

Piston valves are very similar to sliding valves. The sliding piston is now cylindrical and carries a number of “0’-rings (see Figure 9.8). The grooves are replaced by spaces between the “0”-rings,which play the same role of connecting the gas streams coming through the inlet tubings attached to the valve in different patterns. Piston valves are simple to design and build. The different compartments between successive “0’-rings are rather large, however, and make dead volumes which are swept slowly and incompletely, acting in part as small exponential dilution flasks (see Chapter 14). Accordingly the use of piston valves results in tailing peaks and loss of resolution. Furthermore, “0’-rings are made of elastomeric materials which can slowly adsorb and then desorb some compounds. This phenomenon results in analytical errors and memory effects. For these reasons piston valves tend to disappear from manufacturers’ catalogues and to be replaced by sliding valves or rotary valves. 2. Liquid Samples

Injection of liquids appears to be simpler than injection of gases. In fact, although handling liquid samples is a whole lot simpler than handling gas samples, it turns out that the repeatability of gas sample injection volumes is much better References on p. 390.

332

than that of liquid samples. This is in part due to the fact that the volume of the mobile parts of the injection device represents a much larger fraction of the total sample volume for liquid sampling valves or syringes than for gas valves. This area is open for research and improvement of the current devices. Some preliminary results obtained with the recent pulsed injection method are very encouraging. Liquid sample injection is done with either a syringe, a method very popular in laboratories, or with valves. Process control instruments use only valves. a. Syringes and Vaporization Chambers

Syringes have been very popular for the injection of liquid samples in a gas chromatograph since the very early days. The Hamilton syringe is one of the rare devices in chromatography to have been a technical landmark, to have remained almost unchanged and still to satisfy the needs of most analysts. Much technological research and development carried out over the years has allowed improvements of the quality and reductions of the prices of syringes (38). Syringes deliver volumes easily adjustable within a wide range, are rather inexpensive and easy to clean. They are available in a large range of sizes, from 1 pL (total capacity) to several mL. The most popular are the 1 and the 10 pL syringes for liquid samples. For gases all syringes are useful, from the 1 pL syringe used to inject small amounts of pure gases to determine their retention times, to the syringes having a volume of several mL, used to inject samples in trace analysis. Syringe injection of liquid samples, however, requires the use of a vaporization chamber, where the sample undergoes flash vaporization. This chamber, often called the “injector”, is a tube, usually empty, heated at a constant temperature, independent of the column temperature, swept by a stream of preheated carrier gas. The liquid sample is injected through the syringe needle, which has been pushed across the septum, a self-sealing disk closing the top of the injector (see Figure 9.9). This disk is usually made of a thermoresistant polymeric material. The septum is the source of many artefacts, such as base line drifts or the appearance of ghost peaks. These phenomena originate in the septum material (vaporization of plasticizers carried by the sample or its solvent, or bleeding, thermal decomposition or oxidation of the polymer). They have especially adverse consequences in temperature programmed analysis. Then, these volatile products accumulate at the column inlet during cooling periods and between analyses, to be eluted as narrow peaks, among the peaks due to the sample component. Such ghost peaks are detected by running blank analyses, with a pure solvent sample. In some sophisticated equipment, usually dedicated to open tubular columns, an auxiliary gas stream sweeps the septum and is vented. This eliminates the products of septum bleeding, which have no access to the column inlet. For the same purpose, it has been suggested that septa be baked prior to their use, that multilayer septa be used, with a thin Teflon or aluminum foil placed under the polymeric material, or that the septum be protected by a sliding metal porthole, in order to prevent diffusion of oxygen across the septum, towards the column, where it could oxidize the stationary phase and, through a free radical mechanism, considerably amplify the thermal degradation of the column.

333

i

A

Figure 9.9. Syringe Injection. A - Glass Syringe with Needle in the Vaporization Chamber. B - Vaporization Chamber (Vaporizer or Injector). The injector is closed with a rubber septum (a) and is independently heated (b). C - Chromatographic Column.

The repeatability of syringe injection is a function of the syringe capacity, of the fraction of this capacity injected, of the skill of the analyst and of some characteristics of the sample. If the vapor pressure of the sample is hgh, part may vaporize and leak through the needle. The liquid sample may also leak between piston and barrel, under the gas pressure in the injector, when the syringe needle crosses the septum. This latter loss may be limited by greasing the piston with a small amount of vaseline or silicone oil. The problems of the repeatability and reproducibility of sampling injection are discussed in more detail in Chapter 13. b. Automatic Piston Sampling Valves A thin (i.d., ca 2 to 3 mm), air-driven piston has on its side a circular groove, the depth of which determines the sample volume. It slides between a cavity swept by a continuous stream of the analyte and a heated vaporization chamber, where the sample is vaporized and from where it is carried by the mobile phase to the column (see Figure 9.10). In the injection position, the sample groove rests right face to the incoming, pre-heated carrier gas, which favors its rapid vaporization. References on p. 390.

334

Figure 9.10. Piston Valve for the Injection of Liquid Samples. A - Section enclosed in the chromatograph oven. B - Section placed outside. a - Inlet of compressed air (3 to 6 am). b - Jack. c - Articulated piston. d - Leak proof fittings. e - Sample groove. f - Electrical heating. g - Inlet of preheated carrier gas. h - Connecting tube to column. s - Sample stream.

The groove can have different shapes (see Figure 9.11): circular torus, axial cuvet or even a hole pierced across the piston. Each of these designs has problems. The circular torus can cut chips from the material making the seals between the two chambers (see Figure 9.10). To avoid that, the edges of the groove are smoothed, but this is detrimental to the repeatability of the sample volume, This design should be avoided for volumes smaller than 1 pL. The diameter of the hole pierced across the piston must be very small. It is difficult to have a design permitting a correct positioning of the hole face to the heated carrier gas inlet, avoiding progressive misalignment, and ensuring near instantaneous vaporization of mixtures of low vapor pressure components. Slow

335

, , , -

Figure 9.11. Different Pistons for Liquid Sample Injection Valves. A - Circular Groove around the Piston (Volume cu 5 pL). B - Longitudinal Groove, parallel to the piston axis (Volume less than 1 pL). C - Hole across the Piston (Volume 0.5 to 1 pL).

@ I

:I

-0

Figure 9.12. Sliding Valve for the Injection of Liquid Samples. a - Inlet of compressed air. b - Sliding piston, with circular sample holes (Volume cu 1 pL). g - Carrier gas. s - Sample. A Section enclosed in the chromatograph oven. B - Section placed outside. ~

References on p. 390.

336

sample vaporization results in tailing peaks, and loss of resolution. This design is acceptable only for volumes exceeding 1 to 2 pL. The cuvet parallel to the piston axis is used for very small sample volumes, 0.2 to 0.5 pL. Results are satisfactory, provided the sides of the cuvet are parallel to the piston axis (to avoid cutting the Teflon fitting) and the cuvet is placed right in front of the heated camer gas access in the injection position (alignment problem). c. Rotary and Sliding Valves Such valves are still available for liquid injection. Their design is similar to that of rotary and sliding valves for the injection of gas samples. The major difference is in the addition of a vaporization chamber, permitting flash vaporization of the liquid sample when it is injected in the pre-heated carrier gas stream (see Figure 9.12). The main inconvenience of these systems resides in the long time it takes to transfer the liquid sample from the valve to the hot area of the vaporization chamber. A thin liquid sample film stays on the tubing walls and vaporizes slowly. Peaks tend to tail; the lower the component vapor pressure the stronger the band tailing. This phenomenon is detrimental for separation and quantitative analysis. It is more difficult and less repeatable to stop integration on a tailing peak than on a symmetrical one, which has a much sharper decay. d. Pulsed Injection

This technique, invented by Nohl(10) and developed by Coutagne et al. (11) and by Guillemin (12), uses a modified sliding or rotary valve. The liquid sample is pulsed by the rapid expansion of a volume of carrier gas and nebulized into the vaporization chamber, providing for a much faster injection than normal valves (see Figure 9.13). The valve is moved back and forth very rapidly (total motion time less than 1 second). When the valve is in the filling position, a stream of sample sweeps the sampling volume, while the column is normally fed with carrier gas and a small chamber is filled with the carrier gas coming directly from the pressure controller, i.e., at a pressure 2 to 3 atm larger than the normal column inlet pressure. During injection, the normal carrier gas line is interrupted, the gas being vented through a pressure restriction to reduce the intensity of the shock wave in the lines, the sample aliquot is flushed into the vaporization chamber by the expansion of the camer gas contained in the small chamber P (see Figure 9.13). The valve returns rapidly into the filling position and the carrier gas stream resumes for normal elution. The nebulization of the sample permits a very rapid vaporization, by increasing the surface of contact with the hot gas and/or the injector surface. The advantages of this method over classical valve injection are as follows: - It is possible to inject very small sample volumes, 0.2 to a few pL. - The injection is very fast. This permits the achievement of narrower, more symmetrical peaks; it is possible to benefit from the performance of very good columns.

331 S

G'

S

G'

A

B

Figure 9.13. Pulsed Injection of Liquid Samples. S + : Sample stream; G, G' + : Carrier gas streams. P: Reservoir of auxiliary carrier gas, at a pressure 2 to 3 atm above the column inlet pressure. A - Filling of the sample loop with an aliquot of the liquid stream, pressurization of reservoir P, normal flow of carrier gas to the column. B - Injection and nebulization of the sample in the carrier gas stream. The valve returns very rapidly to sampling position. - The tailing of the peak of the main component, or of the solvent, is much reduced. - Very narrow injection bands are obtained. Band width of the injected gas and vapor plug may be as narrow as 200 msec (12). This permits the use of short, very efficient columns, for very fast analysis. - It seems possible to extend this method to macrobore open tubular columns for on-column injection (see Chapter 8). - The reproducibility of the sample size is excellent. Depending on the nature of the compounds used it is between 0.5% and 3% (ll), which is much better than can be obtained with conventional valves. - Compounds which are very viscous and have a low vapor pressure, and hence are considered to be very difficult to inject and analyze by GC, can easily be introduced and lead to satisfactory analyses. A refinement of the method consists in the introduction of a small, measured amount of solvent in the bottom of the gas chamber P, Figure 9.13, where the References on p. 390.

338

d

C

D

B

5 min

I

Figure 9.14. Comparison between the Performance of different Sampling Valves. Analysis of a mixture of glycols. A - Syringe Injection. B - Injection with a Gas Pulse. 1, Air. 2, Water. 3, Methanol. 4, Acetaldehyde. 5, Ethanol. 6, Methyl acetate. 7, Acetic acid. 8, Ethyl acetate. 9, 2-Methoxyethanol. C - Injection with a Liquid Pulse. 1, Air. 2, Water. 3, Ethylene glycol. Column 4 mm i.d., 70 cm long, packed with Chromosorb 102. Carrier gas Helium. Flow rate: 3 L/hour. Temperature: 160 C. Sample size: 0.7 pL. TCD ( i = 250 mA).

pressurized carrier gas is stored prior to flushing the sample aliquot. The value of the carrier gas pressure in this chamber and the time the piston or rotor is kept in the injection position determine the amount of solvent used to flush the sample. This procedure permits the injection of very difficult compounds. As an example, samples of several tens of pL of latex (25% non-volatile material) have been successfully injected, for the determination of the concentration of residual monomer, using pressurized water to flush the sample. The column used was selected so as to withstand the steam injection. Chromatograms on Figure 9.14 have been obtained for a mixture of polar compounds, using different injection modes. The solvent peak is narrower with the pulsed injection, although the amount of solvent injected is larger, because of the solvent flush. The glycol peak on Figure 9.14.C is more symmetrical than with conventional injection.

339

3. Comparison between the Repeatability of the Different Injection Systems This comparison is made separately for the gas and liquid sampling systems. In each case we have developed a procedure to evaluate the repeatability of the valves. a. Gas Sampling Valves A certain volume of gas (the content of the valve sample loop), at the temperature of the laboratory and under atmospheric pressure, is injected repeatedly in the chromatograph. The sample gas stream is stopped for 30 seconds prior to the injection of each sample, to permit equilibration of the pressure in the loop. To avoid back-diffusion of air into the loop, a several meters long tube is placed between the valve exit and the vent (see Chapter 13). The results are reported in Table 9.1.

b. Liquid Sampling Valves

The repeatability of liquid injection is a function of the valve used, but also of the vapor pressure of the sample. The data reported in Table 9.2 have been obtained TABLE 9.1 Repeatability of Gas Sampling Valves * Valve Type Membrane Valve Rotary Valve Sliding Valve Piston Valve

Repeatability (%) Loop Volume 500 pL

Loop Volume 10 p L

1 to2% 0.5% 0.5% 1t o 2 8

1% 1% -

Standard Deviation on 10 Determinations. TABLE 9.2 Repeatability of Liquid Sampling Valves Valve Type

Repeatability Sample Volume 1to2pL

Syringe 10 p L Syringe 1 p L Piston Valve Torus 5 pL Hole 1 pL Cuvet 0.5 pL Sliding Valve ** Pulsed Injection ***

Sample Volume 0.2 to 0.5 p L

5%

10 to 15% 2 to 5% 2 to 5% 1% 5%

0.5%

1%

* Standard Deviation of 10 Measurements.

**

With Band Broadening and Unsymmetrical Peaks.

*** With heavy, viscous compounds, such as glycerol, the repeatability of gas pulsed injection may be only 3%. Using a pulsed solvent injection may improve the repeatability, to less than 1%. References on p. 390.

340

with carbon tetrachloride (b.p. 76.7 O C), using the different sampling systems available. The repeatability of injections of compounds with lower vapor pressure and/or higher viscosity would be uniformly worse for all systems. The injection splitting devices used for open tubular columns are not discussed here. Further details are given in Chapter 8 for the injection systems used with open tubular columns and in Chapter 13 for the repeatability of injection devices used in quantitative analysis.

IV. COLUMN SWITCHING Column switching was first developed by Villalobos (25) for process control analysis, to carry out tasks devoted to temperature programming in laboratory analysis. The advantages of column switching, which permits the use of several columns to achieve the separation of a complex mixture, and offers some of the possibilities of multidimentional chromatography, are such that the method is beginning to spread in analytical laboratories. Process control analysis requiring high stability of the chromatographic data is carried out isothermally. Programmed temperature has been attempted many times, by various manufacturers, but unsuccessfully so far. The problem lies mainly in the lack of reproducibility of the starting temperature from one analysis to the next. Column switching permits the analysis of complex mixtures with components having a wide range of vapor pressures. The compounds of interest may be isolated on one column and separated from closely eluted ones for proper quantitation on another column. Components having very long retention times may be eluted rapidly if they have to move along a short segment of column. The different operations which are usually carried out with column switching are the following: - Backpurging, to eliminate slow eluting compounds of no interest, and to prevent them from polluting and eventually ruining the column, or from causing damaging base line drift. - Backflushing, to elute, via the column inlet to the detector, the heavy components of the sample in a single peak, whose area gives an estimate of the concentration of the “total heavy fraction”. - Heartcutting, to recover a fraction of the sample containing compounds of interest, usually trace components, and reinject them for analysis on another column or, conversely, to eliminate the band of a major component. -Storing, to keep a group of components immobilized in a column, while another group of components is eluted and separated on a different column. This avoids collision in the detector of peaks corresponding to compounds which have been eluted on different column series. - Reversing, to achieve the same function as storing, without needing a compensation column. There are two different approaches to performing column switching, either by using valves on the gas stream or by adjusting the pressure at various points of the

341

gas line, using auxiliary sources of gas. This latter method, referred to as the Deans switching method (13-17), uses valves which are cold and not in contact with the sample components. The two approaches are described and compared in the next sections. 1. Valve Switching

The valves used are very similar to the gas sampling valves described above, except for the number of ports. 6-, 8- and 10-port valves are used. The 8-port valves seem to be the best for most applications. Rotary and sliding valves are preferred, because of the possibility of sample adsorption on membranes or “0”-rings of the other valve types. These valves are available in all kind of materials, permitting the handling of the most corrosive samples, when needed. Each of the five main operations carried out by column switching (backpurging, backflushing, heartcutting, storing and reversing) are illustrated by an example. The experimental conditions selected for all these experiments are the following. Both columns are 1 mm i.d., the first one is 1.16 m long, the second one, 0.84 m long (total length, 2 m). They are both packed with 18 m2/g silica, coated with 1.285% (g/g) Carbowax 20M. The particle size is between 150 and 180 pm. The column temperature is 110°C. The camer gas (helium) flow rate is 0.20 L/hour. A FID is used, with flow rates of 2 L/h for hydrogen and 15 L/h for air. The sample used contains benzene (l), toluene (2), chlorobenzene (3), cumene (4), o-dichlorobenzene (9,and two unknown impurities (6 and 7). a. Backpurging

This procedure permits a reduction of the analysis time by eliminating the compounds which are considered to be unimportant and which are eluted late. After the bands of the interesting compounds havc moved from column 1 to column 2, but when the bands of the late eluting and less important components are still in column 1, the carrier gas stream is reversed in column 1, the components still in this column are vented, while the bands in column 2 are eluted normally (see diagram of the pneumatic circuit Figures 9.15.a and 9.15.b). Simultaneously performing the backpurging of column 1 and the elution of column 2 permits a great reduction in analysis time. All instruments performing automatic process control analysis must have the capability of using this function, in order to avoid the consequences of unexpected peaks appearing at large retention times and disturbing the proper functioning of the data analysis system during the rest of the analytical sequence, or appearing as a base line drift during a further sequence. The backpurging procedure is illustrated in Figures 9.15.a and 9.15.b, using rotary and sliding valves, respectively. In both cases it is necessary to keep the carrier gas flow rate in the second column constant during the analysis, in order to avoid changes in column efficiency and in detector response. This requires that, during the backpurging operation, the pneumatic resistance of the column 1 be References on p. 390.

342

nd L

cot 1

5

6

7

8

1.

G'

q-u@

(b)

G'

col 2

343 Backpurging

3

4 4

5 min

I

15min

Figure 9.16. Backpurgmg illustrated by a Chromatogram obtained with a Test Mixture. Experimental Conditions: Columns, i.d. 1 mm; length 84 cm (column 1) and 116 cm (column 2), packed with 150-180 pm particles of 18 m2/g silica, coated with 1.28% (g/g) Carbowax 20M. Temperature: 110 O C. Carrier gas: helium, 0.20 L/hour. Detector: FID, hydrogen flow rate: 2 L/hour, air: 15 L/hour. Solutes: 1, Benzene; 2, Toluene; 3, Chlorobenzene; 4, Cumene; 5, o-Dichlorobenzene; 6 and 7, unknowns. Chromatogram A - Normal Elution of the Components of the Mixture on the series of two columns. Chromatogram B - Backpurging of the heavy components. Valve switching in B. The peaks of compounds 5 to 7 are eliminated. Calculation of the switching time (See Section IV.3.b). Resolution between peaks 4 and 5 on chromatogram A: 3.70; inlet pressure: 2.90 bar, outlet pressure, 1 bar. x = 43%, L , = 0.84 cm. Switching time: z = 0.52, r L for cumene: 240 sec, t , = 125 sec.

Figure 9.15. Backpurging of the heavy Components of a Mixture, using a Switching Valve. (a) Membrane or Rotary Valve. 0, closed; 0, open. A - Columns 1 and 2 in series. B - Column 1 backpurged with auxiliary carrier gas, (3’; the pneumatic resistance of the valve V, between ports 7 and 8, is equal to that of column 1. (b) Sliding or Piston Valve. A - Columns 1 and 2 in series. B - Column 1 backpurged with auxiliary carrier gas, G’; the pneumatic resistance of thk valve V, between ports 4 and 8, is equal to that of column 1.

References on p. 390.

344

T

T T

T

1-q I L

cot 1

tD b

D

m

compensated by a needle valve properly set, to avoid a major change in the pneumatic resistance of the column system. If the pneumatic resistance of column 1 and of the needle valve are not equal, the switching operation will generate a shock wave in the gas stream and a spurious detector signal or an artefact, whose shape and intensity will depend on the nature of the detector and its sensitivity to flow rate excursions. In the case when a TCD is used, a very sensitive way to check that the two pneumatic resistances, those of column 1 and of the needle valve, have been properly equilibrated is to measure the area of an air sample of constant volume, successively with the carrier gas flowing through columns 1 and 2 and through the needle valve and column 2. If there is a significant difference in the peak area, the carrier gas flow rate is not the same in the two switching valve positions. The use of an 8-port switching valve permits an acceleration of the backpurging, through the use of an auxiliary source of carrier gas, whose flow rate is independent of the column flow rate and can be adjusted separately. Since the components are vented, there is no need to achieve a good column efficiency, and in the interest of speed the carrier gas velocity may be very large. In the case of the example (see Figure 9.16), the analysis time is reduced from 16 to about 5 min, but compounds 5 , 6 and 7 cannot be quantitized.

b. Backflushing Th s procedure is very similar to the previous one. The difference is that the heavy components delayed in column 1 and which will never have access to column 2 are not vented, but sent to a detector, either the same one for both columns or a separate one. In the first case the timing should be arranged to avoid collision of the backflushed band with the eluted bands in the detector. The length of the first column and the switching times are arranged in such a way that the backflushed bands combine into a single composite band whose size gives an approximate value of the total concentration of the backflushed fraction, i.e., of the heavy end of the sample. The determination cannot be exact because the response factors of all the compounds which are mixed in this fraction are different. Figures 9.17.a and 9.17.b illustrate the backflushing operation with rotary and sliding valves, respectively. In this case there is no need for a needle valve to

Figure 9.17. Backflushing of the Heavy Components of a Mixture, using a Switching Valve (a) Membrane or Rotating Valve. 0. closed; 0 , open. A - Normal Elution of the Components of the Mixture. B - Backflushng of the heavy components to the detector. (b) Sliding or Piston Valve. A - Normal Elution of the Components of the Mixture. B - Backflushing of the heavy components to the detector.

References on p. 390.

346

Backflushing 1

A

10 rnin

25min

Figure 9.18. Backflushing illustrated by a chromatogram obtained with a test mixture. Same experimental conditions and mixture as for Figure 9.16. Chromatogram A: Normal elution on the column series. Analysis time 25 min. Chromatogram B: Normal elution until peak 5, included. Backflush starts in B, after 5 min. Peaks 6 and 7 elute in reverse order. in less than 10 min.

maintain a constant flow rate in the column, at the condition that the entire column be backflushed. Figure 9.18 shows the chromatograms obtained with the test mixture. The analysis time is reduced from 24 to 9 min, while the band shape, the detection limit and the precision of the analysis are much improved. c. Heartcutting

The accurate quantitative analysis of trace compounds or minor impurities eluted on the peak tail of a major component or of the solvent is difficult or impossible. The detector may be overloaded (see Chapter lo), the resolution insufficient for the integrator to detect the small peaks (see Chapter 15), the area allocation program may give considerable error (see Chapter 15) or the presence of the large amount of solvent or major component may change the response factor of the analyte (see Chapter 14). For example, the thermal conductivities of vapors are not additive (see Chapter 10). Furthermore, the bar graph record procedure, which represents only the peak height and is basically very inaccurate, is still too often used in process control. It has become 'so entrenched in these rather conservative circles that considerable effort is devoted to making the peak height more representative of the actual

341

component concentration. Since the bar graph represents the observed peak height, without correction for band width, an analysis procedure making the peak height actually representative of the analyte concentration in the original sample is necessary. This can be achieved by collecting the eluate during the elution of the compounds of interest and injecting this mixture of vapors and carrier gas on another column. If the resolution between the analytes and the major component is sufficient, the reinjected sample is considerably enriched in the trace analyte, the separation is greatly improved and the quantitation much more accurate. Figures 9.19.a and 9.19.b illustrate the use of the heartcutting procedure and its implementation with 8-port rotary and sliding valves, respectively. Depending on the position of the solvent or the major component in the chromatogram, the procedure may be carried out differently. The two columns may be placed in series most of-the time, except during the elution of the solvent or major component peak, to vent out most of it. The components of the sample and the small amount of the solvent or major peak which has not been eliminated (because we want to be sure to keep all the interesting analytes inside the system) are then separated on column 2. Alternatively, the two columns may be placed in series only during the elution of a component or a group of components of the sample. The second column is then used to achieve their total separation. In this case, the two columns are usually made with different stationary phases. This method permits a considerable reduction in the analysis time, if the column efficiency, and hence the column length required for the separation, is such that the strongly retained components would take for ever to be eluted. Figure 9.20 shows the chromatogram obtained with the test mixture. Heartcutting has been carried out to eliminate the solvent peak (1) and the first component (2). The analysis time is unchanged. Only very small amounts of the first two components appear on the second chromatogram.

d. Intermediate Storing This procedure permits the analysis of part of the sample on one column, while the other part is stored in a valve loop or in a column, to be analyzed later, on a different column. This procedure affords significant analysis time savings and allows the use of a single detector for the entire analysis. There are two variants in this procedure, depending whether the second group of compounds is immobilized or merely delayed. 1. Dynamic Method or Cutting Column 1 rapidly separates the mixture components into two groups (see Figures

9.21.a and 9.21.b). The lighter ones enter column 2 through which they are eluted and on which they will be separated. The heavier group moves slowly out of column 1 and, when it exits from it, is sent directly to the detector. Columns 1 and 2 must be designed to avoid collision of the two groups of peaks in the detector, which would result in signal interference and a loss of information. The heavier group of compounds is usually eluted after the lighter one. References on p. 390.

348

n l

I ,

349

The chromatogram obtained with the test mixture is shown Figure 9.22.a. Components 3, 4 and 6 are missing from the test mixture. When component 5 is stored, the analysis time is reduced by half. In this case, however, the more retained component 5 is still eluted last. 2. Static Method The procedure is similar to the dynamic method, except that the lighter group of compounds is immobilized in column 2 during the elution of the heavier group through column 1 and the detector. When the last compound of this second group has been detected, elution of the group of light components is resumed on column 2. In this case the heavier group of compounds is detected first. This method should be avoided as much as possible, in spite of its apparent attractiveness. Our experience is that the temporary immobilization of the light analytes on column 2 may result more often than expected in band broadening, i.e., loss of resolution, increase of detection limits (loss of sensitivity), and increase of analytical errors, because of the adsorption of certain compounds on the column paclung material, from which they are not easily desorbed, or of slow reactions of decomposition catalyzed by the support (18). Figure 9.22.b shows the result of static storing carried out on the heavy end of our test mixture. In this case, component 5 is now eluted first, but the analysis is about as fast as with the other storing procedure. e. Column Reversing

This procedure permits a simple reversal in the order of columns 1 and 2, without changing the direction of the carrier gas or the flow rate (see Figures 9.23.a and 9.23.b). This procedure may be used for different aims. Usually, the first column separates the mixture in two groups of components, the light ones which enter column 2 and on which they are separated, and the heavy ones. Before the first heavy component has time to move to column 2, the last light component has been eluted from column 2 and the valve is switched. Then column 1 is placed downstream column 2 and the heavy components elute directly from column 1 to the detector. The advantage of this method is the avoidance of the need for a needle valve to compensate for the pneumatic resistance of the column 2, if it were switched off the gas stream. Another use for this procedure is recycling, when it is not possible to achieve total resolution of a mixture on a column, because the necessary column would be too long to build and would require too large a pressure to operate. ~

Figure 9.19. Heartcutting the main Components of a Mixture, using a Switching Valve. (a) Membrane or Rotary Valve. 0, closed: 0 , open. A - Analysis of the Mixture on Columns 1 and 2 in Series. B - Elimination of the main Component or the Solvent (to be vented out through 4). (b) Sliding or Piston Valve. A - Analysis of the Mixture on Columns 1 and 2 in Series. B - Elimination of the main Component or the Solvent (to be vented out through 4).

References on p. 390.

350 Heart cutting 3

n I

5

AR

-

6 A

14 min I

I

J

Figure 9.20. Heartcutting illustrated by Chromatograms obtained with a Test Mixture. (a) Heartcutting using a Switching Valve. Same experimental conditions as for Figure 9.16, except column lengths: column 1, 1 m; column 2, 2 m. Chromatogram A - Normal elution on the column series. Chromatogram B - Elimination of the solvent peak at its elution off column 1 (step B), followed by elution of the rest of the mixture.

Figure 9.24 shows the chromatogram obtained with a slightly different mixture than the previous figures (9.16, 9.18, 9.20 and 9.22), which contains an unknown impurity eluted before benzene. Again the analysis time of o-dichlorobenzene ( 5 ) is reduced by half, and its peak is sharper and taller.

f: Combination of Switching Procedures It is not infrequent that an analysis requires several switching operations to be carried out properly. Complex analysis may require the use of three to five switching valves. Such strategies must be very carefully studied in advance. Switching procedures seem very simple and attractive on paper, but are very difficult to implement in industrial applications, because of the heavy maintenance required by the valves. They should not be seen as a substitute for chromatographic knowledge and experience and for analytical ingenuity. On the other hand, applications using two valves are common. For example,

I

351

(b)

Heartcutting

DEANS

1

3

6 min

I

I

L

7 min I

I

Figure 9.20 (continued). (b) Heartcutting using the Deans technique. Experimental conditions: column diameter: 1/8 inch, lengths: column 1. 20 cm; column 2, 280 cm. Packing material: Chromosorb P-AW, coated with 4% H,PO, and 10% LAC 446. Temperature: 180°C. Carrier gas: nitrogen, flow rate: 1.10 L/hour. Solutes: 1, Isopropanol; 2, nicotine (0.01%); 3, n-octadecane. Chromatogram A - Normal elution on the column series (A, injection). Chromatogram B - Elimination of the solvent peak at its elution off column 1, followed by elution of the rest of the mixture (B, injection; A, switching of valves VC and VD, Figure 9.26).

backpurging is often combined with heartcutting, storing or reversing. A number of practical applications are discussed and illustrated in Chapter 17. 2. Intermediate Pressure Control (Deans Method) This method can be traced to the pioneering work published by Deans in 1965 (13). Originally designed for process control analyzers and laboratory routine analysis, it spread slowly from control laboratories to analytical laboratories and research groups during the ’seventies. It is now a well-recognized method, which has been the topic of many studies and is implemented by several manufacturers who offer it incorporated in their instruments or as add-ons, known familiarly as “Deans boxes”. Deans has published several critical studies and reviews (14,15)illustrated by many examples of applications (16,17). References on p. 390.

352

G

D b

G

col 1

col2

353

The principle of the method is the use of external electric valves to control the pressure between columns and direct the main carrier gas stream and the auxiliary streams through one of several possible channels. These valves are placed outside the column oven. They do not have to withstand the high temperature and can be operated a million times between failures. The solutes do not flow through them and cannot be adsorbed on their “O”-rings. This method is mainly used to carry out backpurging and heartcutting, for which it is eminently suited. Only one experiment is reported here to illustrate this technique, using a set of experimental conditions similar to those described above (Sections 1V.l.c and IV.2.b), in the case of heartcutting.

a. Backpurging A schematic of the gas circuits needed to apply the Deans method to backpurging is given in Figure 9.25. Two columns are connected. The carrier gas can enter either in A (inlet of column 1) or in D (between columns 1 and 2). Both the main source of carrier gas, in A, and the auxiliary source, in D, have a pressure controller and an electric valve. A needle valve and/or a narrow capillary tube bypasses the electric valve. In B, just before the main carrier gas stream enters the injector, a piece of tubing, with an electric valve and a needle valve, permits a direct connection of the gas stream to vent. The needle valve NB is set so that its pneumatic resistance is lower than that of column 2. Normal elution. The electric valve VA is open, the valves VB and VD are closed. The carrier gas flow rate is controlled by the flow rate controller FA. The gas stream carries the mixture components from the injector to columns 1 and then 2 and the detector. A very small stream of auxiliary carrier gas enters in D; this avoids diffusion of the solutes into the dead end side channel and the subsequent broadening and tailing of the peaks and loss of resolution. When the compounds of interest have moved from column 1 to column 2, it is time for backpurging. Backpurging. The electric valve VA is closed; the valves VB and VD are open. The main carrier gas stream is stopped. A small stream leaks through the bypass of valve VA, to line B, avoiding diffusion of the heavy compounds when they are eluted and contamination of line A. The auxiliary carrier gas stream splits in D, since the pressure in A falls below the pressure in D (the pneumatic resistance of the needle valve NB is lower than that of column 2, while the pressure in D depends on Figure 9.21. Storing one or several Components of a Mixture, using a Switching Valve. (a) Membrane or Rotary Valve. 0, closed; 0 , open. A - Normal Elution of the Sample Components on Column 1 and 2 in series. B - Storing light Components on Column 2, while the heavy Components are directly camed to the Detector. After their elution is finished, column 2 is reconnected to the gas stream and the trapped light components are eluted. (b) Sliding or Piston Valve. See Figure 9.21.a.

References on p. 390.

7

2

Cutting 2

I

5

5

4 min

,

qmin

!mi"

J

1

8 rnin

355

the pressure controller FD, set so that the pressure in D does not change when the three electrical valves are switched). Part of stream D flows along column 2, where the gas velocity remained the same as before and elutes the compounds which were in column 2, at the switching time. The analysis is performed. The other part of the stream D flows through column 1, in the opposite direction than before. The heavy compounds, which have not reached column 2 are eluted backwards and exit through line B. These compounds condense in the line, where it goes out of the oven. A large section of tubing is placed at this level, to avoid plugging of the line. It has to be replaced periodically. Setting the gas pressures. The recommended procedure is as follows: - Open valves VA, close valves VB and VD. - Raise the pressure setting of pressure controller FA to achieve the desired flow rate through columns 1 and 2 (e.g., for a 4 mm i.d. column, approximately 3 L/hour). Note the pressure PD. - Close valve VA, open valves VB and VD. - Raise the pressure setting of pressure controller FD, so that the new pressure PD becomes slightly larger than it was before. - Measure the flow rate at the outlet of column 2 and at the outlet of B. Adjust the pressure setting of FD and the needle valve NB, to achieve the same flow rate at the outlet of column 2 (3 L/hour in the example) and a slightly larger flow rate at the outlet of B. b. Heartcutting

The schematic of the carrier gas lines is given on Figure 9.26; it is similar to the schematic used for backpurging, with the difference that there are two gas lines connecting to the intermediate point, between the two columns. The connections of these gas lines are at both ends of the tubing connecting the two columns. As previously (see Figure 9.25), the main gas circuit contains a source of carrier gas, in A, the injector and the two columns, 1 and 2. All the auxiliary tubings are

Figure 9.22. Dynamic and Static Storing of one or several Components of a Mixture, illustrated by the Chromatogram obtained with a Test Mixture. Same experimental conditions as for Figure 9.16, except the mixture contains only components 1, 2 and 5. (a) Cutting or Dynamic Storing. Chromatogram A - Normal elution on the column series. Chromatogram B - Elution of the first group of peaks on column 2 (step A), followed by elution of the heavy component from column 1 (peak 5, step B). (b) Static Storing. Chromatogram A - Normal elution on the column series. Chromatogram B - Storing of the first group of peaks on column 2 (step A), followed by elution of the heavy component from column 1 (peak 5, step B), and then elution of the light components (peaks 1 and 2) from column 2.

References on p. 390.

356

-D

G a

D

351

Reversing

1

@

@ 5

2 A

L

i,

empty 1 mm i.d. tubes. There is a slight bypass leak around valves VA and VD, to avoid diffusion of the sample components in these tubes and peak tailing. It might seem cautious to add similar leaks around valves VB and VC, where the same phenomenon may take place, but an unknown and probably irreproducible fraction of the sample would be lost, and this would result in unacceptable errors in the quantitative analysis. Normal elution. The electric valve VA is open, the valves VB, VC and VD are closed. The flow rate depends on the pressure set by the pressure controller FA. The main gas stream flows through the injector, columns 1 and 2 and the detector. The components of the mixture are eluted on the two columns. When the band of the Figure 9.23. Column Reversing, using a Switching Valve. (a) Membrane or Rotary Valve. 0, closed; 0, open. A - The light analytes are eluted through column 1 and column 2. B - The column order is reversed. The heavy analytes are eluted directly from column 1 to the detector. The carrier gas flows always in the same direction, through columns 1 and 2. (b) Sliding or Piston Valve. See Figure 9.23.a.

References on p. 390.

358

lI ji

H.Cutting

r

I 1

I

I I

I

I

I I I

I I I I

2

;

0

1

I

I I

I

I

1

L-

Figure 9.25. Deans Method for Column Switching. Backpurging of the heavy Components of a Sample. FA, FD, Pressure Controllers. VA, VB, VD, Solenoid Valves. NB, Needle Valve. PA, PD, Pressure Gauges. Col.1, C01.2, Chromatographic Columns.

solvent or the main component arrives at the connection point between the two columns, the electric valves are switched, to prevent that compound from entering in column 2. Heartcutting. The electric valves VA, VC and VD are open, the valve VB is closed. The main stream of carrier gas continues flowing through column 1 and then exits through line C. The gas flow rate remains the same, because the pressure in C is not changed, due to the proper setting of the pressure controller FD (see below). The components which are still in column 1 are eluted normally, including the compound which we want to eliminate and which elutes through line C, to vent. The auxiliary carrier gas stream enters in D and splits into two parts. One part flows along column 2, in the same direction and at the same flow rate as before, since the pressure in D is the same, through the proper setting of pressure controller FD. The components which are already in column 2 are eluted normally to the detector, but no other component enters the column. The second part of the auxiliary carrier gas stream flows from D to C and there joins the main carrier gas

359 Normal

ILPurgin

ICutting

i

I I

I I I I I

I

Figure 9.26. Deans Method for Column Switching. Heartcutting the main Component of a Sample. FA, FD, Pressure Controllers. VA, VB, VC, VD, Solenoid Valves. NB, NC, Needle Valves. PA, PD, Pressure Gauges. Col.1, C01.2, Chromatographic Columns.

stream, to exit through line C. The purpose of this stream is to avoid diffusion of the main component from C to D and to push its vapor out of the gas stream, through line C. When the elution of the unwanted compound is finished, the electric valves are switched back to their original position, VA is open, VB, VC and VD are closed. Elution of the sample components still contained in column 1 resumes through column 2. The components eluted before and after the solvent or main component of the mixture can be resolved from each other and from the small amount of that unwanted compound which is allowed between columns 1 and 2. Proper timing of the valves switching permits the elimination of between 99% and 99.99% of the unwanted compound. Backpurging. This function can be achieved with the plumbing schematic shown on Figure 9.26, by closing the electric valves VA and VC and opening the valves VB and VD. The system operates as described in the previous section. Setting the gas pressures. The procedure used is similar to the one described in the previous section: - Open valve VA, close valves VB, VC and VD. References on p. 390.

360 - Using pressure controller FA, set the outlet column flow rate and note the pressure PD. - Close valve VA, open valves VC and VD (VB remains closed). Open slightly the needle valve NC. - Using pressure controller FD, set the pressure PD to a value very near the previously noted value for PD. Measure the outlet column flow rate and adjust the pressure PD to achieve exactly the same flow rate as during the first step. - Open valve VA and set the detector output signal at maximum sensitivity. - Check that opening and closing valves VA, VC and VD does not generate any artefact or base line perturbation resulting in an unacceptable error in peak detection or quantitation. - Open valves VA, VC and VD. Set the flow rate at the outlet of line C, using needle valve NC. The recommended flow rates are 3 L/hour for 4 mm i.d. columns and the line B and 2 L/hour for the line C. Figure 9.27 shows the effect of switching the electric valves on a chromatograph using the valve system shown on Figure 9.26, after the pressures have been set as just described. The base line stability is excellent, the recorder sensitivity being 4 X lo-" A full scale. Figure 9.28 illustrates one application of the Deans column switching technique, using a gas chromatograph with two parallel detectors, a gas density balance and a flame ionization detector (see Chapters 10 and 14). On the first set of chromatograms there are three peaks, corresponding to the three components of the sample. On the second set of chromatograms the first peak has been eliminated by heartcutting and the third one by backpurging. There is no artefact on the base line, even on the gas density balance trace, although this detector is very sensitive to flow or pressure fluctuations (see Chapter 10). Figure 9.20.b shows the chromatogram obtained with a test mixture containing isopropanol, nicotine and n-octadecane. A large fraction of component 1, and all the tail of the band, have been eliminated, providing a much better resolution for components 2 and 3, now well placed on a stable base line. A lower detection limit and a more precise analysis are possible. This is a good illustration of the great potential of this technique (37).

c. Advantages of this Method

The Deans method has some considerable advantages over the conventional valve switching methods, which explains why it is becoming extremely popular. On the

L

Figure 9.27. Illustration of the main Advantage of the Deans Method for Column Switching over the Use of Conventional Valves. The base line is very stable (recorder sensitivity, 4 X lo-" A full scale).

361

'ID

3

-I Figure 9.28. Application of the Deans Method of Column Su :hing.

Mixture of Tnchloroethylene (I), 1,2-dichloroethane(2) and 1,1,2-t&hloroethane (3). (a) Analysis of the mixture on a chromatograph using two parallel detectors (FID and GDB). (b) Most of the trichloroethylene is eliminated by heartcutting and all the 1,1,2-trichloroethaneby backpurging.

other hand, there are no disadvantages; even the price and complexity is in favor of the Deans method. The main advantages of practical importance are the following: - There is no other temperature limitation than the one set by the thermal stability of the stationary phase(s) used. The switching valves are cold and the gas going through lines B and C can be cooled before reaching the valves. - The switching times are much shorter than with complex rotatory or sliding valves. Electrical valves are very fast, because of their light weight and small mechanical inertia. The base line is much less perturbed than with conventional valve systems. The method is especially well suited for implementing fast GC analysis. - There is no, or only a very small dead volume. In fact there is a commercial instrument available, using this method for open tubular columns, and the band broadening effect of the required tubings and connections is quite acceptable (19). - The implementation of the method is easy and it is not necessary to purchase expensive parts. In fact, the total cost is less than for a conventional system using two 8-port valves. - The settings of the pressures are easy and fast to perform. - The automation is readily made. References on p. 390.

362

The use of the Deans switching method deserves careful attention. It has proven to be invaluable in process control analysis as well as in routine laboratory analysis. It is widely used in our laboratory, with constant success and we strongly recommend its use. Equipments are commercially available, either as complete gas chromatographs or as specific modules. Various approaches to its implementation in a number of practical cases are described in the literature (19-24). 3. Determination of Switching Times A fruitful use of column switching requires an accurate prediction of the time when a certain band passes by a certain point in the column system and of the resolution between two bands at this point, so that it might be possible to decide exactly when to send the orders to the different valves during the analysis. This also permits the optimization of the length of the various column segments to achieve the shortest possible analysis time. The major difficulty to solve in this kind of calculation comes from the compressibility of gases. As a consequence, the local velocity is much lower at the column inlet than it is at the outlet. The velocity increases slowly at first, then more and more rapidly. The phenomenon is describedin detail in Chapter 2. The diagram on Figure 9.29 shows the plot of the ratio of the local to the outlet carrier gas velocities, versus the column length. Interest in this problem was first limited to industrial analysts dealing with on-line process gas chromatography. It now extends to all those involved in laboratory analysis. Villalobos et al. (25) and Vergnaud et al. (26-28) have discussed the backpurging and backflushing problems, which do not require the determination of the time when the solute passes at some intermediate point in the column, but mere calculation of the effect of flow reversal at some time. Guiochon has calculated

0

0.5

Figure 9.29. Plot of the relative carrier gas velocity (ratio of the local velocity to the outlet gas velocity),

versus the fractional column length (ratio of the abscissa to the column length), for different values of the inlet to outlet column pressure. (after Keulemans, ref. 3).

363

0.5

1

Figure 9.30. Plot of the time at which a band passes by a certain point, versus its fractional abscissa. a - Theoretical values, taking the effect of the pressure gradient into account. b - Plot assuming a negligible compressibility of the mobile phase.

the properties of column series, when the columns have the same cross section area and the same permeability (6,29). More recently, the development of the Deans method and its application to open tubular columns has led to renewed interest. A general theory of the analysis time on a column series has been published by Purnell et al. (30). Other important contributions are due to Ettre and Hinshaw (31) and to Mayfield and Cheder (32). An equation for the prediction of band widths on column series has been recently published by Guiochon and Gutierrez (33). The easiest approach would be the linearization of the band migration. In liquid chromatography the mobile phase is not compressible. The migration distance of the band is proportional to the time elapsed. The error made by using this approximation in gas chromatography is negligible only in the case of very short columns, having a large permeability (i.e., packed with large-sized particles) and when the carrier gas flow rate is low. Otherwise the error becomes important (see Figure 9.30). Band positions can be calculated with relative ease, using equations derived previously in Chapter 2. These equations are summarized in Figure 9.31, to simplify the present discussion. Equation 9 in Figure 9.31 permits the calculation of the exact time at which a band arrives at a certain point of the column. The prediction of the column band width is more difficult and no satisfactory solution has yet been demonstrated. The equation derived by Guiochon and Gutierrez (33) may be the answer, but it needs more systematic experimental investigation. In the mean time, Guillemin has made the reasonable assumption that the resolution between two bands increases in proportion to the square root of the References on p. 390.

364 Under the conditions of gas chromatography, the local velocity of the carrier gas is related to the column characteristics by the Darcy law:

where: u is the local velocity, or velocity at point x , k is the column permeability, independent of the nature of the fluid used (gas, supercritical fluid, liquid), q is the camer gas viscosity, dp/dx is the local pressure gradient. The minus sign indicates that the gas flows in the direction opposite to the pressure gradient, i.e. from high to low pressures. If we assume that the carrier gas is ideal, we have the classical equation: PU = POU, (2) where u, is the outlet gas velocity, while p and po are the local and the outlet pressure, respectively. E l i n a t i o n of u between equations 1 and 2 gives a differential equation: pouon d x = - kp d p

(3) Equation 3 can be integrated between the column inlet and outlet. The result is the relationship between column outlet flow velocity and the column parameters: k (4) u0=(PT - Po') hLP0 where p i stands for the inlet pressure. In practice p, is constant and equal to the atmospheric pressure. Integration of equation 3 between the local point and the column outlet, followed by division of the result by equation 4 and reordering gives:

Equation 5 gives the pressure profile along the column. Combination with equation 2 gives the velocity profile. The gas velocity is by definition: dx u=dt Combination of equations 2.3 and 6 gives: 4qL2 d t = - k(pT-p:)2P2dp

(7)

Integration of equation 7 between the column inlet and outlet permits the calculation of the gas hold-up time:

ro = 48L2( P: - Po') 3k(P2-P,Z)2 Integration of equation 7 between the column inlet and the local point and division of the result by equation 8 gives the time at which the band passes by the point of abscissa x : rx = to

"

p ? - p'--(pz' L 3

I

Pi -Po

P3]3'2

3

(9)

Equation 9 permits the prediction required for calculation of the switching times. Figure 9.31. Equations permitting the calculation of the time when a band passes at a given point of the

column.

365

Figure 9.32. Determination of the point at which a column should be cut to place a switching valve, in order to achieve a resolution of 2.0 between two peaks at this point, when the resolution at column outlet is R , .

elapsed time. It seems from the work of Gutierrez that the error on the resolution should not exceed about 10%.

a. First Problem: Calculation of the Length of Intermediate Column Segments Basically, the problem for the industrial analyst is the determination of the length of the column segment at the end of which a sufficient resolution is achieved between the last band to pass through the switching valve before this valve is actuated, and the first band to pass through the valve after it has switched. This resolution should be large enough to permit proper quantitation, e.g., 2.0 (see Figure 9.32). Then the amount of analyte which does not follow the proper route is negligible. If we assume that the resolution between the two bands is proportional to the time spent, we can write an equation similar to equation 9 in Figure 9.31, by replacing t, by R , and t , by R,, respectively. Solving this equation for x gives:

P : - P,' x is the fraction of the original column length at which a resolution of 2.0 between the two bands considered is achieved. It indicates the point where the column should be cut and the switching valve placed. The resolution R,, at the end of the column is determined experimentally, using the conventional procedure (Chapter 1, Section X). An example is given in the last section of this Chapter. Values of the coefficient x are given in Table 9.3, for all practical combinations of R , and pi, with R , = 2.0. References on p. 390.

366 TABLE 9.3a Value of the Coefficient of Equation 6 Pi

RL 2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

2.90

3.00

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0

0.950 0.948 0.945 0.943 0.941 0.938 0.936 0.934 0.932 0.930 0.927 0.925 0.923 0.921 0.920 0.918 0.916 0.914 0.913 0.911 0.910 0.908 0.907 0.906 0.904 0.903 0.902 0.901 0.900 0.899 0.898 0.897 0.896 0.895 0.894 0.893 0.893 0.892 0.891 0.891 0.890 0.889 0.889 0.888 0.888 0.887 0.887 0.886 0.886 0.885 0.885 0.884 0.884 0.884 0.883 0.883 0.883 0.882 0.882 0.882

0.905 0.901 0.897 0.893 0.889 0.885 0.881 0.877 0.874 0.870 0.867 0.864 0.861 0.858 0.856 0.853 0.851 0.849 0.846 0.844 0.842 0.841 0.839 0.837 0.836 0.834 0.833 0.832 0.830 0.829 0.828 0.827 0.826 0.825 0.824 0.823 0.822 0.821 0.821 0.820 0.819 0.819 0.818 0.817 0.817 0.816 0.816 0.815 0.815 0.814 0.814 0.813 0.813 0.813 0.812 0.812 0.811 0.811 0.811 0.810

0.864 0.858 0.853 0.847 0.842 0.837 0.833 0.828 0.824 0.820 0.816 0.812 0.809 0.805 0.802 0.800 0.797 0.794 0.792 0.790 0.788 0.786 0.784 0.782 0.781 0.779 0.777 0.776 0.775 0.774 0.772 0.771 0.770 0.769 0.768 0.767 0.767 0.766 0.765 0.764 0.764 0.763 0.762 0.762 0.761 0.761 0.760 0.760 0.759 0.759 0.758 0.758 0.757 0.757 0.757 0.756 0.756 0.756 0.755 0.755

0.826 0.820 0.813 0.807 0.801 0.795 0.790 0.785 0.780 0.775 0.771 0.767 0.763 0.760 0.757 0.754 0.751 0.748 0.746 0.743 0.741 0.739 0.737 0.736 0.734 0.732 0.731 0.730 0.728 0.727 0.726 0.725 0.724 0.723 0.722 0.721 0.720 0.719 0.719 0.718 0.717 0.717 0.716 0.715 0.715 0.714 0.714 0.713 0.713 0.712 0.712 0.711 0.711 0.711 0.710 0.710 0.710 0.709 0.709 0.709

0.792 0.784 0.777 0.770 0.763 0.757 0.751 0.746 0.741 0.736 0.731 0.727 0.723 0.720 0.717 0.713 0.711 0.708 0.705 0.703 0.701 0.699 0.697 0.695 0.694 0.692 0.691 0.689 0.688 0.687 0.686 0.685 0.684 0.683 0.682 0.681 0.680 0.679 0.679 0.678 0.677 0.677 0.676 0.675 0.675 0.674 0.674 0.673 0.673 0.672 0.672 0.672 0.671 0.671 0.671 0.670 0.670 0.670 0.669 0.669

0.760 0.752 0.744 0.737 0.729 0.723 0.717 0.711 0.706 0.701 0.696 0.692 0.688 0.684 0.681 0.678 0.675 0.672 0.670 0.668 0.665 0.663 0.662 0.660 0.658 0.657 0.655 0.654 0.653 0.652 0.650 0.649 0.648 0.647 0.647 0.646 0.645 0.644 0.643 0.643 0.642 0.642 0.641 0.640 0.640 0.639 0.639 0.638 0.638 0.638 0.637 0.637 0.636 0.636 0.636 0.635 0.635 0.635 0.635 0.634

0.731 0.722 0.714 0.706 0.698 0.692 0.685 0.679 0.674 0.669 0.664 0.660 0.656 0.652 0.649 0.646 0.643 0.641 0.638 0.636 0.634 0.632 0.630 0.628 0.627 0.625 0.624 0.623 0.621 0.620 0.619 0.618 0.617 0.616 0.615 0.615 0.614 0.613 0.612 0.612 0.611 0.610 0.610 0.609 0.609 0.608 0.608 0.608 0.607 0.607 0.606 0.606 0.606 0.605 0.605 0.605 0.604 0.604 0.604 0.603

0.704 0.695 0.686 0.678 0.670 0.663 0.656 0.651 0.645 0.640 0.635 0.631 0.627 0.624 0.620 0.617 0.614 0.612 0.610 0.607 0.605 0.603 0.602 0.600 0.598 0.597 0.596 0.594 0.593 0.592 0.591 0.590 0.589 0.588 0.587 0.587 0.586 0.585 0.584 0.584 0.583 0.583 0.582 0.582 0.581 0.581 0.580 0.580 0.579 0.579 0.579 0.578 0.578 0.578 0.577 0.577 0.577 0.576 0.576 0.576

0.679 0.669 0.660 0.652 0.644 0.637 0.630 0.624 0.619 0.614 0.609 0.605 0.601 0.597 0.594 0.591 0.588 0.586 0.584 0.581 0.579 0.578 0.576 0.574 0.573 0.571 0.570 0.569 0.568 0.566 0.565 0.564 0.564 0.563 0.562 0.561 0.560 0.560 0.559 0.559 0.558 0.557 0.557 0.556 0.556 0.555 0.555 0.555 0.554 0.554 0.554 0.553 0.553 0.553 0.552 0.552 0.552 0.551 0.551 0.551

0.656 0.646 0.636 0.628 0.620 0.613 0.606 0.600 0.595 0.590 0.585 0.581 0.577 0.573 0.570 0.567 0.565 0.562 0.560 0.558 0.556 0.554 0.552 0.551 0.549 0.548 0.547 0.545 0.544

0.543 0.542 0.541 0.540 0.540 0.539 0.538 0.537 0.537 0.536 0.536 0.535 0.534 0.534 0.533 0.533 0.533 0.532 0.532 0.531 0.531 0.531 0.530 0.530 0.530 0.529 0.529 0.529 0.529 0.528 0.528

361 TABLE 9.3b Value of the Coefficient of Equation 6

P,

RL

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3.90

4.00

1.I

0.634 0.624 0.614 0.606 0.598 0.590 0.584 0.578 0.572 0.567 0.563 0.559 0.555 0.551 0.548 0.545 0.543 0.540 0.538 0.536 0.534 0.532 0.531 0.529 0.528 0.526 0.525 0.524 0.523 0.522 0.521 0.520 0.519

0.614 0.603 0.594 0.585 0.577 0.570 0.563 0.557 0.552 0.547 0.542 0.538 0.535 0.531 0.528 0.525 0.523 0.520 0.518 0.516 0.514 0.513 0.511 0.509 0.508 0.507 0.506 0.504 0.503 0.502 0.501 0.501 0.500 0.499 0.498 0.498 0.497 0.496 0.496 0.495 0.495 0.494 0.494 0.493 0.493 0.492 0.492 0.492 0.491 0.491 0.491 0.490 0.490 0.490 0.489 0.489 0.489 0.489 0.488 0.488

0.595 0.584 0.574 0.565 0.557 0.550 0.544 0.538 0.533 0.528 0.523 0.519 0.516 0.512 0.509 0.507 0.504 0.502 0.500 0.498 0.496 0.494 0.493 0.491 0.490 0.489 0.487 0.486 0.485 0.484 0.483 0.483 0.482 0.481 0.480 0.480 0.479 0.478 0.478 0.477 0.477 0.476 0.476 0.475 0.475 0.475 0.474 0.474 0.474 0.473 0.473 0.473 0.472 0.472 0.472 0.472 0.471 0.471 0.471 0.471

0.577 0.566 0.556 0.547 0.539 0.532 0.526 0.520 0.515 0.510 0.506 0.502 0.498 0.495 0.492 0.489 0.487 0.485 0.482 0.481 0.479 0.477 0.476 0.474 0.473 0.472 0.471 0.469 0.468 0.468 0.467 0.466 0.465 0.464 0.464 0.463 0.462 0.462 0.461 0.461 0.460 0.460 0.459 0.459 0.459 0.458 0.458 0.457 0.457 0.457 0.456 0.456 0.456 0.456 0.455 0.455 0.455 0.455 0.454 0.454

0.560 0.549 0.539 0.530 0.523 0.515 0.509 0.503 0.498 0.493 0.489 0.485 0.482 0.479 0.476 0.473 0.471 0.469 0.466 0.465 0.463 0.461 0.460 0.458 0.457 0.456 0.455 0.454 0.453 0.452 0.451 0.450 0.450 0.449 0.448 0.448 0.447 0.446 0.446 0.445 0.445 0.444 0.444 0.444 0.443 0.443 0.442 0.442 0.442 0.441 0.441 0.441 0.441

0.544 0.533 0.523 0.515 0.507 0.500 0.493 0.488 0.483 0.478 0.474 0.470 0.467 0.463 0.461 0.458 0.456 0.454 0.452 0.450 0.448 0.446 0.445 0.444 0.442 0.441 0.440 0.439 0.438 0.437 0.437 0.436 0.435 0.434 0.434 0.433 0.433 0.432 0.431 0.431 0.431 0.430 0.430 0.429 0.429 0.429 0.428 0.428 0.428 0.427 0.427 0.427 0.426 0.426 0.426 0.426 0.425 0.425 0.425 0.425

0.529 0.518 0.508 0.500 0.492 0.485 0.479 0.473 0.468 0.463 0.459 0.456 0.452 0.449 0.446 0.444 0.442 0.440 0.438 0.436 0.434 0.433 0.431 0.430 0.429 0.428 0.427 0.426 0.425 0.424 0.423 0.422 0.422 0.421 0.420 0.420 0.419 0.419 0.418 0.418 0.417 0.417 0.416 0.416 0.416 0.415 0.415 0.414 0.414 0.414 0.414 0.413 0.413 0.413 0.413 0.412 0.412 0.412 0.412 0.412

0.514 0.504 0.494 0.485 0.478 0.471 0.465 0.459 0.454 0.450 0.446 0.442 0.439 0.436 0.433 0.431 0.428 0.426 0.424 0.423 0.421 0.420 0.418 0.417 0.416 0.415 0.414 0.413 0.412 0.411 0.410 0.409 0.409 0.408 0.408 0.407 0.406 0.406 0.405 0.405 0.405 0.404 0.404 0.403 0.403 0.403 0.402 0.402 0.402 0.401 0.401 0.401 0.401 0.400

0.501 0.490 0.481 0.472 0.464 0.458 0.452 0.446 0.441 0.437 0.433 0.429 0.426 0.423 0.421 0.418 0.416 0.414 0.412 0.410 0.409 0.407 0.406 0.405 0.404 0.403 0.402 0.401

0.488 0.477 0.468 0.459 0.452 0.445 0.439 0.434 0.429 0.425 0.421 0.417 0.414 0.41 1 0.409 0.406 0.404 0.402 0.401 0.399 0.397 0.396 0.395 0.393 0.392 0.391 0.390 0.389 0.389 0.388 0.387 0.386 0.386 0.385 0.384 0.384 0.383 0.383 0.382 0.382 0.382 0.381 0.381 0.380 0.380 0.380 0.379 0.379 0.379 0.379 0.378 0.378 0.378 0.378 0.377 0.377 0.377 0.377 0.377 0.376

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0

0.518 0.518

0.517 0.516 0.516 0.515 0.515 0.514 0.513 0.513 0.513 0.512 0.512 0.511 0.511

0.510 0.510 0.510 0.509 0.509 0.509 0.509 0.508 0.508 0.508 0.508 0.507

0.440 0.440

0.440 0.440 0.439 0.439 0.439

0.400

0.400 0.400 0.400

0.399 0.399

0.400

0.399 0.398 0.398 0.397 0.396 0.396 0.395 0.395 0.394 0.394 0.393 0.393 0.392 0.392 0.392 0.391 0.391 0.391 0.390 0.390 0.390 0.389 0.389 0.389 0.389 0.388 0.388 0.388 0.388 0.388 0.387

368 TABLE 9 . 3 ~ Value of the Coefficient of Equation 6 P,

RL

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.804.90

5.00

1.I

0.476 0.465

0.464 0.454

0.440 0.433 0.427 0.422 0.418 0.413 0.410

0.433 0.422 0.413 0.405 0.398 0.392 0.386 0.381 0.377 0.373 0.370 0.366 0.364 0.361 0.359 0.357 0.355 0.353 0.351 0.350 0.348 0.347 0.346 0.345 0.344 0.343 0.342 0.341 0.341 0.340 0.339 0.339 0.338 0.337 0.337 0.336 0.336 0.336 0.335 0.335 0.334 0.334 0.334 0.333 0.333 0.333 0.332 0.332 0.332 0.332 0.332 0.331 0.331 0.331 0.331 0.331 0.330 0.330 0.330 0.330

0.404

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

0.443 0.432 0.423 0.415 0.408 0.402 0.396 0.391 0.386 0.382 0.379 0.376 0.373 0.370 0.368 0.366 0.364 0.362 0.360 0.359 0.357 0.356 0.355 0.354 0.353 0.352 0.351 0.350 0.349 0.348 0.348 0.347 0.346 0.346 0.345 0.345 0.344 0.344 0.344 0.343 0.343 0.342 0.342 0.342 0.341 0.341 0.341 0.341 0.340 0.340 0.340 0.340 0.339 0.339 0.339 0.339 0.339 0.339 0.338 0.338

0.423 0.413

1.5

0.453 0.443 0.434 0.425 0.418 0.412 0.406 0.401 0.396 0.392 0.389 0.385 0.382 0.380 0.377 0.375 0.373 0.371 0.369 0.368 0.366 0.365 0.364 0.363 0.362 0.361 0.360 0.359

0.414

1.2 1.3 1.4

0.395 0.387 0.380 0.374 0.369 0.364 0.360 0.356 0.353 0.349 0.347 0.344 0.342 0.340 0.338 0.336 0.335 0.333 0.332 0.331 0.330 0.329 0.328 0.327 0.326 0.325 0.325 0.324 0.323 0.323 0.322 0.322 0.321 0.321 0.320 0.320 0.319 0.319 0.319 0.318 0.318 0.318 0.317 0.317 0.317 0.317 0.316 0.316 0.316 0.316 0.316 0.315 0.315

0.405 0.395 0.386 0.379 0.372 0.366 0.360 0.356 0.352 0.348 0.345 0.342 0.339 0.336 0.334 0.332 0.330 0.329 0.327 0.326 0.325 0.323 0.322 0.321 0.320 0.319 0.319 0.318 0.317 0.316 0.316 0.315 0.315 0.314 0.314 0.313 0.313 0.312 0.312 0.312 0.311 0.311 0.311 0.310 0.310 0.310 0.310 0.309 0.309 0.309 0.309 0.308 0.308 0.308 0.308 0.308 0.308 0.307 0.307 0.307

0.397 0.387 0.378 0.370 0.364 0.358 0.353 0.348 0.344 0.340 0.337 0.334 0.331 0.329 0.327 0.325 0.323 0.321 0.320 0.319 0.317 0.316 0.315 0.314 0.313 0.312 0.311 0.311 0.310 0.309 0.309 0.308 0.308 0.307 0.307 0.306 0.306 0.305 0.305 0.305 0.304 0.304 0.304 0.303 0.303 0.303 0.303 0.302 0.302 0.302 0.302 0.302 0.301 0.301 0.301 0.301

5 .O 5.1

5.2 5.3 5.4 5.5

5.6 5.7 5.8

5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0

0.456 0.447

0.406 0.403

0.400 0.398 0.395 0.393 0.391 0.390 0.388 0.386 0.385 0.384 0.383 0.382 0.381 0.380 0.379 0.378 0.377 0.376 0.376 0.375 0.374 0.374 0.373 0.373 0.372 0.372 0.371 0.371 0.371 0.370 0.370 0.370 0.369 0.369 0.369 0.368 0.368 0.368 0.368 0.367 0.367 0.367 0.367 0.367 0.366 0.366 0.366

0.444 0.436 0.429 0.422 0.416 0.41 1 0.407 0.402 0.399 0.395 0.392 0.390 0.387 0.385 0.383 0.381 0.379 0.378 0.376 0.375 0.374 0.372 0.371 0.370 0.369 0.369 0.368 0.367 0.366 0.366 0.365 0.364 0.364 0.363 0.363 0.362 0.362 0.362 0.361 0.361 0.360 0.360 0.360 0.359 0.359 0.359 0.359 0.358 0.358 0.358 0.358 0.357 0.357 0.357 0.357 0.357 0.356 0.356

0.358 0.357 0.357 0.356 0.355 0.355

0.354 0.354 0.353 0.353 0.353 0.352 0.352 0.351 0.351 0.351 0.350 0.350 0.350 0.350 0.349 0.349 0.349 0.349 0.348 0.348 0.348 0.348 0.348 0.347 0.347 0.347

0.396 0.389 0.383 0.377 0.372 0.368 0.364 0.361 0.358 0.355 0.352 0.350 0.348 0.346 0.344 0.343 0.341 0.340 0.339 0.338 0.337 0.336 0.335 0.334 0.333 0.332 0.332 0.331 0.330 0.330 0.329 0.329 0.328 0.328 0.327 0.327 0.327 0.326 0.326 0.326 0.325 0.325 0.325 0.324 0.324 0.324 0.324 0.324 0.323 0.323 0.323 0.323 0.323 0.322 0.322 0.322 0.322

0.404

0.315 0.315 0.315

0.315 0.314

0.301

0.301 0.300 0.300

0.389 0.379 0.370 0.363 0.356 0.350 0.345 0.340 0.336 0.333 0.330 0.327 0.324 0.322 0.320 0.318 0.316 0.314 0.313 0.312 0.310 0.309 0.308 0.307 0.306 0.305 0.305 0.304 0.303 0.303 0.302 0.301 0.301 0.300 0.300 0.300 0.299 0.299 0.298 0.298 0.298 0.297 0.297 0.297 0.297 0.296 0.296 0.296 0.296 0.295 0.295 0.295 0.295 0.295 0.294 0.294 0.294 0.294 0.294 0.294

369 TABLE 9.3d Value of the Coefficient of Equation 6

F,

RL

5.10

5.20

5.30

5.40

5.50

5.60

5.70

5.80

5.90

6.00

0.381 0.371 0.363 0.355 0.349 0.343 0.338 0.333 0.329 0.326 0.323 0.320 0.317 0.315 0.313 0.311 0.309 0.308 0.306 0.305 0.304 0.303 0.302 0.301 0.300 0.299 0.298 0.297 0.297 0.296 0.296 0.295 0.294 0.294 0.294 0.293 0.293 0.292 0.292 0.292 0.291 0.291 0.291 0.290 0.290 0.290 0.290 0.289 0.289 0.289 0.289 0.289 0.288 0.288 0.288 0.288 0.288 0.288 0.288 0.287

0.374 0.364 0.355 0.348 0.342 0.336 0.331 0.326 0.323 0.319 0.316 0.313 0.311 0.308 0.306 0.305 0.303 0.301 0.300 0.299 0.297 0.296 0.295 0.294 0.293 0.293 0.292 0.291 0.291 0.290 0.289 0.289 0.288 0.288 0.287 0.287 0.287 0.286 0.286 0.286 0.285 0.285 0.285 0.284 0.284 0.284 0.284 0.283 0.283 0.283 0.283 0.283 0.282 0.282 0.282 0.282 0.282 0.282 0.282 0.281

0.366 0.357 0.348 0.341 0.335 0.329 0.324 0.320 0.316 0.313 0.310 0.307 0.304 0.302 0.300 0.298 0.297 0.295 0.294 0.292 0.291 0.290 0.289 0.288 0.287 0.287 0.286 0.285 0.285 0.284 0.283 0.283 0.282 0.282 0.282 0.281 0.281 0.280 0.280 0.280 0.279 0.279 0.279 0.279 0.278 0.278 0.278 0.278 0.277 0.277 0.277 0.277 0.277 0.276 0.276 0.276 0.276 0.276 0.276 0.276

0.359 0.350 0.342 0.334 0.328 0.323 0.318 0.314 0.310 0.306 0.303 0.301 0.298 0.296 0.294 0.292 0.291 0.289 0.288 0.287 0.285 0.284 0.283 0.283 0.282 0.281 0.280 0.280 0.279 0.278 0.278 0.277 0.277 0.276 0.276 0.275 0.275 0.275 0.274 0.274 0.274 0.273 0.273 0.273 0.273 0.272 0.272 0.272 0.272 0.272 0.271 0.271 0.271 0.271 0.271 0.271 0.270 0.270 0.270 0.270

0.353 0.343 0.335 0.328 0.322 0.316 0.312 0.307 0.304 0.300 0.297 0.295 0.292 0.290 0.288 0.287 0.285 0.284 0.282 0.281 0.280 0.279 0.278 0.277 0.276 0.275 0.275 0.274 0.273 0.273 0.272 0.272 0.271 0.271 0.270 0.270 0.270 0.269 0.269 0.269 0.268 0.268 0.268 0.268 0.267 0.267 0.267 0.267 0.266 0.266 0.266 0.266 0.266 0.266 0.265 0.265 0.265 0.265 0.265 0.265

0.346 0.337 0.329 0.322 0.316 0.311 0.306 0.302 0.298 0.295 0.292 0.289 0.287 0.285 0.283 0.281 0.280 0.278 0.277 0.276 0.274 0.273 0.273 0.272 0.271 0.270 0.269 0.269 0.268 0.268 0.267 0.267 0.266 0.266 0.265 0.265 0.264 0.264 0.264 0.263 0.263 0.263 0.263 0.262 0.262 0.262 0.262 0.261 0.261 0.261 0.261 0.261 0.261 0.260 0.260 0.260 0.260 0.260 0.260 0.260

0.340 0.331 0.323 0.316 0.310 0.305 0.300 0.296 0.292 0.289 0.286 0.284 0.281 0.279 0.278 0.276 0.274 0.273 0.272 0.270 0.269 0.268 0.267 0.267 0.266 0.265 0.264 0.264 0.263 0.262 0.262 0.261 0.261 0.261 0.260 0.260 0.259 0.259 0.259 0.258 0.258 0.258 0.258 0.257 0.257 0.257 0.257 0.257 0.256 0.256 0.256 0.256 0.256 0.256 0.255 0.255 0.255 0.255 0.255 0.255

0.334 0.325 0.317 0.310 0.304 0.299 0.295 0.291 0.287 0.284 0.281 0.279 0.276 0.274 0.272 0.271 0.269 0.268 0.267 0.265 0.264 0.263 0.262 0.262 0.261 0.260 0.259 0.259 0.258 0.258 0.257 0.257 0.256 0.256 0.255 0.255 0.255 0.254 0.254 0.254 0.253 0.253 0.253 0.253 0.252 0.252 0.252 0.252 0.252 0.251 0.251 0.251 0.251 0.251 0.251 0.250 0.250 0.250 0.250 0.250

0.329 0.320 0.312 0.305 0.299 0.294 0.289 0.285 0.282 0.279 0.276 0.274 0.271 0.269 0.267 0.266 0.264 0.263 0.262 0.261 0.259 0.259 0.258 0.257 0.256 0.255 0.255 0.254 0.253 0.253 0.252 0.252 0.252 0.251 0.251 0.250 0.250 0.250 0.249 0.249 0.249 0.249 0.248 0.248 0.248 0.248 0.247 0.247 0.247 0.247 0.247 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.245

0.323 0.314 0.306 0.300 0.294 0.289 0.284 0.280 0.277 0.274 0.271 0.269 0.266 0.264 0.263 0.261 0.260 0.258 0.257 0.256 0.255 0.254 0.253 0.252 0.251 0.251 0.250 0.250 0.249 0.248 0.248 0.247 0.247 0.247 0.246 0.246 0.246 0.245 0.245 0.245 0.244 0.244 0.244 0.244 0.243 0.243 0.243 0.243 0.243 0.242 0.242 0.242 0.242 0.242 0.242 0.242 0.241 0.241 0.241 0.241

~

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0

370 TABLE 9.3e Value of the Coefficient of Equation 6 Pi

1.1 1.2 1.3 1.4 1.5

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0

RL

6.10

6.20

6.30

6.40

6.50

6.60

6.70

6.80

6.90

7.00

0.318 0.309 0.301 0.295 0.289 0.284 0.279 0.276 0.272 0.269 0.266 0.264 0.262 0.260 0.258 0.257 0.255 0.254 0.253 0.251 0.250 0.249 0.249 0.248 0.247 0.246 0.246 0.245 0.245 0.244 0.244 0.243 0.243 0.242 0.242 0.242 0.241 0.241 0.241 0.240 0.240 0.240 0.240 0.239 0.239 0.239 0.239 0.239 0.238 0.238 0.238 0.238 0.238 0.238 0.237 0.237 0.237 0.237 0.237 0.237

0.312 0.304 0.296 0.290 0.284 0.279 0.275 0.271 0.267 0.264 0.262 0.259 0.257 0.255 0.254 0.252 0.251 0.249 0.248 0.247 0.246 0.245 0.244 0.244 0.243 0.242 0.241 0.241 0.240 0.240 0.239 0.239 0.238 0.238 0.238 0.237 0.237 0.237 0.236 0.236 0.236 0.236 0.235 0.235 0.235 0.235 0.235 0.234 0.234 0.234 0.234 0.234 0.234 0.233 0.233 0.233 0.233 0.233 0.233 0.233

0.307 0.299 0.291 0.285 0.279 0.274 0.270 0.266 0.263 0.260 0.257 0.255 0.253 0.251 0.249 0.248 0.246 0.245 0.244 0.243 0.242 0.241 0.240 0.239 0.239 0.238 0.237 0.237 0.236 0.236 0.235 0.235 0.234 0.234 0.234 0.233 0.233 0.233 0.232 0.232 0.232 0.232 0.231 0.231 0.231 0.231 0.231 0.230 0.230 0.230 0.230 0.230 0.230 0.229 0.229 0.229 0.229 0.229 0.229 0.229

0.303 0.294 0.287 0.280 0.275 0.270 0.266 0.262 0.259 0.256 0.253 0.251 0.249 0.247 0.245 0.244 0.242 0.241 0.240 0.239 0.238 0.237 0.236 0.235 0.235 0.234 0.233 0.233 0.232 0.232 0.231 0.231 0.231 0.230 0.230 0.229 0.229 0.229 0.229 0.228 0.228 0.228 0.228 0.227 0.227 0.227 0.227 0.227 0.226 0.226 0.226 0.226 0.226 0.226 0.226 0.225 0.225 0.225 0.225 0.225

0.298 0.289 0.282 0.276 0.270 0.265 0.261 0.258 0.254 0.252 0.249 0.247 0.245 0.243 0.241 0.240 0.238 0.237 0.236 0.235 0.234 0.233 0.232 0.232 0.231 0.230 0.230 0.229 0.229 0.228 0.228 0.227 0.227 0.226 0.226 0.226 0.225 0.225 0.225 0.225 0.224 0.224 0.224 0.224 0.223 0.223 0.223 0.223 0.223 0.223 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.221 0.221 0.221

0.293 0.285 0.278 0.271 0.266 0.261 0.257 0.254 0.250 0.248 0.245 0.243 0.241 0.239 0.237 0.236 0.235 0.233 0.232 0.231 0.230 0.229 0.229 0.228 0.227 0.227 0.226 0.225 0.225 0.224 0.224 0.224 0.223 0.223 0.222 0.222 0.222 0.221 0.221 0.221 0.221 0.220 0.220 0.220 0.220 0.220 0.219 0.219 0.219 0.219 0.219 0.219 0.218 0.218 0.218 0.218 0.218 0.218 0.218 0.218

0.289 0.280 0.273 0.267 0.262 0.257 0.253 0.250 0.246 0.244 0.241 0.239 0.237 0.235 0.234 0.232 0.231 0.230 0.229 0.228 0.227 0.226 0.225 0.224 0.224 0.223 0.222 0.222 0.221 0.221 0.220 0.220 0.220 0.219 0.219 0.219 0.218 0.218 0.218 0.217 0.217 0.217 0.217 0.217 0.216 0.216 0.216 0.216 0.216 0.215 0.215 0.215 0.215 0.215 0.215 0.215 0.215 0.214 0.214 0.214

0.285 0.276 0.269 0.263 0.258 0.253 0.249 0.246 0.243 0.240 0.237 0.235 0.233 0.232 0.230 0.229 0.227 0.226 0.225 0.224 0.223 0.222 0.221 0.221 0.220 0.219 0.219 0.218 0.218 0.217 0.217 0.217 0.216 0.216 0.215 0.215 0.215 0.215 0.214 0.214 0.214 0.214 0.213 0.213 0.213 0.213 0.213 0.21 2 0.212 0.212 0.212 0.212 0.21 2 0.21 2 0.21 1 0.211 0.21 1 0.21 1 0.21 1 0.21 1

0.280 0.272 0.265 0.259 0.254 0.249 0.245 0.242 0.239 0.236 0.234 0.232 0.230 0.228 0.226 0.225 0.224 0.223 0.222 0.221 0.220 0.219 0.218 0.217 0.217 0.216 0.21 5 0.215 0.214 0.214 0.214 0.213 0.213 0.212 0.212 0.212 0.212 0.211 0.21 1 0.21 1 0.210 0.210 0.210 0.210 0.210 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208

0.276 0.268 0.261 0.255 0.250 0.246 0.242 0.238 0.235 0.233 0.230 0.228 0.226 0.225 0.223 0.222 0.220 0.219 0.218 0.217 0.216 0.215 0.215 0.214 0.21 3 0.213 0.212 0.212 0.21 1 0.211 0.210 0.210 0.210 0.209 0.209 0.209 0.208 0.208 0.208 0.208 0.207 0.207 0.207 0.207 0.206 0.206 0.206 0.206 0.206 0.206 0.206 0.205 0.205 0.205 0.205 0.205 0.205 0.205 0.205 0.204

371 TABLE 9.3f Value of the Coefficient of Equation 6 Pi

RL

7.10

7.20

7.30

7.40

7.50

7.60

7.70

7.80

7.90

8.00

1.1

0.272 0.264 0.257 0.252 0.247 0.242 0.238 0.235 0.232 0.229 0.227 0.225 0.223 0.221 0.220 0.218 0.217 0.216 0.215 0.214 0.213 0.212 0.212 0.21 1 0.210 0.210 0.209 0.209 0.208 0.208 0.207 0.207 0.206 0.206 0.206 0.205 0.205 0.205 0.205 0.204 0.204 0.204 0.204 0.204 0.203 0.203 0.203 0.203 0.203 0.203 0.202 0.202 0.202 0.202 0.202 0.202 0.202 0.202 0.202 0.201

0.269 0.261 0.254 0.248 0.243 0.239 0.235 0.231 0.229 0.226 0.224 0.222 0.220 0.218 0.217 0.21s 0.214 0.213 0.212 0.21 1 0.210 0.209 0.208 0.208 0.207 0.207 0.206 0.206 0.205 0.205 0.204 0.204 0.203 0.203 0.203 0.202 0.202 0.202 0.202 0.201 0.201 0.201 0.201 0.201 0.200 0.200 0.200 0.200 0.200 0.200 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.198

0.265 0.257 0.250 0.244 0.240 0.235 0.231 0.228 0.225 0.223 0.220 0.218 0.217 0.215 0.213 0.212 0.211 0.210 0.209 0.208 0.207 0.206 0.205 0.205 0.204 0.204 0.203 0.203 0.202 0.202 0.201 0.201 0.200 0.200 0.200 0.200 0.199 0.199 0.199 0.199 0.198 0.198 0.198 0.198 0.198 0.197 0.197 0.197 0.197 0.197 0.197 0.196 0.196 0.196 0.196 0.196 0.196 0.196 0.196 0.196

0.261 0.253 0.247 0.241 0.236 0.232 0.228 0.225 0.222 0.220 0.217 0.215 0.213 0.212 0.210 0.209 0.208 0.207 0.206 0.205 0.204 0.203 0.202 0.202 0.201 0.201 0.200 0.200 0.199 0.199 0.198 0.198 0.198 0.197 0.197 0.197

0.258 0.250 0.243 0.238 0.233 0.229 0.22s 0.222 0.219 0.216 0.214 0.212 0.210 0.209 0.207 0.206 0.205 0.204 0.203 0.202 0.201 0.200 0.200 0.199 0.198 0.198 0.197 0.197 0.196 0.196 0.196 0.195 0.195 0.195 0.194 0.194 0.194 0.193 0.193 0.193 0.193 0.193 0.192 0.192 0.192 0.192 0.192 0.191 0.191 0.191 0.191 0.191 0.191 0.191 0.191 0.190

0.254 0.247 0.240 0.235 0.230 0.226 0.222 0.219 0.216 0.213 0.211 0.209 0.208 0.206 0.205 0.203 0.202 0.201 0.200 0.199 0.198 0.198 0.197 0.196 0.196 0.195 0.195 0.194 0.194 0.193 0.193 0.192 0.192 0.192 0.192 0.191 0.191 0.191 0.190

0.251 0.243 0.237 0.231 0.227 0.223 0.219 0.216 0.213 0.21 1 0.208 0.206 0.205 0.203 0.202 0.200 0.199 0.198 0.197 0.196 0.196 0.195 0.194 0.194 0.193 0.192 0.192 0.191 0.191 0.191 0.190

0.244 0.237 0.231 0.225 0.221 0.217 0.213 0.210 0.207 0.205 0.203 0.201 0.199 0.198 0.196 0.195 0.194 0.193 0.192 0.191

0.241 0.234 0.228 0.222 0.218 0.214 0.210 0.207 0.205 0.202 0.200 0.198 0.197 0.195 0.194 0.193 0.191 0.190

0.188

0.248 0.240 0.234 0.228 0.224 0.220 0.216 0.213 0.210 0.208 0.206 0.204 0.202 0.200 0.199 0.198 0.197 0.196 0.195 0.194 0.193 0.192 0.192 0.191 0.190 0.190 0.189 0.189 0.188 0.188 0.188 0.187 0.187 0.187 0.186 0.186 0.186 0.186

0.188

0.185

0.188 0.187 0.187 0.187 0.187 0.187 0.187 0.186 0.186 0.186 0.186 0.186 0.186 0.186 0.185 0.185 0.185 0.185 0.185 0.185 0.185

0.185 0.185 0.185 0.185 0.184 0.184 0.184 0.184 0.184 0.184 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.182 0.182

1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1

5.2 5.3 5.4 5.5 5.6 5.7 5.8

5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0

0.1%

0.196 0.1% 0.196 0.195 0.195 0.195 0.195 0.195 0.195 0.194 0.194 0.194 0.194 0.194 0.194 0.194 0.193 0.193 0.193 0.193 0.193 0.193 0.193

0.190 0.190

0.190 0.190

0.190

0.190 0.190 0.190 0.189 0.189 0.189 0.189 0.189 0.189 0.189 0.188

0.188 0.188 0.188 0.188

0.188 0.188

0.188 0.188 0.187

0.190

0.190 0.189 0.189 0.189 0.188

0.190

0.190 0.189 0.188 0.188 0.187 0.187 0.186 0.186 0.186 0.185 0.185 0.184 0.184 0.184 0.184 0.183 0.183 0.183 0.183 0.182 0.182 0.182 0.182 0.182 0.182 0.181 0.181 0.181

0.181 0.181 0.181

0.181 0.181 0.180 0.180 0.180 0.180 0.180 0.180

0.190

0.189 0.188 0.187 0.187 0.186 0.185 0.185

0.184 0.184 0.183 0.183 0.183 0.182 0.182 0.182 0.181 0.181 0.181 0.181

0.180 0.180 0.180 0.180 0.180 0.180 0.179 0.179 0.179 0.179 0.179 0.179 0.179 0.178 0.178 0.178 0.178 0.178 0.178 0.178 0.178 0.178

372 TABLE 9.3g Value of the Coefficient of Equation 6 Pi

RL

8.10

8.20

8.30

8.40

8.50

8.60

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0

0.238 0.231 0.225 0.220 0.215 0.211 0.208 0.205 0.202 0.200 0.198 0.196 0,194 0.193 0.191 0.190 0.189 0.188 0.187 0.186 0.185 0.185 0.184 0.184 0.183 0.182 0.182 0.182 0.181 0.181 0.180 0.180 0.180 0.179 0.179 0.179 0.179 0.178 0.178 0.178 0.178 0.178 0.177 0.177 0.177 0.177 0.177 0.177 0.176 0.176 0.176 0.176 0.176 0.176 0.176 0.176 0.176 0.175 0.175 0.175

0.235 0.228 0.222 0.217 0.212 0.208 0.205 0.202 0.199 0.197 0.195 0.193 0.192 0.190 0.189 0.188 0.187 0.186 0.185 0.184 0.183 0.182 0.182 0.181 0.181 0.180 0.180 0.179 0.179 0.178 0.178 0.178 0.177 0.177 0.177 0.177 0.176 0.176 0.176 0.176 0.175 0.175 0.175 0.175 0.175 0.175 0.174 0.174 0.174 0.174 0.174 0.174 0.174 0.174 0.174 0.173 0.173 0.173 0.173 0.173

0.233 0.225 0.219 0.214 0.210 0.206 0.203 0.200 0.197 0.195 0.193 0.191 0.189 0.188 0.187 0.185 0.184 0.183 0.182 0.182 0.181 0.180 0.179 0.179 0.178 0.178 0.177 0.177 0.177 0.176 0.176 0.175 0.175 0.175 0.175 0.174 0.174 0.174 0.174 0.173 0.173 0.173 0.173 0.173 0.173 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.171 0.171 0.171 0.171 0.171 0.171 0.171

0.230 0.223 0.217 0.212 0.207 0.203 0.200 0.197 0.195 0.192 0.190 0.189 0.187 0.185 0.184 0.183 0.182 0.181 0.180 0.179 0.179 0.178 0.177 0.177 0.176 0.176 0.175 0.175 0.174 0.174 0.174 0.173 0.173 0.173 0.172 0.172 0.172 0.172 0.171 0.171 0.171 0.171 0.171 0.171 0.170 0.170 0.170 0.170 0.170 0.170 0.170 0.169 0.169 0.169 0.169 0.169 0.169 0.169 0.169 0.169

0.227 0.220 0.214 0.209 0.205 0.201 0.198 0.195 0.192 0.190 0.188 0.186 0.185 0.183 0.182 0.181 0.180 0.179 0.178 0.177 0.176 0.176 0.175 0.174 0.174 0.173 0.173 0.173 0.172 0.172 0.171 0.171 0.171 0.171 0.170 0.170 0.170 0.170 0.169 0.169 0.169 0.169 0.169 0.168 0.168 0.168 0.168 0.168 0.168 0.168 0.168 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167

0.224 0.217 0.212 0.206 0.202 0.198 0.195 0.192 0.190 0.188 0.186 0.184 0.182 0.181 0.180 0.179 0.178 0.177 0.176 0.175 0.174 0.174 0.173 0.172 0.172 0.171 0.171 0.170 0.170 0.170 0.169 0.169 0.169 0.168 0.168 0.168 0.168 0.168 0.167 0.167 0.167 0.167 0.167 0.166 0.166 0.166 0.166 0.166 0.166 0.166 0.165 0.165 0.165 0.165 0.165 0.165 0.165 0.165 0.165 0.165

'

8.70

8.80

8.90

9.00

0.222 0.215 0.209 0.204 0.200 0.196 0.193 0.190 0.188 0.185 0.183 0.182 0.180 0.179 0.178 0.176 0.175 0.174 0.174 0.173 0.172 0.171 0.171 0.170 0.170 0.169 0.169 0.168 0.168 0.168 0.167 0.167 0.167 0.166 0.166 0.166 0.166 0.165 0.165 0.165 0.165 0.165 0.165 0.164 0.164 0.164 0.164 0.164 0.164 0.164 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163

0.219 0.212 0.207 0.202 0.197 0.194 0.191 0.188 0.185 0.183 0.181 0.180 0.178 0.177 0.175 0.174 0.173 0.172 0.172 0.171 0.170 0.169 0.169 0.168 0.168 0.167 0.167 0.166 0.166 0.166 0.165 0.165 0.165 0.164 0.164 0.164 0.164 0.164 0.163 0.163 0.163 0.163 0.163 0.162 0.162 0.162 0.162 0.162 0.162 0.162 0.162 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161

0.217 0.210 0.204 0.199 0.195 0.192 0.188 0.186 0.183 0.181 0.179 0.177 0.176 0.175 0.173 0.172 0.171 0.170 0.170 0.169 0.168 0.167 0.167 0.166 0.166 0.165 0.165 0.164 0.164 0.164 0.163 0.163 0.163 0.163 0.162 0.162 0.162 0.162 0.161 0.161 0.161 0.161 0.161 0.161 0.160 0.160 0.160 0.160 0.160 0.160 0.160 0.160 0.159 0.159 0.159 0.159 0.159 0.159 0.159 0.159

0.214 0.208 0.202 0.197 0.193 0.189 0.186 0.183 0.181 0.179 0.177 0.175 0.174 0.173 0.171 0.170 0.169 0.168 0.168 0.167 0.166 0.166 0.165 0.164 0.164 0.163 0.163 0.163 0.162 0.162 0.162 0.161 0.161 0.161 0.160 0.160 0.160 0.160 0.160 0.159 0.159 0.159 0.159 0.159 0.159 0.158 0.158 0.158 0.158 0.158 0.158 0.158 0.158 0.157 0.157 0.157 0.157 0.157 0.157 0.157

313

b. Second Problem: Calculation of the Transit Time on an Intermediate Column Segment The practical problem for the analyst is the determination of the time at which the most important peak exits from the column segment operated with the inlet pressure pi and an intermediate pressure. Only the retention time on the total column is known. This transit time can be easily derived from the equations discussed Chapter 2, relating the local pressure to the column characteristics (see equation 9, Figure 9.31):

t . r 3 A = t,A

P3 - P,’

(7)

We can also derive the transit time, knowing that the retention time of a retained compound, A, is proportional to that of the non-retained band or gas hold-up. Thus:

where k i is the column capacity factor for compound A and to is given by equation 9 in Figure 9.31. Values of the coefficient of tL,A in equation 7 are reported in Table 9.4, for all practical combinations of values of p i and x / L . c. Third Problem: Calcdation of the Retention Time on a Column having an Outlet Pressure above Atmospheric

It is sometimes required to use a precolumn and a column made with different stationary phases. The retention time on the precolumn can be related to the retention time on this column alone and to the values of the inlet and outlet pressures, provided the outlet flow velocity (i.e., the mass flow rate) through the column remains the same in both cases. The retention time of a compound on the precolumn alone is:

where j is the James and Martin pressure correction factor corresponding to the inlet and outlet pressure used (see Chapter 2). When the precolumn is placed before the column, but the mass flow rate is kept the same (same flow velocity at the outlet of the last column, i.e., under atmospheric pressure), the retention time becomes:

(10) References on p. 390.

374

TABLE 9.4a Value of the Coefficient of Equation 9

* 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.OO

P, 1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

0.0209 0.0417 0.0626 0.0834 0.1042 0.1249 0.1456 0.1663 0.1869 0.2075 0.2280 0.2486 0.2690 0.2895 0.3099 0.3302 0.3506 0.3709 0.3911 0.4113 0.4315 0.4516 0.4717 0.4918 0.5118 0.5318 0.5518 0.5717 0.5916 0.6114 0.6312 0.6510 0.6707 0.6904 0.7100 0.7296 0.7492 0.7687 0.7882 0.8076 0.8270 0.8464 0.8657 0.8850 0.9043 0.9235 0.9427 0.9618 0.9809 1 .oooo

0.0217 0.0433 0.0649 0.0864 0.1079 0.1293 0.1506 0.1719 0.1931 0.2142 0.2352 0.2562 0.2771 0.2980 0.3187 0.3394 0.3601 0.3806 0.4011 0.4215 0.4419 0.4622 0.4824 0.5025 0.5226 0.5426 0.5625 0.5823 0.6021 0.6218 0.6414 0.6610 0.6805 0.6999 0.7192 0.7384 0.7576 0.7767 0.7957 0.8147 0.8336 0.8524 0.8711 0.8897 0.9083 0.9268 0.9452 0.9635 0.9818

0.0224 0.0447 0.0670 0.0891 0.1112 0.1332 0.1550 0.1768 0.1985 0.2201 0.2416 0.2630 0.2843 0.3055 0.3266 0.3476 0.3685 0.3894 0.4101 0.4307 0.4512 0.4716 0.4919 0.5121 0.5322 0.5522 0.5721 0.5919 0.6116 0.6312 0.6507 0.6701 0.6893 0.7085 0.7276 0.7465 0.7653 0.7841 0.8027 0.8212 0.8396 0.8579 0.8760 0.8941 0.9120 0.9298 0.9475 0.9651 0.9826 1.oooO

0.0230 0.0460 0.0688 0.0915 0.1141 0.1 366 0.1590 0.1812 0.2034 0.2254 0.2473 0.2691 0.2907 0.3123 0.3337 0.3550 0.3761 0.3972 0.4181 0.4389 0.4596 0.4801 0.5005 0.5208 0.5409 0.5610 0.5809 0.6006 0.6203 0.6398 0.6591 0.6783 0.6974 0.7164 0.7352 0.7539 0.7724 0.7908 0.8090 0.8271 0.8451 0.8629 0.8806 0.8981 0.9154 0.9326 0.9497 0.9666 0.9834 1.oooO

0.0236 0.0471 0.0704 0.0936 0.1167 0.1397 0.1625 0.1851 0.2077 0.2301 0.2523 0.2745 0.2964 0.3183 0.3400 0.3615 0.3829 0.4042 0.4253 0.4463 0.4671 0.4877 0.5082 0.5286 0.5488 0.5689 0.5887 0.6085 0.6281 0.6475 0.6667 0.6858 0.7048 0.7235 0.7421 0.7606 0.7788 0.7969 0.8148 0.8326 0.8501 0.8675 0.8847 0.9017 0.9186 0.9352 0.9517 0.9680 0.9841

0.0241 0.0480 0.0718 0.0955 0.1190 0.1424 0.1656 0.1886 0.2115 0.2343 0.2569 0.2793 0.3016 0.3237 0.3456 0.3674 0.3890 0.4105 0.4318 0.4529 0.4738 0.4946 0.5152 0.5356 0.5559 0.5760 0.5959 0.6156 0.6351 0.6545 0.6737 0.6926 0.7114 0.7300 0.7484 0.7667 0.7847 0.8025 0.8201 0.8375 0.8548 0.8718 0.8886 0.9051 0.9215 0.9376 0.9536 0.9693 0.9847

0.0245 0.0489 0.0731 0.0972 0.1211 0.1448 0.1684 0.1918 0.2150 0.2380 0.2609 0.2836 0.3062 0.3285 0.3507 0.3727 0.3945 0.4161 0.4376 0.4588 0.4799 0.5008 0.5215 0.5420 0.5623 0.5824 0.6023 0.6220 0.6415 0.6608 0.6799 0.6988 0.7175 0.7360 0.7542 0.7722 0.7900 0.8076 0.8250 0.8421 0.8590 0.8757 0.8921 0.9083 0.9242 0.9399 0.9553 0.9704 0.9853

0.0249 0.0497 0.0743 0.0987 0.1229 0.1470 0.1709 0.1946 0.2181 0.2414 0.2646 0.2875 0.3103 0.3329 0.3552 0.3774 0.3994 0.4212 0.4428 0.4642 0.4854

1.m

1

0.0252 0.0504 0.0753 0.1oOo 0.1246 0.1489 0.1731 0.1971 0.2209 0.2445 0.2678 0.2910 0.3140 0.3368 0.3594 0.3817 0.4039 0.4258 0.4476 0.4691 0.4904 0.5114 0.5323 0.5529 0.5733 0.5935 0.6135 0.6332 0.6526 0.6719 0.6908 0.7096 0.7281 0.7463 0.7643 0.7820 0.7994 0.8166 0.8335 0.8501 0.8665 0.8826 0.8983 0.9138 0.9289 0.9438 0.9583 0.9725 0.9864 1.oooO

0.0256 0.0510 0.0762 0.1012 0.1261 0.1507 0.1751 0.1994 0.2234 0.2472 0.2708 0.2942 0.3174 0.3403 0.3631 0.3856 0.4079 0.4300 0.4518 0.4735 0.4949 0.5160 0.5370 0.5577 0.5781 0.5983 0.6183 0.6380 0.6574 0.6766 0.6956 0.7143 0.7327 0.7508 0.7687 0.7862 0.8035 0.8206 0.8373 0.8537 0.8698 0.8856 0.9011 0.9162 0.931 1 0.9455 0.9597 0.9735 0.9869 1.oooo

1.oooo

l.m l.m

0.5064

0.5272 0.5477 0.5681 0.5882 0.6082 0.6279 0.6473 0.6666 0.6856 0.7045 0.7230 0.7414 0.7595 0.7773 0.7950 0.8123 0.8294 0.8463 0.8629 0.8792 0.8953 0.9111 0.9267 0.9419 0.9569 0.9715 0.9859

.oooo

315 TABLE 9.4b Value of the Coefficient of Equation 9

PI

X

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

0.0258 0.0516 0.0770 0.1023 0.1274 0.1523 0.1770 0.2014 0.2257 0.2497 0.2735 0.2971 0.3204 0.3435 0.3664 0.3891 0.4116 0.4338 0.4557 0.4775 0.4990 0.5202 0.5412 0.5620 0.5825 0.6027 0.6227 0.6424 0.6618 0.6810 0.6999 0.7185 0.7369 0.7549 0.7727 0.7902 0.8073 0.8242 0.8407 0.8569 0.8728 0.8884 0.9036 0.9185 0.9330 0.9472 0.9610 0.9744 0.9874

0.0261 0.0521 0.0778 0.1033 0.1286 0.1537 0.1786 0.2033 0.2277 0.2519 0.2759 0.2997 0.3232 0.3465 0.3695 0.3923 0.4149 0.4372 0.4593 0.4811 0.5027 0.5240 0.5451 0.5659 0.5864 0.6067 0.6267 0.6464 0.6659 0.6850 0.7039 0.7225 0.7407 0.7587 0.7764 0.7937 0.8108 0.8275 0.8439 0.8599 0.8756 0.8910 0.9060 0.9206 0.9348 0.9487 0.9621 0.9752 0.9878 1.oooo

0.0263 0.0525 0.0785 0.1042 0.1298 0.1551 0.1801 0.2050 0.2296 0.2540 0.2781 0.3020 0.3257 0.3491 0.3723 0.3952 0.4179 0.4403 0.4625 0.4844 0.5061 0.5275 0.5486 0.5695

0.0266 0.0529 0.0791 0.1051 0.1308 0.1563 0.1815 0.2065 0.2313 0.2558 0.2801 0.3042 0.3280 0.3515 0.3748 0.3979 0.4207 0.4432 0.4655 0.4875 0.5092 0.5307 0.5518 0.5727 0.5934 0.6137 0.6337 0.6535 0.6729 0.6920 0.7109 0.7294 0.7475 0.7654 0.7829 0.8001 0.8169 0.8334 0.8495 0.8653 0.8806 0.8956 0.9102 0.9244 0.9381 0.9514 0.9643 0.9767 0.9886 1.oooo

0.0268 0.0533 0.0797 0.1058 0.1317 0.1573 0.1828 0.2079 0.2328 0.2575 0.2820 0.3061 0.3301 0.3538 0.3772 0.4003 0.4232 0.4458 0.4682 0.4903 0.5121 0.5336 0.5548 0.5758 0.5964 0.6168 0.6368 0.6566 0.6760 0.6951 0.7139 0.7324 0.7505 0.7683 0.7858 0.8029 0.8196 0.8360 0.8520 0.8676 0.8829 0.8977 0.9121 0.9260 0.9396 0.9526 0.9652 0.9773 0.9889 1.m

0.0269 0.0537 0.0802 0.1065 0.1325 0.1583 0.1839 0.2092 0.2343 0.2591 0.2836 0.3080 0.3320 0.3558 0.3793 0.4026 0.4255 0.4482 0.4707 0.4928 0.5147 0.5362 0.5575 0.5785 0.5992 0.6196 0.6397 0.6594 0.6789 0.6980 0.7167 0.7352 0.7533 0.7711 0.7885 0.8055 0.8222 0.8384 0.8543 0.8698 0.8849 0.8996 0.9138 0.9276 0.9409 0.9538 0.9661 0.9779 0.9892 1.oooo

0.0271 0.0540 0.0807 0.1071 0.1333 0.1593 0.1850 0.2104 0.2356 0.2605 0.2852 0.3096 0.3338 0.3576 0.3813 0.4046 0.4277 0.4504 0.4729 0.4952 0.5171 0.5387 0.5600 0.5811 0.6018 0.6222 0.6423 0.6620 0.6815 0.7006 0.7194 0.7378 0.7559 0.7736 0.7909 0.8079 0.8245 0.8407 0.8565 0.8719 0.8868 0.9014 0.9154 0.9291 0.9422 0.9548 0.9669 0.9785 0.9895

0.0272 0.0543 0.081 1 0.1077 0.1340 0.1601 0.1859 0.21 15 0.2368 0.2618 0.2866 0.3111 0.3354 0.3594 0.3831 0.4065 0.4296 0.4525 0.4750 0.4973 0.5193 0.5410 0.5623 0.5834 0.6042 0.6246 0.6447 0.6645 0.6839 0.7030 0.7218 0.7402 0.7582 0.7759 0.7932 0.8101 0.8266 0.8428 0.8585 0.8738 0.8886 0.9030 0.9170 0.9304 0.9434 0.9558 0.9677 0.9791 0.9898 1.oooo

0.0274 0.0546 0.0815 0.1082 0.1347 0.1609 0.1868 0.2125 0.2379 0.2630 0.2879 0.3125 0.3369 0.3609 0.3847 0.4082 0.4314 0.4544 0.4770 0.4993 0.5213 0.5431 0.5645 0.5856 0.6064 0.6268 0.6469 0.6667 0.6862 0.7053 0.7240 0.7424 0.7604 0.7781 0.7953 0.8122 0.8286 0.8447 0.8603 0.8755 0.8903 0.9046 0.9184 0.9317 0.9445 0.9568 0.9685 0.9796 0.9901 1.oooo

0.0275 0.0548 0.0819 0.1087 0.1353 0.1616 0.1876 0.2134 0.2389 0.2642 0.2891 0.3138 0.3383 0.3624 0.3863 0.4098 0.4331 0.4561 0.4788 0.5012 0.5232 0.5450 0.5665 0.5876 0.6084 0.6289 0.6490 0.6688 0.6883 0.7074 0.7261 0.7445 0.7625 0.7801 0.7973 0.8141 0.8305 0.8465 0.8621 0.8772 0.8918 0.9060 0.9197 0.9329 0.9455 0.9576 0.9692 0.9801 0.9904 1

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50

0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00

1.m

0.5900

0.6103 0.6304 0.6501 0.6695 0.6887 0.7075 0.7261 0.7443 0.7622 0.7798 0.7970 0.8140 0.8306 0.8468 0.8627 0.8782 0.8934 0.9082 0.9225 0.9365 0.9501 0.9632 0.9759 0.9882 1.m

1.oooo

.oooo

376

TABLE 9.4 Value of the Coefficient of Equation 9

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4.0

0.0276 0.0551 0.0822 0.1092 0.1358 0.1622 0.1884 0.2143 0.2399 0.2652 0.2903 0.3150 0.3395 0.3638 0.3877 0.4113 0.4347 0.4577 0.4804 0.5029 0.5250 0.5468 0.5683 0.5895 0.6103 0.6308 0.6509 0.6707 0.6902 0.7093 0.7280 0.7464 0.7643 0.7819 0.7992 0.8159 0.8323 0.8482 0.8637 0.8787 0.8933 0.9073 0.9209 0.9340 0.9465 0.9585 0.9698 0.9805 0.9906

0.0277 0.0553 0.0826 0.1096 0.1364 0.1629 0.1891 0.2151 0.2407 0.2662 0.2913 0.3162 0.3407 0.3650 0.3890 0.4127 0.4361 0.4592 0.4820 0.5045 0.5266 0.5485 0.5700 0.5912 0.6120 0.6326 0.6527 0.6725 0.6920 0.7111 0.7298 0.7482 0.7661 0.7837 0.8009 0.8176 0.8339 0.8497 0.8652 0.8801 0.8946 0.9086 0.9221 0.9350 0.9474 0.9592 0.9704 0.9810 0.9908 1.m

0.0278 0.0555 0.0829 0.1100 0.1368 0.1634 0.1897 0.2158 0.2416 0.2671 0.2923 0.3172 0.3418 0.3662 0.3902 0.4140 0.4374 0.4606 0.4834 0.5059 0.5281 0.5500 0.5716 0.5928 0.6137 0.6342 0.6544 0.6742 0.6937 0.7128 0.7315 0.7498 0.7678 0.7853 0.8025 0.8191 0.8354 0.8512 0.8666 0.8815 0.8959 0.9098 0.9232 0.9360 0.9483 0.9600 0.9710 0.9814 0.9911 1.m

0.0279 0.0557 0.0831 0.1103 0.1373 0.1640 0.1904 0.2165 0.2423 0.2679 0.2932 0.3182 0.3429 0.3673 0.3914 0.4152 0.4387 0.4619 0.4848 0.5073 0.5296 0.5515 0.5731 0.5943 0.6152 0.6357 0.6559 0.6758 0.6952 0.7143 0.7330 0.7514 0.7693 0.7868 0.8040 0.8206 0.8368 0.8526 0.8679 0.8827 0.8971 0.9109 0.9242 0.9369 0.9491 0.9606 0.9715 0.9818 0.9913

0.0280 0.0558 0.0834 0.1107 0.1377 0.1644 0.1909 0.2171 0.2430 0.2687 0.2940 0.3191 0.3438 0.3683 0.3924 0.4163 0.4398 0.4631 0.4860 0.5086 0.5309 0.5528 0.5744 0.5957 0.6166 0.6372 0.6574 0.6772 0.6967 0.7158 0.7345 0.7528 0.7707 0.7882 0.8053 0.8219 0.8381 0.8539 0.8691 0.8839 0.8982 0.9119 0.9252 0.9378 0.9499 0.9613 0.9721 0.9821 0.9915

0.0281 0.0560 0.0836 0.1110 0.1381 0.1649 0.1914 0.2177 0.2437 0.2694 0.2948 0.3199 0.3447 0.3692 0.3934 0.4173 0.4409 0.4642 0.4872 0.5098 0.5321 0.5541 0.5757 0.5970 0.6179 0.6385 0.6587 0.6786 0.6981 0.7172 0.7359 0.7542 0.7721 0.7896 0.8067 0.8232 0.8394 0.8551 0.8703 0.8850 0.8992 0.9129 0.9261 0.9386 0.9506 0.9619 0.9725 0.9825 0.9916 1.m

0.0282 0.0562 0.0839 0.1113 0.1384 0.1653 0.1919 0.2183 0.2443 0.2700 0.2955 0.3207 0.3455 0.3701 0.3944 0.4183 0.4419 0.4653 0.4882 0.5109 0.5333 0.5553 0.5769 0.5982 0.6192 0.6398 0.6600 0.6799 0.6994 0.7185 0.7372 0.7555 0.7733 0.7908 0.8079 0.8244 0.8405 0.8562 0.8714 0.8861 0.9002 0.9138 0.9269 0.9394 0.9513 0.9625 0.9730 0.9828 0.9918

0.0282 0.0563 0.0841 0.1116 0.1388 0.1657 0.1924 0.2188 0.2449 0.2707 0.2962 0.3214 0.3463 0.3709 0.3952 0.4192 0.4429 0.4662 0.4893 0.5120 0.5343 0.5564 0.5780 0.5994 0.6203 0.6410 0.6612 0.6811 0.7006 0.7197 0.7384 0.7566 0.7745 0.7920 0.8090 0.8255 0.8416 0.8573 0.8724 0.8870 0.9012 0.9147 0.9277 0.9401 0.9519 0.9630 0.9734 0.9831 0.9920

0.0283 0.0564 0.0843 0.1118 0.1391 0.1661 0.1928 0.2193 0.2454 0.2713 0.2968 0.3221 0.3470 0.3717 0.3960 0.4201 0.4438 0.4672 0.4902 0.5129 0.5353 0.5574 0.5791 0.6004 0.6214 0.6421 0.6623 0.6822 0.7017 0.7208 0.7395 0.7578 0.7756 0.7931 0.8101 0.8266 0.8427 0.8583 0.8734 0.8880 0.9020 0.9155 0.9285 0.9408 0.9525 0.9635 0.9739 0.9834 0.9921

0.0284 0.0565 0.0844 0.1121 0.1394 0.1665 0.1932 0.2197 0.2459 0.2718 0.2974 0.3227 0.3477 0.3724 0.3968 0.4209

1.m

l.m l.m

l.m l.m

1.m

0.4446 0.4680 0.4911 0.5139 0.5363 0.5584 0.5801 0.6015 0.6225 0.6431 0.6634 0.6833 0.7027 0.7218 0.7405 0.7588 0.7767 0.7941 0.8111 0.8276 0.8437 0.8592 0.8743 0.8888 0.9029 0.9163 0.9292 0.9415 0.9531 0.9640 0.9743 0.9837 0.9923 1.m

377 TABLE 9 . 4 Value of the Coefficient of Equation 9

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

5.0

0.0284 0.0567 0.0846 0.1123 0.1397 0.1668 0.1936 0.2201 0.2464 0.2723 0.2980 0.3233 0.3484 0.3731 0.3975 0.4216 0.4454 0.4688 0.4920 0.5147 0.5372 0.5593 0.5810 0.6024 0.6234 0.6441 0.6644 0.6842 0.7037 0.7228 0.7415 0.7598 0.7777 0.7951 0.8120 0.8285 0.8446 0.8601 0.8751 0.8897 0.9036 0.9170 0.9299 0.9421 0.9536 0.9645 0.9746 0.9840 0.9924 1.m

0.0285 0.0568 0.0848 0.1125 0.1399 0.1671 0.1940 0.2205 0.2468 0.2728 0.2985 0.3239 0.3490 0.3737 0.3982 0.4223 0.4461 0.4696 0.4927 0.5156 0.5380 0.5601 0.5819 0.6033 0.6243 0.6450 0.6653 0.6852 0.7047 0.7238 0.7425 0.7608 0.7786 0.7960 0.8129 0.8294 0.8454 0.8610 0.8760 0.8904 0.9044 0.9177 0.9305 0.9427 0.9541 0.9649 0.9750 0.9842 0.9926 1.oooo

0.0285 0.0569 0.0849 0.1127 0.1402 0.1674 0.1943 0.2209 0.2472 0.2733 0.2990 0.3244 0.3495 0.3743 0.3988 0.4230 0.4468 0.4703 0.4935 0.5163 0.5388 0.5609 0.5827 0.6041 0.6252 0.6459 0.6662 0.6861 0.7056 0.7247 0.7434 0.7616 0.7795 0.7969 0.8138 0.8303 0.8463 0.8617 0.8767 0.8912 0.9051 0.9184 0.9311 0.9432 0.9546 0.9654 0.9753 0.9845 0.9927 1.oooo

0.0286 0.0570 0.0851 0.1129 0.1404 0.1677 0.1946 0.2213 0.2476 0.2737 0.2995 0.3249 0.3501 0.3749 0.3994 0.4236 0.4475 0.4710 0.4942 0.5170 0.5396 0.5617 0.5835 0.6049 0.6260 0.6467 0.6670 0.6869 0.7064 0.7255 0.7442 0.7625 0.7803 0.7977 0.8146 0.8311 0.8470 0.8625 0.8775 0.8919 0.9057 0.9190 0.9317 0.9437 0.9551 0.9658 0.9756 0.9847 0.9928 1.oooo

0.0286 0.0571 0.0852 0.1131 0.1406 0.1679 0.1949 0.2216 0.2480 0.2741 0.2999 0.3254 0.3506 0.3754

0.0287 0.0571 0.0853 0.1132 0.1408 0.1682 0.1952 0.2219 0.2484 0.2745 0.3003 0.3259 0.3511 0.3759 0.4005 0.4248 0.4487 0.4722 0.4955 0.5184 0.5409 0.5631 0.5849 0.6064 0.6275 0.6482 0.6685 0.6884 0.7080 0.7271 0.7458 0.7640 0.7818 0.7992 0.8161 0.8325 0.8485 0.8639 0.8788 0.8932 0.9070 0.9202 0.9328 0.9447 0.9560 0.9665 0.9762 0.9851 0.9931 1.oooO

0.0287 0.0572 0.0854 0.1134 0.1410 0.1684 0.1955 0.2222 0.2487 0.2749 0.3007 0.3263 0.3515 0.3764 0.4010 0.4253 0.4492 0.4728 0.4961 0.5190 0.5416 0.5638 0.5856 0.6071 0.6282 0.6489 0.6692 0.6891 0.7087 0.7278 0.7465 0.7647 0.7825 0.7999 0.8168 0.8332 0.8491 0.8645 0.8794 0.8938 0.9075 0.9207 0.9333 0.9452 0.9564 0.9668 0.9765 0.9853 0.9932 1.oooo

0.0288 0.0573 0.0856 0.1135 0.1412 0.1686 0.1957 0.2225 0.2490 0.2752 0.301 1 0.3267 0.3519 0.3769 0.4015 0.4258 0.4497 0.4734 0.4966 0.5196 0.5421 0.5644 0.5862 0.6077 0.6288 0.6495 0.6699 0.6898 0.7093 0.7284 0.7471 0.7654 0.7832 0.8006 0.8174 0.8338 0.8497 0.8651 0.8800 0.8943 0.9081 0.9212 0.9337 0.9456 0.9567 0.9672 0.9768 0.9855 0.9933 1.oooo

0.0288 0.0574 0.0857 0.1137 0.1414 0.1688 0.1960 0.2228 0.2493 0.2755 0.3015 0.3271 0.3523 0.3773 0.4019 0.4263 0.4502 0.4739 0.4972 0.5201 0.5427 0.5649 0.5868 0.6083 0.6294 0.6502 0.6705 0.6904 0.7100 0.7291 0.7478 0.7660 0.7838 0.8012 0.8181 0.8345 0.8503 0.8657 0.8806 0.8949 0.9086 0.9217 0.9342 0.9460 0.9571 0.9675 0.9770 0.9857 0.9934 1.oooo

0.0288 0.0574 0.0858 0.1138 0.1416 0.1690 0.1962 0.2230 0.2496 0.2758 0.3018 0.3274 0.3527 0.3777 0.4024 0.4267 0.4507 0.4744 0.4977 0.5206 0.5432 0.5655 0.5874 0.6089 0.6300 0.6508 0.671 1 0.6910 0.7106 0.7297 0.7484 0.7666 0.7844 0.8018 0.8186 0.8350 0.8509 0.8663 0.881 1 0.8954 0.9091 0.9221 0.9346 0.9464 0.9575 0.9678 0.9773 0.9859 0.9935 1.oooo

0.4oOo

0.4242 0.4481 0.4716 0.4949 0.5177 0.5403 0.5624 0.5842 0.6057 0.6268 0.6475 0.6678 0.6877 0.7072 0.7263 0.7450 0.7633 0.781 1 0.7985 0.8154 0.8318 0.8478 0.8632 0.8781 0.8925 0.9064 0.9196 0.9322 0.9442 0.9555 0.9661 0.9759 0.9849 0.9930 1.oooo

378 TABLE 9.4e Value of the Coefficient of Equation 9 x

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40

0.42 0.44 0.46 0.48 0.50

0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.OO

PI

5.1

5.2

5.3

5.4

5.5

5.6

5.7

0.0289 0.0575 0.0859 0.1139 0.1417 0.1692 0.1964 0.2233 0.2499 0.2761 0.3021 0.3278 0.3531 0.3781 0.4028 0.4271 0.4512 0.4748 0.4982 0.5211 0.5438 0.5660 0.5879 0.6094 0.6306 0.6513 0.6717 0.6916 0.7112 0.7303 0.7490 0.7672 0.7850 0.8023 0.8192 0.8356 0.8514 0.8668 0.8816 0.8959 0.9095 0.9226 0.9350 0.9468 0.9578 0.9681 0.9775 0.9861 0.9936

0.0289 0.0576 0.0860 0.1141 0.1419 0.1694 0.1966 0.2235 0.2501 0.2764 0.3024 0.3281 0.3534 0.3785 0.4032 0.4275 0.4516 0.4753 0.4986 0.5216 0.5442 0.5665 0.5884 0.6099 0.6311 0.6518 0.6722 0.6922 0.7117 0.7308 0.7495 0.7678 0.7856 0.8029 0.8197 0.8361 0.8520 0.8673 0.8821 0.8963 0.9100 0.9230 0.9354 0.9471 0.9581 0.9683 0.9771 0.9862 0.9937 1

0.0289 0.0576 0.0860 0.1142 0.1420 0.1695 0.1968 0.2237 0.2504 0.2767 0.3027 0.3284 0.3538 0.3788 0.4035 0.4279 0.4520 0.4757 0.4990 0.5221 0.5447 0.5670 0.5889 0.6104 0.6316 0.6524 0.6727 0.6927 0.7122 0.7313 0.7500 0.7683 0.7861 0.8034 0.8202 0.8366 0.8524 0.8678 0.8825 0.8968 0.9104 0.9234 0.9358 0.9474 0.9584 0.9686 0.9779 0.9864 0.9938

0.0290 0.0577 0.0861 0.1143 0.1421 0.1697 0.1970 0.2239 0.2506 0.2769 0.3030 0.3287 0.3541 0.3791 0.4039 0.4283 0.4524 0.4761 0.4995 0.5225 0.5451 0.5674 0.5894 0.6109 0.6321 0.6528 0.6732 0.6932 0.7127 0.7318 0.7505 0.7688 0.7866 0.8039 0.8207 0.8371 0.8529 0.8682 0.8830 0.8972 0.9108 0.9238 0.9361 0.9478 0.9587 0.9688 0.9781 0.9865 0.9938

0.0290 0.0577 0.0862 0.1144 0.1423 0.1699 0.1971 0.2241 0.2508 0.2772 0.3032 0.3290 0.3544 0.3795 0.4042 0.4286 0.4527 0.4765 0.4998 0.5229 0.5456 0.5679 0.5898 0.6114 0.6325 0.6533 0.6737 0.6936 0.7132 0.7323 0.7510 0.7693 0.7870 0.8044 0.8212 0.8375 0.8534 0.8687 0.8834 0.8976 0.9112 0.9241 0.9365 0.9481 0.9590 0.9691 0.9783 0.9867 0.9939 1.oooo

0.0290 0.0578 0.0863 0.1145 0.1424 0.1700 0.1973 0.2243 0.2510 0.2774 0.3035 0.3292 0.3547 0.3798 0.4045 0.4290 0.4531 0.4768 0.5002 0.5233 0.5460 0.5683 0.5902 0.6118 0.6330 0.6537 0.6741 0.6941 0.7136 0.7328 0.7515 0.7697 0.7875 0.8048 0.8216 0.8380 0.8538 0.8691 0.8838 0.8980 0.9115 0.9245 0.9368 0.9484 0.9592 0.9693 0.9785 0.9868 0.9940 1.oooo

0.0291 0.0290 0.0579 0.0578 0.0864 0.0864 0.1147 0.1146 0.1426 0.1425 0.1703 0.1701 0.1976 0.1975 0.2247 0.2245 0.2514 0.2512 0.2778 0.2776 0.3039 0.3037 0.3297 0.3295 0.3552 0.3549 0.3803 0.3801 0.4051 0.4048 0.4296 0.4293 0.4537 0.4534 0.4775 0.4772 0.5009 0.5006 0.5240 0.5236 0.5467 0.5463 0.5690 0.5687 0.5910 0.5906 0.6126 0.6122 0.6338 0.6334 0.6542 0.6546 0.6745 0.6749 0.6945 0.6949 0.7141 0.7145 0.7336 0.7332 0.7519 0.7523 0.7701 0.7706 0.7883 0.7879 0.8056 0.8052 0.8221 0.8225 0.8384 0.8388 0.8542 0.8546 0.8695 0.8698 0.8842 0.8846 0.8983 0.8987 0.9119 0.9122 0.9248 0.9251 0.9371 0.9374 0.9489 0.9487 0.9595 0.9597 0.9697 0.9695 0.9789 0.9787 0.9871 0.9869 0.9941 0.9942 1.oooo 1

1.m

.oooo

1.oooo

l.m

5.8

5.9

6.0

0.0291 0.0579 0.0865 0.1148 0.1427 0.1704 0.1978 0.2248 0.2516 0.2780 0.3042 0.3300 0.3554 0.3806 0.4054 0.4299 0.4540 0.4778 0.5012 0.5243 0.5470 0.5694 0.5914 0.6129 0.6341 0.6549 0.6753 0.6953 0.7149 0.7340 0.7527 0.7709 0.7887 0.8060 0.8228 0.8392 0.8550 0.8702 0.8849 0.8990 0.9126 0.9254 0.9377 0.9492 0.9600 0.9700 0.9791 0.9872 0.9942

0.0291 0.0580 0.0866 0.1148 0.1428 0.1705 0.1979 0.2250 0.2518 0.2782 0.3044 0.3302 0.3557 0.3808 0.4057 0.4302 0.4543 0.4781 0.5016 0.5246 0.5474 0.5697 0.5917 0.6133 0.6345 0.6553 0.6757 0.6957 0.7153 0.7344 0.7531 0.7713 0.7891 0.8064 0.8232 0.8395 0.8553 0.8706 0.8852 0.8994 0.9129 0.9257 0.9379 0.9494 0.9602 0.9701 0.9792 0.9873 0.9943

.oooo l.m 1.oooo

319 TABLE 9.4f Value of the Coefficient of Equation 9 x

PI 6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

7.0

~

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00

0.0291 0.0580 0.0866 0.1149 0.1429 0.1706 0.1980 0.2251 0.2519 0.2784 0.3046 O.GO4 0.3559 0.3811 0.4059 0.4304 0.4546 0.4784 0.5019 0.5250 0.5477 0.5700 0.5920 0.6136 0.6348 0.6557 0.6761 0.6960 0.7156 0.7348 0.7534 0.7717 0.7895 0.8068 0.8236 0.8399 0.8556 0.8709 0.8856 0.8997 0.9132 0.9260 0.9382 0.9497 0.9604 0.9703 0.9794 0.9874 0.9944 1 .oooo

0.0291 0.0580 0.0867 0.1150 0.1430 0.1707 0.1982 0.2253 0.2521 0.2786 0.3047 0.3306 0.3561 0.3813 0.4062 0.4307 0.4549 0.4787 0.5021 0.5252 0.5480 0.5704 0.5924 0.6140 0.6352 0.6560 0.6764 0.6964 0.7160 0.7351 0.7538 0.7720 0.7898 0.8071 0.8239 0.8402 0.8560 0.8712 0.8859 0.9000 0.9134 0.9263 0.9385 0.9499 0.9606 0.9705 0.9795 0.9875 0.9944 1 .0000

0.0292 0.0581 0.0867 0.1151 0.1431 0.1709 0.1983 0.2254 0.2522 0.2787 0.3049 0.3308 0.3563 0.3815 0.4064 0.4309 0.4551 0.4789 0.5024 0.5255 0.5483 0.5707 0.5927 0.6143 0.6355 0.6563 0.6767 0.6967 0.7163 0.7354 0.7541 0.7724 0.7901 0.8074 0.8242 0.8405 0.8563 0.8715 0.8862 0.9003 0.9137 0.9265 0.9387 0.9501 0.9608 0.9707 0.9797 0.9876 0.9945 1.oooo

0.0292 0.0581 0.0868 0.1151 0.1432 0.1710 0.1984 0.2256 0.2524 0.2789 0.3051 0.3310 0.3565 0.3817 0.4066 0.4312 0.4553 0.4792 0.5027 0.5258 0.5486 0.5709 0.5929 0.6146 0.6358 0.6566 0.6770 0.6970 0.7166 0.7357 0.7544 0.7727 0.7905 0.8077 0.8245 0.8408 0.8566 0.8718 0.8865 0.9005 0.9140 0.9268 0.9389 0.9504 0.9610 0.9709 0.9798 0.9877 0.9945 1 .m

0.0292 0.0582 0.0868 0.1152 0.1433 0.1711 0.1985 0.2257 0.2525 0.2791 0.3053 0.3312 0.3567 0.3819 0.4068 0.4314 0.4556 0.4794 0.5029 0.5261 0.5488 0.5712 0.5932 0.6149 0.6361 0.6569 0.6773 0.6973 0.7169 0.7361 0.7547 0.7730 0.7908 0.8080 0.8248 0.8411 0.8569 0.8721 0.8867 0.9008 0.9142 0.9270 0.9392 0.9506 0.9612 0.9710 0.9799 0.9878 0.9946 1.m

0.0292 0.0582 0.0869 0.1153 0.1434 0.1711 0.1986 0.2258 0.2527 0.2792 0.3054 0.3313 0.3569 0.3821 0.4070 0.4316 0.4558 0.4797 0.5032 0.5263 0.5491 0.5715 0.5935 0.6151 0.6364 0.6572 0.6776 0.6976 0.7172 0.7363 0.7550 0.7733 0.7910 0.8083 0.8251 0.8414 0.8572 0.8724 0.8870 0.9010 0.9145 0.9273 0.9394 0.9508 0.9614 0.9712 0.9801 0.9879 0.9946 1 .oooo

0.0292 0.0582 0.0869 0.1153 0.1434 0.1712 0.1987 0.2259 0.2528 0.2793 0.3056 0.3315 0.3571 0.3823 0.4072 0.4318 0.4560 0.4799 0.5034 0.5265 0.5493 0.5717 0.5938 0.6154 0.6366 0.6575 0.6779 0.6979 0.7175 0.7366 0.7553 0.7736 0.7913 0.8086 0.8254 0.8417 0.8574 0.8726 0.8872 0.9013 0.9147 0.9275 0.9396 0.9510 0.9616 0.9713 0.9802 0.9880 0.9947 1 .m

0.0292 0.0582 0.0870 0.1154 0.1435 0.1713 0.1988 0.2260 0.2529 0.2795 0.3057 0.3316 0.3572 0.3825 0.4074 0.4320 0.4562 0.4801 0.5036 0.5268 0.5496 0.5720 0.5940 0.6156 0.6369 0.6577 0.6782 0.6982 0.7178 0.7369 0.7556 0.7738 0.7916 0.8089 0.8257 0.8419 0.8577 0.8729 0.8875 0.9015 0.9149 0.9277 0.9398 0.9511 0.9617 0.9715 0.9803 0.9881 0.9948 1.m

0.0293 0.0583 0.0870 0.1154 0.1436 0.1714 0.1989 0.2261 0.2530 0.2796 0.3059 0.3318 0.3574 0.3827 0.4076 0.4322 0.4564 0.4803 0.5038 0.5270 0.5498 0.5722 0.5942 0.61 59 0.6371 0.6580 0.6784 0.6984 0.7180 0.7372 0.7559 0.7741 0.7919 0.8091 0.8259 0.8422 0.8579 0.8731 0.8877 0.9017 0.9151 0.9279 0.9400 0.9513 0.9619 0.9716 0.9804 0.9882 0.9948 1.oooo

0.0293 0.0583 0.0870 0.1155 0.1436 0.1715 0.1990 0.2262 0.2531 0.2797 0.3060 0.3319 0.3576 0.3828 0.4078 0.4324 0.4566 0.4805 0.5040 0.5272 0.5500 0.5724 0.5945 0.6161 0.6374 0.6582 0.6787 0.6987 0.7183 0.7374 0.7561 0.7743 0.7921 0.8094 0.8262 0.8424 0.8582 0.8733 0.8879 0.9020 0.9154 0.9281 0.9402 0.9515 0.9620 0.9717 0.9805 0.9883 0.9949 1.0000

380

If we assume that the column capacity factor does not change when the carrier gas pressure increases, the retention times on the precolumn alone and on the precolumn placed at the top of the series of columns are related by: t;

j J

=t R T i

The correction factor j decreases with increasing value of the inlet to outlet pressure ratio. It also decreases with increasing inlet pressure at constant flow rate: the gas being compressible, it takes a large number of moles to fill a certain volume, such as the column gas hold-up, when the pressure increases. If the precolumn is very short compared to the column, it may be possible to neglect its pneumatic resistance and to replace j by 1 in equations 9 and 11, which simplifies them greatly. Values of the correction factor j are given in Table 9.5. d, Examples of Application

In an analysis of chlorinated hydrocarbons, it is desired to backpurge compounds heavier than 1,Zdichloroethane (included). The last compound eluted and quantitated will be dichloromethane (see Figure 9.33). I . Determination of the Length of an Intermediate Column Segment The column length is 4 m. The resolution between dichloromethane and 1,2-dichloroethane is 5.0. The inlet pressure is measured at 2.9 atm, i.e., the absolute value of the inlet pressure is 3.9 atm. The outlet pressure is atmospheric. In order to achieve a clean separation between the dichloromethane which has to be eluted entirely to achieve accurate quantitation, and the 1,2-dichloroethane, which will be backpurged, it is necessary to achieve a resolution of at least 2.0 at the position of the switching valve. In this case equation 6 gives x = 30.3%. The valve will be placed between a first segment of 1.20 m and the rest of the column. Experimental results show that the resolution after a 1.20 m long column is 2.30, which exceeds the specifications. Such a result is not unusual. NB. It is possible to arrive at the same result by using data in Table 9.3 rather than equation 6. Read the value of x at the intersection of the column pi = 3.90 and the line R , = 5.0. The value x = 30.31 is found, hence the column should be cut at the distance 4 X 30.31/100 = 1.20 m. 2. Determination of the Switching Time

Valve switching must be done after the band of dichloromethane has entirely moved into the second segment of the column. The determination of the switching time will be done using the time at which the peak of this compound is entirely recorded (see Figure 9.33).

381

TABLE 9.5 Values of the James and Martin Coefficient Pi/Po 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55

i 0.951661 0.928725 0.906593 0.885245 0.864661 0.844817 0.825688 0.807248 0.789473 0.772337 0.755813 0.739879 0.724508 0.709677 0.695364 0.681546 0.668202 0.655312 0.642857 0.630816 0.619174 0.6079 12 0.597014 0.586466 0.576251 0.566356 0.556768 0.547474 0.538461 0.529718 0.521235 0.513000 0.505004 0.497237 0.489690 0.482355 0.475223 0.468286 0.461538 0.454970 0.448577 0,442352 0.436288 0.430379 0.424621 0.419007 0.413533 0.408194 0.402985 0.397901

1/i 1.050793 1.076744 1.103030 1.129629 1.156521 1.183687 1.211111 1.238775 1.266666 1.294771 1.323076 1.351572 1.380246 1.409090 1.438095 1.467251 1.496551 1.525988 1.555555 1.585245 1.615053 1.644973 1.675000 1.705128 1.735353 1.765671 1.796078 1.826570 1.857142 1.887793 1.918518 1.949315 1.980180 2.011111 2.042105 2.073160 2.104273 2.135443 2.166666 2.197942 2.229268 2.260642 2.292063 2.323529 2.355038 2.386590 2.418181 2.449812 2.481481 2.513186

(Continued on p. 382) References on p. 390.

382 TABLE 9.5 (continued)

Pi/Po 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.15 4.80 4.85 4.90 4.95 5 .OO 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00

i 0.392938 0.388092 0.383360 0.378737 0.374220 0.369805 0.365489 0.361269 0.357142 0.353105 0.349155 0.345289 0.341506 0.337801 0.334174 0.330621 0.327140 0.323730 0.320388 0.317112 0.313901 0.310752 0.307664 0.304635 0.301664 0.298748 0.295887 0.293079 0.290322 0.287615 0.284957 0.282347 0.279783 0.277264 0.274789 0.272356 0.269966 0.267616 0.265306 0.263034 0.260800 0.258603 0.256442 0.254317 0.252225 0.250167 0.248141 0.246148 0.244186

1/.i 2.544927 2.576702 2.608510 2.640350 2.672222 2.704123 2.736054 2.768013 2.800000 2.832013 2.864052 2.896116 2.928205 2.960317 2.992452 3.024610 3.056790 3.088990 3.121212 3.153453 3.185714 3.217994 3.250292 3.282608 3.314942 3.347293 3.379661 3.412044 3.444444 3.476859 3.509289 3.541734 3.574193 3.606666 3.639153 3.671653 3.704166 3.736692 3.769230 3.801781 3.834343 3.866917 3.899502 3.932098 3.964705 3.997323 4.029951 4.062589 4.095238

383

TABLE 9.5 (continued) P,/Po

j

1/ j

6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.60 6.65 6.70 6.75 6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 7.30 7.35 7.40 7.45 7.50

0.242254 0.240352 0.238479 0.236634 0.234817 0.233028 0.231265 0.229528 0.227817 0.226130 0.224468 0.222830 0.221215 0.219623 0.218053 0.216506 0.214980 0.213475 0.211990 0.210526 0.209081 0.207656 0.206250 0.204863 0.203494 0.202143 0.200809 0.199493 0.198193 0.196911

4.127895 4.160563 4.193240 4.225925 4.258620 4.291324 4.324036 4.356756 4.389485 4.422222 4.454966 4.487719 4.520479 4.553246 4.586021 4.618803 4.651592 4.684388 4.717190 4.750000 4.782815 4.815637 4.848466 4.881300 4.914141 4.946987 4.979840 5.012698 5.045562 5.078431

This time is 11 minutes. With the values of the inlet (3.9 atm) and outlet pressures (1.0 atm), the fractional time at the end of the 1.20 m long segment is 39.6%, assuming j = 1 for the first segment ( L = 1.20 m), corresponding to a time of 4.35 minutes. Experimental results (see Figure 9.33) show a time of 4.20 minutes. The difference of 0.15 minutes (9 seconds) is inconsequential. The analyst must check his results, however, by measuring the elution times of the critical compound out of the column and the relevant column segments, by slightly changing the switching time and measuring the repeatability of the peak area, which is the critical parameter in this exercise. NB. The ratio z = t , , / t , , can be obtained from the data in Table 9.4, by reading it at the intersection between column pi = 3.90 and line x=0.30. The value z =0.3960 is found. Hence the retention time should be 11 X 0.3960=4 min 35/100.

References on p. 390.

384

a

R-5

b

~ : 4 m

L : 1.20 rn

R i2.30

I I /

___r_

Figure 9.33. Example of the Determination of the Point to cut a Column and place a Switching Valve. a - Chromatogram obtained on the total column. b - Chromatcgram obtained with the first segment ( L ~1.20m, see text).

V. ANCILLARY EQUIPMENT The chromatographic column must be kept at constant temperature during the course of an analysis, because the retention times depend very strongly on the temperature (see in Chapter 3). Temperature fluctuations play a significant role in the error made when determining retention data, as does the temperature gradient along the column. Similarly, the detector signal and the detector response depend on the temperature of the sensing element, which must be kept as nearly constant as possible. A chromatograph also requires a flow meter to permit easy, proper setting of the carrier gas flow rate and a sure control of its stability. 1. Oven and Temperature Control

The requirements depend to some extent on the use made of the equipment. The collection of accurate retention data requires much lower temperature fluctuations than most analytical applications. It seems, however, that the following specifications would be adequate for most applications: - temperature fluctuations smaller than 0.2" C, - temperature gradient in the oven such that the maximum temperature difference between two points of the column be smaller than 0.2" C,

385 - maximum temperature 400°C for a laboratory chromatograph (450°C if the aluminum clad open tubular silica columns become popular), 250 O C for an on-line process chromatograph, - the size of the oven and of its door must permit easy access to the column, the detector and the valves for assembly, changes and maintenance. In most cases air baths are used; liquid baths are reserved for applications where an extremely stable column temperature is required and isothermal operation is carried out. The very small heat capacity of air makes it difficult to achieve temperature stability and stable gradients. On the other hand it permits easy adjustment of the temperature setting and rapid temperature programming. Temperature gradients inside the oven are a direct consequence of the heat losses through the wall. Homogeneous insulation and a leakproof door are required for satisfactory performance. A very fast circulation of air, with a carefully designed and built fan and baffle system, avoiding any stagnant air pocket of significant size is also a very important feature of satisfactory ovens. For the same reason, coiled columns are preferred to long U-shaped columns, permitting a more compact oven design. Chromatographs designed for temperature programming contain two different ovens, one for the column, the temperature of which can be programmed, the other for the detector, which must be kept isothermal at an adjustable temperature. Often the sampling system is also kept isothermal. Simple, inexpensive chromatographs, as well as the complex, sophisticated, costly process chromatographs operate isothermally and use a single oven. The oven of a normal chromatograph is usually 28 cm W, 22 cm D, 36 cm H, with a volume of 22 L. Process chromatographs, using a number of valves for column switching, are larger, about 38W x 25D x 40H, and of 38 L capacity. Chromatograph ovens are electrically heated. This requires that the process chromatographs be designed to be explosion proof. To avoid the difficulties associated with the use of electrical current in a dangerous atmosphere, Annino has designed a gas chromatograph which does not require any electrical power (34). Air circulation is forced by high power fans or blowers (laboratory GC) or by air ejectors (process GC) - efficient but very noisy devices. The ovens are constructed with thin stainless steel sheets and high quality quartz wool insulating panels. Laboratory chromatographs work in a rather stable atmosphere compared to process instruments, which are often exposed to weather fluctuations and which require a better thermal insulation.

2. Temperature Control

The temperature control is very important, since it determines the reproducibility of retention data. It is also important for quantitative analysis, especially trace analysis. Very often there is a small stationary phase bleed, resulting in a background signal. In such a case, temperature fluctuations result in a base line noise which increases rapidly with increasing amplitude of the temperature fluctuations. References on p. 390.

386

a. Isothermal Analysis

The oven temperature is measured by a thermal sensor. An electronic circuit continuously adjusts the power supplied in order to keep the signal of the sensor constant. In theory it is not necessary that the sensor be accurate to achieve a good stability of the oven temperature. The sensor should be located in the place where temperature is the most sensitive to changes in the heating power, to minimize temperature fluctuations of the column. Accordingly it is a good idea to use two different sensors, one for the control, the other for the measure of the column temperature. These sensors are located in different places in the oven. It is cautious to measure the temperature stability over both the short and long term for a new oven, and also the temperature gradient inside this oven, which requires the use of half a dozen sensors, temporarily located in various places in the oven and easily introduced through the injection port. Modem electronics permits an easy control of the temperature. Using differential, proportional and integral control permits the achievement of fluctuations smaller than 0.1" C over the short term and negligible in the long run. Temperature gradients are more difficult to master. A very careful design of the oven, of the blower location, and of the air ducts is required, to ensure laminar flow along the oven wall and to avoid stable eddies where the temperature could easily drop by more than 10O C. b. Temperature Programming

Temperature programming is used to analyze complex mixtures containing compounds with a wide range of vapor pressure. At a temperature at which the column could resolve the light components, the retention times of the heavy ones would be prohibitively long and it would be nearly impossible to detect their wide, low bands. At a temperature where the heavy components could be resolved and eluted in a reasonable time the light components would be eluted with the inert tracer. Temperature programming permits the elution of all components in a reasonable time, while achieving good resolution and rather small detection limits. This technique is reserved for laboratory applications. The difficulties encountered in achieving the proper level of repeatability of the temperature profile have prevented its successful use in process control analyses. Temperature programming was first studied by Griffiths, James and Phillips (36), who used ballistic programming: the oven being cold, the mixture was injected and the power switched on to the oven heating system. The temperature program resulted from the thermal inertia of the oven and was not highly reproducible. The development of electronic controllers permitting the achievement of linear programming of the oven temperature has ensured the popularity of the method. An excellent discussion of the method and its problems, advantages and drawbacks can be found in the monograph by Harris and Habgood (35). Modern techniques of digital electronic and microcomputers permit the achievement of complex temperature programs, with several linear ramps of different slopes and hold-up periods

387

TABLE 9.6 Reproducibility of Retention Times (sec) in Temperature Programming *

n-Alkanes

c 12 C 14 C 16 c 18

Run No. 1

2

3

4

5

6

780 914 1032 1155

780 913 1031 1153

779 913 1029 1151

779 912 1030 1152

779 912 1030 1152

779 913 1029 1152

Obtained in 1987 with a modem chromatograph.

during whch the temperature is kept constant. After the run is over, the oven temperature should be returned to the exact value of the starting temperature desired. The reproducibility of chromatographic results requires the proper reproducibility of the heating rate and of the initial temperature. Modem electronic technology has permitted the achievement of an extremely good reproducibility of the heating rate. It has proven extremely difficult to reach a comparable level of reproducibility for the starting temperature, especially with chromatographs located in workshops or in the plant. The starting temperature depends on the nature of the materials used for the thermal insulation of the oven, on the ambient temperature, the humidity (which modifies the thermal properties of the insulating material), etc. Cooling may be required, and a stream of cold air, sometimes at a subambient temperature, has to be provided. Whereas satisfactory results may be obtained in the laboratory, the environmental conditions in the plant change too rapidly, too often and too much, from day to night, during the space of a few hours or around the year, to permit the achievement of the reproducibility required for proper quantitative analysis. The lack of reproducibility of the temperature programs explains why better quantitative results are obtained with isothermal analysis than with temperature programming. In addition, temperature programming provides frequent thermal shocks to the column, which ages faster, and systematic fluctuations of the carrier gas flow rate, which cannot be completely corrected by the use of a flow rate controller (see above, Section 11.3). Typical figures regarding the repeatability of retention times are given in Table 9.6. c. Design of a Modern Gas Chromatographfor Temperature Programming

A laboratory gas chromatograph designed to work in temperature programming (PTGC) incorporates two ovens and a dual column circuit. The first oven is designed to operate isothermally and houses the detectors and the sampling system. T h s ensures proper reproducibility of the sample size injected and of the response factor, which is necessary for quantitative analysis. The second oven contains two identical columns and can be temperature programmed. References on p. 390.

388

Each gas circuit contains a sampling system, a column and a detector. If a TCD is used, one column is connected to the measuring cell(s), the other one to the reference cell(s). With an ionization detector, a differential dual detector is used. This design permits the correction of base-line drifts due to various reasons, essentially to column bleeding. A FTGC is normally equipped with a flow rate controller. As discussed above (Section 11.4), this device permits a control of the mass flow rate of carrier gas during the analysis. The volume flow rate increases, due to the thermal expansion of gases, but this is rather beneficial, since diffusion coefficients also increase with increasing temperature, so the optimum carrier gas flow velocity increases with increasing temperature. The resulting performance is much better than with a pressure controller. Then the gas velocity would decrease with increasing temperature, due to the increasing viscosity of the camer gas. The column oven is built with material having a low heat capacity, such as thin stainless steel sheets, and thermal insulation is provided by panels of quartz wool. In the first experiments, the temperature program was ballistic, i.e., the full power of the oven was switched on and the temperature raised freely. As was recognized by the pioneers, this method is not conducive to good reproducibility. Now linear temperature programmers are available which provide advanced control of the oven temperature, using proportional and differential control algorithms. Modem computer-controlled FTGC affords the possibility to combine successive linear ramps and isothermal periods during the same run, and to reset the oven at the same, set initial temperature, after cooling down. Programming rates from 0.5 to 50 O C/min are available. The time required for cooling down the oven temperature is short, especially for chromatographs which may open and close automatically via a trap door. No more than 10 minutes is required for cooling the oven from 400°C to 50"C,but another 10 minutes may be required to reach a temperature of 30°C. Several minutes is also required to stabilize the temperature to the starting value for the new analysis. A discussion on the reproducibility of the temperature program, of the chromatographic data and the quantitative results is provided in the previous section. The use of a microcomputer controlled FTGC permits an excellent reproducibility of the retention data obtained with open tubular columns, whose thermal inertia is very small. d. Other Parameters in Programmed Temperature Gas Chromatography

The choice of the stationary phase is very important, since the nature of this phase determines the maximum temperature at which the column can be raised. The vapor pressure of the stationary phase must be low, to avoid phase bleeding, detector foul-up and possible detector overloading. To avoid the possible consequences of the repeated thermal shocks on the column, the.packing should be carefully conditioned before use. This can be done by keeping the column isothermally at a temperature slightly above the temperature limit observed in programming, under constant stream of carrier gas, until the

389

bleeding stops and the base line stabilizes. Sometimes a satisfactory result is achieved by applying successive temperature programming sequences. The selection of the support is also important, since catalytic decomposition may be promoted at high temperature, during the end of each analytical run. The phase becomes very fluid at the end of the run and this may explain a progressive degradation of performance of open tubular columns. The best results seem to be obtained with weekly cross-linked polymers, or with materials for modified gas-solid chromatography (see Chapter 7). The stability of the carrier gas flow rate is also important for the achievement of reproducible results, especially if concentration-sensitive detectors, such as the TCD, have to be used. Unfortunately, the accuracy of most flow rate controllers used in the available instruments is limited to a few percents for flow rates of the order of 1 to 3 L/hour. The consequences are less important when the FID is used. e. The Future of Temperature Programming

PTGC is a very powerful technique. It provides the only analytical method which may answer a question which is more and more frequently asked of the analysts, to provide management with a balance of the plant. This requires the complete analysis of the different effluents, from the permanent gases to the heavy components. The drawback of the method is its current lack of accuracy. Owing to new technological developments, especially to the use of open tubular columns, stable, cross-linked, stationary phase and computer-controlled chromatographs, applications in process control analysis may appear in the near future. This would bring a welcome alternative to the column switching approach which cannot provide the same flexibility nor permit the analysis in a single run of the components of a complex mixture with a wide range of vapor pressures.

3. Flow Meters After thirty years of progress and developments, the same device is still in use for the determination of gas flow rates: the soap bubble flow meter. Rotameters or ball flow meters have been abandoned because of their cost, lack of precision, and inaccuracy. They have to be recalibrated for each gas used, the measurement depends on the gas pressure and is not linear. They must be placed before the sampling system, to avoid pollution by analytes, which would make the ball stick to the wall, but as their indications depend on the local pressure, they can hardly give better than a two bit number (no flow, small, moderate and large flow rate). The soap bubble flow meter uses a calibrated pipet, equipped at its bottom with a rubber reservoir of soap solution. A measurement is made by forcing the gas stream to bubble in the solution for a short time. The soap film rises and the time necessary for it to pass between two marks defining a known volume permits the calculation of the flow rate. The measurement is independent of the nature of the gas. For good accuracy it must be corrected for the surface tension of the soap film, the References on p. 390.

390

atmospheric pressure, the temperature and the water partial pressure. Since the gas passes over a water solution, it cannot be perfectly dry. Then care must be taken to make sure that it is saturated with water vapor. Fluctuations of the carrier gas flow rate should not exceed 0.2%. The main drawback of the soap bubble flow meter is that it is an integrated measurement over a fairly long period of time, and thus it does not permit the study of short-term fluctuations. Also, its accuracy is limited by the slow diffusion of the carrier gas through the soap film. Column switching requires an exact measurement of the flow rate in the two branches of the gas circuit. A slight difference between the flow rates in both circuits would result in base line shifts or other artefacts at the time of column switching, including possible distorsions in the shape of the peaks eluted shortly afterwards. The most accurate method for equilibrating the pneumatic resistances consists in an injection of a sample of pure gas, such as air or ethylene, successively on both gas circuits. When using a concentration detector, the areas of the two peaks should be identical. A slight adjustment of the needle valve to compensate for differences in pneumatic resistances of the two circuits permits a correction and the achievement of equal flow rates in both branches. LITERATURE CITED (1) J. Janak, Mikrochim. Acta, 1038 (1956). (2) R. Annino, C. Caffert and E.L. Lewis, Anal. Chem., 58,2516 (1986). (3) A.I.M. Keulemans, Gas Chromatography, Reinhold, New York, NY, 1959. (4) C. Vidal-Madjar, M.F. Gonnord, F. Benchah and G. Guiochon, J . Chromatogr. Sci., 16,190(1978). (5) W.E. Harris and H.W. Habgood, Programmed Temperature Gas Chromatography, Wiley, New York, NY, 1966. (6) G. Guiochon, Chromatographic Reuiews, M. Lederer Ed., Elsevier, Amsterdam, The Netherlands, Vol. 8, 1966,p. 1. (7) M. Goedert and G. Guiochon, J. Chromarogr. Sci., 7, 323 (1969). (8) M. Thizon, C. Eon, P. Valentin and G. Guiochon, Anal. Chem., 48, 1861 (1976). (9) P.G. Jeffery and P.J. Kipping, in Gas Analysis by Gas Chromatography, Pergamon, London, UK, 1964. (10) A. NOH, Spectra-Physics, Private Communication, 1975. (11) M. Beche, Y. Claret and D. Coutagne, Analusis, 8, 31 (1980). (12) C.L. Guillemin, Unpublished Data. (13) D.R. Deans, J. Chromatogr.. 18,477 (1965). (14) D.R. Deans, Chromatographia, I, 18 (1968). (15) D.R. Deans, in Gas Chromatography 1968, C.L.A. Harbourn Ed., The Institute of Petroleum, London, UK, 1969,p. 447. (16) D.R. Deans, M.T. HucMe and R.M. Peterson, Chromatographia, 4 , 279 (1971). (17) D.R. Deans and I. Scott, Anal. Chem., 45, 1137 (1973). (18) C.S.G. Phillips, in Gas Chromatography 1970, R. Stock Ed., The Institute of Petroleum, London, UK,1971,p. 1. (19) F.Mullet and M. Oreans, Chromatographia, 10, 473 (1977). (20) G. Schomburg and E. Ziegler, Chromatographia, 5, 96 (1972). (21) G. Schomburg, H.Husmann and F. Weeke, J. Chromatogr., 99,63 (1974). (22) G. Schomburg, H. Husmann and F. Weeke, J. Chromatogr., 112,205 (1975). (23) A. Ducass, M.F. Gonnord, P. Arpino and G. Guiochon, J. Chromatogr., 148,321 (1978).

391 (24) J. Sevcik, J. Chromatogr., 186, 129 (1979). (25) R. Villalobos, R.O. Brace and T. Johns, in Gas Chromatography, H.J. Noebbels, R.F. Wall and N. Brenner Eds., Academic Press, New York, NY, 1961. (26) J.M. Vergnaud, Bull. SOC.Chim. France, 1914 (1962). (27) J.M. Vergnaud, E. Degeorges and J. Normand, Bull. SOC.Chim. France, 1904 (1964). (28) J.M. Vergnaud, J . Chromatogr., 19, 495 (1965). (29) J. Krupcik, J.M. Schmitter and G. Guiochon, J. Chromatogr., 213, 189 (1981). (30) J.H. Purnell, M. Rodriguez and P.S. Williams, J. Chromatogr., 358, 39 (1986). (31) L.S. Ettre and J.V. Hinshaw, Chromatographia, 10, 561 (1986). (32) H.T. Mayfield and S.N. Cheder, J. High Resolut. Chromatogr. Chromarogr. Commun., 8, 595 (1985). (33) G. Guiochon and J. Gutierrez, J. Chromatogr., 406, 3 (1987). (34) R. Annino, C. Caffert and E.L. Lewis, Anal. Chem., 58, 2516 (1987). (35) W.E. Harris and H.W. Habgood. Programmed Temperature Gas Chromatography, Wiley, New York, NY, 1966. (36) J.H. Griffiths, D.H. James and C.S.G. Phillips, The Analyst, 77, 897 (1952). (37) P. Guillermard, Private Communication, 1987. (38) C. Hamilton, Private Communication, 1987.

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CHAPTER 10

METHODOLOGY Detectors for Gas Chromatography TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. General Properties of Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Classificationof Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Concentration Detectors ........................................... b.MassFlowDetectors ............................................. c OtherDetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Sensitivity and Response Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.DetectionLdt ................................................... a. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Analyte Dilution during the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . Dynamic Linear Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Base Line Stability ....................... ....................... a. Short Term Stability. Noise . . . . . . . . . . . . . . . ....................... b. Long Term Stability. Drift ......................................... 7. Contribution to Band Broadening ...................................... a. ResponseTime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b . Detector Cell Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Repeatability of the Response ......................................... 9. Predictability of the Response ......................................... 10. Maintenance and Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. The Gas Density Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. DetectorPrinciple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Parameters Affecting the Response ..................................... a. Nature of the Carrier Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Reference Gas Flow Rate .......................................... c. Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Intensity of the Bridge Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . e. Design Parameters .................... ........................... 1. Sensing Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Internal Geometry of the Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . Sensitivity. Detection Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Linearity . ............................................. 7. Detector St ............................................. 8. Prediction of the Response Factors ....................... ... 9. Maintenance and Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. The Thermal Conductivity Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Detector Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Parameters Affecting the Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Nature of the Carrier Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Carrier Gas Flow Rate ............................................

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395 397 397 398 399 400 400 401 402 403 404 405 407 407 408 408 408 409 410 410 410 411 411 412 414 414 415 417 418 418 418 418 419 419 420 420 421 422 422 423 423 426 426 427

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c. Nature of the Sensors ............................................. d Intensity of the Bridge Current ...................................... e Internal Geometry of the Channels ................................... 3. Classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Prediction of the Response Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b First Empirical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Second Empirical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d.ThirdMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Maintenance and Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Flame Ionization Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. DetectorPrinciple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Parameters Affecting the Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Temperature of the Flame ......................................... 1 Hydrogen Flow Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . AirFlowRate ................................................ 3 Carrier Gas Flow Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Polarization Voltage of the Collecting Electrodes ......................... 3. Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Prediction of the Response Factors ..................................... a. Molar Relative Response Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Weight Relative Response Factor .................................... 8. Maintenance. and Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TheElectronCaptureDetector ........................................... 1 Detector Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Constant Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. PUlsedVoltage .................................................. c Constantcurrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Parameters Affecting the Response ..................................... a. Nature of the Carrier Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Carrier Gas Flow Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Temperature ................................................... d Polarization Voltage of the Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . Linearity ........................................................ 7 Prediction of the Response Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Maintenance and Cost .............................................. The Thermoionic Detector .............................................. 1. DetectorF’rinciple ................................................. a. SolidPhaseReactions ............................................ b.GasPhaseReactions .................. ........................... c. Photcevaporation ............................................... 2 Parameters Affecting the Response ..................................... a Nature of the Alkaline Salt Used ..................................... b. Hydrogen and Air Flow Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Carrier Gas Flow Rate ............................................

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427 428 429 431 431 432 432 432 433 434 434 436 436 437 431 440 440 440 441 442 442 443

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395 3. Classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . 4. Selectivity . . . . ............................................. 5. Sensitivity . . . . ............................................. . . .. . . . . . . . . . . . . . 6. Linearity.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Prediction of the Response Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Maintenance and Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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VII. The Flame Photometric Detector . . . . . . ............................ ..................... 1. Detector Principle . . . . . . . . . . . . . 2. Parameters Affecting the Response . . . . . . ............... a. Photomultiplier Voltage . . . . . . . ..................... b. Gas Flow Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Classification. . . . . . .. . .. .. 4. Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Sensitivity.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . 6. Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Prediction of the Response Factors . . . . . . . . . . . . . . . , . . . . . , . . . . . . . . . . . . . . . 8. Maintenance and Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. The Photoionization Detector . . . . . .................................... 1. Detector Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Parameters Affecting the Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Classification.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . Sensitivity.. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Prediction of the Response Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Maintenance and Cost . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX. The Helium Ionization Detector . . . . . ... .. ........,...... .......... . . . .. 1. Detector Principle . . . . . . . . . . . . .. . . . . . . . . . . . . . 2. Parameters Affecting the Response . . . . . . . . . . . ........... . . .. a. Purification of Helium . . . . . . . b. Other Parameters Affecting the Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. 3. Classification. . . . . . . . . . . . . . . . . , 4. Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Sensitivity.. . . . . . . .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Prediction of the Response Factors . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Maintenance and Cost . . . . . . . . . . ......................... Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . .

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471 471 471 472 472 474 474 474 475 476 476 476 476 476 477

INTRODUCTION Together with the chromatographic column, the detector makes up the hard core of the chromatograph. The column separates the components of the mixture; the detector makes the analyst aware of the results of this separation. It provides information in a usable format, as electric voltages or pulses which can be collected, stored and handled by a variety of devices, such as recorders, integrators and computers. It constitutes the interface between the chemical world of samples, resolved components and mixtures of gases and vapors, on the one hand, and the abstract world of numbers, concentrations, specifications and regulations on the other. Without a detector, chromatography could only be a separation or a preparative technique. References on p. 477.

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The use of a detector is what makes the “modern” generation of chromatographic instruments different from the chromatographic apparatus which was used during the first half of the century. The birth of modern chromatography can thus be traced to the seminal paper of Martin and James on gas chromatography (1). They were the first to put a detector on-line with a column. That was also the only way to make gas chromatography practical, as illustrated by the severe difficulties encountered in trying to quantitatively condense the vapors of the separated components at the outlet of the column in preparative gas chromatography (2). In this chapter we first review the general characteristics and properties of detectors (Section I). Then we review the principle, properties and main implementations of the most important detectors used in gas chromatography: - the gas density balance (GDB), which is the only detector for gas chromatography whose response can be calculated from the physical properties of the camer gas and the compounds considered (molecular weight), and does not vary with the ambient parameters of the detector (Section II), - the thermal conductivity detector (TCD), which is a universal detector and is still widely used for the analysis of gases and for the analysis of organic compounds when sensitivity is not an issue (Section 111), - the flame ionization detector (FID), the most popular detector for gas chromatography, for its reliability and its sensitivity in the detection of organic vapors (Section IV), - the electron capture detector (ECD), a very selective detector for compounds having conjugated double bonds or a electron systems, or halogen atoms (Section

V), - the thermoionic detector (TID, Section VI) and the flame photometric detector (FPD, Section VII), two other popular, very selective detectors for compounds having either phosphorus or nitrogen atoms (TID) or sulfur or phosphorus atoms (FPD). - the photometric ionization detector (PID, Section VIII) and the helium ionization detector (HID, Section IX), two non-selective detectors, useful in special applications. Given the fact that there are entire books devoted to the properties of detectors for gas chromatography (3, 4), that there is extensive literature on each of the detectors just mentioned and also on a number of other detectors, some of them being manufactured, the present review cannot be anything other than a cursory review of the topic for the busy analyst. The reader who needs more information is referred to the pertinent literature, which we have tried to quote in the sections dealing with each detector. The more sophisticated “ hyphenated techniques”, which can be viewed by chromatographers as the use of spectrographs as detectors, are discussed in Chapter 12, since they are used mostly to acquire qualitative information for the identification of unknown components present in analyzed mixtures. The most important of these techniques use mass spectrometers, Fourier transformed infra-red spectrometers, nuclear magnetic resonance spectrometers and inductively coupled plasma spectrometers coupled to a gas chromatograph. These instruments are very complex

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and expensive, they require the permanent attention of skilful specialists and, with the exception of GC-MS, are little used to perform quantitative analysis in routine laboratories, or not used at all for this purpose.

I. GENERAL PROPERTIES OF DETECTORS There has been a large number of reviews published in this field (5-11) and many lists of important properties have been given. These properties include: - the sensitiuity, which relates the detector response to the amount of the corresponding compound introduced. The sensitivity is thus in general a function of the compound considered. - the signal noise of the detector, which combined with the sensitivity sets the detection limit of the corresponding compound. - the selectiuity of the detector expresses the relative sensitivity of the detector for two compounds or possibly two classes of compounds. It can be expressed by the ratio of the detector sensitivities for these compounds. - the linearity of the detector response indicates whether the detector response vanes linearly with increasing sample size and, if it does, within which range. The dynamic linear range of the detector is the range of sample size for which a signal is detected, which is a linear function of the sample size. - the contribution of the detector to band broadening is the increase in the band variance, which is due to its passage through the detector. It should be small compared to the variance originating in the column (see Chapter 4). It is characterized mainly by the response time and the detector cell volume. - the ease of operation and the reliability of the detector are very important factors to consider. They are difficult to quantify and depend more than the previous properties on the specific implementation considered. We here examine these various properties in detail. It is useful to discuss first, however, the classification of chromatographic detectors depending on the general property of their response, function of the analyte concentration in the mobile phase, or of the mass flow rate of analyte to the detector. 1. Classification of Detectors

There are detectors whose response is proportional to the concentration of the analyte in the carrier gas (such as the thermal conductivity detector, the gas density detector and the ultrasonic detector) and there are those whose response is proportional to the mass flow rate of analyte to the detector cell (such as the flame ionization detector, the thermoionic detector and the mass spectrometer). Other more complex detectors are those which are not linear (such as the flame photometric detector in the sulfur mode or the UV absorption photometer) and those whose response depends on the carrier gas flow rate (such as the electron capture detector). We discuss here the relationship of peak area to amount of analyte for these detectors (12). References on p. 477.

398

a. Concentration Detectors

A concentration detector is non-destructive. The signal is proportional to the concentration of the analyte in the carrier gas inside the detector cell. If the carrier gas flow is abruptly interrupted the detector signal remains constant until the flow resumes. If a gas stream with a constant concentration of analyte is passed through the detector the signal is constant, proportional to the concentration used, and independent of the carrier gas flow rate, at least as long as convection does not appreciably perturb the response mechanism (12,13). The relationship between the detector signal, y , and the concentration, C, is written:

where f is the response factor (see Section 1.3). Integration of this relationship during the elution of the peak corresponding to an analyte gives:

If the response factor is constant, independent of the time, of the flow rate, or of other parameters which can change during the course of an analysis, the RHS of equation 2a is equal to the product of the (constant) response factor and the peak area, as measured on the chart of the recorder or as calculated by a digital integrator (i.e., the integral of the signal as a function of time). On the other hand, the sample size (in moles or weight unit) is equal to the integral of the concentration as a function of the volume of carrier gas swept through the detector cell. Thus equation 2a becomes: JCdt

=J

C dV T =f A

(3)

If the carrier gas flow rate, F,, is constant during the analysis, it can be withdrawn from the integral and becomes a factor in the LHS of equation 3. Since the integral of the concentration as a function of the carrier gas volume is equal to the amount, m ,of analyte, we have:

m =fAF,

(44

The peak area, A, observed for a given amount of analyte is inversely proportional to the carrier gas flow rate, since the slower the flow rate, the longer the analyte stays in the detector.

399

The peak height can be derived from the general equation relating the height of a Gaussian distribution to the characteristics of the peak (see Chapter 1, equation 39):

Combination with equation l a gives the peak height, h,,,,:

h,

=

C,/f

=

mfi f V R G

h is proportional to the sample size and to the square root of the plate number and inversely proportional to the response factor and to the retention volume (13). For a given column, this volume is a function of temperature only. At or around the optimum flow rate, where N is maximum, the peak height will not vary for small changes in the flow rate. However, it will be seriously affected by temperature fluctuations, which explains conflicting observations regarding the reproducibility of peak height measurements, as reported in the early literature. b. Mass Flow Detectors A mass flow detector is destructive: usually the analyte molecules react and are transformed into ions which are collected and counted. Instead of being a voltage, as with most concentration detectors, the primary signal of a mass flow detector is usually an intensity (the electronics associated with the detector often transform that current into a voltage). The signal is proportional to the mass flow rate of analyte swept by the carrier gas into the detector cell. If the carrier gas flow is abruptly interrupted, the detector signal falls rapidly to zero and remains at this value until the flow resumes. The variation of the signal when flow is stopped and resumed follows an exponential profile, with a time constant equal to the detector response time. If a gas stream with a constant concentration of analyte is passed through the detector, the signal is proportional to the concentration used, but also to the carrier gas flow rate. In fact it is proportional to the mass flow rate of analyte (12).

The relationship between the detector signal and the mass flow rate is written now (compare to equation la): dm dt

-

=fv

Integration of this relationship during the elution of the peak corresponding to an analyte gives:

References on p. 411.

The LHS of equation 2b is the analyte amount while the RHS is the product of the response factor by the peak area. Thus: m=fA

(4b)

With a mass flow detector the peak area observed for a constant amount of analyte is independent of the flow rate, which certainly reduces the extent of errors in quantitative determinations. On the other hand, the height of the peak obtained with a mass flow detector is a function of the carrier gas flow rate. Since the band width increases constantly with decreasing flow rate while the area remains constant, the peak height must decrease. Trace analysis will be easier at large carrier gas flow rates, since there is less time for diffusion and dilution of the analyte in the carrier gas. One must avoid, however, an excessive flow rate which would cause a significant increase of the signal noise.

c. Other Detectors The response of these detectors is more complex, because in principle they are not linear (e.g. the flame photometric detector in the sulfur mode, which gives a quadratic response, or the absorption photometric detectors, which gives a logarithmic response), or because the response factors depend on the carrier gas flow rate. In this last case, the use of an auxiliary stream of scavenger gas, the flow rate of which is adjusted to keep constant the flow rate of the gas stream through the detector, could bring the detector back into one of the two main categories previously described. Another interesting, complex situation is that of the electron capture detector which, in the cases where it is coulometric, i.e., when each analyte molecule entering the detector captures an electron, is a mass flow detector. But if the reaction yield is very low, as happens with some compounds and some implementations, the response is proportional to the reaction rate, i.e., for a first order reaction, to the concentration. In intermediate cases (large but not total reaction yield), the response is complex and often puzzles the investigator. The ambient parameters of these detectors must be carefully controlled. It is especially important to keep the carrier gas flow rate constant or at least to maintain constant the total flow rate of gas through the detector. 2. Selectivity

In spectrometric methods of analysis, selectivity usually characterizes the extent to which the detector response depends on the concentration of the analyte of interest, as opposed to interferences. Interferences in chromatography being usually other analytes, incompletely resolved by the column, the term is used here with a slightly different meaning. Most detectors give responses which vary widely from one compound to another. The selectivity characterizes this effect. It is rarely quantitated, in part because the numbers depend on the exact compound used. Even for a class of compounds, the

401

response factors vary significantly from one compound to the next. There is no agreement in the literature on a parameter nor on a set of figures for the most common detectors. The selectivity of a detector for two compounds could be the ratio of their response factors. Ratios exceeding 1 X lo4 are not rare with some detectors (ECD, TID). It would be useful to have non-selective detectors, which would have the same response factor for all compounds, on either a weight or a mole number basis, and selective detectors, the selectivity factor of which could be adjusted, so the response factor would be very large for a group of compounds and negligible for all others. Such ideal detectors do not exist. Non-selective detectors respond to the mobile phase as well. Accordingly, they are sensitive to changes in its density and the detector signal fluctuates with variations in the temperature and pressure of the detector cell. This limits their sensitivity (see further in this section). Properties like density or thermal conductivity vary from one compound to the other, so the response factor of even a non-selective detector may vary over a range of 1 to several tens. Except for the gas density detector, for which the relative response of two compounds is accurately predicted, it is not possible to derive even an approximate estimate of the quantitative composition of a mixture without prior calibration. The response of some selective detectors depends on some parameter which permits a certain adjustment of the selectivity. This is possible with spectrometric detectors and also, to a degree, with the electron capture detector. On the other hand, the flame ionization detector is very selective for organic compounds, but much less from organic compound to organic compound. The mass spectrometer is both very selective, in the selected ion monitoring mode, and relatively non-selective in the total ion current mode. This explains the great success of the coupling of gas chromatography and mass spectrometry. 3. Sensitivity and Response Factor

The term of sensitivity is quite ambiguous in chemical analysis and especially in chromatography. It has been used to describe the response factor of a detector and its relationship with other parameters of the analysis. This is the topic which is briefly discussed here. It is more commonly used as a poorly chosen synonym for detection limit. The difficulty with these terms is that when the sensitivity improves (“becomes better”), the detection limit decreases. More importantly, the detection limit depends both on the signal noise and on the detector response, which is what the first acception of the word “sensitivity” was used to describe. The sensitivity, S, is the ratio of the signal obtained to the concentration of the analyte in the carrier gas (concentration detectors) or to its mass flow rate to the detector (mass flow detectors). Thus we have:

s = -Y

= c

(7) References on p. 417.

402

It has been shown by Dimbat, Porter and Stross that the sensitivity of a detector can be calculated by the following equation (14):

s, = A c1c2c3 m where: - m is the amount of the compound injected (mg), - A is its peak area (cm2), - C, is the sensitivity of the recorder used (mV/cm on the ordinate axis), - C2 is the inverse of the speed of the paper chart on the recorder (min/cm), - C3 is the carrier gas flow rate at the detector temperature and atmospheric pressure (mL/min). S, is the absolute response factor, F, of the compound considered (see Chapter 13, equation 3a). It is equal to the inverse of what we call, for practical reasons, the response factor (see Chapter 13, Section 11.1). For a mass flow detector a similar definition of the sensitivity is: S--

Y

- dm/dt

(9)

and the sensitivity is calculated from:

where A, C,, C2 and m have the same meaning as for equation 8. These relationships are somewhat obsolete, as is the use of paper chart recorders to collect quantitative data. They are still found in the literature and may prove useful occasionally. For reasons which are discussed in Chapter 13, we prefer to use the response factor, defined as the ratio of the amount of analyte, Q,to the corresponding peak area, A :

Q =fA

(11)

The response factor is thus the inverse of the sensitivity, as discussed in equations 7 to 10 above. It is totally incorrect to use the name sensitivity to mean the ability of a detector to give a signal above the background noise for very small concentrations of analyte. The proper term is the detection limit, defined in the following section. 4. Detection Limit

This property relates to the analysis of traces, where the signal is small and often of the same order of magnitude as the base line noise. It is usually accepted that the detection limit corresponds to a signal which is equal to a certain number of times

403

-?-----

2R,

-

-I--

l-- - 7-Rn

6

5

4

3

2

1

Figure 10.1. Base line noise and detection limits.

the base line noise (15). Difficulties arise with the choice of this number and the definition of the base line noise. The noise is defined from the standard deviation of the base line signal over a certain period of time (of the order of the base width of the peaks of the analytes considered). What experimentalists often call “the noise” is the “width” of a noisy base line and is close to four times the standard deviation of the background signal. Figure 10.1 illustrates a very common situation in trace analysis. It has been shown by Rogers (16) that if a peak is equal to twice the standard deviation of the noise it will be barely detected some of the time. If the peak is five times the standard deviation of the noise, it will be detected most of the time. If the peak exceeds ten times the standard deviation of the noise, it will always be detected (16). It is thus prudent to adopt for the definition of the detection limit a factor of five or ten times the noise (standard deviation). If the noise is determined from the width of a base line, a factor 2 seems adequate. a. Definitions

Conventionally, the detection limit of a chromatographic detector is defined as the analyte concentration (for a concentration detector) or the analyte mass flow (for a mass flow detector) which gives a signal equal to twice the detector base line noise (15). The detection limit of an analytical procedure depends on the response factor of the detector at low analyte concentration, on the detector noise and on the properties of the chromatographic system used, which makes the detection limit one of the most complex and least understood issues of gas chromatography. References on p. 411.

404

b. Analyte Dilution during the Analysis

Chromatography is a separation technique. But, to separate the components of a mixture, it is necessary to supply the amount of Gibbs free energy required to compensate for the decrease in entropy due to the separation (which is equal to minus the mixing entropy). In isocratic, isothermal chromatography, this is provided by the dilution of each component of the separated mixture in the mobile phase. As a consequence, the eluate is more diluted than the sample introduced into the column. Chromatography is, in fact, a selective dilution technique (17). The dilution factor can be calculated by an approximation of a Gaussian profile, from the equation relating the maximum concentration of the analyte in the eluate, C,, and which is obtained from the area of the Gaussian curve is the volume standard deviation, u,, of the elution band), as discussed in Chapter 1. This is equation 5 above. The sample mass is the product of its concentration, C,, by the sample volume, Vo. Thus equation 5 becomes:

(&/a

We know that, in order for the contribution of the injection band width to be neghgible compared to that originating in the column, the ratio of the sample volume to the volume standard deviation of the zone should be less than 1/5 (see below, Section 1.7). If we desire that no band width be increased, this relationship must hold for the non-retained peak as well and the ratio V,/u, will then be equal to 1/5(1 k') if the largest possible sample volume is injected. Then the dilution ratio becomes:

+

CM -=-

0.080

Co

1+k'

which may easily be as low as 1 to 2% (for k' between 3 and 9). This means that if the detector has a detection limit of 1 ppm (in the mobile phase, in the detector cell), the detection limit will be 50 to 100 ppm in the actual sample. The incautious analyst may be disappoinied. If we accept overloading of the column, a larger sample volume can be introduced. Guiochon and Colin (17) have shown that the minimum dilution ratio is given by:

where:

- h is a numerical factor depending on the injection technique used, usually around 2,

405

- B is the square root of the relative loss of column efficiency which we can accept and sets a limit to its overload. With a typical value of 0.3 for B (i.e., a 9% loss in the number of plates), the dilution ratio can be as low as 4.2. It is not always possible to inject the larger possible sample size permitted by a certain loss in plate number, because the loss is going to be larger for all the compounds which are less retained, and this may be unacceptable. Care must be taken, especially in trace analysis, to inject the largest possible sample volume.

5. Dynamic Linear Range The response of a detector is ideally linear, i.e., the signal is proportional to either the conc2ntration of analyte in the carrier gas or to its mass flow rate. Then, under constant experimental conditions, the peak area is proportional to the sample size. This is true with most detectors, but only within a limited range of sample sizes. The current practice when studying the linear behavior of a detector is to plot the detector response (peak height or peak area) versus the sample size in double logarithmic coordinates. This may be misleading, since it dampens the fluctuations. It has been shown in a number of cases that the response deviates markedly from linearity, but progressively, and S-shaped curves have been reported. These phenomena are clearly seen on plots of the ratio of the peak area to the sample size versus the logarithm of the sample size, and large ranges of sample sizes can easily be explored. The non-linear behavior of electronic devices or components may explain many of these observations. If the response of the detector, y, is linear and equal to kC (for a concentration detector) at small concentrations, the deviation from linearity may be characterized by :

sy=

~

kC-y Y

The detector is called non-linear if 6 y exceeds 5% (or sometimes 10%)(see Figure 10.2). The dynamic linear range of the detector is the ratio of the concentration for which this happens to the detection limit of the same compound. It is not a property characterizing the detector alone, since it is a function of the compound selected for the measurements. In general, however, the order of magnitude remains the same for all compounds. Deviations from a linear response may originate (i) in the basic physical laws governing the detector principle, (ii) in the principle adopted for the specific implementation used and (hi) in the particular design of the instrument. Examples are as follows: (i) The flame photometric detector in the sulfur mode uses a second order reaction. The response is proportional to the square of the sulfur concentration. The ECD is an absorption detector, its response is logarithmic and can be considered to be linear only at low concentrations (or rather at low values of the signal). References on p. 477.

406

Figure 10.2. Linear range of the detector response.

(ii) The TCD measures the variation in the current across the diagonal of a Wheatstone bridge. This current results from the change in the resistance of the sensor resistor in the measure cell, when the heat conductivity of the gas varies, resulting in a change of the resistor temperature, hence of its resistance. The linearity of a Wheatstone bridge is limited, however, and if the sensor resistance becomes too large, deviation from linear response will occur. The corresponding concentration range depends on the exact design selected and the elements used. (iii) The FID collects charge carriers generated by the combustion of organic compounds. The current flows through a large resistor. If the sample size increases beyond some limit, the number of charge carriers increases, and the voltage drop across the resistor decreases, and the charge carriers accumulate around the collecting electrode, generating a space charge. Deviation from linear response occurs. The range of concentration depends on the shape and position of the collecting electrode and on the characteristics of the resistor. Finally, the peak height does not increase linearly with the sample size as soon as the column is overloaded and the band profile becomes broader because the equilibrium isotherm is not linear (see Chapter 5). The peak area continues to increase linearly with increasing sample size, however. The recent advent of computers makes the use of non-linear detectors possible. The major difficulty in the use of the signal of a non-linear detector is that the peak area cannot be calculated by the simple time integration of the detector signal. The signal has first to be processed, to generate a second signal, proportional to the analyte concentration or mass flow rate. This last signal can be integrated. This

407

procedure is too tedious to be carried out manually, hence our profound reluctance to use non-linear detectors. But computers can do that very well and very fast. This would permit the use of non-linear detectors, on the condition that the characteristics of their response be as stable as those of linear detectors, so that they do not need to be recalibrated too often. Unfortunately, the use of relative responses and relative response factors would become impossible. 6. Base Line Stability

Most detectors give a background signal and the response to the elution of analytes through the detector cell appears above this background. It is easy to suppress the background electrically, but all fluctuations of the background perturb the signal and interfere with the analytical results. These fluctuations may be classified into three groups, depending on their frequency. Low frequency fluctuations are referred to as base line drifts. High frequency fluctuations are called noise. To some extent it is possible to considerably reduce the effect of noise and base line drift. Intermediate fluctuations, with a frequency of the order of the inverse of the width of the peaks recorded are almost impossible to correct for. In principle, noise and base line drift can be eliminated by making a Fourier transform of the chromatogram, replacing the parts at high and low frequency, which do not contain useful information on the analysis performed, by a base line and making the inverse Fourier transform to the time domain. More sophisticated forms of filtering the signal in the frequency domain are available (18). a. Short Term Stability, Noise

The noise has a critical influence on the detection limits. Reducing the intensity of the noise is the first thing to do to solve difficult trace analysis problems. Noise origmates in the electronics associated with the detector or in fluctuations of the physical parameters of the detector environment. It must be noted, however, that in their report on the use of a very carefully built and controlled TCD, Goedert and Guiochon were disappointed to note that no significant decrease in the detector base line noise was observed when the temperature of its block was controlled within 0.001" C, the detector pressure within 0.01 mbar, the flow rate within better than 0.05% and the bridge voltage within better than 0.01% (19). In the TCD at least, noise probably comes from turbulence due to heat convection in the gas phase and from resistor noise. This illustrates our dramatic lack of understanding of the physics of detectors used in GC. Noise can be corrected for by integration, which drastically reduces its direct contribution to measurement errors. Another contribution of the noise to the error on the peak area is much more difficult to correct. It results from random interaction with the algorithm detecting the peak. Using the first derivative of the signal, these algorithms are very sensitive to noise. This is why the determination of the peak height of trace components is often more precise than the determination of their peak area. References on p. 411.

408

6. Long Term Stability. Drift

The base line drift can introduce major errors in the determination of the peak areas, but this can be corrected more or less satisfactorily (see Chapter 15). Otherwise the effect of base line drift is rather cosmetic. Base line drifts have their origin in fluctuations of the carrier gas flow rate and in fluctuations of the detector and column temperature. In temperature programming analysis there is almost always a major drift at the end of the analysis, signaling the beginning of liquid phase bleeding. Short term drifts, with a period between 1/5 and a few standard deviations of the peaks on the chromatogram, are very difficult to identify and correct for, unless they are periodic.

7. Contribution to Band Broadening When the analytes have left the column, the chromatography mechanism which was building up the separation ceases to operate. There is a strong axial concentration gradient, however, and diffusion proceeds to mix the compounds separated on the column. Thus, connecting tubes between column and detector should be short and the detector should be designed in such a way that these phenomena are minimized. This means using small cell volumes and a rapid response. The band variance recorded by the data system is the sum of contributions which may be ascribed to the column itself, to the injection system and to the detector (see Chapter 4, Section XI). As far as these contributions are independent, the variance contributions are additive (see Chapter 1).The contribution of the detector can be separated into two parts, the one originating in the finite volume of the detector cell, where the separated compounds can actually be remixed, at least to some extent, and the other due to the finite rate of response of the detector signal, which is delayed and does not reflect the rapid change in the composition of the carrier gas in the detector cell, but lags behind. a. Response Time

If we assume the concentration profile at column exit to actually follow a Gaussian profile, it is possible to calculate the profile of the detected peak, the increase in retention time, and column plate height and to relate the height of the recorded peak to the maximum concentration of the band at column exit (20,21). All these changes are function of the detector time constant. The area of the band is unchanged. The first moment of the band increases by an amount equal to the time constant and the second moment by an amount equal to the square of the time constant:

409

where M I and M 2 are the first and second moment determined for the recorded peak, respectively, u , the standard deviation of the band profile at column exit and r , the detector time constant. It is shown that if the response time of the detector is smaller than 0.2 times the standard deviation of the concentration profile of the band, the retention time is increased by an amount equal to the time constant, while the relative reduction of the peak height is practically equal to the relative increase in the band width (21). If the output peak height is required to be a certain fraction, @, of the true peak height:

or:

Similarly, if the loss of apparent column efficiency is not to exceed a fraction O2 of the true column efficiency, the time constant should be smaller than

eu = e-

tR

fi

In practice, the time constant of the detector should be smaller than 1/5 the standard deviation of the narrowest peak which will be analyzed, or 1/20 its base line width (20-22). For packed columns response times of the order of 0.2 to 0.5 sec are required, for open tubular columns, response times of 0.1 sec or below are necessary for fast analysis, while for long, high efficiency columns, the response time can be larger, up to 1 second.

b. Detector Cell Volume The band of analyte eluted from the column does not migrate through the detector cell as a cylinder. Some mixing takes place (22). In the most unfavorable case, when the cell behaves as an exponential mixing chamber, Sternberg (21) has shown that the time variance contribution of the remixing of the eluted band with pure carrier gas in the detector cell is given by:

.,'= vd2

-

D2

where uc is the contribution to the band variance, Vd is the detector cell volume and D the camer gas flow rate. If this contribution is not to exceed a fraction O 2 of the References on p. 477.

410

band variance created by the column, the detector cell volume should be smaller than (22):

where d , is the column diameter, z, the total packing porosity (ca OM), k’, the column capacity factor for the compound considered, L, the column length and H, the HETP. Equation 22 gives volumes of the order of 0.5 mL for conventional packed columns and 0.002 mL for classical open tubular columns.

8. Repeatability of the Response Ideally, the detector response should be highly repeatable. This means that all the parameters which influence the response factors have been identified and are controlled within satisfactory limits. This may be a problem for some detectors, and a number of implementations available from manufacturers do not fully meet the criteria for acceptable performance in quantitative analysis. In a number of cases simple modification, such as the replacement of the flow rate or pressure controller by a more accurate one, or more complex changes, such as the use of temperature controlled pressure controllers, of a controlled reference pressure for the pressure controllers or for the column outlet pressure, permit a considerable increase in the performance of detectors. It should be stressed that in quantitative gas chromatographic analysis, as in other circumstances, the quality of an instrument can be no better than the quality of the weakest component.

9. Predictability of the Response It would be extremely useful to have a universal detector available, the response of which can be predicted from known molecular properties of the analytes. The response factor of the detector would then be calculated, and the need for calibration would be eliminated. There is no such detector available. At least, for some detectors, such as the GDB, the relative response factors can be calculated. This makes calibration much easier and also permits the rapid, simple calibration of other detectors. In most cases, however, the responses measured do not agree satisfactorily with the responses calculated from the molecular properties of analytes, using the relationship derived from the detector principle. This means that the detector behavior is more complex than its principle and is not fully understood. 10. Maintenance and Cost

Detectors must be practical, easy to maintain, not too expensive and without serious constraints. Detectors for industrial applications must be easy to maintain

411

by non-specialists in a workshop environment. They must stabilize rapidly and be rather insensitive to the fluctuations of ambient parameters. Detectors using radioactive sources will be avoided in such a case. Some potentially very interesting detectors have been abandoned because of unusual difficulties encountered in their use. The most famous case in point is the Argon Ionization Detector, also called the “Lovelock detector”. This detector was excellent in many respects. It is more sensitive than the flame ionization detector, potentially faster (i.e. with a shorter response time) and certainly more practical to use, since it requires only one source of gas, the carrier gas. Unfortunately, it was sensitive to various pollutants, especially stationary phase bleeding and water vapor, it had a non-linear response and a rather capricious behavior in the hands of analysts who were not fastidiously careful and clean. The detector cell should be easy to disassemble, clean, bake and reassemble. After such a treatment, the response factors should not have changed drastically, even though a recalibration is acceptable. The detector electronics should supply signals in digital as well as analog form, and the time constant should be easily adjustable. 11. Conclusion

A number of detectors, governed by entirely different principles, are available. The most important only are reviewed here. Most of them are commercially available from many different manufacturers. Some implementations are profoundly different from the average and provide an unusual performance. Accordingly, it may be difficult to choose a detector. Non-technical considerations like price, quality of service available locally, etc. are also important. There does not seem to be any very important technical problem which remains unsolved in gas chromatography. For most volatile compounds, organic as well as inorganic, there are very sensitive detectors. A number of classes of compounds have selective detectors, although the search for detectors with a tunable selectivity has been elusive. Detectors, however, are fast enough and have cells small enough for the most demanding conditions. Trace problems where the real difficulties come with a lack of detector sensitivity are rare.

11.

THE GAS DENSITY BALANCE

The Gas Density Balance was first designed and built by A.J.P. Martin (23,24) in 1955, as the first detector dedicated to gas chromatography. Very difficult to build at the time, more difficult still to equilibrate and set properly, this detector was rapidly abandoned for the Thermal Conductivity Detector, which was more sensitive, much simpler and easier to operate. The only model commercially available at present was designed in 1960 by Neirheim (25) and developed by Gow-Mac Instrument (Bound Brook, NJ, U.S.A.). A “mass detector” using the exceptional property of the GDB of being able to supply the molecular weight of an unknown References on p. 477.

412

after proper calibration, was developed in the early 'seventies and presented at the Pittsburgh Conference by a now defunct company. The relative lack of success of the GDB, in spite of an attractive set of properties, is due to the lack of sensitivity of the only available implementation of the device. 1. Detector Principle

The principle is the same for the two designs, by A.J.P. Martin and by Neirheim. We shall describe and discuss only the simpler design of Neirheim. The design is illustrated Figure 10.3. It is the gas stream equivalent of a Wheatstone bridge. The stream of carrier gas eluting from the column enters at c. A stream of pure reference carrier gas enters at a. Both streams mix and exit through the port at d. Both gas streams split when they enter the detector, one stream flowing upward, the other downward. The two streams of pure carrier gas pass over two sensors, bl and b2, resistors cooled by the gas stream flowing over them and heated by the electrical current. These two resistors are placed in the opposite branches of a Wheatstone bridge, which measure the variation of their temperature, i.e., of the velocity of the carrier gas in the two branches of the GDB. When pure camer gas elutes from the column, the flow rates are equal in the two branches of the balance. The balance and the electric bridge are equilibrated. When a compound elutes and its density is larger than that of the carrier gas, the eluate stream does not split equally between the upward and the downward branches. The mobile phase is heavier than the pure camer gas coming from the right channels, and its flow rate in the downward tube becomes larger than its flow rate in the upward tube. As a consequence, the flow rate of pure carrier gas over sensor b l decreases, while its flow rate over sensor b2 increases. It can be shown

d

Figure 10.3. Schematics of the Gas Density Balance. a - Inlet of the reference carrier gas. bl, b2 - Flow rate sensors. c - Column effluent inlet. d - Gas outlet. (Gow-Mac model 373).

413

that the total flow rate of the pure carrier gas stream remains constant (25). The signal of the detector results from the disequilibrium in the electric Wheatstone bridge, caused by the change in carrier gas flow rate over sensors b l and b2, and hence in their resistance. A similar phenomenon occurs when an analyte elutes whch has a density smaller than that of the carrier gas. Now the flow rate of eluate in the upward channel is larger and the flow rate of pure carrier gas over sensor b2 becomes lower than the flow rate over sensor bl. It is very important to observe that only pure carrier gas flows over the flow rate sensors b l and b2, so their response results only from the change in the flow rate in the corresponding channels, not from a change in the composition, hence in the thermal conductivity of the gas. Neirheim has shown that the change in carrier gas flow rate in each channel (positive in one channel, negative in the other) is given by the following equation, which neglects the compressibility of the gases: rgd

SD = - S p (

128qL

H, - H , )

(23)

\

4

\

:I

20 rnin

15

10

5

50'C

I

Figure 10.4. Chromatogram obtained with the GDB (Figure 10.3), for a 5 pL sample of a mixture of

chloroalkanes: 1 = 1,l-Dichloroethylene. 2 = I,l-Dichloroethane. 3 = 1,2-DichIoroethane. 4 = Carbon Tetrachloride. 5 = Trichloroethylene. 6 = 1,1,2-Trichloroethane. 7 = Tetrachloroethylene. 8 = 1,1,2,2-Tetrachloroethane.9 = Pen tachloroethane. Camer gas: Nitrogen. Flow Rates: Reference: 6 L/hour, Column: 4.5 L/hour. Column: 4 mm id., 2 m long, packed with 60-80 mesh Chromosorb P coated with 158 Apiezon M. Temperature programmed from 50 to 170 C at 7 C/min. Detector: Gow-Mac 2 WX wires, current: 150 mA, temperature: 220 O C. References on p. 477.

414

where: - g is the gravity constant, - d is the inner diameter of the horizontal channels containing the sensors b l and b2, - 6 p is the variation of density of the eluate, proportional to the concentration of analyte and to the difference between the molecular weights of camer gas and analyte, - q is the viscosity of the carrier gas, - L is the length of the horizontal channels b l and b2, - H, - H , is the vertical height between the inlet port of the eluate, c, and the sensor b l . The balance should have wide and short horizontal channels to connect the two gas streams, reference pure carrier gas and eluate, and a great height. Back diffusion of the analyte vapor to the sensors should be prevented, however, to avoid a complex response depending on two different mechanisms. Whereas the principle of the GDB should be carefully reinvestigated, it is most probable that modern technology could provide another, more sensitive, better-suited sensor for the measurement of the pressure differential than the anemometer used in the implementations described so far. It seems also that the balance design should be optimized for a given camer gas. A complete theory of the response of the GDB has been published recently (160). Its results are in full agreement with our conclusions. Figure 10.4 shows a chromatogram obtained for a mixture of chlorinated hydrocarbons. 2. Parameters Affecting the Response A detailed study of the properties of the GDB Gow-Mac model 373 has been carried out by Guillemin et al. (26-28), who recognized the great importance of having an absolute detector for calibration. Rules regarding the use of the GDB in quantitative analysis were derived from this study. There are two kinds of parameter affecting the response of the GDB: those which can be adjusted and optimized by the analyst, such as the nature of the carrier gas, the reference gas flow rate, the temperature of the detector and the bridge current; and those which are determined by the design and construction of the detector.

a. Nature of the Carrier Gas

Equation 23 shows that the detector response is proportional to the difference in density between the camer gas and the analyte vapor. Assuming that both follow the ideal gas laws, the weight response factor, as defined above (see Section 1.3, equation 11) is proportional to: Pa

- Ma - Ma- M8

41 5

Figure 10.5. Chromatogram obtained with a GDB using H, as carrier gas. Sample: 0.25 mL of a mixture of air, chlorine and hydrochloric acid. Flow Rates: Reference: 44 L/hour, Column: 5 L/hour. Column: 4 mm i.d., 5 m long, packed with 40-60 mesh Chromosorb T, coated with 15% GESF 96. Temperature: 53OC. Detector: Cow-Mac GDB model 373, 4 WX wires, current: 320 mA. Temperature: 53OC.

where pa and pg are the densities of the analyte and the carrier gas, respectively, and Mu and Mg their molecular weights (the molar response factor would be 1/( Mu M, 1). For a given sample size, the peak area will be larger (see equation 23), and the response factor smaller (see equation 24), when the difference Mu- M g is largest. From the point of view of detector sensitivity, the best carrier gases are thus hydrogen and helium. For example, with carbon tetrachloride ( M = 154) the response factors with hydrogen, helium and nitrogen are 1.013, 1.027 and 1.222, respectively. The use of light gases deserves a careful study. As noted above, the back diffusion of analyte vapor to the sensors (bl or b2, on Figure 10.3) could change the response mechanisms, modify the response factors and nullify the important advantage of the GDB. Guillemin et al. (28) have shown that these phenomena do not take place and that the GDB behaves as predicted by the theoretical model based on its design when the Reynolds number in the horizontal channels where the sensors are placed is equal to 20. Provided this condition is fulfilled, the response of the GDB with hydrogen is maximum (see next section) and follows the relationship discussed in this section. Figure 10.5 shows a chromatogram obtained with hydrogen as a carrier gas. b. Reference Gas Flow Rate As shown on Figure 10.6, there is an optimum flow rate for the reference carrier gas stream that depends on the nature of the carrier gas (28). Studies have been References on p. 477.

416

Figure 10.6. Plot of the peak area versus the reference flow rate for a GDB. Influence of the nature of the carrier gas: SF,, C02, N,, Ar. Sample: 1 pL 2-Methylpentane.

made using argon, nitrogen, carbon dioxide and sulfur hexafluoride. The result shows that the optimum flow rate corresponds in each case to the same value of the Reynolds number: UdP Re= 1

where: is the camer gas viscosity, is the diameter of the horizontal channels containing the flow rate sensors (see Figure 10.3), - p is the carrier gas density, - u is the average velocity of the carrier gas in the horizontal channels. For the Gow-Mac GDB model 373, the optimum Reynolds number is 20. Since the flow rate in each channel is equal when the eluate is pure carrier gas, the optimum flow rate will be: -1 -d

where s is the cross section area of the horizontal reference channel. For the

417

TABLE 10.1 Flow Rate Characteristics of a Gas Density Balance Carrier Gas Helium (He) Hydrogen (H,) Nitrogen (N,) Argon (Ar) Carbon Dioxide (CO,) Sulfur Hexafluoride (SF,) Bromotrifluoromethane (CBrF, ) Dichlorodifluoromethane (CCI *F,) Chloromethane (CH,Cl)

M 4 2 28

40 44 146 149 121 50.5

b.p. ("C)

d (g/L)

Viscosity (PP)

Flow Rate

Reynolds Number

- 269

0.178 0.090 1.25 1.78 1.97 6.16 8.71 6.33 *** 3.58

196 89 176 221 148 180 168 127 106

50 44 6 6 4 1.3 0.87 0.9 1.34

20 20 20 ** 22.5 ** 23.5 ** 20 ** 20 20 20

- 253 - 196 - 186 - 78 - 64 - 58 - 30 - 24

-

Optimum Flow Rate in L/hour. ** Experimental values. Other values of Reynolds number used for calculation. Constants from Handbook of Chemistry and Physics, CRC, Cleveland, OH, except gas specific gravities, from Matheson Data Book (1961). *** CF,CI, is not an ideal gas. Otherwise d would be 5.30 g/L.

Gow-Mac GDB model 675 the optimum Reynolds number is 10 and the detection limits are larger than for the GDB model 373. Further experiments have shown that equation 26 extends to light carrier gases as helium and hydrogen. The corresponding flow rates are large. With the detector used (Gow-Mac model 373), the optimum flow rate - which is approximately 6 L/hour for nitrogen and argon - becomes 44 L/hour and 50 L/hour for hydrogen and helium, respectively. Nevertheless, the noise and base line drift remain comparable to what is observed with the other carrier gases. Table 10.1 shows a list of the gases which are potential candidates for use with the GDB and their relevant physical properties. The column flow rate does not influence the response factor. The GDB being a concentration detector, the peak area decreases in proportion to the inverse of the carrier gas flow rate. It is better, however, to keep the column flow rate smaller than the reference flow rate (27). The carrier gas flow rate is measured first, with the reference stream switched off. Then the sum of the two flow rates is measured with a convenient flowmeter.

c. Temperature The response of the GDB is strongly temperature dependent. The effect of temperature comes from three different sources (see equation 23). The density of gases decreases with increasing temperature, their viscosity increases and the response of the flow rate sensors decreases. The first two effects are readily seen in equation 23. If the density of gases decreases, so will the difference between the density of two gases. The difference between the temperature of the sensing resistor and that of the carrier gas flowing around it decreases with increasing temperature, resulting in a proportionally lower response. References on p. 477.

418

An increase in the detector temperature from 60 to 300 O C results in a decrease of the absolute response factors, of the peak heights and areas by approximately a factor 5. The temperature of the GDB must be carefully controlled to maintain constant the response factors, absolute and relative. d. Intensity of the Bridge Current

The response of the GDB is proportional to the variation of the flow rate in the two horizontal channels between which the stream of reference carrier gas is split. The change in flow rate is sensed by resistors which are placed in a Wheatstone bridge and heated by a current. The detector response will thus also depend on the response factor of the bridge. The response factor of the GDB is proportional to the amount of heat dissipated in the gas stream. It increases approximately as the square of the bridge current (the resistance of resistors varies with temperature). Since the resistors are placed in the gas stream, they can dissipate a larger amount of energy than similar sensing elements placed in the cells of a TCD. Especially with gases having a large thermal conductivity and used at a large flow rate, such as hydrogen and helium, very high bridge currents are used (more than 350 mA). e. Design Parameters

The GDB’s designed by both A.J.P. Martin and Neirheim use anemometry as the detection principle of the changes in flow rates in the inner channels of the balance induced by the elution of an analyte. Although other methods of sensing these changes are possible, they would not change the general properties of the detector. 1. Sensing Elements Creitz has studied the details of anemometric detection as a method of improving the sensitivity of the detector (29,30). Since the resistance of normal resistors (wires) increases linearly with temperature, while that of thermistors decreases exponentially with increasing temperature, thermistors are preferred for balances used at low temperatures and wires for balances used at high temperatures. Most GDB use four sensing elements. When four sensors are used, they are placed in the opposite diagonals of the Wheatstone bridge, in order to improve the response. The gain is a factor 1.5, not 2 as expected. The two resistors being placed in series, the gas has been already heated by the first one when it passes over the second one. The energy flux dissipated by this second resistor is smaller, hence the decrease in the response.

2. Internal Geometry of the Channels The most important design parameter which could be adjusted in equation 23 is the height of the gas column. Using a home made detector, with adjustable height, Guillemin (31) has been able to show that the detector response increases in proportion to the height, as predicted by equation 23. Unfortunately, the response

,

419

Model 373

Gas density balances

Figure 10.7. Comparison between the sensitivity of two

GDB.

Carrier gas: Nitrogen. Detectors: 2 W 2X wires. Current: 150 mA.

time also increases, which limits the potential advantage of tall detectors. They would also be difficult to integrate into a gas chromatograph. Even to control their temperature properly would not be easy. In opposition to some statements found in the literature (30), it has been shown that proper adjustments of the dimensions of the inner tubings of the balance permit an increase in the response and in the dynamic linear range. Data in Figure 10.7 show a response larger by a factor 3 than the response obtained with the standard Gow-Mac detector (31).

3. Classification The GDB is a concentration detector (see equation 23). The areas of the peak obtained are inversely proportional to the gas flow rate. The sensitivity is derived from measurements using the equation of Dimbat, Porter and Stross (equation 9). 4. Selectivity

The GDB is a selective detector, but the degree of selectivity is very small. The response factor depends on the molecular weight of the analyte and on the difference between the molecular weights of the analyte and the carrier gas (see equation 24). But it is impossible to detect ethylene (M = 28) when nitrogen is used as carrier gas, and very difficult to detect ethane or oxygen. For the quantitative analysis of mixtures, the carrier gas will be chosen so that its molecular weight is as remote as possible from that of the sample components. Hydrogen will often be the best choice. For mixture of light gases containing hydrogen, helium, ammonia, methane, etc., sulfur hexafluoride could provide excellent results (see Figure 10.3, ref. 28). References on p. 411.

420

TABLE 10.2 Dynamic Linear Range of a Gas Density Balance for Different Carrier Gases Carrier Gas

Maximum Linear Concentration

Detection Limit 6 (PP4

Dynamic Linear Range

Helium Nitrogen Sulfur Hexafluoride

3.54% 3.545% ** 3.5% ***

1.4 3.1 33

25,000 10,Ooo

1,Ooo

Corresponding to an injection of 0.6 rnL of CCl,F, and a column flow rate of 3 L/hour.

** Corresponding to an injection of 0.6 mL of CCI,F, and a column flow rate of 3 L/hour. *** Corresponding to an injection of 0.08 mL of Nitrogen and a column flow rate of 0.5 L/hour. Concentration in the carrier gas, in the detector cell.

5. Sensitivity. Detection Limits The GDB model 373 should be used with optimum reference gas flow rate (Re = 20) to maximize the response. Similarly, the carrier gas flow rate should be adjusted to the value giving the maximum column efficiency, and the maximum peak height, when a concentration detector is used. The detector should also be used at the lowest temperature compatible with the application in mind. Finally, the bridge current will be adjusted as high as possible. The combination of these different settings will ensure the maximum response for the detector and the lowest possible detection limits. It is especially important with the GDB, because the detector is not very sensitive. The GDB is approximately 10 times less sensitive than a TCD using the same sensing elements. The detection limits reported as concentrations in the sample analyzed are around 100 ppm. Detection limits expressed as concentration of the analyte in the carrier gas are of course much lower; they are of the order of 5 ppm. Some data are reported in Table 10.2.

6. Linearity The dynamic linear range of the GDB has been determined for three different carrier gases: helium, nitrogen and sulfur hexafluoride (see Table 10.2). The maximum concentration corresponding to a linear response was derived using the equation derived by Toth, Kugler and Kovats (32):

c,,, = T108 2MVin, P where: - w is the sample size, - M is the molecular weight, -

-

T is the temperature,

P is the pressure (mm Hg),

ynnis the volume between the inflexion points of the peak.

421

We observe that the maximum concentration is the same with all three carrier gases, but the noise level is different, and so is the dynamic linear range. In most cases a dynamic linear range of the order of 10,000 can be expected.

7. Detector Stability. Noise As can be seen on Figure 10.3, the carrier gas and the reference gas streams merge orthogonally. Although these gas streams are laminar, the interaction between them generates stationary waves which is the origin of most of the noise. The larger the ratio of the column flow rate to the reference flow rate, the larger this effect and the larger the noise. Since the optimum reference flow rate decreases rapidly with increasing reference gas molecular weight, much more rapidly than the column optimum flow rate (see Table lO.l), the noise will be larger with the denser gases, for which the ratio of the two flow rates tends to be close to 1 (see Table 10.2). For example, with sulfur hexafluoride, the noise level decreases markedly when the carrier gas flow rate is decreased from 4 L/hour to 0.4 L/hour (column optimum flow rate), as illustrated by Figure 10.8. The reference gas flow rate is 1.3 L/hour. The ratios of reference to measurement flow rates are 0.325 and 3.25, respectively. With hydrogen, however, the reference flow rate has to be 44 L/hour, while the column flow rate is 10 times smaller. The GDB is sensitive to vibrations, which generate noise. Pressure fluctuations also create noise and drift. A “muffler”, a series of pneumatic capacitors (tubes, i.d. cu 3 cm, length 20 cm) and resistors (tubes, i.d. ca 1 mm, length 20 cm) effectively protects against pressure variations due to people traffic in and out the laboratory and around the GDB.

Figure 10.8. Influence of the flow rates in the two gas channels on the noise of the GDB (28). (Reprinted from Journal of Gas Chromatography, 4, 338 (1966).)

References on p. 411.

422

8. Prediction of the Response Factors The relative response factors of the GDB are predictable with great accuracy. This is the only such detector available in gas chromatography, which explains why we consider it to be very important. Its use permits rapid and precise calibration of other detectors. The composition of mixtures can be derived safely from chromatograms, with simple calculation procedures such as corrected area normalization, the use of which is dangerous with other detectors. The precision achieved is of the order of 1%,a figure which depends essentially on the precision of area determination (see Chapter 14). Data in Table 10.3 show results obtained in the calibration of binary and ternary mixtures, using different carrier gases. The average deviation is 0.6%. 9. Maintenance and Cost

One of the main drawbacks of the GDB, besides its rather poor detection limits, is the large amount of gas required to operate it. Not mentioning sulfur hexafluoride, with helium and hydrogen the flow rates required are one order of magnitude larger than those required to operate a TCD. This is costly on the long run and explains why the detector is not widely used. On the other hand, the use of the GDB permits a drastic reduction of the cost of calibrations, which may be performed much more rapidly, with only the pure products, without preparing calibration mixtures (see Chapter 14). TABLE 10.3 Accuracy of a Gas Density Balance (28) Carrier Gas

Analyte

Sample Composition

Response Factor

Measured Concentration **

Error

co2

1,l-Dichloroethane Trichloromethane 1,2-Dichloroethane

5.47 24.25 70.28

1.80 1.58 1.80

5.42 24.52 70.06

0.90 1.10 0.30

SF,

1,l-Dichloroethane Trichloromethane 1,2-Dichloroethane

5.47 24.25 70.28

2.10 4.50 2.10

5.48 23.84 70.68

0.20 1.70 0.60

He

Dichlorodifluoromethane (CCl 2F2) Dichlorotetrafluoroethane (C2CI F4)

11.15

1.03

11.21

0.55

88.85

1.02

88.79

0.07

42.30

1.014

42.66

0.85

57.70

1.011

57.33

0.65

H2

Trichlorofluoromethane (CC1,F) Dichlorotetrafluoroethane (C2C12F4)

*

Composition of the calibration mixtures, w/w (%).

** Average of 3 determinations. *** Difference between measured and true value.

*

Sampling by continuous vaporization of the liquid sample (see Chapter 13). (Reprinted from Journal of Gas Chromatography, 4, 338 (1966).)

***

423

111.

THE THERMAL CONDUCTIVITY DETECTOR

The thermal conductivity detector (TCD) was introduced as a sensor of the composition of a gas stream by Shakespeare in 1921 (33). It was used as a detector for gas chromatography very early and permitted the first series of major developments in this area. Although it has long lost the position of most prominent detector to the FID, it remains important for the analysis of gases, to which the FID does not respond, of simple mixtures, which do not require the use of open tubular column for their separation nor great detection sensitivity, and for many industrial applications, for safety reasons. 1. Detector Principle

The principle is based on the variation of the thermal conductivity of a mixture with its composition. If a resistor is heated by a current and cooled by a gas stream passing by, the equilibrium temperature depends on the composition of the gas. The resistance of the resistor, in turn, depends on its temperature. The variations of this resistance are easy to record. The schematic of a TCD cell is shown on Figure 10.9. A metal block contains a number (2 or 4, usually) of cavities, or cells, which are swept by the carrier gas. Each contains a sensing element, either a wire (Figure 10.9) or a thermistor. The resistors are connected to form a Wheatstone bridge, so that 1 or 2 cells each form a diagonal of the bridge. The cell(s) in one diagonal are swept by pure carrier gas, either upstream of the sampling device, or in a parallel, auxiliary stream (see Figure 10.10). The other cell(s) are swept by the column eluent. At the beginning of the analysis the bridge is equilibrated. The elution of a vapor out of the column results in a change of the thermal conductivity of the gas mixture, a variation of the corresponding resistance and a disequilibrium of the bridge. The current recorded is a measure of the concentration of the vapor in the eluent.

Figure 10.9. Schematics of a thermal conductivity cell.

References on p. 477.

424

This measurement procedure permits the automatic correction for drifts resulting from the variations of the gas flow rate, the change in the block temperature, etc. The response of the TCD has been actively studied since the beginning of gas chromatography (33-39). The response observed is a combination of effects, due to heat conduction and heat convection, which are difficult to account for accurately. Thus, the response of the detector cannot be completely predicted. The energy flux generated by electric current in the resistor must be equal, at equilibrium, to the energy flux lost by thermal conductivity: I ~ R

9 = - =J

W T W -

T,)

where: - I is the bridge current, - R is the resistance of the thermal sensor, - J is Joule constant, - h is the thermal conductivity of the gas mixture, - G is a geometrical constant, - Tw and T, are the temperatures of of the wire and the cell, respectively.

Figure 10.10. Schematics of the Wheatstone bridge of a TCD. a - Attenuation of the signal. b - Connection to recorder or integrator. c - Galvanometer. d - Control of the bridge current. e - Voltage supply. R1,R2 - Reference cells. R3, R4 - Measure cells.

425

The geometrical constant can be calculated by integration only for very simple cell designs. For a linear wire in the center of a cylindrical tube, neglecting the end effects, we have:

where: - L is the wire length, - rc and r, are the radii of the cell and the wire, respectively. Dal Nogare and Juvet (35) have derived an equation relating the detector response to its parameters:

where: - I/ is the detector output voltage, - a is the thermal coefficient of the

resistance of the sensing element,

- E is the bridge voltage, R , is the resistance of the sensing element at 0 ° C X is the mole fraction of analyte in the carrier gas, A, and A, are the thermal conductivity of the analyte and carrier gas, respectively. Finally, Littlewood (39) has derived a more complete and complex equation relating the response factor to the molecular parameters of the camer gas and the analyte: -

where: - ug and ua are the molecular diameters of the carrier gas and the analyte, respectively ( ug,, = ( ug u,)/2). - M, is the molecular weight of the analyte, - R , and R, are the resistances of the two sensing elements in a two cell TCD. The first term in equation 31 accounts for the variation of the thermal conductivity with composition of the vapor. It is valid only if the molecular weight of the analyte is much larger than that of the camer gas (e.g., with He carrier gas). The second term of equation 31 accounts for the variation of the temperature of the resistor with the thermal conductivity of the gas contained in the detector cell. The third term accounts for the variation of the resistance of the sensing element with its temperature and the fourth term accounts for the relationship between the bridge output voltage and the change in the resistance.

+

References on p. 411.

426

Equation 31 has been studied in detail by Goedert and Guiochon (19) during their investigation of the sources of errors in the measurement of sample composition with a thermal conductivity detector. Although a general agreement has been found, some discrepancies remain. They may be due to the fact that the TCD does not respond uniquely to changes in the thermal conductivity of the column eluent. There are also energy losses from the sensing element due to heat convection, which depends on the density of the gas.

2. Parameters Affecting the Response The nature and the flow rate of carrier gas can easily be changed and adjusted by the analyst. The nature of the sensing elements can also be changed, although this cannot be a frequent operation. The design of the detector, and its geometry are forced upon him by the manufacturer. a. Nature of the Carrier Gas For proper performance, the thermal conductivity of the camer gas should be very different from that of the analytes. Table 10.4 gives values of the thermal conductivities of some gases and vapors. Hydrogen and helium, which have a thermal conductivity much larger than that of most vapors, are preferred. With gases like nitrogen or argon, which are sometimes used, poor results are often obtained. The differences between the thermal conductivities of the carrier gas and the analytes are small, the detector responses are low and the detection limits TABLE 10.4 Thermal Conductivity of Gases and Vapors Gas or Vapor

x

Hydrogen Helium Methane Ammonia Air Nitrogen Ethane Acetylene Propane +Butane Methanol n-Pentane Carbon Dioxide Ethanol n-Hexane Acetone Chloromethane Trichloromethane

7.1 5.53 1.45 1.04 1 0.996 0.97 0.9 0.832 0.744 0.127 0.702 0.7 0.7

0.662 0.557 0.53 0.328

Relative to the Thermal Conductivity of air. Handbook of Chemistry and Physics, CRC, Cleveland. OH.

421

high. Furthermore, there are vapors which have a thermal conductivity larger than that of nitrogen or argon, while others have a lower thermal conductivity and still others have the same thermal conductivity. These last compounds are not detected. The others gve either positive or negative peaks. It is unpleasant to have to record peaks detected on both sides of the base line. Complex chromatograms become very difficult to understand, especially when some bands are incompletely resolved (41-47). Finally, it has been reported that sometimes with argon and rather frequently with nitrogen, the thermal conductivity of the mixture of carrier gas and analyte vapor does not vary linearly with its composition. There are even maxima in the plot of the thermal conductivity of the gas mixture versus its composition. In such a case doublets are recorded when pure compounds are eluted (36,41). Such “M” shaped peaks are a serious source of difficulty in quantitative analysis, since the peak area does not represent the amount of analyte (42). They are avoided by using helium or hydrogen as carrier gas, except for the analysis of one of these gases, in which case argon or nitrogen should be used. In practice, helium is often preferred as being less dangerous, but it is also more expensive. Some artefacts have been blamed on the catalytic hydrogenation of analytes on the TCD wires, which would be another reason to prefer helium. b. Carrier Gas Flow Rate

The TCD can work over a large range of carrier gas flow rates, especially if the detector design is symmetrical. The detector being a concentration detector, the peak area is proportional to the inverse of the carrier gas flow rate. This relationship postulated by Keulemans et al. (48) has been established experimentally by Net0 et al. (49) and Guiochon (13) and demonstrated theoretically by Halasz (12) and by Guiochon (13). Usually the flow rate will be selected to be equal or slightly larger than the optimum column flow rate, to provide maximum sensitivity.

c. Nature of the Sensors There are two kinds of sensing elements commonly used in the TCD, metallic wires or thermistors (ceramic beads). The resistance of the former increases linearly with increasing temperature. The resistance of the latter decreases exponentially with increasing temperature. Accordingly, a given detector using thermistors can be used in a much narrower temperature range than a wire detector. When the resistance of the thermistor has been reduced by an order of magnitude, the sensitivity of the device becomes too low. Wires can be in about any shape, but spirally coiled wires are by far the most popular: they provide the proper resistance and can be placed in a very small cell. Wires for TCD have been made out of platinum, tungsten, rhenium, nickel, tungsten-rhenium alloy, golden tungsten or Teflon-clad tungsten, for some special applications. Oxidation is the main limitation to a long wire life and, for this reason, traces of oxygen or oxidizing vapors should be avoided in the camer gas. The bridge References on p. 411.

428

Figure 10.11. Plot of the current in the TCD bridge as a function of the wire temperature, for different carrier gases (38). (Reprinted from Journal of Gus Chromutogruphy, 4, 273 (1966).)

voltage should always be switched off before the flow of carrier gas to the chromatograph is stopped. Otherwise back diffusion of air will provide rapid destruction of the wires. The sensing elements are incorporated in a Wheatstone bridge as illustrated in Figure 10.11. The higher the symmetry of the block design the better. This will smooth the temperature gradient in the detector block and reduce base line drifts. The temperature of the detector is usually maintained about equal to that of the column, to avoid condensation of the vapors of high boiling analytes in the detector. The temperature of the detector block and of the wires should not be excessive, however. Otherwise noise and drift could result from the pyrolysis, polymerization or polycondensation of analytes on the wires, or from the presence of coatings of pyrolysis or condensation products. An efficient cleaning procedure for TCDs is described below, Section 111.8. Thermistors are metal oxide beads or ceramics which have a strong negative temperature coefficient for their resistance. They are extremely small, a fraction of a millimeter in diameter, and permit the design of extremely small TCD, with very small cell volumes, which can be used with open tubular columns. The variation of resistance with temperature is strongly non-linear, which creates serious difficulties in quantitative analysis, because the detector is linear in only a very narrow sample size or concentration range, and results are very difficult to correct for. Quantitative analysis carried out with a wire TCD can be quite accurate. Quantitative analysis carried out with a thermistor TCD is rarely accurate at all. d. Intensity of the Bridge Current This is in practice the most important of the parameters of the TCD that the analyst may control. The bridge current determines the temperature of the sensing

429

element and the energy flux sent to the detector block. The temperature of the sensing element must be very stable, so the bridge voltage must be carefully controlled. Goedert and Guiochon (19) have found that the error propagation coefficient for the bridge voltage is 3.5, a value somewhat exceeding the one predicted by equation 31 (i.e., 3). Since the bridge current determines the energy flux generated by the sensing element, it will be larger with helium as carrier gas than with nitrogen since, the thermal conductivity of the former gas being larger, it permits the achievement of the same wire temperature while generating a larger amount of energy. Equation 31 shows that the response is proportional to the bridge voltage &d to the square of the bridge current (see Figure 10.11). This in agreement with the results of Mellor (50), but Harvey and Morgan (51) have reported a multiplication of the response by a factor 5.7 when the current is doubled, while Goedert and Guiochon (19) have found the signal to increase as the 3.5 power of the bridge voltage. Equation 31 predicts a power of 3. Since the bridge current is proportional to the bridge voltage, these last two results are in fair agreement. e. Internal Geometry of the Channels A large number of geometrical designs have been experimented with for the thermal conductivity detector. This work has been driven by the search for a good compromise between a short response time and a low noise level. The noise of a TCD results in large part from the interaction between the wire and eddies in the turbulent gas flow sweeping the wires. These eddies result in unstable heat losses, hence temperature, of the sensor resistance. TCDs can be arranged in three different classes: - direct flow cells, - semi-diffusion cells, - diffusion cells. Only direct flow and semi-diffusion cells are used with analytical gas chromatographs (see Figure 10.12 schematics of these cells). Diffusion cells, which can easily accommodate huge flow rates and very large vapor concentrations have been used essentially with preparative chromatographs. The direct flow cells have very short response times but are noisy, while semi-diffusion cells have a longer response time and are much more stable. The progressive development of the instrument industry and the coming of new generations of controllers have permitted considerable improvements to the stability of the temperature of the detectors and of the carrier gas flow rate, resulting in a wider use of direct flow cells. Originally used only on laboratory instruments, direct flow cells tend now to replace semi-diffusion cells on process control equipment, which has to carry out measurements under less stable environmental conditions. Systematic studies (52) on the response factors of direct flow and semi-diffusion cells have demonstrated significant differences between multicell TCDs having their cells placed in parallel or in series (see Figure 10.12). The geometrical constant in equation 30, as well as the response factor given by equation 31, assume that the detector sees the whole amount of analyte injected References on p. 411.

430

:j I; b

I

1

A Figure 10.12. Geometric design of commerciallyavailable TCDs (by permission of Carlo Erba, Gow Mac and Bendix). A - Semi-diffusion, parallel cells. B - Semi-diffusion, serial cells. C - Semi-diffusion, serial cells. D - Flow-through, parallel cells. E - Flow-through, serial cells.

with the sample and separated from the other components by the column. This is approximately true only with direct flow cells placed in series. With all other geometrical designs, part of the sample is not seen by the detector. The flux of analyte towards the sensor is given by the following equation:

where: - N2 is the number of moles of analyte, - D2,1is the diffusion coefficient of the analyte in the pure carrier gas, - P (= p1 + p 2 ) is the total pressure, - p l and p 2 are the partial pressures of the carrier gas and the analyte, respectively, - e is the distance along the cell, from the port connecting it to the carrier gas stream. The flux of analyte towards the sensing element is very fast in the case of a series of direct flow cells. It is slower in the case of a semi-diffusion cell. The diffusion of analyte into the cell is fast when the peak begins to elute, because the concentration

431

gradient (dp,/dz) is large and increasing. It becomes slower and slower when the peak is going, because the analyte concentration in the mobile phase is small and getting smaller and the distance over which diffusion takes place is long. Thus, the phenomenon produces a decreased response and a tailing peak. The response factors decrease in the following order: serial flow-through cells, parallel flow-through cells, serial semi-diffusion cells, parallel semi-diffusion cells. This is in agreement with the values of the response factors given in Chapter 15 for the different TCD cells. The smallest values of the response factors (largest area per unit sample amount) are obtained with the flow through serial cells and the greatest for the parallel semi-diffusion cells. The difference between the extreme values of the response factors of detectors of different geometrical designs for the same compounds is 18%.The difference between the response factors of designs C, D and E (see Figure 10.12) is only 6%. Consequently, the response factors, must be measured for each new detector design. Tabulated response factors, even relative response factors, are of limited interest. Further studies of the response factor of the TCD and its relationship with various design parameters are discussed in Chapter 15. 3. Classification

The TCD is a typical concentration detector, as has been demonstrated by various studies (12,13,50). The peak area is inversely proportional to the flow rate (see Section 1.l.a). 4. Selectivity

The TCD is a very weakly selective detector. The response is proportional to the difference between the molar thermal conductivity of the carrier gas and the partial molar thermal conductivity of the analyte at infinite dilution. As a first approximation, this difference can often be replaced by the difference between the thermal conductivity of the carrier gas and the pure analyte vapor. For camer gases such as hydrogen or helium, and organic vapors, this relationship is reasonably accurate. The thermal conductivities of most organic vapors being comparable, the relative response factors are close to unity. Calibration is necessary, however, because thermal conductivities of analytes are too different from each other. With carrier gases such as nitrogen or argon, or for gases with comparable thermal conductivities, such as hydrogen or neon analytes in helium carrier gas, the partial molar thermal conductivity of the analyte at infinite dilution is too different from the thermal conductivity of the pure vapor, and the relative response factors can be quite different from unity. Also, as noted above, the partial molar thermal conductivity varies rapidly with concentration, even at very low concentrations, resulting in response factors changing markedly with concentration and in strongly distorted band profiles. References on p. 411.

432

5. Sensitivity In optimal conditions, with hydrogen used as carrier gas and a rather high bridge current, the TCD is about 10 times more sensitive than the GDB and the detection limit is of the order of 30 ppm in a sample. In favorable cases it can be below 10 PPm. The main sources of base line instability, either noise or drift, are: - the temperature fluctuations of the cells. The detector temperature must be controlled very carefully. The response of the detector is a measure of the change in the temperature of the sensing element, and any temperature fluctuation will appear as a noise or a drift. - the temperature fluctuations of the sensing elements. For the same reason, the temperature of the sensors must be very stable, which requires the use of a highly stable voltage supply. - interaction between the carrier gas stream and the sensors. Turbulence of the gas flow, due to the use of too large a gas flow rate, results in the appearance of a strong base line noise. - mechanical vibrations. The transmission of mechanical vibrations from other instruments on the same bench or from the oven fan must be avoided by using proper dampening. In some cases, insulation of the detector from the rapid temperature fluctuations of an air bath and from mechanical vibrations have reduced the noise level by one order of magnitude. The problems associated with the determination of the response factors of different TCDs, having various internal geometries, and their stability are discussed in Chapter 14 (Sections 111.2 and 111.4), with emphasis on accuracy and precision of quantitative analysis. 6. Linearity

The linear dynamic range of the TCD is of the order of lo4, which is rather reasonable for a gas chromatography detector. Deviations from linear response may come either from a non-linear relationship between the thermal conductivity of the mixture of carrier gas and analyte vapor and its composition, or from the increasing contribution of other sources of thermal losses of the sensing element when the thermal conductivity of the gas in the cell decreases and the temperature of the sensor increases. Heat conductivity through the electrical insulator of the sensors may be important.

7. Prediction of the Response Factors Several methods have been used to obtain an estimate of the relative response factors. The theoretical study of heat transfer shows that the relationship between the thermal conductivity of a vapor and its other molecular properties is complex and that it is not possible to predict this parameter accurately. It is not even possible to predict simply the thermal conductivity of a gas mixture, knowing that

433

of its pure components. Empirical relationships have been used, with limited success. Calibration with authentic compounds is more accurate and reliable than the use of predicted response factors. a. Theoretical Background

The prediction of the thermal conductivity of gases and vapors has been one of the favorite topics of the kinetic theory of gases (55). It has proved to be more challenging than the prediction of heat capacity and viscosity, which are related parameters. Even for monatomic gases, the only prediction of the molecular kinetic theory of gases which is born out by experimental results is the independence of the thermal conductivity of the pressure (55). This result still holds for polyatomic gases at low pressures (up to a few atmospheres). The Chapman-Enskog theory accurately predicts the thermal conductivity of monatomic gases. For polyatomic gases, an equation due to Eucken gives an estimate of the thermal conductivity: k = (C,+ g)q

(33)

where: - Cp is the molar thermal capacity of the gas under constant pressure, - R is the universal ideal gas constant, - M is the molecular weight of the gas, - I) is the viscosity of the gas. Although the error is only 3% for oxygen, it is already 20% for steam (55). The use of equation 33 is certainly not recommended for the prediction of the thermal conductivity of complex organic vapors, the molecules of which may have a large number of internal degrees of freedom. A more accurate method for polyatomic and polar gases has been suggested (56). Its use is difficult and requires the knowledge of other physico-chemical properties of the vapor, which are rarely available for the analytes a chromatographer has to work with. Relating the thermal conductivity to the viscosity and the viscosity to the collision function and the parameters of the Lennard-Jones potential for the vapor is very satisfying for. the physical chemist but of little practical value to the analyst. The kinetic theory of gases has also permitted the derivation of a relationship between the thermal conductivity of a mixture, that of the pure components and the composition of the mixture (5537). We report the equation here only to show that a linear relationship should not be expected. n

kmix=C j=l

xiki n

Cxjqj

(34)

j=1

References on p. 477.

434

where the x i (and x i ) are the mole fraction of the components of the mixture, and k i the thermal conductivity of the pure components. aj, are given by:

where: - q is the viscosity of the vapor - M is its molecular weight.

of the corresponding compound,

Equation 35 shows that the thermal conductivity of a binary mixture cannot be expected to vary linearly with its concentration, except at very low concentrations. Furthermore, even in this concentration range, the response factor is not the difference between the two thermal conductivities. For a binary mixture of carrier gas ( 8 ) and analyte ( a ) , with a very small concentration of analyte, equation 34 becomes:

This equation explains why a direct attempt at predicting the response or relative response factors will fail: we know neither the thermal conductivity nor the viscosity of the analytes we have to work with. b. First Empirical Method

The first attempt at predicting response factors empirically consists in assuming that the relative response factors are equal to unity. Since the thermal conductivity of hydrogen or helium is an order of magnitude higher than that of organic vapors, this should give at least a reasonable approximation. It turns out that this approximation is fairly good. Calculations of the composition of authentic mixtures by area normalization, on a weight basis, gives results which rarely deviate from the true composition by more than 15 to 20% (14,53,54). Calculations made on a molar basis are less accurate (53). This method fails completely when nitrogen or argon are used as carrier gases. Other approaches have to be used, but there is little reason to use these gases in gas chromatographic analysis. c. Second Empirical Method A method for the calculation of relative molar responses ( R M R ) has been derived by Messner et al. (58), following the work by Rosie and Grob (59) on the response of the TCD for homologous series. The RMR of the members of an homologous series relative to benzene is given by:

RMR = A

+ BM

(37)

435

TABLE 10.5 Determination of the Relative Molar Response of a TCD Analyte

Range

A

B

Alkanes Alkanes Methylalkanes Dimethylalkanes Trimethylalkanes l-Olefins Methylbenzenes Mono-n-alkylbenzenes Mono-sec-alkylbenzenes Ketones Primary Alcohols Secondary Alcohols Tertiary Alcohols n-Alkyl Acetates n-Alkyl Ethers

C1-C3 C3-C10 c4-c7 c5-c7 C7-C8 C2-C4 c7-c9 c7-c9 C9-C10 C3-C8 C2-C7 c3-c5 c4-c5 C2-C7 C4-C10

20.6 6.7 10.8 13.0 13.9 13.0 9.7 17.9 18.1 35.9 34.9 33.6 34.9 37.1 43.3

1.04 1.35 1.25 1.20 1.16 1.20 1.16 1.06 1.04 0.861

0.808 0.857

0.808 0.841 0.886

Range of homologous compounds used for the determination of the coefficients A and B (58). (Reproduced from Anulyrical Chemistry, 31, 230 (1959).)

where A and B are numerical coefficients and M the molecular weight of the compound. Values of A and B for a number of homologous series are given in Table 10.5. They permit the calculation of the response factor of the members of these series relative to benzene (RMR = loo), in helium carrier gas. The response factors obtained are constant over a large range of values of the flow rate (58). The relative response factors with hydrogen can be assumed to be equal to those with helium (58). Gassiot-Matas and Condal-Bosch (60) have shown, however, that a better result is obtained by using the following conversion: RMR(H,)

= 0.86RMR(He)

+ 14

A large number of experimental results have been published by Dietz (61) and permit the calculation of RMR or R WR (relative weight response). The conversion of one to the other is given by:

R WR

= RMR/M

(39)

Some excellent results have been reported (62) in the use of the data published by Messner et al. (58), but there are sometimes important differences between the RMR predicted from their data and experimental values (63,64). There are two reasons which may explain these differences. First, the results have been obtained using the instrumentation available at the time. Peak areas have been obtained by manual integration (see Chapter 15). The errors are much more important than those made using modern methods (see Chapters 15 and 16). The constants A and B (Table 10.5) should be determined again, with better accuracy and precision. References on p. 477.

436

Furthermore, we have shown that there are significative differences between responses obtained with different TCDs, depending on their geometrical design. The data published (58) do not mention the detector design. They can be expected to be very good with some detectors, much less so with others. Finally, the precision which can be expected from these predicted response factors is not much better than the one obtained on the simple assumption that the factors are equal to unity. They may be between 10 and 15%.

d. Third Method This method has been rarely used. It was originally suggested by Littlewood (65) and has been studied in detail by Barry and Rosie (66-68). The R M R is determined from parameters related to the molecular structure:

[

aa+ ag

RMR=100 ‘biag]

[

Ma- Mg

‘I4

Mb-Mg]

where IJ is the molecular diameter and the subscripts a, g and b stand for the analyte, the carrier gas and benzene, the reference, respectively. Although a good agreement between predicted and measured relative response factors was observed, the method is of little practical use. The accuracy depends on the accuracy of the molecular diameters which depends considerably on the source consulted, and only very few molecular diameters are available in the scientific literature. 8. Maintenance and Cost

The TCD is simple, its cost is low and little maintenance is required. Wires have to be changed periodically, which is easy. Wire life can be extended by following some simple rules: - The carrier gas should always sweep the detector when the power is on. The power must be switched off before the gas valves are closed. - Traces of oxygen in the carrier gas should be carefully eliminated (see Chapter 9). We have found the following cleaning procedure for the detector wires and cells to be very efficient and harmless to the sensors. The column is replaced by an empty metal tube of comparable diameter and length. Tube and detector are heated to cu 200OC. A large volume syringe (10 mL) is used to inject water as a continuous stream. The steam and the water droplets vaporizing on the metal surface by calefaction tear off deposits of pyrolyzed or polymerized organic stuff from the detector cell walls and the wires. The rate of water injection must be adjusted to achieve proper cleaning without harming the wires.

437

IV. THE FLAME IONIZATION DETEmOR The flame ionization detector (FID) has been the most popular detector for gas chromatography during the last fifteen years and nothing suggests that this position will ever be challenged. The reasons for this preference come from the high sensitivity, the linearity and the reliability of this very simple detector. Although the circumstances surrounding the origin of the FID have been controversial at times, it is now recognized that it was invented by McWilliam (69,70), following some pioneering work by Harley and Pretorius (71) and Ryce and Bryce (72). The serendipitious effect of the simultaneous discovery and implementation of the open tubular columns by Golay (see Chapter 8) and the FID by McWilliams in 1958 has been crucial to the rapid development of gas chromatography. Should we have to teach gas chromatography to an intelligent being on a different planet, it would probably suffice to send the references 1 and 70 of this chapter and reference 1 of Chapter 8. 1. Detector Principle

The combustion of hydrogen and of a few other gases (NH,, CO) gives no or practically no ions (73). The combustion of organic compounds gives a small number of ions (a few ions per million molecules). These ions can be collected with an appropriate electrical field and the current measured. In practice, all that is necessary is a burner (called a jet), fed with a mixture of hydrogen and carrier gas, at constant flow rate, and surrounded by electrodes (see Figure 10.13). The column effluent is mixed with the hydrogen just upstream of the jet. The jet is placed in an enclosed box, to protect the flame from drafts. Air (generally preferred to oxygen, for the sake of simplicity) arrives concentrically at the burner, through a sintered metal disk, which provides a laminar flow around the flame (flow turbulences produce noise). An electrical field is applied either between two parallel electrodes placed on both sides of the flame or between the jet and a

C

Figure 10.13. Schematics of the Flame Ionization Detector.

References on p. 477.

438

collecting electrode made of a ring or a cylindrical mesh, surrounding the flame. The FID uses a diffusion flame with which the current produced is higher than with a premixed flame. The mechanism of the formation of the ions collected is still controversial and open to speculation. This is related to the fact that the combustion of organic vapors gives a very small number of ions: a few ions per million molecules burned (see below, Sections IV.2 and IV.7). The sensitivity of the detector results from the near absence of other charge carriers in the flame and from the ease with which the few ions formed can be collected and counted with little noise resulting from the detector electronics. The formation of ions in flames is a phenomenon known long before GC was invented (74), and used in the design of flame sensors. Stern (74) suggested for the origin of these ions the thermal ionization of small graphite particles or carbon aggregates, whose work function is compatible with the order of magnitude of the current collected. The formation of carbon aggregates under the conditions of the FID, in a very lean flame, is impossible, however. Furthermore, the ions are not formed in the hotter part of the flame, nor is the current collected from the very hot flame of carbon disulfide very large (75). Accordingly, Calcotte (75,76) suggested that the formation of ions results from chemi-ionization: the energy released in some strongly exothermic reaction steps is retained by one of the fragments as internal vibrational energy and results in the decomposition of the fragment into ions before random thermalization has time to occur. The ionization process would thus be a first order reaction, which explains the linear response of the FID, and the ionization mechanism would be placed in a low probability reaction pathway, which would explain the low ion yield. A thorough discussion by Lovelock et al. (77) concludes in the same way, and all experimental results obtained so far have agreed with these conclusions. However, the exact nature of the reaction step leading to the formation of ion fragments has long eluded our understanding. A very detailed study of the response of the FID made by Sternberg et al. (78) has brought definite proof of the chemi-ionization mechanism and suggested a possible mechanism. Some more recent publications (79-81) have complemented their conclusions which remain nevertheless totally valid. The oxidation mechanism of organic vapors in an air flame can be briefly summarized as follows (see Figure 10.14): - Zone A . In the jet, the carrier gas and the hydrogen are mixed by diffusion. - Zone B. The pyrolysis reactions begin slowly. Methane and possibly free radicals CH, are formed by cracking in a hydrogen rich atmosphere, in an almost quantitative way. - Zone C. The center of the flame is hot (1,500 to 2,000 K) and contains no oxygen at all. Pyrolysis reactions take place rapidly, giving free radicals CH, CH, and CH,, in their ground state. - Zone D. Chemical ionization would take place there, between CH free radicals in the ground state and atomic oxygen or excited molecules of oxygen, following: CH + O* + CHO+ + e-

(41)

439

t F

A

A

L

I

I

1000

diffusion flame

I

2000

OC-

Figure 10.14. The different zones in a diffusion flame (78.84). See text for explanations.

The ions formed would react immediately with water to gve: CHO++ H,O

+

H,O++ CO

(42)

The rate constant for reaction 41 is much lower than for the other reactions of CH, with oxygen for example, and for other channels of the CH/O reaction. The fate of CH radicals in the flame depends on other reactions than 40 and the ionization yield is very low. - Zone E . This zone is very rich in oxygen. Complete combustion of carbon and CO into CO, and of H into H,O takes place rapidly. - Zone F. This is the zone where the combustion products diffuse into air and cool down. Recently, Cool and Tjossen (82) have shown that the rate constants for the chemi-ionization reactions:

+

CH( A 2 A ) 0 + CHO+

+ e-

(43)

and: CH( B ’ X )

+0

+

CHO+

+ e-

(44)

are approximately 2,000 times larger than the rate constant for reaction 41 in the temperature range where the FID operates (ca 2,000 K). A pulsed tunable dye laser was used to saturate the transitions CH A + X or CH B + X and establish References on p. 477.

substantial populations of the excited species in lean methane flames. The enhancement of the electrical current measured constitutes both a demonstration of the validity of the mechanism of formation of ions in the FID postulated by Sternberg et al. (78), and the first workable idea which may possibly help one day to improve considerably the response of the FID. In conclusion, the response of the FID to various analytes will depend on their ability to give CH(X) free radicals during their combustion. All the alkyl carbons have nearly the same probability to react in this way. Partially oxidized carbon atoms, such as those belonging to carbonyls, carboxylic acids, or nitriles have a very low or negligible probability. Carbon atoms bound to a chlorine atom, a hydroxyl or an amine group have an intermediate probability. We understand how it might be possible to build a table of increment contributions to the response factor which will permit an approximate prediction of the relative response factors (see Section IV.7). 2. Parameters Affecting the Response

There are two types of parameter which determine the response of the FID, those which can be set by the analyst, essentially the flow rates of the gases (79-81,83,84), and those which are chosen by the manufacturers (geometrical design, polarization of the electrodes) (69-77,85,86). a. Temperature of the Flame

The mechanism of the response of the FID depends on chemical reactions taking place in a flame. Accordingly, parameters which affect the flame temperature may change the absolute or relative response factors. Those parameters which are accessible to the analyst are essentially the flow rates of the three gases, hydrogen, air and carrier gas. The geometrical design, such as the size, thickness and nature of the components of the detector, especially of the jet may also have some influence. 1. Hydrogen Flow Rate The detector response varies with the hydrogen flow rate (see Figure 10.15). The plot of the response versus the hydrogen flow rate has a maximum (83). The optimum hydrogen flow rate depends on the nature of the analyte (see Figure 10.15). It is larger for haloalkanes than for paraffins. This explains why it is not infrequent to observe the maximum of the response for a flow rate different from the one given by the manufacturer in the instrument manual. The difference may be important. In trace analysis it is recommended to optimize the flow rates for maximum response to the trace compound(s). Usually, the following set of flow rates gives good results, not too far from the optimum: - Hydrogen flow rate: 2 L/hour. - Carrier gas (nitrogen): 3 L/hour, for a 4 mm i.d. column. - Air: 15 L/hour.

441

I

1

I

I I

2. Air Flow Rate A large excess of air is recommended. This permits an easy elimination of the combustion products and the steam, the condensation of which should be avoided in the detector. Major damage resulting from corrosion would rapidly take place. Too large an air flow rate results in the appearance of eddies and turbulent flow in the detector case, resulting in excessive base line noise. In extreme cases, the flame could be blown out and extinguished. The results published (78) tend to show that the plot of the FID response versus the air flow rate is very flat beyond a flow rate of 15 L/hour (see Figure 10.16). The phenomenon is general, but the exact number depends on the geometrical design of the detector. FID designed for use with open tubular columns have narrower jets and usually require lower flow rates than those dez gned for conventional packed columns.

I n

AD" 0

0

He

H

30

20 30 40

o 60 A 90

a

rnl/rnin

u

1

I

I

0

200

400

Figure

I

GOO A i r rate,

I

800 /min

I 1000

ml 10.16. Plot of the response of a FID versus the flow rate of air (78). References on p. 477.

442

3. Carrier Gas Flow Rate An increase of the carrier gas flow rate must result in a certain decrease in the flame temperature. It is not sure, however, because of the complexity of the reaction pathway, in which direction the response will change if the flame temperature decreases. The prediction that an increase in carrier gas flow rate must result in a decrease of the response because of the dilution of the ions and the decrease of reaction rates is not entirely credible (84). Experimental results show that plots of detector response versus carrier gas flow rate exhibit a maximum at a flow rate and for a response which depend on the nature of the carrier gas (81). The variation of response around the maximum is slow, however, and the corresponding flow rate should be chosen. This may require an additional stream of make-up inert gas to the detector, to permit the separate optimization of the carrier gas flow rates through the column and the detector. The detector response is a complex function of all three flow rates. While the air flow rate should merely exceed a certain threshold value (around ca 15 L/hour for conventional detectors), the other two flow rates cannot be optimized separately. The optimum hydrogen flow rate is a function of the carrier gas flow rate used, and vice versa. The best way to optimize the flow rates in practice is to use a “Simplex” linear program approach (85) or one of its software implementations for personal computers (86). b. Polarization Voltage of the Collecting Electrodes

The collection of the ions formed during the combustion of the analyte must be complete. This requires a proper design of the shape of the electrodes and a sufficient electrical field between the electrodes. When the concentration of analyte increases in the camer gas to the jet, the number of charge carriers formed increases, the electrical field decreases and a space charge builds up around the collecting electrode. If this charge is too large or extends too far from the electrode, electrical leaks take place and the detector response is no longer linear. After experimenting with a variety of designs, manufacturers have almost all adopted a cylindrical electrode, in sheet metal or gauze, placed about 5 mm above the jet tip and negatively polarized, surrounding a grounded or positively polarized jet. An ignitor, a small wire which can be heated red hot with an appropriate current, is placed just below the flame and permits an easy start-up. The electrical circuit is closed with a high impedance resistor, of the order of 1 Tohm (1 10l2 ohm). The background current of the FID is of the order of 0.1 nA and the base line noise around 0.1 pA (87). A current of 0.1 nA through a 1 Tohm resistor generates a 100 V voltage drop. The polarization voltage should exceed this value for good dynamic linear range. Many authors have studied the influence of the polarization voltage (83,84,87-91), of the distance between electrode and jet tip (83,88) and of the geometry of the electrodes (88,91) on the detector response. Since the collection yield depends on the electrical field, and thus only indirectly on the voltage, and on the geometrical design, it is not surprising that the conclusions are somewhat contradictory.

-

443

Figure 10.17. Plot of the current of a flame ionization detector versus the polarization voltage (84). Below 90 volts the proportion of ions collected increases with the voltage. It reaches 100% around 90 V for this particular detector. Between 90 and 300 V, all the ions are collected and the current is constant. Above 300 V, collisions between accelerated primary ions and neutral molecules in the detector generate secondary ions and the current increases exponentially.

For an ionization detector, the plot of the current versus the voltage is typically as shown on Figure 10.17 (77). When the voltage is such that the ions formed are entirely collected, the response is constant (see the plateau on the curve, Figure 10.17). If the voltage is lower than a certain threshold, part of the ions escape uncollected. If the voltage is higher than a certain limit, the energy of the ions, accelerated in the electrical field, becomes large enough to ionize neutral molecules when collisions take place. These secondary ions are accelerated and collected, hence the exponential rise of the response. For maximum dynamic linear range, the voltage of a FID should be selected to be close to the limit above which secondary ions are formed. When the analyte amount is small, all the ions are collected and no secondary ions are made. When the analyte concentration increases, the effective polarization voltage decreases, because of the ohmic loss in the huge load resistor. For example, Bruderreck et al. (87) experienced non-linear behavior of their FID under conditions when the polarization voltage is 225 V and the current 200 to 500 nA. With a load resistor of 1 Tohm, the voltage drop in the resistor would be 200 V at 0.2 pA. It is not surprising that a current larger than cu 0.5 pA cannot be measured. Finally, the response time of the detector is given by the product RC of the load resistance by the input circuit capacity. To achieve a 10 msec response time with a 1 Tohm input resistance requires a very small capacity. 3. Classification

The FID is the typical mass flow detector (12). The signal results from the oxidation of the analyte which is destroyed. A number of ions are formed during the References on p. 477.

444

process. They are collected. The intensity of the current is proportional to the mass flow of analyte to the detector. The response depends only weakly on the carrier gas flow rate, at least around the optimum. 4. Selectivity

The FID is a selective detector, but as it is selective for organic molecules, and as its response is of the same order of magnitude for practically all organic compounds, it is traditionally considered as a highly non-selective detector. The FID responds to all organic compounds, with only an extremely small number of exceptions, for very simple carbon compounds: there is no response for carbon dioxide; there is practically no response for carbon monoxide, carbon disulfide, carbon oxysulfide (COS), formaldehyde, formic acid, formamide and hydrocyanic acid (HCN). The response for ketones, aldehydes and halogensubstituted compounds is smaller than for the corresponding alkanes having the same skeleton, but the difference decreases with increasing molecular weight. There is no response for almost all inorganic compounds, such as H,S, SO,, SO,, H,O, NH,, NO, NO,, N20,SiCl,, Cl,, HCl. 5. Sensitivity

The FID is an extremely sensitive detector. The detection limits depend very much on the chromatographic conditions used. Analyte mass flow rates as small as 1g/sec have been successfully detected (89). In practice, the detection limits for trace compounds are easily around a few ppb (concentration of trace component in the original sample). The noise depends to a large extent on the purity of the gases used. Thus, whereas it is typically around 0.5 pA when working under good conditions with conventional equipment, it can be reduced to less than 0.01 pA by using an adsorbent column and passing all gases (carrier gas, hydrogen, air) through a molecular sieve trap at low temperature. The design of good amplifiers (rather, impedance converters) for the FID is complex. The currents detected are large and the background must be compensated. The achievement of a small response time with the huge load resistance used requires extremely small capacity for the connection. This can be done by placing a preamplifier on the detector itself. Finally, the coupling with the mains supply is an important source of noise which must be eliminated. The advent of computers in the analytical laboratory has required the design of advanced electronics with lower noise levels in the 1-10 Hz range, which is one of the unsung feats of the chromatographic instrument industry. The problems associated with the determination of the response factors of the flame ionization detectors and the stability of their response are further discussed in Chapter 14 (see Sections 111.3 and 111.4), with emphasis on the precision and accuracy of quantitative analysis.

445

6. Linearity The FID is probably the chromatographic detector which has the widest dynamic linear range, in excess of 1 lo6 (87,90). In practice this would mean that it would be possible to carry out quantitative determinations by internal normalization of the corrected peak areas for the main component and a trace at the ppm level. This would not be prudent, however. The response of the FID may appear to be linear on a double logarithm plot (log of peak area versus log of sample size), but over such a huge range, minor deviations go unnoticed. Plots of the ratios of the peak area to the sample size (i.e. of the response factor) versus the logarithm of the sample size are more revealing. Oscillations take place which may be due to changes in the characteristics of the electronics with increasing current. The dynamic linear range can be increased only by reducing the noise, although it might be conceivable to increase the polarization voltage at high detector signal. The noise can be reduced by careful handling of the detector and its environment: - The stream of air in the detector shoud be laminar. All turbulences should be avoided. - The gases used must be very pure. They must be filtered over sintered metal frits to eliminate dust-generating spikes. Passing the gases over a bed of activated carbon or molecular sieves at low temperature may also markedly reduce the noise. The adsorbents in these beds must be regenerated from time to time. - The detector, and especially its jet, must be ultrasonically cleaned periodically. - Overly volatile stationary phases must be avoided. Combustion of the stationary phase vapor generates noise and drifts. Small changes in the carrier gas flow rate or in the column temperature result in very large drifts. - The air used must be carefully selected. If it is taken from the laboratory room it must be passed over an activated charcoal bed. Even so, the entrance of a smoker to the laboratory might be recorded by the gas chromatograph. If proper care is taken, it is not impossible to achieve a noise as small as 0.05 to 0.1 PA.

-

7. Prediction of the Response Factors The mechanism of the response of the FID being barely understood, and the rate constants of the reaction involved being largely unknown, it is impossible to predict the relative response factors. It is generally accepted, however, that for hydrocarbons the response is proportional to the number of carbon atoms in the molecule. It is about 20 mC/g of carbon for good detectors, with few ion leaks. Sternberg et al. (78) have calculated the contribution to the response of the various carbon atoms in a molecule, depending on the nature of their substitue'nts. Some substituents, atoms or groups of atoms, decrease the probability that the oxidation of the carbon atom involved results in the formation of an ion. Table 10.6 lists the contributions thus determined for a number of atoms to the response factor. References on p. 411.

446 TABLE 10.6 Atomic Increments for the Response to the FID (after ref. 78) Contribution (Effective Carbon Number)

Atom

Type

C C C C C C

Aliphatic Aromatic Olefinic Acetylenic Carbonyl Nitrile

0 0 0 0

Ether Primary Alcohol Secondary Alcohol Tertiary Alcohol and Esters

-1 - 0.60 - 0.75 - 0.25

CI

-0.12 (each)

c1

2 or more on an aliphatic C on an olefinic C

N

Amines

Same as for alcohols

1

1 0.95

1.30 0

0.30

+0.05

a. Molar Relative Response Factor

The molar relative response factor is the factor by which the area ratio of two peaks must be multiplied to obtain the ratio of the molar concentrations of these two compounds. It can be obtained easily from the data in Table 10.6. The number of effective carbon atoms of the compound analyzed and of the standard are cakulated by summing up the contributions given in the Table. The relative molar response factor is the ratio of these two numbers. As an example, 3-methylpentane has an effective carbon number of 6 (each alkyl carbon = 1); acetaldehyde, an effective carbon number of 1 (CH, = 1, CO = 0). The molar response factor of acetaldehyde (analyte) relative to 3-methylpentane is 6. A discussion of the comparison between the response factors measured experimentally and those obtained using the data and the method of Sternberg et al. is given in Chapter 14. Examples of calculations of Sternberg response factors are given in Figure 10.18. b. Weight Relative Response Factor

The weight relative response factor is the factor by which the area ratio of two peaks must be multiplied to give the concentration ratio of the two compounds. The weight response factor of a compound 2 relative to a standard 1 is calculated by determining first the molar response factor, then by multiplying it by the ratio of the molecular weight. Thus, the weight response factor of acetaldehyde relative to 3-methylpentane is 6 X 44/86 = 3.070.

447 Figure 18.A. Relative weight response factors. The calculation of the relative weight response factors of two compounds requires the determination of the effective carbon atom numbers of both compounds ( E C A N ) . The relative weight response factor is then given by: f

'/I-

ECAN, M 2 ECAN, M I

Example. Reference compound: 3-methylpentane (M= 86). Analyte: acetaldehyde (M = 44). ECAN of 3methylpentane: 6 ECAN of acetaldehyde: 1 (See Table 10.6. CHO = 0). Relative weight response factor:

f

"I-

6x44 - -= 3.07 1x86

Numerous values calculated by this method are reported in Table 14.8. Figure 18.8. Relative molar response factors. The relative molar response factor is given by the relationship: ECAN,

f2h = ECAN, Example. In the previous case of the response of acetaldehyde relative to 2-methylpentane, the molar response factor is:

Figure 10.18. Example of the calculation of response factors after Sternberg.

8. Maintenance and Cost The FID is very simple, rugged and easy to build in a laboratory equipped with a modest workshop. The maintenance is very simple and limited to periodically cleaning the jet by sonication and dusting the silica powder produced by oxidation of the silicon polymers used as stationary phases. The cost of the electronics associated with the detector is significant, as it is still now a rather delicate subsystem, because of the drastic specifications of sensitivity and response time imposed by chromatography. Because of all its properties the FID has achieved universal acceptance by analysts, even in process control applications, where an explosion proof design is mandatory. V. THE ELECIXON CAPTURE DETECTOR The principle of the electron capture detector (ECD) was suggested for the first time by Lovelock in 1958 (93,94). Lovelock and Lipsky (95) described the first ECD in 1960 and Lovelock (96) discussed the phenomenon of electron capture. A number of important reviews have been published (97-99). The ECD has become the References on p. 477.

448

classical detector for molecules having a strong electron affinity, such as polynuclear aromatic hydrocarbons, molecules with systems of conjugated double bonds or compounds having several halogen atoms, among which are a number of well-known pollutants and pesticides. The sensitivity of the detector is extremely high. The detection limits can be ten thousand times lower with the ECD than with the FID. Conversely, the ECD is the most difficult detector to handle, requiring extreme care and cleanliness. The response is still the topic of research and controversies (92). 1. Detector Principle The detector principle is based on the huge difference between the recombination rates of positive and negative ions on the one hand, and positive ions and electrons on the other. A radioactive source, originally %Sr, then 3H as a hydride of titanium or a lanthanide, now 63Ni,placed in a small chamber swept by the carrier gas, emits electrons which collide with the molecules of carrier gas and ionize them. The charge carriers formed drift slowly in a weak electrical field (see below), and after a number of collisions, the electrons lose most of their energy, until they retain only the thermal kinetic energy. Eventually they are collected by the electrodes and a certain, steady background current is recorded. When an analyte is eluted which has a significant electron affinity, its molecules react with electrons and capture them, giving rise to the formation of negative ions. Negative ions drift much more slowly in the electrical field and react much more rapidly with positive ions than electrons. Thus, the current observed decreases by the amount corresponding to the number of electrons captured. The response of the ECD follows a law similar to the Beer-Lambert relationship in absorption spectroscopy:

where: - I is the current observed when the concentration of analyte in the carrier gas is

c,

Z,, is the ionization current with pure carrier gas, - d is the distance between the electrodes in the ECD, - K is a response factor, function of the electrical field, the temperature, the -

carrier gas, and the analyte. Equation 45 does not provide a linear response, except at very small concentrations, when the exponential function is equivalent to (1- KCd). There are other sources of non-linear response, however, as we discuss below (Section V.6). Although equation 45 is generally valid, at least within a certain concentration range, there are still extensive controversies in the literature regarding the response mechanism, the exact relationship between the response of the ECD and the kinetics of the various reactions involving electrons which take place inside the ECD and

449

regarding the dependence of the response factor K on the various parameters. It does not seem there is any method to predict even an order of magnitude for the response factor. The main reaction taking place in the ECD, between the molecules of analyte and the electrons can be one of two types: e-

+ AB

+ AB-

(46)

or : e - + AB + A B - + A + B-

(47)

In the first case, the anion formed is stable until it reacts with a cation. This is the case for PNA's and a number of conjugated molecules. In the second case, the anion is unstable and one bond breaks very rapidly. This is the case for most halogen substituted compounds. A halogen atom is lost as a halide ion. The activation energy is different with the two mechanisms and so is the temperature dependence of the response (100). The various implementations of the ECD can be sorted into two different classes, those where the two opposite electrodes are planar and parallel (96), and those

A

eye C

Figure 10.19. Schematic of the ECD. (A) Concentric electrodes. (B) Parallel plates electrodes. a - Gas outlet. a' - Metal grid. b - Radioactive metal foil. c - Gas inlet (from column). d - Teflon. Electrical insulation. e - Brass.

References on p. 477.

450

where they are cylindrical and concentric (95) (see Figure 10.19). The design of the ECD cell is extremely simple in both cases. In the former case the electrical field is constant and the results seem to be better (77). As for many electrochemical detectors, it is possible to operate the ECD in the amperometric mode or in the coulometric mode. Although excellent results have been published by Lovelock (101) using a coulometric ECD, this mode is not generally possible, and the reaction is often incomplete. This phenomenon explains in part some of the contradictions found in the literature regarding relative responses of analytes. Finally, three different techniques are used to measure the detector signal: constant polarization voltage, pulsed polarization voltage and constant current. Now most manufacturers use only the third method. a. Constant Voltage

In this first method, the earliest used, a constant, relatively low (10 to 20 V, usually) voltage is applied to the detector cell and the variations of the current during band elution are recorded. Negative ions may be collected, in spite of their different velocity than electrons and of their fast rate of recombination with positive ions. When this phenomenon takes place, sensitivity and dynamic linear range are reduced. In other instances, positive ions may accumulate around the cathode and form a space charge, preventing their total collection. This also affects the dynamic linear range, which rarely exceeds 100 in this mode. b. Pulsed VoItage

In this second method, narrow (0.5 to 1 psec), rectangular pulses of constant maximum voltage (ca 50 V) and constant frequency (5,000 to 20,000 Hz) are applied to the electrodes, and the current intensity is measured. During most of the time, electrons are not accelerated by an electric field and their average energy is close to thermal. They are more easily captured by analyte molecules. Also negative ions more readily react and combine with positive ions. If the values of the pulse height and width are properly chosen, most negative ions are too heavy to be accelerated and collected. Also the internal polarization is reduced (lesser space charge). The sensitivity is improved, there are fewer spurious peaks and the dynamic linear range is increased to a few hundreds, which is still insufficient for most applications. c. Constant Current

In the last, more recent method, the pulse frequency is constantly adjusted, by a feedback mechanism, in order to keep the current constant, and the frequency is measured (77,157). With this system, when the band of an electron capturing compound enters the detector cell the concentration of thermal electrons decreases as well as the number of charge carriers collected during each voltage pulse. The

451

feedback mechanism increases the pulse frequency, which remains inversely proportional to the density of electrons in the detector cell, i.e., to the concentration of the analyte in the eluate. Thus, the use of a pulsed voltage permits the rapid thermalization of electrons between the voltage pulses, followed by the total collection of the remaining electrons by the high voltage pulse. This avoids reactions of analytes with high energy electrons and also limits the effect of a space charge build-up on the response. The variable frequency ECD has a wider dynamic linear range than the constant frequency ECD, of the order of 10,000, which is a considerable improvement and justifies the exclusive use of this method for quantitative analysis. 2. Parameters Affecting the Response A number of publications have studied in detail the influence of the detector parameters on its response. It is not possible to present here a complete discussion or review. We draw essentially on the works already quoted (92-101) and on the papers by Devaux and Guiochon (102-104). a. Nature of the Carrier Gas

The carrier gas must exhibit a very small electron affinity but its molecules must also give inelastic collisions with the electrons to thermalize them rapidly. For this reason, either nitrogen or argon doped with ca 5% methane are used. From a chromatographic point of view nitrogen, which has a larger diffusion coefficient and a lower viscosity, should be preferred. The carrier gas must be very dry and must contain a low concentration of oxygen. Water vapor has a very large electron affinity and its presence in the carrier gas reduces the density of electrons in the detector cell, hence the response factors. Before entering the chromatograph, the carrier gas flows through a molecular sieve trap. This trap must be regenerated periodically, by heating to 350-400O C under a carrier gas stream directly vented to atmosphere, not through the detector. Also, the pressure and/or flow rate controllers must have metal membranes. The injection port septum must be protected. b. Carrier Gas Flow Rate

The detector responds to the concentration of analyte in the carrier gas. Accordingly, it is a concentration detector and the peak area decreases with increasing flow velocity (105). The response factor depends on the density of thermal electrons in the cell, and this density is a function of the flow rate (104,106). Thus, the ECD is not as easy to understand as the TCD. It may be necessary, with certain columns whch are operated at a low flow rate, to use a secondary gas stream, to permit an independent adjustment of the flow rates through the column and the detector cell. References on p. 417.

452

c. Temperature

The temperature dependency of the response of the ECD has been well documented for the conventional direct voltage mode. Systematic investigations have been carried out on selected compounds and the results reported by plotting In( KT3’’) versus 1 / T , where K is the response factor and T the absolute temperature (96,158,159). The results obtained show that the detector temperature can be optimized for maximum response. Also, depending on the temperature range at which the chromatograph must be operated for optimum analytical performance, different reagents should be used to selectively prepare an electron absorbing derivative. Figure 10.20 shows a plot of the detector signal for a stream of camer gas spiked with a constant concentration of 1-chlorobutane, versus the polarization voltage (constant voltage), at three different temperatures (102). The higher the temperature, the lower the voltage at which the current plateau is reached. At voltages lower than the one for which the plateau is reached, the current varies rapidly with the

1

10

20

1

I

30 Volts I

t

Figure 10.20. Plot of the background current of the ECD versus the polarization voltage, at different cell temperatures (after 102). Constant polarization voltage. (Reprinted from Bulletin de la Sociiti Chimique de France. 4. 1404 (1966).)

453

temperature. In the case of Figure 10.20, it is multiplied by 2 for a temperature increase of 108OC. It has been shown that, in extreme cases, the signal may be multiplied by 10,OOO for a temperature increase of 2OO0C, i.e., by 1.047 for a temperature increase of 1' C (107). This implies that the detector temperature should be controlled within 0.1" C in order to achieve a reproducible response. In practice, the analyst will set the detector temperature in order to maximize the response of the trace components searched for, or in some cases to minimize the response of some interfering compound. Sometimes the temperature dependence is used for qualitative analysis. d. Polarization Voltage of the Electrodes

In the constant voltage mode, the plot of the response factor versus the polarization voltage exhibits a maximum (see Figure 10.21). This is the result of the superposition of two phenomena. On the one hand, the higher the polarization voltage, the higher the electron energy and the lower the probability of their capture by analytes. On the other hand, the fraction of electrons collected increases with increasing polarization voltage, as well as the background current. The dynamic linear range is wider at high voltages (102). In the pulsed voltage mode, the response factor increases with the pulse frequency. For 1 chloro-alkanes, the optimum conditions are a pulse period of 50 psec, a pulse duration of 0.5 psec and a polarization voltage of 24 V (103).

t

K

107(mole/cm3)-1

Figure 10.21. Plot of the response factor of the ECD versus the polarization voltage (after 102). Constant polarization voltage. Carrier gas plus 7.8. lo9 mole/mL 1-chlorobutane. (Reprinted from Bulletin de la Swi'bC Chimique de France, 4, 1404 (1966).)

References on p. 477.

454

3. Classification The ECD is a concentration detector, but the electron density, and hence the response factor, is a function of the flow rate. This makes the exact flow rate dependence of the peak area difficult to predict, and requires a careful control of the carrier gas flow rate through the detector cell.

4. Selectivity The ECD is extremely selective. The response for hydrocarbons without conjugated double bonds is very small, while the ECD is very sensitive to traces of compounds having highly conjugated double bond systems, halogen atoms or other electronegative groups such as phenols, conjugated carbonyls, nitrates, etc.

5. Sensitivity The ECD is extremely sensitive to polychlorinated molecules. For example, 0.1 pg of lindane can be detected (108). For this reason, the ECD is the choice detector for the analysis of pesticides residues, of polychlorodiphenyls or polychlorodioxins in food. The sensitivity for water vapor and even for oxygen (the detection limit of this non-retained compound is around 1 ppm) explains why extreme care should be taken to avoid diffusion of these gases from the atmosphere of the laboratory to the carrier gas stream, through septa, pressure or flow rate controllers membranes, etc. The base line noise of the ECD is usually of the order of 1 PA. It depends essentially on the purity of the gases used, particularly on their water content, on the degree of column bleeding and the nature of the volatile products generated by the stationary phase (vapor or decomposition products), and on the procedure followed for column conditioning. Temperature fluctuations are amplified by the exponential dependence of the retention volumes on column temperature, so if a vapor is carried through the column by the carrier gas or generated inside the column, the outlet flux increases exponentially with temperature. 6. Linearity The dynamic linear range of the ECD is rather narrow, which is its main drawback. It does not exceed a few hundreds for the constant voltage mode, about 1,OOO for the constant period pulsed voltage and a few thousands to maybe 10,000 for the variable frequency pulsed mode. This has some important, unpleasant consequences. Because the response factors of different components of the same mixture may be very different, it will be rare that the quantitative analysis of all these components can be performed at the same time. For a given injection, some components will not be detected, while the response of the ECD for other ones will exceed the range of linear responses. A number of successive injections, the use of different standards,

455

and several calibrations will be required, which drastically complicates the task of the analyst. This explains the popularity of the more complex variable frequency pulsed voltage mode, because the dynamic linear range is much wider. 7. Prediction of the Response Factors The response of the ECD is impossible to predict. There is no valid relationship between the structure and the response factor. It was hoped that derivatives prepared by reacting compounds which give no response or very weak response to the ECD with halogen-rich reagents would all have nearly the same response. This did not work out. For example the N-trifluoroacetyl or N-heptafluorobutyryl derivatives of the different proteinic amino acid methyl esters exhibit markedly different responses, while the N-acetyl derivatives of most amino acids give weak or negligible responses. Similarly, the derivatives prepared by reacting chloromethyl-dimethylchlorosilane with alcohols or polyols have unpredictable relative responses, TABLE 10.7 Order of Magnitude of the Electronic Affinities of Compounds belonging to Different Families (after refs. 109 and 110) Chemical Family

Relative Response

Examples

Alkanes, alkenes, alkynes, simple aromatic hydrocarbons, aliphatic ethers, esters, dienes.

0.10

n-Hexane, benzene, Cholesterol, Benzyl alcohol, Naphthalene.

Aliphatic alcohols, amines, ketones, aldehydes, nitriles, monofluoro, monochloro derivatives.

1.o

Vinyl chloride, ethyl acetoacetate, chlorobenzene.

10.0

Cis-, trans-stilbene, azobenzene, acetophenone.

Enols, oxalic esters, monobromo, dichloro derivatives, hexafluoro derivatives. Acyl chlorides, anhydrides, barbiturates, thalidomide, lead alkyls, hydroxychloro derivatives.

100

Ally1 chloride, benzaldehyde, azulene, benzoyl chloride, lead tetraethyl.

Monoiodo, dibromo, trichloro, mononitro derivatives. Pesticides. Cinnamaldehyde.

Cinnamaldehyde, nitrobenzene, CHCI,, (2%.

1,2-Diketones, quinones, fumaric, pyruvic esters, diiodo, tribromo, polychloro, dinitro derivatives. Organo mercury compounds.

Dini trobenzene, Diiodobenzene, Dimethyl fumarate, CCI,.

Response relative to chlorobenzene ( = 1). (Reprinted from Nuture, 183, 729 (1961) and 193, 540 (1962)) References on p. 417.

456

even if the corresponding derivatives of trimethylchlorosilane give no response. The electron capture energy of a compound depends essentially on the energy of the LUMO of its molecule, something even quantum mechanical calculations do not predict too well as yet. A number of relative response factors are found in the scientific literature. They have been determined under certain experimental conditions and are valid only in very similar conditions. They show extremely large differences between the absolute TABLE 10.8 Relative Response Factors of Various Compounds on an Electron Capture Detector (after ref. 103) Compound 1-Chlorobutane 2-Chlorobutane 1-Chloro-2-methylpropane

2-Chloro-2-methylpropane 1-Chloropentane 1-Chlorohexane 1-Chloroheptane 1-Chlorooctane 1,2-Dichloroethane 1,4-Dichlorobutane 1,l-Dichlorobutane rrans-1,2-Dichloroethylene cis-1,2-Dichloroethylene Chloroform Carbon tetrachloride 1-Bromopropane 1-Bromobutane Bromocyclopentane 1-Bromo-2-propene 1,l-Dibromoethane 1-Iodobutane Benzene Toluene 2-Fluorotoluene 4Fluorotoluene Chlorobenzene Bromobenzene I-Butanol Di-n-butyl ether Acetone Methyl butyrate 2,3-Butanedione n-Heptyl trifluoroacetate n-Propyl pentafluoropropionate

Response Factor 1.0 2.0 1.7 12 1.o 1.1 1.5 1.6 190 15 110 370 90 60000 400000

255 280 280 4000

11oooo 90000

0.06 0.2 0.55 0.55 15 450 1.o 0.6

0.5 0.9 50000 4.5 450

Standard: 1-chlorobutane. Detector temperature: 190OC. pulse voltage: 50 V. Pulse period: 50 psec. Pulse width: 0.5 psec. (Reprinted from Journal 01Gar Chromarography, 5, 341 (1967)J

457

response factors of closely related compounds under the same experimental conditions. They also show strong differences between the absolute response factors of a compound in different conditions. Data published by Lovelock (109), by Lovelock et al. (110) and by others (111-115) substantiate these conclusions. Data in Tables 10.7 and 10.8 give the order of magnitude of the response of the ECD for different chemical classes. They may be used only as an estimate of the probable order of magnitude of the relative response of two compounds. Similarly, data in Table 10.8 are given to illustrate the large and rather unpredictable variation of the ECD response from compound to compound. Devaux and Guiochon (103) have shown that: - the relative response factors vary with the pulse frequency, - they depend hardly at all on the pulse width, - they are constant for voltages below 20 V (20 V/cm); they can be multiplied by a few units when the electrical field becomes higher, - they increase with increasing temperature, between 120 and 215 O C. The use of numerical values of the response factors found in the literature must be strongly discouraged, even if they are relative response factors for closely related compounds, even if the exact conditions under which these factors have been determined can be duplicated. It is difficult to duplicate the trace composition of the carrier gas.

8. Maintenance and Cost Maintenance of the ECD is more important and difficult than that of any other gas chromatographic detectors (except maybe the electrochemical detectors). It is necessary to carefully control the column bleeding and avoid its condensation inside the detector, where residues can easily polymerize, under the influence of radiation or electronic bombardment, into an insoluble deposit, near impossible to eliminate and which interferes with the proper functioning. Care should be taken not to cause leaks of radioactive material. It has been rumored, for example, that most of the 63Nisource of an ECD used in a European laboratory to detect volatile metal chelates (fod) was lost, following reaction of the nickel with an excess of free fod. Heating above a certain temperature limit of detectors using a metal hydride as radioactive source can result in the loss of tritium to the environment and a reduction of the detector response. With proper care regarding the elimination of oxygen and water from the camer gas, the ECD can be used for control and routine analysis in the laboratory. Its use in process control analysis remains difficult and should be avoided.

VI. THE THERMOIONIC DETEmOR This detector derives from work done to reduce to practice a detector based on the Beilstein test. A copper wire heated in a Bunsen burner flame gives a very intense green light in the presence of chlorine or bromine. This phenomenon was References on p. 411.

458

used by Lebbe and Chovin (116) and by Gunther et al. (117) to identify chlorinated compounds in complex mixtures. Looking at a flame during the elution of a sample was not very practical, however. Cremer et al. (118) described a detector using an anode heated to 900OC. It emits positive ions. The current is considerably increased in the presence of halogenated compounds. The modem thermoionic detector derives directly from the pioneering work by Karmen and Giuffrida (119,120), who observed that the electrical conductivity of a flame in the presence of alkaline salts is enhanced by the combustion of compounds containing halogens, phosphorus or nitrogen. 1. Detector Principle

Although the detector works very well and is rather widely used as a selective detector for C1, Br, I, N and P, its mechanism is still controversial. Basically the TID is a modified FID, where a platinum eletrode coated by an alkaline salt is heated by the flame (see Figure 10.22). Many different implementations of the TID have been designed, however, incorporating for example two flames, the second swept by the combustion products of the first, or an electrically heated salt crystal, or a ceramic bead impregnated with a salt, and various salts have been used. It seems that, one way or another, the combustion of the derivative containing P, N, Br or C1 enhances the volatility of the salt. Brazhnikov, Gur’ev and Sakodinskii (121,122) have separated the possible mechanisms into three categories: - solid phase reactions, - gas phase reactions, - photoevaporation. We briefly review these mechanisms.

.

Air

4 C

Figure 10.22. Schematics of the Thennoionic Detector. a - Jet (positively polarized). b - Alkaline salt. c - Collection electrode.

459

a. Solid Phase Reactions

Karmen (119) used two successive flames, one above the other. The lower flame heated the salt. If the upper flame is fed with dilute chloroform vapor, no response is observed. If the lower flame receives these vapors, a large response is recorded. Karmen suggested that chlorine in the flame would increase the rate of vaporization of the solid salt. With phosphorus, on the other hand, both the rate of vaporization and the ionization yield would increase, explaining the very large response for this element. b. Gas Phase Reactions

According to Page and Woolley (123), there are free alkaline metal atoms (A) in the flame, which are ionized by collisions with gas molecules:

A catalytic reaction involving phosphorus or halogen atoms could take place in the reducing region of the flame, causing an increase in the number of ions formed:

A+2H+A++e-+H2

(49)

Kolb et al. (124,125) suggested a more detailed mechanism, to explain the response observed with a detector using a ceramic bead impregnated with RbCl, heated by the Joule effect and polarized negatively. The background current would result from a recycling of the rubidium between the bead and the flame. Free rubidium atoms vaporize, are ionized by ternary collision with two free hydrogen atoms, resulting in the formation of a hydrogen molecule, and the positive rubidium ion is collected by the electrode (see Figure 10.23). Free radicals resulting from the pyrolysis of organic compounds containing phosphorus or nitrogen would react with rubidium atoms and ionize them:

Only compounds pyrolyzing in the flame to give free radicals would give a large response to the TID. Nitro derivatives would pyrolyze to give NC; cyan0 radicals. Phosphorus derivatives would form intermediate radicals such as PO; PO; and PH;. For other compounds a negligible response would be observed. c. Photoevaporation

According to Brazhnikov et al. (122), the mechanism involves absorption by the salt surface of photons emitted by the flame during the combustion of organophosphorus compounds, followed by the vaporization of atoms from the salt surface and by their dissociation. References on p. 411.

460

f

R'

Rb+

\

R-

Rb

*

Figure 10.23. Principle of the response mechanism of the TID (after 124). The cycle of reactions takes place at the alkaline salt surface. (Reprinted from Journal of Chromatographic Science, 12, 625 (1974).)

In a more recent publication, Brazhnikov and Shmider (126), summarizing the results of most previously published studies (123-128) as well as those of new investigations, elect a gas phase reaction. They note that the rate of vaporization of the salt remains unchanged when phosphorus or nitrogen derivatives are introduced into the flame. It seems that thermal ionization takes place in the flame, where reactions between the vapor of the alkaline salt and hydrogen atoms are allowed by thermodynamics. During the combustion of these compounds the following reactions would take place: - formation of heavy ions as intermediate combustion products of phosphorus and nitrogen derivatives. - these heavy ions react with alkaline atoms to form even heavier ions. - the alkali metal salts are active inhibitors of combustion, and their presence reduces the flame temperature. The combination of these reactions controls the flame temperature, the efficiency of the ionization of the salt vapor and of the aerosol particles. When the phosphorus or nitrogen compounds enter the flame, the concentration of alkaline metal is reduced, the flame temperature increases and the ionization efficiency increases considerably, hence the detector signal. We are still far from a detailed understanding of the detector mechanism and the calculation of response factors does not seem feasible. 2. Parameters Affecting the Response

Like the FID, the TID will give a response depending on the flow rates of hydrogen, carrier gas and air, on the polarization voltage of the electrodes and on the geometry of the detector. It will also depend on the nature of the salt used.

461 TABLE 10.9 Relative Response Factors of the TID for Phosphorus and Chlorine (after ref. 129)

Salt

Relative Response *

LiCl NaCl A1,0, +Na,SO,

10.0 7.6-40 ** 6.4

RbCl CSCl

11.0

7.4-14

**

* Relative response of triethyl phosphate to butyl chloroacetate (in weight P / weight Cl). ** Values measured at higher temperature. (Reprinted from Journal of Gas Chromatography, 3, 336 (1965).)

a. Nature of the Alkaline Salt Used

Karmen (129,130) has shown that the response of the TID for phosphorus derivatives is always much larger than that for chlorine derivatives, sometimes up to 10 times larger or more (see Table 10.9). Other authors reached the same conclusions (124,131,132). Rubidium seems to give larger responses than other alkaline elements (133) and rubidium sulfate has been generally adopted in TID. Potassium chloride and cesium chloride are also used. The alkaline salt is held by the collecting electrode. It is placed as a coating, a crystal or a pellet, a glass or a ceramic bead impregnated with the salt. b. Hydrogen and Air Flow Rates

Since the response of the TID is a function of the amount of alkaline salt present in the flame, it will depend on its temperature, i.e., on the hydrogen and air flow rates (119,133-136). The influence of the hydrogen flow rate on the response is very strong. A change of the flow rate by 0.01 L/min results in a base line shift (108). Extremely stable flow rates must be achieved and the best flow rate controllers must be used on both hydrogen and air streams (122). In practice, the optimum flow rates for maximum response are 25-30 mL/min for hydrogen and 250-300 mL/min for air when helium is used as carrier gas and 35-40 mL/min for hydrogen and 200-250 mL/min for air when nitrogen is used as carrier gas. c. Carrier Gas Flow Rate

Although nitrogen, helium or argon can be used as carrier gas, the absolute and the relative responses depend on the nature of the gas. With helium the response for phosphorus derivatives can be up to 100 times larger than with nitrogen or argon, which may be due to the heat conductivity. By contrast, the response for nitrogen compounds is larger with nitrogen and argon than with helium. References on p. 477.

462

3. Classification The TID, like the FID, is a mass sensitive detector. 4. Selectivity

The response of the TID is much larger for phosphorus and nitrogen derivatives than for other organic compounds, except those containing halogens, which also give a significant response. Schmitter et al. (137) claimed that the response of the TID is 10,000 times larger for benzoquinolines than for phenanthrene, thus permitting the easy detection of ma-aromatic compounds in heavy distillation cuts. For this reason, the TID is largely used in the analysis of traces of residues of pesticides, herbicides, fungicides and related compounds in environmental samples, water, soils, etc. and in food products. TABLE 10.10 Detection Limits of the TID for some Heterocyclic Compounds Name

Structure

Detection limit

Barbitural

Folpet

Dyrene Cl CI

Atrazine

Amphetamine

In femtogram per second (see 138). (Reprinted from Journal of Chromarogruphy, 134, 57 (1977).)

463

5. Sensitivity The TID is very sensitive to the phosphorus and nitrogen derivatives, more sensitive than the FID. The response can be 50 to 100 times larger for nitrogen compounds and 500 to 1,000 times larger for phosphorus compounds. Table 10.10 contains detection limits for some typical compounds. In most cases, it will be easy to achieve detection limits corresponding to concentrations in the original sample much below 1 ppb.

6. Linearity The dynamic linear range is of the order of 10,000, but it may vary from one compound to the next. It should always be determined during calibration of the detector. 7. Prediction of the Response Factors The mechanism being still controversial, and the kinetics of the reaction involved being largely unknown, it is not surprising that it has proven impossible to predict the response of the TID. Calibrations must be carried out for each compound. It has been observed, however, that the response factors vary over extended periods of time, thus making necessary a periodic repetition of the calibration of a given detector. Response factors obtained with one detector should not, however, be used with another detector without extreme caution.

8. Maintenance and Cost The maintenance required by the TID is important. The detector must be cleaned periodically, much more often than a FID employed with similar samples, to eliminate all kinds of deposits. A solvent unreactive towards the alkaline salt should be used. The salt bead or pellet should be replaced as soon as the response shows an important trend towards a decrease. Before that, the centering of the pellet or bead should be checked. The TID is not used in process control analysis and its use is not recommended. VII. THE FLAME PHOTOMETRIC DETECTOR The flame photometric detector (FPD) is extremely selective for phosphorus and sulfur. It is the only selective and sensitive detector which may be used with an on-line process control gas chromatograph. This is due to its excellent stability and rather low maintenance cost. The concept of the FPD was first disclosed in a German patent in 1962, by Draeger and Draeger (139). In 1966, Brody and Chaney (140) built a FPD and used it for gas chromatographic analysis. References on p. 411.

464

1. Detector Principle

It is based on the collection of the light emitted at characteristic wavelengths when substances containing sulfur or phosphorus are burned in a hydrogen rich flame. A schematic of the most popular implementation is shown on Figure 10.24. The light emitted is collected in a photomultiplier. A filter or a monochromator may be used to separate the signals due to sulfur and phosphorus, with bands centered at 394 and 526 nm, respectively. Another version uses two photomultipliers, one on each side of the burner, with filters permitting the collection of the S and P signals simultaneously (141). The main characteristic features are that the response is larger for phosphorus than for sulfur compounds, that it is linear for phosphorus and quadratic for sulfur compounds and that the emission bands overlap, so it is necessary to compare the two signals, at 394 and 526 nm, respectively, for qualitative identification. Correct identification as a sulfur or phosphorus detector is possible only if the band eluted is pure. 2. Parameters Affecting the Response

These parameters are the polarization voltage of the photomultiplier and the flow rates of the gases sent to the flame. a. Photomultiplier Voltage

A plot of the signal to noise ratio of the FPD versus the polarization voltage of the photomultiplier is reported on Figure 10.25. It was obtained by Brody and

Air

t

column

Figure 10.24. Schematic of the Flame Photometric Detector. a - Burner. b - Mirror. c - Glass window. d - Optical filter. e - Photomultiplier.

465

-

H

1

401 35 1

.-8 <-0 301 C 0)

.G 2 5 1 C

.s

201

,o 151

k a

-

101

”! 51

7 1

I

I

800

900

1000

Voltage on PM t u b e

Figure 10.25. Influence of the photomultiplier voltage on the response of the FPD. Plot of the response to a 40 pL sample containing 1.26 ppm of Parathion versus voltage. Dotted line shows the ratio of the noise when the flame is on to the dark current noise. (After ref. 140.) (Reprinted from Journal of Gas Chromafography,4, 42 (1966).)

Chaney (140), who injected constant volumes of an acetone solution containing a trace amount (1.26 ppm) of parathion. The maximum response is obtained at 750 V. b. Gas Flow Rates

The response seems to be rather insensitive to the variation of these flow rates. The carrier gas flow rate may vary from 20 to 200 mL/min without causing any significant change in the response. An air flow rate of about 200 mL/min and a hydrogen flow rate of 175 to 200 mL/min are necessary for good operation conditions, but the exact values are not critical.

3. Classification The FPD is a mass sensitive detector. 4. Selectivity

The FPD is selective to either phosphorus or sulfur, depending on the wavelength which is monitored. According to Beroza and Bowman (141,142), a considerable selectivity can be achieved, the ratio of the response for a P or S derivative to the response for an anologous compound where this atom is replaced by CH, being of the order of 50,000. References on p. 477.

466

Unfortunately, the emission bands of S and P in the detector overlap, so the responses interfere and it is necessary for proper qualitative analysis that sulfur and phosphorus derivatives be separated completely (143). Consequently, the formal identification of a compound as a P or S derivative can rarely be made using merely the information supplied by this detector.

5. Sensitivity Brody and Chaney (140) have determined the detection limits of the FPD for parathion (0,O-diethyl 0-(p-nitrophenyl) phosphorothioate, C,,H,,NO, PS) and malathion (S(1,2-bis(ethoxycarbonyl)ethyl) 0,O-dimethyl phosphorothioate), using both the phosphorus filter (526 nm) and the sulfur filter (394 nm). In the first case the detection limit for these two compounds is 5 ppb, in the second case it is only 0.6 ppm. 6. Linearity The response of the detector in the phosphorus mode is not linear over a large concentration range, only 2 to 3 orders of magnitude. The response for sulfur is quadratic, attesting to the fact that a second order reaction is responsible for the production of photons. In both cases proper, repeated calibration is required.

7. Prediction of the Response Factors The response of the FPD is not predictable. Absolute calibration of the detector response for all compounds involved in the analysis is required, because of the narrow range of linear response. 8. Maintenance and Cost Users of FPD in process control analyzers report that this detector does not require more maintenance than the FID. Its cost is comparable. This is probably the best choice for automatic control analyses of traces of P and S compounds, in spite of its shortcomings in quantitative analysis.

VIII. THE PHOTOIOMZATION DETEaOR This detector was originally described by Lovelock in the early 'sixties (7,144), but became commercially available only in 1977. The reasons for the failure of the first attempts were related to the lack of stability of the low wavelength UV sources available at that time and the difficulties in operating the detector cell under vacuum. These shortcomings have been circumvented by using sealed UV lamps and by making the ionization chamber work under atmospheric pressure (145,146).

467

1. Detector Principle A cross-sectional view of the detector is shown in Figure 10.26. The process of photoionization involves the absorption of a photon by the molecule of analyte and its dissociation into an electron and an ion:

The ions formed are collected by polarized electrodes. The ionization potential of the analyte must be lower than the energy of the photon (7). Thus the detector requires the use of a source of high energy UV photons. Some degree of selectivity is provided by the selection of the light energy. For instance, permanent gases, water and the C, to C, alkanes have ionization potentials which are > 12.98 eV, 12.59 eV and 10.6 eV, respectively. They will not respond to a PID equipped with a 10.2 eV light source. Only compounds with an ionization potential below 10.2 eV will do. Ionization potentials for selected compounds are given in Table 10.11. Theoretical considerations reported by Freedman (147) suggest that the response of the PID should be related to the ionization potential through the photoionization cross-section, according to the following expression:

Z = 1, FqaNL [ A B ]

(52)

where I, is the initial intensity of the flux of photon, F, the Faraday, q. the

1,'I t

5

Figure 10.26. Schematic of the photoionization detector. 1 - Ion collection electrode. 2 - Accelerating electrode. 3 - Sealed UV lamp. 4 - Ionization chamber. 5 - Sample inlet. 6 - Sample outlet. 7 - Hated body.

References on p. 477.

468 TABLE 10.11 Ionization Potential of Selected Compounds (after ref. 146) Compound Diethyl sulfide m-Xylene Dimethyl sulfide Toluene Cyclohexene 1,fButadiene Benzene Pyridine Trichloroethylene Ally1 alcohol Acetone Methyl ethyl ketone Tetrahydrofuran Cyclohexane Vinyl chloride Carbon disulfide Acrolein n-Hexane Ethyl alcohol Ethylene Oxygen Water Carbon dioxide Methane Carbon monoxide Nitrogen

Ionization Potential lev) 8.43 8.56 8.68 8.82 8.94 9.07 9.25 9.32 9.45 9.67 9.69 9.53 9.54 9.88 9.95 10.08

10.10 10.17 10.48 10.51 12.07 12.59 12.80 12.98 14.01 15.55

(Reprinted from Journal of Chromatography, 134. 49 (1977).)

photoionization efficiency, u, the absorption cross-section of the analyte, N, the Avogadro number, L, the path length of the light across the cell and [AB] the concentration of analyte in the cell. The product qu is the photoionization cross section of the molecule.

2. Parameters Affecting the Response The characteristics and the performance of the PID have been studied by Driscoll et al. (145,146,148). Their work has shown that the only parameter which affects the response is the flow rate of carrier gas. There is no restriction on the choice of this gas among the classical ones, since their ionization potentials are high, much higher than the energy provided by the UV lamps (10.2 ev). Since the PID is probably a concentration-sensitive detector, the peak area increases with decreasing carrier gas flow rate. A plot of the response versus the carrier gas flow rate is given in Figure 10.27.

469 15

0

?

a

10

5

1,

0

I

I

I0

I

50 100 Flow r a t e (ml/min)

Figure 10.27. Influence of the carrier gas flow rate on the response of the PID. Plot of the response (peak area, arbitrary unit) to a 0.5 mL sample of air containing 1 ppm benzene, versus the flow rate. (After ref. 146). (Reprinted from Journal o/ Chromatography, 134, 49 (1977).)

3. Classification The PID seems to be a concentration-sensitive detector. A very small fraction of the analyte entering the cell is destroyed by the reaction, which results from the absorption of high energy UV radiation. Thus, the response should follow Beer’s law. Data are lacking to permit a final conclusion. 4. Selectivity It is formally a selective detector, since a response is obtained only with the compounds which have an ionization potential below the energy of the UV photons generated by the lamp. Thus, some compounds elicit no response at all, others have an enormous response. This detector is well suited to the analysis of most organics, inorganics and organometallics. Few restrictions have been recorded, except the lightest alkanes. A list of compounds which do not respond to the PID is given in Table 10.12. References on p. 471.

470

TABLE 10.12 List of Important Compounds which give No Response with the PID Oxygen Nitrogen Carbon monoxide Carbon dioxide Water Sulfur dioxide Methane Acetylene Methyl chloride Carbon tetrachloride Chloroform 1,2-Dichloromethane Formamide Formaldehyde

5. Sensitivity

One of the most significant features of the PID is its high sensitivity to most organic compounds: their detection limits are typically 10 to 50 times lower than those of the FID for the same compounds (145-149). This is due to a larger response and a lower signal noise. For P and S compounds, the PID can be 2 to 10 times more sensitive than the FPD. For instance, the PID is particularly suitable for the detection of PH,, ASH,, NH,, IH, I,, SeH,, TeH,, etc. in the ppb range.

3 I

I

6

7

I

I

8 Carbon number

9

Figure 10.28. Plot of the relative molar response of the PID to aromatic hydrocarbons versus the

ionization potential (descendingcurve) and versus the carbon atom number (ascending curve). (After ref. 147).

(Reprinted from Journal of Chromatography, 190, 263 (1980).)

471

Optimization of the selectivity and sensitivity of the detector is possible by selecting the lamp used among those available, with emission bands centered at energies of 9.5 to 11.7 eV. Traces of water in the carrier gas may drastically reduce the response of the PID. The carrier gas must be very thoroughly dried, if the detector is used in low trace detection.

6. Linearity The PID is one of the most linear detectors. Its dynamic linear range seems to exceed 10,000,000, extending from 2 pg to 30 p g , according to the manufacturer. For this reason the detector is exceptionally suited to quantitative analysis of trace or ultra-trace components. 7. Prediction of the Response Factors It is not possible to calculate the response factors by any known approach. Calibration is thus mandatory. Some practical suggestions may be derived, however, from the work of Freedman (147) and of Driscoll (145,146.148). There is a close correlation between the relative molecular response factor and the ionization potential, itself a function of the number of carbon atoms, as illustrated in Figure 10.28 for aromatic hydrocarbons. Thus, the response factor of homologs increases with the number of carbon atoms, parallel to the decrease of the ionization potential. Driscoll et al. (148) have determined the ratio of the relative response factors of a number of compounds with the FID and the PID. They have observed that the PID is less than two times more sensitive than the FID for alkanes, between two and four times more sensitive for alkenes and between five and ten times more sensitive for aromatic hydrocarbons. The molecular response factors, relative to benzene, of a number of compounds have been determined by Langhorst (149). From the data obtained, it has been concluded that the sensitivity of the PID depends on the chemical structure of the molecule: carbon atom number, nature and position of functional groups, nature and position of double bonds or conjugated double bonds. 8. Maintenance and Cost

The earlier versions of the PID could not be operated above 225 O C, because of the presence in the ionization chamber of Teflon parts, used for electrical insulation. This limitation has been eliminated by the redesign of the detector cell and the use of ceramic parts. The newer versions may work at temperatures well above 300 O C, which enlarges the range of applications. The PID is simple, rugged, safe and needs little maintenance. If it had appeared twenty years earlier, it probably would have become one of the most popular detectors. References on p. 411.

412

IX. THE HELIUM IONIZATION DETECTOR The helium ionization detector (HID) is a variant of the original Lovelock or argon ionization detector (7,150), which was developed in the late 'fifties and eventually supplanted by the FID, in spite of some serious advantages, such as a lower detection limit, larger current and background noise (with a better signal-tonoise ratio for a given sample size), resulting in the possibility to use a faster electronic amplifier (i.e. an impedance converter), and no need for additional gases to operate the detector. Unfortunately, the argon ionization detector suffers from a few major drawbacks which explain why it disappeared. (i) It is not linear. The response is in fact exponential and various schemes have been used to linearize its response with only moderate success. The dynamic linear range is much smaller than for the FID. (ii) It is very sensitive to trace impurities, including water vapor. It is easily fouled up by deposits, such as those resulting from stationary phase bleeding. It has to be cleaned often. Otherwise its behavior may be quite irreproducible at times, especially when it is not treated with consideration. (iii) It uses a radioactive source. These drawbacks are found to an even greater degree with the helium ionization detector (151-153). The HID, however, is very sensitive to permanent gases, and is the only sensor permitting their detection at the trace level. While detection limits are of the order of 10 ppm with the TCD, they are of the order of 1 ppb with the HID (151-156). This detector is very difficult to operate properly, however, and can be quite temperamental. 1. Detector Principle

When high energy radiations collide with any molecule in the gas phase (primary collisions), ionization ensues with a high probability (7). If the gas is in an electric field, the ions formed are accelerated, drift along the field, acquire energy and, further, secondary collisions can transfer some of that energy to the collision partner. Rare gas molecules may be excited up to a metastable level during such low energy collisions. In fact the cross sectional area for these secondary collisions is quite large. Thus, a certain density of metastable rare gas atoms is formed in the detector cell. These atoms can transfer their energy to organic molecules during tertiary collisions. If the ionization potential of these molecules is lower than the energy of the metastable atom, the colliding molecule is ionized (7,150). In the HID the primary collisions are between the helium atoms and p particles provided by radioisotopes of strontium or nickel or by tritium. The metastable helium atoms formed during secondary collisions have an energy of 19.8 eV. They can ionize every known molecule, except 3He and Ne (see Table 10.13). The ions produced by tertiary collisions are collected by the electrodes and the background current, resulting from the collection of the ions produced during the primary collisions, and a small fraction of the secondary collisions, is increased. This provides the detector signal. The detector is usually a solid metal cylinder, grounded with a coaxial negative electrode, polarized to a voltage between 500 and

473

TABLE 10.13 Ionization and Excitation Potentials of Permanent Gases Potential (eV)

GiU

Ionizaiion Potential Helium Neon Argon Nitrogen Carbon dioxide Carbon monoxide Krypton Hydrogen Oxygen Sulfur dioxide Xenon

24.5 21.5 15.7 14.5 14.4 14.1 13.9 13.5 13.5 13.1 12.1

Excitation Potential Helium Argon

19.8 11.5

2,000 V. This electrode is hollow and serves to introduce the column effluent (see

Figure 10.29). The higher the voltage, the larger the response. Several factors limit the sensitivity and the linearity of the response. Trace components of the camer gas are ionized, increasing the background signal and the noise. Their presence increases the detection limits. Ultratrace analyses require the use of extremely pure helium. The elution of a compound to which the detector responds results in an increase of the number of charge carriers accelerated by the polarization field, hence an PTFE insulator

Gas

Scale 1 cm

Figure 10.29. Schematic of the helium ionization detector. (After ref. 154). (Reprinted from Journal oj Chromatography, 14, 387 (1964).) References on p. 477.

414

increase in the density of the metastable excited helium atoms. Because of this snowball effect the response is not linear, but increases very rapidly and becomes infinite (electrical discharge) for a finite analyte concentration (this is the principle of the counters for ionizing radiations). The consequences of the snowball effect are reduced by the use of a high resistance in series with the detector, and by the design of the detector cell, where the negative electrode is withdrawn from the chamber into a recess in an insulating material, to promote the build-up of a space charge. These design features increase the concentration range over which the response is nearly linear. 2. Parameters Affecting the Response

Besides the physical parameters which affect the performance of any ionization detector, the purity of the carrier gas is of extreme importance, as noted in the section above (151-156). a. Purification of Helium Berry (152)and Bourke et al. (154)have carefully studied the influence of the helium purity on the accuracy and sensitivity of the HID. To reach the very lowest possible detection limits, they advised the purification of helium in four different stages: - cooled molecular sieve traps, to remove the bulk of the water and carbon dioxide, and the traces of condensable gases. - titanium chips at 800 O C, for removing the nitrogen. - hopcalite, an alloy of copper and manganese, for trapping traces of oxygen as CuO, oxidizing hydrogen into water and CO into C 0 2 . - molecular sieve traps, for removing water and carbon dioxide formed in the previous stages. In order to avoid possible back diffusion of traces of air through plastic or elastomer parts or through fittings, the entire instrument must be protected. Only metal parts will be used. Flow rate and pressure controllers will incorporate metal membranes. The chromatograph is placed in a double enclosure, swept by the flow of carrier gas exiting from the column. b. Other Parameters Affecting the Response

Bourke et al. (154) investigated the different parameters which influence the value of the background current of the HID: pressure, helium flow rate, temperature, polarization voltage. The background current was found to be inversely proportional to the pressure in the range from 730 to 800 mm Hg (see Figure 10.30). It increases with increasing voltage, up to 1250 V, which is the maximum limit before spark discharge occurs (see Figure 10.30). The influence of the helium flow rate parallels that of the pressure (see Figure 10.30). The operating conditions recommended by Bourke et al. are 765 mm Hg,23°C and lo00 V. The value of the helium flow rate should be chosen within the range

475 4 . 6 7 x la8

4.67 I

16’

r

-

@

c 01

L 3

u

4 . 6 7 I 16”

730

740

750

760

770

780

790

Pressure, rnrn Hg

Figure 10.30.Influence of the helium pressure and flow rate and of the voltage on the background current of the HID. (After ref. 154). (Reprinted from Journal of Chromurogruphy, 14, 387 (1964).)

where its variations do not affect the background current. This study does not deal with the detector response, but the results obtained by Excoffier (156) who tried to optimize the signal-to-noise ratio, were similar.

3. Classification

The helium detector is a mass sensitive detector, as are most ionization detectors, because the analyte is destroyed during the reaction. References on p. 477.

416 TABLE 10.14 Detection Limits of the HID for Permanent Gases (after ref. 156) Gas

Detection Limit (ppb)

Hydrogen Oxygen Nitrogen Carbon monoxide Carbon dioxide Methane

20 3

15 3 0.8 3.5

4. Selectivity The HID responds to all gases and vapors, except neon, which is the only compound to have an ionization potential higher than the excitation potential of the metastable excited helium, 19.8 eV. The response factors vary greatly from one compound to another, which means that the HID is somewhat selective.

5. Sensitivity The HID is one of the most sensitive detectors, if it is used with highly pure helium. It performs especially well with traces of permanent gases. When it is optimized, detection limits below or around 1ppb are achieved for H,, 4, Ar, N,, CO and CO,. Table 10.14 summarizes the detection limits reported by Hartmann and Dimick (155).

6. Linearity Hartmann and Dimick (155), using an exponential dilution flask to generate binary gas mixtures of known composition, have found that the dynamic linear range of their HID was about 10,000.

7. Prediction of the Response Factors Response factors are not predictable and vary greatly from one compound to another, so calibration is in order. With such an extremely sensitive detector, calibration must be made using an exponential dilution flask (see Chapter 14, Section 1.l.b). According to Bourke et al. (154), the calibration curves and the relative response factors seem to be stable over long periods of time. 8. Maintenance and Cost

As with other extremely sensitive detectors, the HID requires to be operated and maintained with considerable care. Ultrapure helium must be used, columns should

477 TABLE 10.15 Comparison between the Performance of the main Gas Chromatographic Detectors (after ref. 108) Detectors

Sensitivity

Detection Limit **

Dynamic Linear Range

Selectivity

Gas Density Balance Thermal Conductivity Electron Capture Flame Ionization Thermoionic Photometric Photoionization Helium

1,000 10,Ooo 800 1.10-~ 2.10-2 4.10-’

2.10-~ 2.10-6 2.10-1’ 2.10-~ 3.10-l’ 2.10-~

5,000 50,Ooo

N N Y N Y Y Y Y

2,000 1,~,oOO 10,000 none 1.10’ 10,Ooo

In mVXmL/mg for concentration detectors (except ECD, mAxmL/mg), in C/mg for mass flow detectors (FID, TID). ** In mg/mL for concentration detectors, in mg/sec for mass flow detectors. (Reprinted from Analytical Chemistty, 43, 113A (1971).)

be well conditioned prior to their use on the gas chromatograph, tubings and accessories should be well cleaned and dried before assembling. For these reasons the HID is difficult to incorporate in an on-line process control gas chromatograph. It remains a laboratory detector, in spite of the need of process engineers for a detector with its kind of performance.

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481

CHAPTER I 1

QUALITATIVE ANALYSIS BY GAS CHROMATOGRAPHY

The Use of Retention Data TABLE OF CONTENTS Introduction

.....................................

1. Absolute Retention Data 2. Relative Retention Data

.............

482

......................... ...........

4. Retention Index Increments

.................... ............. ...............................

..........................

c. Contribution of Mixed Mechanisms

.....

...........................

a. Fluctuations of Ambient Parameters . . . . . . . . . . . . . . . . . ......... b. Errors of Measurements . . . . . . . ........................... 3. Accuracy of Derived Retention Data . . . . . . . . . . . . . . . . . . . . . .......

.......... b. LostPeaks ..................... c. Movingpeaks . . . . . . . . . . . . . . . . . 1. Use of Special Plots of the Retention Data

........................ ............................... ......

................... .............

a. Effect of Carbon Chain Length in Homologous Series . . . . . . b. Correlation with Vapor Pressure and Boiling Point . . . . . . . .

a. Homologous Series . . . . . . . . . . . . . . . . . . . . . . . . . b. Functional Group Contributions . . . . . . . . . . . . . . .

498 499 499

.............

............

508

...........

.............. ..............

492 493 493 493 495 497

501 501 503

.................

4. Classification of Stationary Phases

489 490

...........................

.....

515 517

482

5. Selection of Phases ................................................... a. TheNearestNeighbor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Numerical Taxonomy. .............................................. 6. Practical Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literaturecited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

523 523 524 526 526

INTRODUCIlON

~

Chromatography is a very powerful separation technique but it offers only very limited help in answering the question that immediately follows the achievement of a successful separation: “What is that?” It does not even give a ready answer to the question whether two compounds, one known, the other not, are identical or whether all the components of a mixture have been separated. The reason for the extreme difficulty, if not the total impossibility of achieving formal identification by gas chromatography is of course the small amount of information contained in a chromatogram, and the lack of accuracy in the determination of the retention data. Accordingly, the use of gas chromatography alone to identify compounds in a mixture tends to be limited to the determination of which peak corresponds to a certain compound known to be present in the mixture analyzed. When a truly unknown compound appears in a chromatogram, the analyst usually does not strive to accumulate a number of retention data on different stationary phases to attempt its identification. He merely goes and asks for a GC-MS or a GC-FTIR analysis (see Chapter 12). From the spectra obtained the identification is carried out much faster, with much greater reliability and at much lower cost. Although the practical, useful applications of qualitative analysis by gas chromatography are rather limited, as explained, considerable attention has been paid, and much work has been done on the systematic acquisition of a large data bank of retention data and on the study of relationships between these data and the physico-chemical properties of the analytes. This situation certainly contrasts with the one found in quantitative analysis, where the applications are extremely important and widespread, but where relatively little systematic effort has been invested by the scientific community. This is due to the ease with which retention data can be measured, to the immense number of possibilities, combining the few hundred stationary phases described and the ten thousand or so compounds amenable to gas chromatography and to the fact that considerable hope was once vested in the possibilities of using chromatographic data for identification purposes. This work is still useful for the characterization and selection of stationary phases and for a rapid estimate of the retention data of new compounds, helping the analyst in his rapid screening of the available stationary phases and the choice of those most appropriate for the trial of new separations. The literature on the determination and use of retention data is of tremendous size. It is impossible for us to offer a thorough survey of the field and to attempt to do justice to the many interesting papers published in this area. Indeed, more than in most other chapters, our prejudices and our ignorance are reflected in this one.

483

For further complementary details, the reader is referred to the excellent monograph by Leathard and Shurlock (l), which deals essentially with this aspect of gas chromatography, and to a more recent review published by Leathard (2).

I. CHARACTERIZATION OF COMPOUNDS BY RETENTION DATA As discussed in Chapter 1, there are two kinds of retention data: absolute and relative ones. Both can be used for qualitative analysis, but relative retention data are easier to measure and are more accurate, as the influence of a number of experimental parameters cancels out. The parameters characterizing the retention of a compound are summarized in Table 11.1, together with the equations which relate them to the data which can be measured directly and to the relevant thermodynamic data.

1. Absolute Retention Data Although absolute retention data are difficult to measure with any accuracy, the direct comparison between the retention time of an authentic compound and the retention times of the different components of a mixture is probably the most widely used method of qualitative analysis. The retention times are measured in immediate succession, on the same column, under exactly the same experimental conditions. This procedure permits a rapid and reasonably reliable identification of the peaks of the compounds which are known to be present in the mixture analyzed. It permits us to rule out the presence of a compound at a certain concentration level in a mixture, if a peak of corresponding size does not appear at the proper time on TABLE 11.1 Definition of Retention Data I.

Experimental Data, Absolute Retention Time True Retention Time Column Capacity Factor

11. Experimental Data, Relative Relative Retention Retention Index

1,

1; = 1,

- 1,

k’ = t;/t,,,

Chapter 1, Section VI.l Chapter 1, Section VIII.3 Chapter 1, Section VIII.7

Eq. 1.31

Chapter 1, Section X.l Chapter 1, Section X.2

111. Experimental Data, Corrected Retention Volume True Retention Volume Net Retention Volume Specific Retention Volume

VR = t RFo VL = 1, jFo VN = 1; jFo Vg = 273VNPo/(760mT)

Chapter 1, Section VIII.4 Chapter 1, Section VI11.3 Chapter 1, Section VIII.5 Chapter 1, Section VIII.6

IV. Thermodynamic Parameters Partition Coefficient

KR =

a = 1;*/1;,

v,/y

KR = RT/(~~OPO)

Adsorption Coefficient

K A = vN/A,

Chapter 3, Section A.111 Chapter 3, Section A.111 Chapter 3, Section B.1

References on p. 526.

484 ADSORPTION

PART IT ION

u 5:1024

5 rnin

1

Figure I I . I . Chromatograms showing the influence of the sample size on the retention time.

the chromatogram of the mixture. This method, however, does not permit a formal identification, for mere statistical reasons, because the peak capacity of even the best columns is small (a few hundreds at most) compared to the number of compounds they can elute under a given set of experimental conditions. The amount of compound injected with the mixture and separately, as a solution in a pure solvent, should be as similar as possible. Retention times change quite markedly with sample size, due to the combination of column overloading (non-linear behavior of the equilibrium isotherm) and sorption effect (see Chapter 5). The kind of results which may be obtained and which could lead to erroneous conclusions if this rule is not followed is illustrated in Figure 11.1. To avoid these problems, and as an additional security against fluctuations of experimental conditions, some people use a spike method. A small amount of the authentic compound whose presence in a mixture is to be tested is added to the mixture. Ideally the addition should be just enough to double the concentration of the compound of interest. The mixture is run on an efficient column and the unknown is assumed to be identical to the authentic compound if no doublet is observed. This is a very unsafe practice, which leads to unreliable, questionable results (3). . Comparison between net or specific retention volumes measured on a given column in the laboratory and tables of retention volumes compiled from the

485

literature or acquired previously is also possible, but still much more risky. In practice, retention is much more often than is actually realized by analysts, the result of mixed mechanisms. This is not necessarily bad, as long as the proper separation is achieved. It makes very difficult to duplicate the column prepared by the independent author who has measured the retention data. The same products and procedure should be used, but this does not guarantee an exact replication, as manufacturers improve their products and change their process periodically. Furthermore, temperature gradients (4), temperature and flow rate fluctuations also alter retention times in a fashion which is difficult to duplicate. From this standpoint, the replication of relative retention data is much easier. More confidence about the identity of two compounds is legitimate if the coincidence between retention data persists on a set of dissimilar stationary phases, regardless of the temperature. Therefore, a compilation of retention data related to the most widely used phases may be used to derive some clues regarding the sample composition. Some work has been done in this fied by Pierotti et al. as early as 1956 (5). Still, in addition to their lack of reproducibility, absolute retention data suffer from the laborious procedure of measurement which must be followed to tabulate them, and which can be avoided only in the case of the direct comparison of data measured in immediate succession. Parameters such as inlet and outlet pressure, column temperature, carrier gas volume flow rate, and mass of stationary phase must be accurately measured, which is difficult in many application laboratories. Relative retention data are easier to measure and more accurate. They are rightly preferred. 2. Relative Retention Data

Relative retention times (see Chapter 1, equation 30) are easy to measure and are much more reproducible than absolute retention volumes. Especially, the apparatusto-apparatus and the laboratory-to-laboratory reproducibility are considerably better. Relative retention data found in the literature can be used with more confidence than absolute retention volumes, although tables of the latter can be easily converted in tables of relative retention. Difference in column temperatures may be corrected if the relative retentions are available at several temperatures. A plot of the logarithm of the relative retention versus the inverse of the absolute temperature may be interpolated to provide a value at the same temperature as used for the measurements. Determination of relative retentions are made easy by the availability of programmed integrators which print on the analysis report both the absolute retention time and the retention time relative to any preselected standard. The choice of this standard is the curse of the method. Ideally, the standard should be similar to the compounds of interest, have a retention time of the same order of magnitude, and be easily resolved from them. This means that most often data of different origins are reported to different standards, in spite of various recommendations (6). To avoid the use of too many standards, Evans and Smith (7) have suggested the use of retention data relative to n-nonane, arbitrarily chosen as primary standard. References on p. 526.

486

This raises serious experimental problems as many compounds are eluted far from n-nonane. The problem could be solved by measuring separately the retention relative to the nearest n-alkane, and the slope of the plot of the logarithm of the retention time of n-alkanes versus their number of carbon atoms. Then: I

ax,c9

#

t R . X fR,.z

= II l R , z tR,9

where: - fA,x is the true retention time (see equation 7 in Chapter 1) of the studied compound, is the true retention time of the n-alkane with z carbon atoms, is the true retention time of n-nonane. This procedure is theoretically sound, but has turned out to be both clumsy and rather imprecise, especially for compounds carrying a polar group. A major breakthrough was made by Kovats (8), who suggested bracketing the pertinent peak between two n-alkanes and taking them both as standards. The properties of the retention index are discussed in the next section. In general, the precision of the determination of relative retentions is no better than 38,for values between 0.2 and 5. For values out of that range, the precision becomes poor and another standard must be used. A better precision, exceeding l%, may be obtained with very carefully controlled instruments, most often well-designed, home-made or modified gas chromatographs (4,9,10).Excellent flow rate and temperature control are required (see Section 11.2 below). Recommendations regarding the determination and publication of retention data have been published (6911). Relative retention data, as well as absolute data, fail to give enough information to permit a reasonably secure identification of an unknown compound because they contain too little information. James and Martin (12)and James (13) have suggested a potentially very powerful approach. Data obtained on different stationary phases may be combined. A compound is thus characterized by one point in a space which has as many dimensions as there are phases on which relative retention data are available. Such bidimensional plots have been used by Cartoni et al. (14) and many others. Most recent applications of chemometrics to the study of retention data can be traced to this seminal work.

3. Properties of Retention Indices Retention indices are defined by Kovats (8,15,16)by reference to two standards, the n-alkanes whose peaks bracket the band of the compound of interest (see equation 31 in Chapter 1). The retention index is given by:

481

where: - Z ( X ) is the retention index of compound X, - tA(,) is the true retention time of compound X , - Pz and Pz+l are the two n-alkanes which are eluted just before and just after the peak of compound X . The rationale behind this definition is that, for homologous series, the logarithm of the true retention time increases linearly with the number of carbon atoms of the alkyl chain, except for the first two or three members of the series:

where the coefficients a and b depend on the stationary phase and on the nature of the chemical group bound to the alkyl chain. However, a is very close for all series. This relationship makes the series of n-alkanes a uniform scale for the determination of relative retention data. Furthermore, we have shown (see Chapter 3) that the logarithm of the true retention time is proportional to the variation of the Gibbs free energy, A G ( X ) associated with the passage of a mole of solute X from the mobile to the stationary phase (at infinite dilution). This Gibbs free energy varies linearly with the number of carbon atoms in an homologous series. This makes the retention index a measure of the variation of free energy of retention:

z( x ) = 1002 + 100

AG( X ) - AG( P,)

W e + ,- )A G W

(4)

An excellent, comprehensive review (with 96 pages and 1392 references, it is rather a book) has recently been published by Budahegyi et al. (17). It discusses all the aspects of the system, the measurement of indices as well as their use in qualitative analysis. Probably due to the conditions under which the authors work, and the immense difficulties they have to gain access to a mass spectrometer, however, they have underestimated the impact of GC-MS on the use of retention indices for qualitative analysis, and overestimated the practical importance of retention indices. The advantages of the retention indices over the other methods using relative retention data made them very popular before the advent of modern GC-MS intrumentation. Their determination is long and tedious, especially in the case of compounds in complex mixtures, when the sample and a mixture of n-alkanes must be analyzed during successive runs. Precision becomes poor for polar compounds analyzed on polar stationary phases, in which the n-alkanes are sparingly soluble. As their retention takes place mainly by adsorption at the gas-liquid interface, the value of the retention index very much depends on the coating ratio (16-18). The temperature dependence is increased. The sample size and the nature of the support also have a significant influence (19-23). Data banks of retention indices are available (24,25). After a period of great popularity, especially in Europe (26,27), the use of References on p. 526.

488

retention indices has declined over the last ten years, spectroscopic methods being much faster and surer. One of the major reasons for the advantages of retention indices over other relative retention data is their low temperature dependence. This comes in part from the use as a reference of an n-alkane with a size similar to that of the analyte, in part from the use of a logarithm in the definition. Free energies vary only linearly with temperature. Accordingly, one can expect an Antoine-type relationship (28): I=A+-

A T+ C

(5)

where A, B and C are coefficients independent of the temperature. In a narrow temperature range, the variation can be approximated by a linear dependence. The coefficient dZ/dT varies from 0.05 K-' for branched alkanes to a few units per Kelvin for polar compounds. Tables have been published (see Table 11.2). The use of the value of dl/dT for identification purposes has been suggested. It gives some indications on what kind of compound an unknown cannot be, but little information on what it can be, unless the variation dZ/dT is very small. Furthermore, the dependence is not truly linear, as predicted by equation 5 , and as confirmed by experimental results (29,30).Moller (31) has measured the retention indices of 14 common drugs on OV-1 and 0-17, at temperatures ranging from 150 to 270 O C, and found a non-linear dependence. He also showed that interlaboratory deviations are much smaller between data measured at the same temperature than between data extrapolated to the same temperature. This certainly makes sense, but too often the fact remains overlooked. Since there is a definite temperature variation of the retention indices, the question arises as to what temperature the indices should be tabulated for. Wehrli and Kovats (15) suggested 130 O C. Although measurements are easy at this temperature, for the compounds they studied, it is impractical to adopt a universal temperature. There are many compounds for which retention data cannot be measured at such a low temperature, and extrapolation of an index-versus-temperature plot would be cumbersome and imprecise. It is not surprising that the agreement between values of the retention index of a compound measured under isothermal conditions and in temperature programming TABLE 11.2 Variation of the Retention Indices with Temperature Compound Class

100 dl/dT

Isoalkana 1-Alkenes Other alkenes Monocyclic Hydrocarbons Bicyclic Hydrocarbons

o* 4 -14f 3 -15f 24 - 70* 120 - 170 f 220

Reference 62. Carbowax 2OM and Emulphor 0.

489

is only fair (see Chapter 3, Section C), unless care is taken to account for their exact temperature dependence. 4. Retention Index Increments

Wehrli and Kovats (15) suggested a procedure for the identification of unknown compounds based on the use of retention indices measured on two different, standard stationary phases, one non-polar, the other one polar. They selected for a systematic study Apiezon L stop-cock grease as the non-polar phase and Emulphor 0, a partly terminated polyethylene glycol, as polar phase. They tabulated the increment:

AZ= Zp- Z A

(6)

where Z p and Z A are the retention indices at 130 O C of the same compound on the two phases. Unfortunately these two products are poorly-defined mixtures of large molecules. Certain batches of Apiezon L have been shown to be contaminated by polar oxidation products, which have to be removed by liquid chromatography over Fluosil. Production of Emulphor 0, which was not intended by the manufacturer to be used in gas chromatography, was discontinued. The concept of retention increments, however, was very fruitful and easy to extend. Polymethylsiloxanes of various origins and molecular weight, squalane and other heavy hydrocarbons have been used as non-polar phases. Virtually every polar phase has been used to determine sets of retention index increments. A I is a precious measure of the strength of polar interactions in solution. For monofunctional molecules, it characterizes to some extent the nature of the chemical groups involved. Typical values of the range of retention index increments, as measured by Wehrli and Kovats (15), are reported in Table 11.3. Prediction of the retention index increments on the basis of structure retention relationships has been attempted (15). Success was achieved in the case of monofunctional terpene derivatives. The case of TABLE 11.3 Retention Index Increments Compound Class

AI

Nitriles and Nitro Compounds Alcohols Alkyl Formates Alkyl Acetates Alkyl Butyrates Aldehydes and Ketones Alkyl Bromides and Chlorides Ethers Olefins Naphthenes

340-410 300-360 200-280 160-200 180-250 170-260 120- 180 60-100 30- 50 20- 50

I(Emu1phor 0)- [(Apiezon L), after ref. 15. References on p. 526.

490

polyfunctional compounds, which is of major practical importance, is too complex to be dealt with by this approach. The retention index increments of the different functions are not additive; the functional groups interact and correction coefficients would have to be included in the calculation. Finally, the prediction becomes inconclusive. 5. Conclusion

Retention indices have become the most practical way of reporting retention data. The temperature at which the indices are measured should be selected so as to permit direct experimental determination of the index (as opposed to extrapolation) for the largest possible number of compounds. Identification schemes based on the comparison between the retention indices measured for an unknown on two or more different stationary phases, and the value of the retention index increment calculated by combination of the increment contributions for different possible structures of this unknown give results which are inconclusive at best, and are dubious in most cases. Since the main virtue of the retention index system is the availability of a readily extendable series of standards, defining a scale permitting the easy comparison of the retention data of a large number of compounds, other, similar retention index systems have been suggested and used for the study of polar solutes which are analyzed with stationary phases on which alkanes are retained more by adsorption at the gas-liquid interface than by dissolution in the bulk. For example, various authors have used the J-indices, with the alkanol series (32), the carbon number or the equivalent chain length, with the n-fatty acid methyl esters (33-39, the steroid numbers (36,37) and the phenyl numbers (38). These systems are useful in particular cases but lack generality. Because the retention index system has become so enormously popular in some circles, a word of caution is necessary. The retention indices do not contain any information which was not available in the retention volumes. The advantage of the index system is in the ease of the calculation, handling and storage of the data. As for any system of retention data, the indices characterize a compound by a mere number of limited accuracy, however, which is not sufficient to permit any valid identification of a total unknown. Before discussing the relationships between structure and retention further, it is necessary to discuss the precision and accuracy of the data used, and the procedures required to improve the quality of these data. 11. PRECISION IN THE MEASUREMENT OF RETENTION DATA

Depending on the experimental conditions under which retention data are determined, their precision and accuracy may vary considerably. It is pointless to use any procedure to handle these data, which would require a precision better than the one available. The sources of errors are numerous and some of them are difficult

491

to control. We separate the errors originating in the chromatographic system proper, which are mainly systematic errors, from the instrumental errors, most of which are random. 1. Sources of Error Originating from the Chromatographic System

The main sources of errors associated with the lack of definition or reproducibility of the chromatographic system are (i) the column overloading, resulting in an incorrect definition of the data measured, (ii) the slow change in the properties of the stationary phase, resulting in a drift of the retention volume, (iii) any significant adsorption on one or several interfaces involved in the chromatographic column, and (iv) the determination of the dead volume or gas hold-up time, which again results in an incorrect definition of the data measured. These errors can be controlled to some extent, when they have been identified. a. Column Overloading

In analytical chromatography, it is always assumed that the retention times are independent of the sample size. This is not true. As a general rule, the retention time depends on the sample size. It may increase or decrease with increasing sample size, depending on the curvature of the isotherm at the concentration origin, and on the average density (i.e., average pressure, Po/’) of the camer gas (see Chapter 5). In some range of sample size, however, the variation of the retention time is too small to be significant. This range is small for compounds having a low vapor pressure, i.e., for strongly retained compounds, the same for which a rather large sample size is required for detection. Indeed, the compromise between a sample size low enough to avoid column overloading, but large enough to permit detection of the compound band and precise determination of its retention time may be difficult or even impossible to find out, especially when a TCD is used. The chromatograms on Figure 11.1 illustrate the difficulties encountered, and the kind of bands an overloaded column may generate (see Chapter 5 , Section I11.2.a). An error of this type can be detected by running systematic determinations of the retention times of series of compounds with sample sizes varying by at least one order of magnitude.

b. Change in the Properties of the Stationary Phase The chemical composition and amount of the stationary phase contained in a gas chromatographic column is prone to change progressively, but steadily, especially at high temperature. Consequently, the retention volumes will also change. Depending on the reactions taking place in the column, the slow pyrolysis of the stationary phase may have more or less serious consequences. Losses of stationary phase by vaporization are the least consequential. All retention volumes vary similarly and relative retention data, as well as retention References on p. 526.

492

indices, hardly change, at least as long as the phenomenon is not severe enough to leave some fraction of the surface bare or to change markedly the surface area of the gas-liquid interface (39). When the stationary phase decomposes thermally, its composition and structure may vary, for example when a polymeric phase decomposes by a random process. A variation of 100 units of the retention indices of fatty acid methyl esters on poly-diethylene glycol succinate, at 150O C has been observed over a period of six months (40). In this case, obviously, the use of the retention data determined and stored in a data bank for identification purposes is improper. The catalytic effect of the support, or of certain impurities present on the surface of some supports, may enhance the thermal decomposition of the stationary phase. Similarly, the presence of trace amount of oxygen in the carrier gas may have a very serious influence on the stability of retention data and on the useful column lifetime. This is because a number of pyrolysis reactions are sensitized or triggered by an autoxidation mechanism. The use of an entire stainless steel instrument, the replacement of standard elastomeric membranes on pressure and/or flow rate controllers by steel membranes (performing less but totally impermeable to oxygen), and the use of a metal cover to protect the septum when it is not in use, may greatly improve the long-term repeatability of retention indices. The use of well-defined chemicals as liquid phases, rather than of polymers, is another method to limit the extent of these progressive changes in the nature of solute-solvent interactions, by reducing the rate of the stationary phase oxidation. It is strongly recommended to periodically run a standard sample mixture and to check the variation of retention data of these compounds. c. Contribution of Mixed Mechanisms

Adsorption of the analyte at the various interfaces - gas-liquid, liquid-solid, gas-solid - in the chromatographic column contributes to the overall retention. From the analyst’s point of view, adsorption is not necessarily bad. It has been shown in Chapter 7 that the phenomenon can be profitably used by permitting unusual selectivities, which could not be obtained otherwise. The difficulty, for identification purposes, comes from the extreme difficulty of properly reproducing the relative importance of various interfaces. This makes the use of retention data taken from the literature highly questionable. Data measured on another column, often prepared with a different support, or a similar support differently treated, are difficult to compare, and often do not agree at all. Furthermore, in a large number of cases, the indications found in the literature are insufficient to permit even an attempt at reproducing the column. Additional difficulties arise because of the poor definition of many commercial grades of polymers which are not intended to be used as stationary phases for GC, such as the drift in their properties during the last thirty years, and the changing nature of additives. Adsorption changes the retention times of polar and non-polar compounds to a different extent, and thus has a serious effect on retention indices. The shifts observed may be large enough to mislead the analysts completely (41,42). Analysts

493

should know the importance of a change in the nature of the support or in the phase ratio, and the possibility of using these phenomena to reverse elution orders or considerably improve some separations. The importance of adsorption on the retention data of the compounds under study may be checked by measuring these data on different columns prepared with the same liquid phase coated on different supports. The near identity of the retention data on several different columns could be considered as validating the assumption of pure partition. This problem has been discussed at length by Berezkin (43), in relation to the role of the chromatographic support.

d. Measurement of the Gas Holdup Time No truly inert compound exists. Depending on the detector used, it is common practice to consider nitrogen (TCD), methane (FID), oxygen (ECD) as a suitable inert tracer for the determination of the column gas hold-up time. Although the solubility of these gases in the stationary phase is very small, it is not zero and, in some cases, it is not even negligible. There are some doubts regarding the use of the gas hold-ups determined directly. On the other hand, there are no direct data on the solubility of these gases in organic solvents. It has been suggested that a calculation method be used instead, based on the assumption of the linearity of a plot of the logarithm of the retention time of homologous compounds, versus their number of carbon atoms (44,45). Details of the experimental procedure are given by Kaiser (46). This is a very dangerous method. It takes a long series of homologous compounds to determine the gas hold-up with a reasonable precision, as has been demonstrated in liquid chromatography, where a similar problem arose (47). There is no serious theoretical justification to the additivity of the free energy of dissolution on which this rule is based, and it is certainly not applicable to the first few members of any homologous series. The systematic error may be very important. Unless extreme caution is taken, the error is probably much larger than the one achieved by direct determination with the proper inert tracer. 2. Instrumental Sources of Error

The main contributions to this type of error are the errors of measurement, usually caused by excessive signal noise, the errors associated with the definition of the retention time and the time origin, and, finally, the errors arising from random fluctuations and drift of the experimental conditions, such as column temperature, temperature gradient, inlet pressures or flow rate, etc. a. Fluctuations of Ambient Parameters

The precision of the retention time measurements has been studied in detail by Goedert and Guiochon (48). Differentiation of the relationship between the retenReferences on p. 526.

494 TABLE 11.4 Specificationsregarding the Stability of a Gas Chromatograph for the Measurement of Precise Retention Ties* Precision required **: Relative Fluctuations (%a) of Outlet Pressure Pressure Drop Temperature *** Error of Measurement (W)

1%

0.01%

25

0.25 0.0055 0.001 0.005

0.55

0.1 0.5

After ref. 48.

** Standard Deviation of a Series of Measurements. *** i.e., 0.4' C at 127 'C. tion time and the experimental parameters (see Chapter 2, equation 9):

provides the basis for this study. An evaluation of the error propagation coefficients permits the assessment of the contributions of these parameters. Typical results are summarized in Table 11.4.The results are similar for all compounds, except so far as the temperature is concerned. Specifications regarding temperature control will be tighter for high boiling compounds, which have a larger vaporization enthalpy. The table demonstrates that a 1% standard deviation on the measurements of retention times is relatively satisfactory, and requires a rather good control of the column inlet and outlet pressures and of the temperature (48). The allocation of the different contributions to the total error performed in Table 11.4 is somewhat arbitrary. It has been done on an equal basis for each of the parameters; the value of the acceptable level of fluctuation of this parameter has been derived then from the corresponding error propagation coefficient already obtained from equation 1.Although other compromises are possible, balancing the specifications differently, there is, in practice, little flexibility and the final results are not much affected. Accordingly, there is little utility in considerably improving the quality of the temperature control when the pressure control is neglected, a comment which could have been made about more than a few commercially available instruments. The influence of short term fluctuations of the temperature and of thermal gradient on the accuracy of retention time measurements has also been studied by Goedert and Guiochon (49). They have shown that, because of the non-linearity of the relationship between the column capacity factor and the temperature, the time-averaged temperature measured at a point in the column is different from the temperature corresponding to the average retention time or capacity factor. This limits the permissible amplitude of the short term fluctuations which can be tolerated. Gradients have a similar effect, since they are seen as a time fluctuation

495

by the moving analyte band (49). Their influence is more pernicious, as they are more difficult to detect. It is difficult to measure the column temperature at different points, with different sensors, which have to be calibrated. Their effect is important, however. It can be minimized by coiling the column and placing its axis parallel to the direction of the temperature gradient. Flow rate and pressure controllers are usually the weakest part of gas chromatographic instruments. This is due in part to the less glamorous status of a (low tech) plumber compared to that of a (high tech) electronic specialist. Unfortunately there is no cheap, convenient system of pressure or flow rate control. Finally, most pressure controllers work by reference to an external pressure, most often the atmospheric pressure. Thus, a normal inlet pressure controller tries, in fact, to keep the pressure differential between column inlet and outlet pressures constant. Should the column outlet pressure need to be controlled, for the sake of carrying out very precise measurements, the outlet pressure controllers have to be designed to work by reference to vacuum, while the inlet pressure controller will work by reference to the outlet pressure (4). This combination minimizes the errors made. b. Errors of Measurements

Systematic errors of measurements are associated with the definition of the time of origin (injection) and the retention times, and with the clock precision and accuracy. Random errors result from the contribution of signal noise and originate in various parts of the data acquisition hardware and software (4,48). The importance of the precision and accuracy of the time origin, i.e., the moment when the injection is actually performed is quite obvious. Great care should be paid to the reliability and repeatability of the injection devices used (see Chapters 8 and 9), as they can be the source of significant errors (51). The precision of the time clock used is also a possible contribution to the total error. Retention distances measured on a paper chart have a limited precision. For this reason also, numerical data acquisition, using a computer or a modem electronic integrator permits a serious improvement in the precision of the data recorded. As discussed in the previous section, there is no compound for which the column capacity factor is truly null. Methane and nitrogen are sufficiently retained by most stationary phase for the true retention data to be in error, especially in the range of k’ values below 1 (52,53). Various corrections can be made. They are certainly necessary when accurate data are needed. As stated above the often used (52,54) correction based on the linearity of the plots of true retention data of n-alkanes versus the number of their carbon atoms is fallacious. The accuracy of the determination is very poor, unless extreme care is taken to overcome the major pitfalls described by Grushka et al. (47). Retention data measured or calculated by independent methods can be used with better success (53). The error made on the estimation of the gas hold-up is more important than has been recognized by many authors. It may account for a large part of the discrepancies between retention data of hydrocarbons measured on non-polar stationary phases by different authors. Finally, the effect of the precision on the determination of the retention time of References on p. 526.

496

the analyte band should be assessed. Too often the time of peak maximum is determined for peaks which are obviously unsymmetrical. This is very wrong, as exemplified by the data on Figure 11.1. The measurement of the peak mass center or first moment is more difficult. It is an improvement only when certain causes of band tailing are prevalent, such as an injection with an exponential decay, or a slow, first-order kinetics of equilibrium between the mobile and the stationary phase. There is no advantage in measuring the peak first order moment, rather than the time of its maximum, in the case of an unsymmetrical peak resulting from column overload (non-linear isotherm, see Chapter 5). Furthermore, the determination of the peak first moment is easy only when data are acquired with a computer, and when the program either has a feature permitting this calculation or allows access to the raw data. A last difficulty with the determination of moments is the fact that any deviation of the detector response from linear behavior contributes to an important systematic error, while the effect on the retention time of a band maximum is much smaller. The origins and the magnitude or the errors made on the measurements of retention data have been discussed by Cram et al. ( 5 9 , Goedert and Guiochon (4,48,49), and Petitclerc and Guiochon (56), using computer simulations of the measurement process, and comparisons of the precision actually achieved with that predicted by the simulations. Even for symmetrical peaks, the effect of noise on the precision of the retention time of the peak maximum may be important (lo), unless curve fitting is used (i.e., the data points which are larger than 0.9 or 0.95 times the largest data point are fitted on a parabola, and the best estimate of the peak height and retention time are the coordinates of the maximum of the parabola obtained). Some electronic integrators introduce a bias due to the definition they use in practice, the retention time being the moment when the signal differential reaches some negative threshold level (48). In the case of data acquired with a computer, the density of data points collected during the elution of the peak should be sufficient (about 20 points per standard deviation of the Gaussian peak) (10,55,56,58). The influence of the time window during which data are collected and of the signal-to-noise amplitude ratio have also been studied in detail. The time window during which the integration is performed should be such that the ratio of the signal at both ends of the window to the peak maximum be equal to the value of the relative error which has been accepted (55). Finally, the random error due to the detector noise is inversely proportional to the signal to noise ratio (10). Retention data have been measured with an extremely high precision by different groups (10,49,55,56,58,59). The reproducibility achieved is better than 1 part in 10,000 (relative standard deviation). There have been few useful applications of this work in analytical practice, because there are few chromatographic phase systems which are reproducible or even repeatable at this level. Only adsorption on graphitized carbon black or on Molecular Sieves seems to fulfill this condition (60). A precision of 0.1% would be quite useful in practice and does not seem to be very difficult to achieve, with some care and a minimum understanding of the error problems in analytical chemistry and, more specifically, in chromatography.

497

3. Accuracy of Derived Retention Data In the previous subsections we have discussed the measurement of the retention times, which are the data directly derived from the chromatographic experiments, the sources of the errors made, the precision and accuracy of the data obtained. In practice, however, retention times and relative retention times are not the most widely used retention data. It is necessary to examine how the errors made in the measurement of retention times influence the precision of the derived data (see Chapter 1, Section VIII). We discuss here the errors in the retention indices and the errors in the retention volumes. The relationship between the error made in the retention indices and the error made in the retention times is quite straightforward (61), albeit rather complex. Two conclusions are important. First, because of the definition of the retention indices, using a logarithmic relationship with the relative retention times of the analyte and n-alkanes, and because of the properties of the differential of a logarithm, the absolute error made on the retention index is proportional to the relative error made on the determination of a relative retention time. Errors on the retention indices are of the order of a few hundredths of a unit to a few units, depending greatly on the column efficiency, which directly influences the precision with which the band maximum may be located. Finally, when precise data are needed, it is better to use an interpolated scale for the frame of reference, i.e., to calculate the relative retention of two successive n-alkanes from the slope of the plot of the logarithm of the retention time of a series of n-alkanes versus the number of carbon atoms in their chain, rather than to take the relative retention of the two alkanes eluted immediately before and after the analyte. This permits a reduction of the total error, as shown by statistical calculations and simulation (54). The determination of precise retention volumes is difficult. The retention volume is obtained as the product of the retention time by the flow rate, measured independently. The fluctuations of the flow rate are averaged in both determinations, but this cancels out their influence on the product only to some extent. The two averages are usually taken over different time scales, the retention time is of the order of several minutes or several tens of minutes, while a flow rate determination takes less than a minute. Furthermore, the averaging process is different, the flow rate being measured at column outlet, while the retention time depends on the average velocity. The compressibility of the carrier gas makes the column to behave as a resistor-capacitor circuit, an excellent device to dampen the effects of fluctuations, especially short term ones. While the random error on the retention volumes depends on the flow rate fluctuations, the accuracy is directly determined by the accuracy of the flow rate determination. It is extremely difficult to calibrate flow meters with an error less than 0.2 to 0.5%.Absolute retention data are very difficult to measure accurately. For example, to study the predictions of statistical models of adsorption on graphitized carbon black, Vidal-Madjar et al. preferred to use AC, rather than the entropy. AC, can be obtained directly from the variation of the adsorption enthalpy with temperature, a procedure which requires only the accurate measurement of retention times (60). References on p. 526.

498

4. Artefacts A variety of phenomena may lead to erroneous results, because peaks appear which do not correspond to components of the mixture analyzed, because existing components may give no peak or because peaks corresponding to true components appear where they were not expected. These artefacts were reported very early on. Burchfield and Storrs (131) have suggested a general approach. The most serious problem raised by artefacts is the difficulty in predicting them. Their harmfulness is seriously enhanced by the complacency of analysts. a. Ghost Peaks

These are peaks which appear on the chromatogram, look genuine, contrary to spikes or slow base line drifts, but do not correspond to any component of the sample. They may be completely unrelated to the sample or may result from the disappearance of sample components. The most simple case of real ghost peaks is observed in temperature programming, when compounds resulting from the slow thermal degradation of the injection septum are trapped at the column inlet during the periods when the column is cold and are eluted as components of the next sample run (132). Septa should be treated carefully and preconditioned if needed. Some well designed instruments keep the septum at a relatively cold temperature, by placing the septum at a distance from the injection port, by providing a heat sink and, possibly, by forcing a stream of cold carrier gas just above it. This has the additional advantage of reducing the extent of oxygen contamination of the carrier gas. Septa lined on the inner side by a thin Teflon layer are offered for use at high temperature. Many ghost peaks originate from pyrolysis reactions, isomerizations or adsorption/desorption phenomena in the injection port or on the top of the column. Many samples contain a small amount of non-volatile material. These compounds accumulate in the injection port, broil and generate tars and charcoal products which may react with sample components, dissolve them or adsorb them. Memory effects have been often reported. They are due to the adsorption of a polar compound from a previous sample, followed by its desorption upon injection of another polar compound. For example, Smith and Gosnell (133) observed that the injection of a series of identical samples of dilute propionic acid resulted in the elution of peaks of increasing size, tending rapidly towards a limit. If a series of samples of valerianic acid is then injected, chromatograms are obtained exhibiting two peaks, one for each acid. The size of the propionic acid peak decreases rapidly, while the size of the valerianic acid peak increases. Carefully and frequently cleaning the injection port permits an almost total elimination of this kind of problem. A good solution is having a glass insert in the injection port, and changing it often. A similar phenomenon of repetition has been reported by Kaye (134), but it was attributed to the adsorption of a particular solute on the wall of the tube connecting the column and the detector. When performing the analysis of naphthalene with a

499

UV spectrophometer as detector, it was observed that a small naphthalene peak was eluted in the same time as the solvent, a saturated hydrocarbon, giving no response with this detector. In this case, the adsorption of naphthalene cannot take place in the sampling port or on the column. In the former case, the extra naphthalene peak would be eluted with the retention time of naphthalene; in the latter with an intermediate retention time. The size of this ghost naphthalene peak depends on the size of the original naphthalene injection and on the time elapsed. It appears that many ghost peaks can be generated during trace analysis, when samples diluted in polar solvents, and especially water, are analyzed. The solvent vapor may desorb a large number of compounds trapped in the column. It has been reported that the front of the elution peak of methanol, ethanol and propanol on some polyethylene glycol phases contains a small amount of methyl, ethyl or propyl formate, formed by chemical reaction with the formic acid or formaldehyde contained in some polyethylene glycol samples (135,136). This might result in erroneous analyses. b. Lost Peaks These are essentially due to thermal decomposition or isomerization. Terpene derivatives are especially sensitive to thermal degradation and to reactions of isomerization catalyzed by the support and have often been used for the study of the sources of artefacts. Such effects may originate in the injection port, the column, the detector. It has been shown that commercial phthalates used as stationary phases contain enough acidic residues to catalyze the isomerization of a-pinene into P-pinene (137). Proper treatment of the solid support used to make the column is essential (see Chapter 6). Some stationary phases may become highly reactive at high temperatures. Polyesters, for example, may react with alcohols or esters and absorb them irreversibly (135). Unsaturated fatty acid methyl esters could be lost on polyester columns at 240 O C. It seems that it would be better to use these phases at relatively low temperatures, with a low coating ratio, in order to minimize the possible reactions. Reactions, such as pyrolysis or catalytic hydrogenation, may also take place in the detector, e.g., on the hot wires of thermal conductivity detectors. This phenomenon has detrimental effects only if fractions are collected for further identification. c. Moving Peaks

In most cases, bands move in the chromatogram because the column is aging. In gas-liquid chromatography this is due to vaporization and pyrolysis of the solvent. The relative retentions of some compounds may drift considerably. This should be avoided by keeping the column temperature below the recommended limit. Retention times may also change with the sample size (see Figure 11.1). In gas-solid chromatography, the progressive poisoning of the adsorbent surface References on p. 526.

500

by traces of high boiling or strongly sorbed compounds may also take place. These phenomena are much less important in gas modified layer chromatography, especially if the carrier gas contains steam (see Chapter 7).

111. COMPARISON BETWEEN

RETENTION DATA

In the simple case, the use of retention data for identification purposes involves merely a comparison between the retention time of an unknown and that of a series of authentic compounds. Since the essential ability of chromatography is to separate substances, a negative conclusion - these two compounds can be separated, thus they are different - can be reached with certainty. A positive identification, on the other hand cannot; there are just too many compounds which may have the same retention time. The odds can be improved very simply, by just measuring the column efficiency for the unknown and for the mixture containing both the unknown and the suspected compound in the same amounts. If the measured efficiency is the same and if its precision is about 108,the compounds could not be resolved with a resolution unity, by a column about 10 times more efficient than the column used. We must emphasize again that a positive result for this test is not a proof that the two compounds are identical. In many cases, unfortunately, the authentic compounds one might need are not available. There is not enough information available about what the unknown might be, authentic compounds are expensive, on back order, or just not available, tables of retention data found in the literature are not reliable, the stationary phase used is not available or the results cannot be duplicated. It might be considered to be useful to organize the immense amount of data available in the literature and to attempt to draw relationships between structure and retention. This would conceivably permit the prediction of the retention data of unavailable compounds, the comparison of these results with the retention time of the unknown and the elimination of a number of possible choices, now become improbable. Charts have been widely used in these applications, because vision permits the rapid understanding of complex relationships and the easy observation of outliers or inconsistent results. From these charts various equations, most of them purely empirical, can be derived for the prediction of retention data. Initially, these methods were based on the use of additive contributions to the retention indices, related to the presence of various molecular features. Later the whole armory of chemometrics has been brought into play. By and large the results of these efforts has been vastly disappointing. Most published work is based on rather small data sets. A vast majority is devoted to compounds with a single functional group, and only one or very few such groups are considered. The results are then as brilliant as they are useless in practice. The basic problem, in our opinion, is that there is just too little information in the retention data to warrant the success of any identification scheme based on its use.

501

1. Use of Special Plots of the Retention Data Various relationships between retention indices and other molecular properties, or between retention indices on various phases have been studied. The most important ones involve the chain length, its connectivity, the vapor pressure, the refraction index, the dipole moment, and retention indices on other phases. a. Effect of Carbon Chain Length in Homologous Series

According to Martin (63), the free energy of interaction between a solute and a sdvent, i.e., the molar free energy of dissolution of the solute, i , in this solvent, j , is an additive function of the interactions of each individual segment of the solute molecule with the solvent. If the solute molecule is, for example, CH3-(CHz),,-X,we have: A G ( i , j )= A G ( C H , , j ) + n A G ( C H , , j ) + A G ( X , j )

(8)

The first correlation between retention data and physical characteristics of the analytes was derived by James and Martin (57), who showed that a plot of the logarithm of the relative retention of normal fatty acids on silicon oil (with stearic acid to deactivate the solid support) versus the number of carbon atoms is a straight line (see Figure 11.2). As usual, the relationship does not hold for the first two terms. Later, Ray (138) showed that the same relationship is valid for many homologous series (see Figure 11.3). log (R.V.)

4.0

3.5

30

2.5 A Q

n-acids iso-acids

2 .o

1.5

1.O

0 2 4

6

8 10 12 14 16 C atoms

Figure fl.2. Plot of the logarithm of the corrected retention volume of carboxylic acids versus the number of carbon atoms. Stationary phase: silicone oil and stearic acid. After James and Martin (57).

References on p. 526.

502

Figure 11.3. Plot of the logarithm of the retention volume of different compounds versus the number of CH, in their alkyl chain. After Ray (138). 1 - n-alkanes, 2 - n-alkanols, 3 - n-alkyl formates, 4 - n-alkyl acetates, 5 - n-alkyl propionates, 6 - methyl n-alkyl ketones.

Since the retention indices are related to the free energies of dissolution, we may as well write:

The first consequence of this equation is to predict that the retention indices of homologous compounds will vary linearly with the number of carbon atoms in the chain, a result which has been verified many times, for example by Arakelyan and Sakodinski (64) who found it to hold for over 18 different homologous series on many stationary phases. There is so far no exception known. However, the relationship is not expected to hold too well for small values of n, for which interactions between the groups X and the CH2 groups are not negligible. Equation 9 cannot be accurate either. If it were, the plots of the retention indices of homologous compounds versus the number of their carbon atoms would be parallel for all series, which is not true. Furthermore, esters such as alkyl acetates and fatty acid methyl esters would have the same retention index for a given total carbon atom number. Such isomeric esters are not easy to separate, but they can often be resolved. Although the retention indices seem to satisfy equation 9, there is a definite curvature in the plots of the logarithm of the retention volume or time, versus the number of carbon atoms in any homologous series. This has been shown and

503

discussed by Golovnia and Grigoryeva (65), and is easy to check using McReynolds data or any other set. The same is also true of the logarithm of the vapor pressure, which underlines a very general phenomenon, which could be related to the progressive passage of the molecule from a rod-like structure to a random coil, as the carbon number increases. Finally, it is not really difficult to identify a member of an homologous series, but this is rarely a problem of major importance. Other relationships, useful for less trivial compounds, must be sought. b. Correlation with Vapor Pressure and Boiling Point As we have seen above, within an homologous series, the logarithm of the retention volume, the retention index, and the logarithm of the vapor pressure vary linearly with the number of carbon atoms. It is to be expected that the retention data will be related to the vapor pressure at the column temperature. This is to be expected also from equation 7 in Chapter 3 , which relates the column capacity factor to the vapor pressure and the activity coefficient at infinite dilution. In fact, it could be expected that the same correlation between log P o and I would hold for branched alkyl derivatives, at least as long as the group X does not become sterically hindered by the alkyl chain. This is in agreement with the fact that, at infinite dilution, the activity coefficient of homologous compounds is nearly the same. Many conclusive examples of the correlation between retention index and vapor pressure have been reported (64,66). Leathard and Shurlock (1) have proposed the following equation to account for the correlation between the specific retention volumes, V,, and the boiling points, T,, of analytes:

log

v, = log- 273R MS

where: - k is the Trouton constant, - T, is the boiling point of the solute, - Ms is the molecular weight of the liquid phase, - y," is the activity coefficient of the solute at infinite dilution. This equation is mostly valid for non-polar or slightly polar compounds. Then, the Trouton constant is approximately equal to 23 cal/mole K and the activity coefficient at infinite dilution is not too far from unity. Neither the correlations of the boiling point or the vapor pressure with the retention data (logarithm of the retention volume or the retention index) is very good. They assume that the changes in the logarithm of the activity coefficients at infinite dilution are small compared to the variations of the vapor pressure, which is not always exact. These correlations should not be ignored, however, as they often give surprisingly good results, as exemplified by Figure 11.4. The linearity of the plot observed on this Figure deserves some comment, since equation 10 has been derived for non-polar solutes. For alkanols, Trouton's law is not valid, and the

-

References on p. 526.

504

Figure 11.4.Plot of the retention index on Apiezon L versus the boiling point. The dotted line connects the n-paraffins. Group 1, hydrocarbons, alkyl chlorides and bromides. Group 2, esters, ketones and aldehydes. Group 3, alcohols. Reproduced from Z.Anal. Chem. (140) by permission of Springer Verlag, Berlin.

activity coefficient at infinite dilution is far from unity since strong association takes place between the solute and the stationary phase. However, the strength of the hydrogen bonds, either alcohol-alcohol (AH ca 5.7 kcal/mole) or alcohol-ether (AH ca 2.5 kcal/mole) is relatively independent of the size of the alkyl group. Thus, both the pseudo Trouton coefficient and the activity coefficient remain approximately constant for the whole series of primary alcohols. Many other examples have been reported by Arakelyan and Sakodinski (64). c, Correlation between Retention Data on

Two Different Phases

Whenever any of the relationships just discussed hold for a given set of compounds on two different stationary phases, a plot of the logarithm of the retention

505

iso- iodides X’

volume of one compound on one phase versus the logarithm of its retention volume on the other phase is also linear. According to equation 7 in Chapter 3, we have:

where: - Q, is a numerical coefficient, a function of the design of the two columns, i.e., their respective phase ratios, - M(1) and M ( 2 ) are the molecular weights of the two stationary phases, - y(1) and y ( 2 ) are the activity coefficients at infinite dilution of the analyte in the two stationary phases. As long as the ratio of the activity coefficients remains constant, i.e., for chemically similar compounds, the plots of k’(1) versus k’(2) will be linear. The first graphical relationship of this kind was proposed by James (67) as early as 1952 (see Figure 11.5). It can be most helpful for recognizing that a certain compound does not belong to a given chemical family. If one phase is selective (i.e., polar), and the other is weakly polar or non-polar, the points corresponding to compounds belonging to different chemical groups will lie in different regions of the diagram. Retention data obtained on two different phases can thus permit the classification of the components of a mixture. This method is quite similar to the one developed by Wehrli and Kovats (15), based on the use of differences between the retention indices of a compound on two stationary phases.

d. Use of Three Stationary Phases The use of only two phases, one non-polar and one polar, may not permit a sufficient differentiation between the compounds studied. In such a case, the selection of two polar phases capable of giving different types of interactions, such as an electrodonor and an electroacceptor phase, may permit a much better characterization of the compounds studied. Then a tridimensional plot is necessary. References on p. 526.

506

/

D

0.30

N

Figure 11.6. Triangular diagram based on the retention indices of cornpounds on three different stationary phases. The homologous compounds are located on straight lines originating at the mass center of the triangle. G, mass center of the complete triangle. The triangle is enlarged for clarity. 1, alcohols. 2, trimethylsilyl ethers. 3, acetates. 4, trifluoroacetates.6, pentafluoropropionates. 7, butyrates. 8, heptafluorobutyrates. After ref. 40.

Coincidence between the points representing an unknown and a reference compound now offers a significant probability (still far from unity though) that they are identical. Furthermore, the area of the diagram where the point corresponding to a compound lies gives some clues as regards its chemical nature, especially if it is a monofunctional compound (it is too bad that most compounds that are difficult to identify are polyfunctional ones). Ideally, the three phases should be selected so that there is no correlation between the retention data or at least the activity coefficient contribution (orthogonal set). Thus, their selectivities are very different. Brown (68) has suggested the use of Apiezon L (non-polar phase), trinitrobenzene (electron acceptor stationary phase) and Reoplex 400 (polypropylene glycol adipate, electron donor). This is a good set, but cannot be generally used because of the poor thermal stability of the last two phases. Azen and Gushchin (69) have suggested the replacement of Reoplex 400 by triethylene glycol diethyl ether. Other systems can be used. Rules for the selection of a set of phases as nearly orthogonal as possible are discussed later in this Chapter. Normalization of the data (68), for example the use of the following set of coordinates:

J,

=

J -

-

12

I,

+ I, + I3

I,

+ I , + l3

13

507

permits the use of a triangular, planar plot, which is much easier to handle than a three-dimensional plot (see Figure 11.6). It can be shown that on such a diagram the plots representing an homologous series should be straight lines going through the mass center of the triangle (40). Although it has been advocated by some authors (70), the use of four or more phases is rare and the trouble seems to be out of proportion to the return. e. Use of Non-homologous Series

Identification by coincidence of the points corresponding to an unknown and a reference compound is not restricted to homologous series, but most of the correlations described here are valid only for the members of these series and do not apply accurately to other compounds. In particular they do not describe the behavior of positional isomers or branched alkyl chains. Such secondary effects cannot, as a rule, be taken into account properly in terms of two- or three-dimensional plots. An exception is provided by the effects of substituents on aromatic rings which can be fairly well described in terms of the Hammett equation, as shown by Karger et al. (71):

where: - the subscripts 1 and 2 stand for the substituted and unsubstituted ring compound, respectively,

20'1. EGSS-X o t 168°C

_L

-0.4

Figure 11.7. Plot of the logarithm of the ratio of the activity coefficients at infinite dilution of phenol to substituted phenols, versus the Hammett substituent constant. 1, m-CH3. 2, p - C H , . 3, m-C2H5. 4, p-C2H5.5, m-i-C3H7.6, p-i-C3H7. 7, m-t-C,H,. 8. p-t-C,H,. 9, m-F. 10, p-F. 11, m-CI. 12, p-CI. 13, m-Br. 14,p-Br. 15, m-OCH,. 16, p-OCH,. 17, p-n-C3H7. 18, H.

References on p. 526.

508

- a, is the chromatographic substituent parameter, which depends only on the nature of this substituent group, not on the nature of the stationary phase, - @ is a solvent parameter, - b is a third parameter, independent of the electronic factors considered. Figure 11.7 illustrates the application of equation 13 to the retention of a number of phenols on EGSS-X at 168OC. Other correlations have been reported, as well as the temperature effect on the chromatographic substituent parameter (72). 2. Use of Additive Contributions to Retention Indices As explained above, the most practical way to handle large banks of retention data is by using retention indices. Since these indices are related to the Gibbs free energy of dissolution in the stationary phase (see equation 4), it is normal also to search for application of the empirical rule of free energy linear relationships (63). The literature dealing with this topic is extremely abundant and we do not attempt to review it. The reader is referred to papers by Leathard and Shurlock (1) and Takacs and Kralik (61) for comprehensive reviews and to papers by Carr et al. (50), Kovats (8,15), Ettre (73), Hoken (74), Keller (75), Rohrschneider (76), Schomburg and Dielmann (77) and Takacs (78) for some of the basic ideas. The principle of the method is to divide the analyte molecule in a series of segments (i.e., CH,, CH,, aromatic ring, functional groups, etc.), whose interactions with solvent molecules can be considered independently, calculate the interaction free energy, or index contribution, and add them up. In spite of its apparent crudeness, this model usually gives fairly good results for non-polar or weakly polar solutes on non-polar stationary phases. The contributions of dispersion forces are additive, but interactions of a polar nature are more difficult to account for. Even modest changes in the electronic distribution of the molecule, due to interaction between remotely placed substituted functional groups will cause important changes in the retention index that this model is unable to account for. Chromatography is a very powerful separation method, which can separate compounds which differ little in their Gibbs free energy of dissolution. Only sophisticated methods may predict retention data with an accuracy compatible with the analyst needs. The model discussed here is essentially empirical, with no serious theoretical background. It may work in some cases, but this is no guarantee it will do in others. Accordingly, one should be very cautious not to expand it too far, nor extrapolate its results. Finally, it should not be forgotten that in many cases the analyst uses mixed mechanisms to achieve a separation. Retention may occur by dissolution and adsorption at the gas-liquid interface, for example. In such a case, the accurate prediction of the retention volume on the bulk liquid phase would be of little help to predict the retention time observed. a. Homologous Series

The simplest correlation deals with members of homologous series, analyzed on the same phase, at the same temperature. The retention index increases by 100 units

509

No. of C atoms

Figure 11.8. Plot of the retention indices of compounds belonging to different chemical groups versus the number of carbon atoms. Top, polar column Ipoly(neopentylglyco1 sebacate)]; bottom, apolar column (silicone gum SE-30). Analytes, di and trialkyl esters. After ref. 84.

TABLE 11.5 Effect of Branching on the Retention Indices of Alkanes Structural Feature 2-Methylalkane 3-Methylalkane 4-Methylalkane 5-Methylalkane 2,2-Dimethylalkane 2.3-Dimethylalkane 2.4-Dimethylalkane

Retention Index Contribution **

- 36

- 30 -41 - 45

- 80

- 39 - 67

After ref. 79. Difference between the retention index of the isomer and that of the alkanes having the same number of carbon atoms. *t

References on p. 526.

510

each time the chain is increased by one CH, group. This relationship does not hold for the first three of four members (15). Furthermore, it has been found that the increment is close to but significantly different from 100. Figure 11.8 illustrates this correlation for a few homologous series, with compounds having between 4 and 8 carbon atoms. The span of carbon numbers which can be investigated at any given temperature on a certain column rarely exceeds 6 to 8, because of the exponential increase of retention times with temperature. The a value of two successive homologs is usually around 1.7. Branched chain hydrocarbons or functional derivatives are less retained than the linear isomers. The decrease in retention index corresponding to a given type of branching is fairly constant, as a result of the linear free energy relationship (12,63). Table 11.5 shows some data taken from Schomburg (79,80). It takes a rather large number of branchings to achieve a decrease in the retention index by more than 100 units. This permits some estimate of the proportion of branched isomers in a complex mixture. Note, however, that phytane is eluted before n-tetradecane, and there is overlap between the weakly branched iso-octanes (methylheptanes) and the highly branched iso-nonanes (tetramethylpentanes) (81). b. Functional Group Contributions

A functional group contribution may be calculated from the difference between the retention indices of the compound and the parent saturated hydrocarbon (82). Whereas the CH, contribution is always very near 100, the group contribution depends very much on the nature of the stationary phase, sometimes on the nature of the support and the stationary phase loading. An example of the application of the method has been given by Schomburg (79) and reported by Ettre (83). It deals with the prediction of the retention index of 5-hexenylcyclopropaneat 80 O C on squalane (experimental index: 895.3). From the retention indices of hexylcyclopropane (I= 913.0) and of 1-octene (I= 782.7), the contributions of the functional groups are calculated for cyclopropyl ( + 13.0) and for an a double bond ( - 17.3). The calculated index for 5-hexenylcyclopropane is thus 895.7, in excellent agreement with the experimental value. This type of correlation works very well for moderately polar compounds, having an important hydrocarbon skeleton, with one functional group or several such groups which do not interact. This seriously limits the range of useful applications mainly to the identification of compounds in petroleum distillates and in some petrochemicals. For example, Zulaica and Guiochon (84) have shown how to predict the retention indices of a variety of esters and diesters on two different phases, SE-30 and polyethylene glycol sebacate, using the sum of chain and functional group contributions. It results from the linear free energy relationship that, if R and S are two different chemical groups, each of which may be very complex, the retention indices of the compounds R-R, S-S and R-S are related by:

511

This phenomenon has been verified by Evans and Smith (7). The groups R and S must not be conjugated, however. This would create an additional contribution for one of the compounds which would have no equivalent in the other two. Thus, for example, the retention indices of aldehydes should be calculated from that of CHO-CH,-CH,-CHO, not from that of CHO-CHO. This method has been used by Evans and Smith (7) and by Antheaume and Guiochon (141) for the identification of the derivatives of many homologous series. This method cannot account simply for the effects of positional isomerism and chain branching. Structure retention relationships are required which have been investigated by many scientists. c. Constitutive Relationships

These relationships are also based on the additivity rule, but each segment of the analyte molecule is given a certain weight, which depends upon the immediate environment of this segment. Tables of values characterizing structural groups have been calculated by Castello et al. (85) to predict the retention indices of branched chain paraffins. Schomburg (79,80) has used the same approach. Takacs et al. (88-90) have extended the method to a wide variety of hydrocarbons, including various cyclic and aromatic hydrocarbons and olefins. Table 11.6 illustrates the power of the method, applied to non-polar hydrocarbons on squalane. The complexity of the method, on the other hand, becomes a serious drawback to its widespread use, together with the increasing effect of experimental errors on the precision of the increments. Highly accurate measurements, such as those carried out by Walraven et al. (91) and by Rijks et al. (92), are necessary for any successful application of the method. Conversely, such measurements may reveal new phenomena, such as the tile effect, a slight shift of the plots of retention indices of homologous series of branched alkanes. The applications of molecular topology, as developed by Dubois (93-96) and applied by Chastrette (97-100) and by Chretien (101) seemed to be quite promising, in spite of the computational problems. This method uses the DARC topological TABLE 11.6 Comparison between Measured and Calculated Retention Indices of some Hydrocarbons Retention Indices **

Compound

2,4,4-Trimethylpentane 1-Methylcyclopentane 1,I ,3-Trimethylcyclopentane 2-Methyl-2-butene 2-Methyl-1-butene Benzene Toluene

Measured

Calculated

715 629 724.6 514 487 640 147

715.1 628.5 723.8 513.5 487.1 640.2 145.3

After ref. 89.

** On squalane at 50

C.

References on p. 526.

512

system (93), which allows the description of the entire structure of any molecule by a unique number, and the drawing of the structure of the molecule corresponding to any number satisfying a simple set of rules. This system gives a considerable flexibility in the correlation of any type of experimental data with the molecular structure. The power of the method is such that it can be applied to polar systems as well (99,100). Some applications to retention indices (101-103) have led to interesting results. In spite of early promises, this work has not developed much. The application to a new stationary phase requires the accurate determination of a large number of data. The extension to polar and to multifunctional compounds is difficult. On the other hand the advances made during the last fifteen years in the spectrometric methods and their interfacing with chromatography, has made the use of complex methods based on retention data rather obsolete. d. Retention Index Increments between Two Phases

In their early paper, Wehrli and Kovats (15) observed that the difference between the retention indices of a compound on two different stationary phases is a constant for series such as R-A, where A is a functional group and R an alkyl group with more than three carbon atoms and which does not sterically hinder A. This is, of course, another consequence of the additivity rule. From this observation, Kovats derived the idea to relate the structure of a compound to its retention increment, I,, - ZA, the difference between its retention indices on a polar and an apolar phase. Wehrli and Kovats have shown that the retention increment may be calculated using additivity and combination rules which take into account the contributions of the different segments of the molecule (15). Extensive tables of data are included in this early work. Unfortunately, the polar phase chosen, Emulphor 0, was an industrial polycondensate whose production was discontinued long ago. This method could have been useful for the identification of unknowns, or more exactly for the choice between several possible formulas for that unknown, especially in connection with the similar methods applied to each of the retention indices, as discussed in the previous sections. The major problems that the systematic use of such an approach would raise have never been satisfactorily solved. First, the selection of a few different, standard stationary phases, universally accepted, should be made, as well as the choice of a few reference temperatures (130 O C, chosen by Kovats, is good for terpene derivatives and many chemicals; it is rather low for sesquiterpenes and many other compounds). Then, very complete tables of retention indices on these phases should become available. But, in practice, the major roadblock is found even before the retention indices are measured. If we have a mixture of even moderate complexity, how are we going to find out which peak on the first chromatogram corresponds to the same compound as a certain peak on the second one? The method used by Scott (104) for the identification of impurities in paraffin oil is tedious, time consuming and cumbersome; it cannot be recommended for systematic applications. Scott prepared a series of twenty-one columns with mixed

513

liquid phase coatings, from pure apolar ( A ) to pure polar (P),with the composition of the intermediate columns given by 0.05nA + 0.05(20 - n ) P . Analysts have found a much better way to solve this problem, using an on-line coupling of a mass spectrometer to a gas chromatograph. The mass spectra provided by this instrument permit a rapid, usually accurate solution to the problem of deciding which peaks on different chromatograms correspond to the same compound, and whether these peaks are singlets or multiplets. At the same time these spectra give much more information regarding the identity of this compound than the retention indices, except for some closely related isomers, for which chromatographic retention data supplies very valuable information. Typical examples are geometrical isomers of multisubstituted aromatic rings or enantiomers. Finally Kovats (105) has suggested, for identification purposes, the use of the retention index increment between two phases of similar polarity and different molecular weight. The increment is small, but the same rules apply. On the other hand, the identification of the peaks on the chromatograms corresponding to the same compound is much easier, provided the mixture is not too complex. This method has not been widely used. e. The Rohrschneider Method of Predicting Retention Increments

Rohrschneider (106,107) has shown that it is possible to determine with sufficient precision a set of numbers characterizing each stationary phase (x”, y ” , z ” , us, s”) and a set of numbers for each compound ( u , , b,, c,, d , , e , ) , so that the retention index increment of the compound i on the stationary phase s is given by: A Z s ( i )= I ” - Z A

= u,xs

+ b,y” + c i z s+ d,uS+ e,s”

(15)

In this equation A refers to the non-polar stationary phase. Rohrschneider chose squalane, which is an excellent phase for use at temperatures below about 100 O C. This arbitrarily restricts the method to applications involving light compounds, which are less numerous, have fewer isomers and are easier to resolve than heavier compounds. Thus the method is of no great potential use in real practice. If we measure the retention index increments of 5 solutes on one stationary phase, we have 5 equations and 30 unknown constants. Whatever the number of solutes studied, the number of coefficients to be determined is much larger than the number of equations. To resolve from this indeterminacy, Rohrschneider proposed selecting five “polarity probe solutes”, having widely different physico-chemical properties, and ascribing arbitrary coefficients to them (see Table 11.7). Each of these solutes will probe one particular different aspect of the molecular interactions (dispersion, polarizability, dipolar, electron-donor, electron-acceptor, hydrogen bonding, etc.), although it is of course impossible to separate the different forces completely. The choice of the probe solute is arbitrary. It is sound, but again suffers from the choice of a system which can be used only at low temperature. It is now possible to determine the coefficients of each new stationary phase, by running the five polarity probe solutes and measuring their retention indices. In References on p. 526.

514

TABLE 11.7 Coefficients of the Rohrschneider Polarity Probe Solutes Probe Solute

Coefficients b

a

Benzene Ethanol Methyl ethyl ketone Nitromethane Pyridine

0 100 0 0 0

100

0 0 0 0

d

c

0 0 100

0 0

e

0 0 0 100

0 0

0

100

0 0

turn, the values of the coefficients of any new solute can be derived from their retention indices on six different stationary phases, squalane and five polar phases for which the Rohrschneider constants are known and which are selected so as to be as widely different as possible. Then the calculation of the retention index of this compound on any stationary phase for which the Rohrschneider coefficients are known is straightforward. Some manufacturers (notably, Supelco, Bellefonte, PA, U.S.A.) give these coefficients for each stationary phase they sell. Values for a few common phases are given in Table 11.8. The results of this method seem to be quite good. The agreement between calculated and measured values of indices is within about 10 units, which is more than satisfactory, given the accuracy of the determinations of the retention data required for the application of the method. The main drawback of this method, compared to the other ones previously discussed in this section is that it does not allow the prediction of the retention indices of compounds from their chemical structure alone. Retention data on six phases are required before any prediction is made. Although data can be found in the literature, it is usually too scattered and of uneven, and often unchecked, accuracy for use. The method is thus tedious to use, and has found its main field of application in the comparison and selection of stationary phases. An additional drawback is the temperature dependence of the Rohrschneider coefficients and the fact that the polarity probe solutes and the non-polar phase chosen for the implementation of the method are suitable only for use at low temperature. The selection of probe solutes and a non-polar phase suitable for high temperature gas chromatography has been attempted several times (39), but no system has gained wide recognition, which probably demonstrates that there is no real need for such a system. TABLE 11.8 Rohrschneider Coefficients for some Compounds Probe Solute

Coefficients b

a

Cyclohexane Acetone Chloroform At 13OoC.

32.06

- 5.3 69.71

- 22.47

-4.61 28.91

c

d

e

- 21.64

4.07 7.90 53.05

29.72 5.64 - 6.29

94.94 - 72.62

515

f: Conclusion Considerable work has been invested in the selection of methods permitting the prediction of retention data. Scientists from industrial research laboratories were very much involved in this work in the 'sixties. Their contribution has been remarkable. The further work makes great use of the data bank collected by McReynolds and of the Rohrschneider method. The retention index system itself was designed by Kovats when trying to solve a problem of major practical importance, the complete analysis of essential oils (8). In the 'seventies, GC-MS instruments became available. They do not always permit a rapid, unambiguous identification of the components of a complex mixture, but they are so much more powerful for the identification of compounds separated by gas chromatography than any method using retention data, that the thrust of the effort moved to this area. In the only cases when retention data are needed, for the identification of isomers having similar spectra (e.g., alkyl aromatics or hetero-aromatics), these data are measured on the column used for the analysis, using authentic compounds. Accordingly, research in this area has been limited to people who have no access to mass spectrometers and to chemometricians trying to test a new procedure. This seems an obvious application of the Rohrschneider approach, since equation 15 is the product of a one line and a one column matrix. Unfortunately, in both cases, only simple problems have been tackled, involving monofunctional compounds, using small data sets, rarely exceeding thirty compounds and making measurements of questionable accuracy (adsorption of either the polar compounds at the gas-non-polar phase interface or on the surface of its support, or of the non-polar compounds at the gas-polar stationary phase interface makes all the determinations dependent on the phase ratio and nature of the support used;. i.e., the reproducibility of the data is limited). Recently two papers have been published by Carr (50,109) which may bring some new light and open new approaches. First, a new set of data has been acquired (50). Great attention has been paid to the design of the chromatograph and the measurement process in order to achieve a marked improvement on the accuracy of McReynolds data. GC instrumentation has been much improved during the last twenty years. Then a method of prediction of retention data based upon the work done in chemical engineering for the prediction of phase equilibria has been described (109). This could prove useful in the long run, although any prediction of retention data, in order to be useful, must be very accurate, because of the high separation power of gas chromatography. As for taking into account both solubility and adsorption data, it seems to be a very ambitious program, which does not appear to be supported by any major need in the foreseeable future.

IV. CLASSIFICATION AND SELECTION OF STATIONARY PHASES In the early days of gas chromatography, much effort was devoted to a search for a polarity scale, which would have permitted an easy comparison between the References on p. 526.

516

stationary phases and a simple explanation of their selectivity (110). Things would really have been wonderfully simple, had a single number been able to express the effect of column selectivity, i.e., account for the activity coefficient (see equation 7 in Chapter 3). It took years before the hopelessness of that quest was fully realized. The complexity of molecular interactions is much too great to be readily accounted for. The following forces have been identified by physical chemists: dispersion forces, dipole-dipole interaction, dipole-quadrupole interactions, hydrogen bonding. In most cases all of them are involved in the interaction between a solute molecule and a molecule of stationary phase, but the relative values of the contributions to the Gibbs free energy varies from compound to compound, making the polarity approach overly simplistic, compared to an approach such as the one proposed by Rohrschneider (see section above and below). The dispersion or Van der Waals forces are the most general source of molecular interactions. They result essentially from the basic asymmetry of matter, which makes positive charges occupy minuscule volumes, as large as atomic nuclei, while negative charges are distributed over comparatively huge molecular volumes, ten thousand times larger in dimensions, a few million million times larger in volume. As a consequence, the sum total of the electrostatic interaction energy between two molecules (i.e., the sum of the interaction energies between the nuclei, between the nuclei and the electrons and between the electrons themselves) cannot be zero at short distances. The residual energy is negative and results in an attraction which decays very rapidly with increasing distances and is responsible for the cohesion of non-polar liquids and solids. In addition to those ever-present dispersion forces, molecules which have a dipole moment, i.e. for which the centers of positive and negative charges do not coincide, interact and attract each other through normal electrostatic forces. Such forces are responsible for the relatively high boiling points of SO, or acetone. Other molecules do not have a dipole moment but have an electronic system which is more or less delocalized and sensitive to external electrostatic influence. The molecule is said to be polarizable and may interact rather strongly, i.e., more strongly than if only dispersion forces were involved, with polar molecules. A case in point is the interaction between benzene and acetone. Finally, compounds which carry OH or NH groups may interact with other molecules having atoms with unshared electron pairs and partially share the hydrogen atom with them. This is the hydrogen bond effect, which results in a stronger molecular interaction energy than the other forces previously described. In almost all cases, several different forces contribute to the overall retention, and the relative importance of the different contributions varies from one compound to the other, making prediction of the relative retention of a series of compounds an almost impossible task. Short of achieving this goal, the analyst would like some information regarding the relative selectivity of several stationary phases for some groups of compounds, in order to be able to make an educated selection between the nearly 300 stationary phases available. A number of schemes have been devised to answer this complex, somewhat ill-defined question. The first approach was suggested by Kovats, as a direct

517

consequence of his work on the retention index increment. He defined the retention index dispersion as the set of retention index increments obtained when considering the long chain, normal alkyl members of the main homologous series, i.e., n-alkyl benzenes, n-alkanols, n-alkanals, n-2-alkanones, methyl-n-alkoxylates (i.e., n-alkyl fatty acid methyl esters), n-1-chloroalkanes, etc. This certainly permits instructive comparisons between a few phases, especially if they are somehow related and rather close in their solubility properties, but it is too complex an approach for a systematic study of the behavior of the 300 different phases which have been described in the literature. More sophisticated methods have been described for this latter purpose. All of them use retention indices and increments and so are directly derived from Kovats’ early work. Most of them make use of the tables of retention data published by McReynolds (25), as a basis for their calculation, to be used as “training sets”. 1. Characterization by the Rohrschneider Coefficients

As described in the previous section, it is possible to characterize a stationary phase by the set of five coefficients which permit an exact prediction of the retention index increments of benzene, ethanol, methyl ethyl ketone, nitromethane and pyridine, using equation 15 and the set of values given in Table 11.7 for the coefficients of these five polarity probe solutes (106,107). While the selection of these five probe solutes has undoubtedly been dictated by solid chemical intuition, and makes sense, it is also completely arbitrary. This makes the phase polarity factors, as these coefficients are known, purely empirical and somewhat difficult to use for the characterization and classification of the stationary phases. The system is made workable, however, by the profound differences between the five probe solutes. Benzene is a weak, soft base; ethanol is an amphoteric compound (it behaves as a base or an acid, depending on the chemical environment) which is easily involved in hydrogen bonding; nitromethane is rather strongly polar, has some weak acid-base character and has no mobile hydrogen; pyridine is a strongly TABLE 11.9 Rohrschneider Coefficients for some Stationary Phases Liquid Phases Apiezon L Methylphenyl silicone oil (DC-710) Methylphenyl silicone oil (OV-17) Fluorosilicone oil Polyphenyl ether (5 rings) Nitrile silicone gum (XE-60) Polyoxyethylene sorbitan monooleate (Tween 80) Carbowax 20M

Coefficients X

Y

Z

U

U

0.32 1.05 1.30 1.41 1.75 2.08 2.14

0.39 1.50 1.66 2.13 2.27 3.85 4.2

0.25 1.61 1.79 3.55 2.34 3.62 2.78

0.48 2.51 2.83 4.73 3.26 5.33 5.2

0.55 1.90 2.47 3.04 2.84 3.45 3.65

3.18

5.33

3.81

7.02

5.04

At 13OoC. All these coefficients depend on the temperature. References on p. 526.

518

polar compound and a strong proton acceptor. Methyl ethyl ketone, which is somewhat polar and slightly basic, does not seem to add much to the spectrum of molecular interactions probed, but its use gives some flexibility to the system, as its properties are intermediate between those of the other solutes. The values obtained for a number of conventional stationary phases are reported in Table 11.9. One of the advantages of this system is to demonstrate clearly that many phases are very similar, quite a few are indeed duplicates, with different names but practically identical retention patterns. This system also allows a rapid selection of phases with widely different retention properties, to be used in multidimensional chromatography when needed. The predictive value of the Rohrschneider system being practically limited as well as the value of the information obtained concerning the detail of the phase characteristic, some refined versions of this approach have been proposed. 2. The McReynolds System

According to McReynolds (108), an expanded probe solute set made of the following ten solutes should be preferred: benzene, butanol, 2-pentanone, nitropropane, pyridine, 2-methyl-2-pentano1, iodobutane, 2-octyne, 1,Cdioxane and cis-hydrindane. Since there are now ten probe solutes, there are, of course, ten coefficients in the solute matrix and ten in the stationary phase matrix and the retention index increments on ten different phases are required to get the system started. Compared to the Rohrschneider system, the changes involve the replacement of nitromethane, ethanol and 2-butanone by their larger molecular weight homologs nitropropane, butanol and 2-pentanone7 and the addition of five solutes. The substitution does not result in any loss of precision in spite of the lower polarity of the new solutes. On the other hand retention data for these compounds are easier to obtain, because they are much less volatile and their retention indices are larger. We note in passing that to solve the same problem of the high volatility and small retention time of the Rohrschneider probe solutes, which prevents their use for high temperature studies, Thizon et al. (39) have replaced most of the compounds by dimers. In their study of the thermal stability of stationary phases, they have used diphenyl, 1,4-butanediol, methyl laurate, and 4,4’-bispyridinyl. Dinitroalkanes are hard to find. Methyl laurate should have been replaced by dimethyl adipate, in order to keep the approach self-consistent. The addition of 1-iodobutane gives better results in the prediction of the retention increments of halogen derivatives. The addition of 2-methyl-2-pentanol improves the quality of the prediction of the retention increments of branched compounds, especially among alcohols. According to McReynolds himself (108), the stepwise addition of l,rl-dioxane, 2-octyne and cis-hydrindane results only in minor improvements of the predictability of the whole system. Certainly the most striking advantage of the phase classification method designed by McReynolds is the availability of the constants for the whole set of the 226 phases studied, a vast majority of the phases in current use. This work has become

519

TABLE 11.10 McReynolds Constants* for Frequently used Liquid Phases Phases Squalane Apiezon L (treated on Fluosil) Methyl silicones SE30 ov-1 DC 410 DC 200 ov-101 SF96 UCW 982 Dexsil 300 Methylphenyl silicone DC 550 (25%phenyl) Dinonyl phthalate Methylphenyl silicone (50%) DC 710 OV-17 Tnfluoropropyl silicone QF-1 ov-210 Tricresyl phosphate Polyphenyl ethers 0s-138 PPE-20 Carbowax 20M Carbowax 2OM-TPA Polyethylene glycol adipate Carbowax 1540 Diethylene glycol succinate

N,N-Bis-(2-cyanoethyI)formamide

**

1

2

3

4

5

6

7

8

9

1

0 1 32 35 32

0 1 22 28 24

0 1 15 19 16

0 2 32 37 31

0 2 42 47 43

0 1 13 16 13

0 0 35 36 32

0 1 11 11 10

0 1 31 33 30

53

44 44

64 64 66 66 67 61 66 148

41 42 46 43 43 36 42 96

31 32 34 33 33 31 33

3 4 4 3 4 0 4

22 23 23 23 23 21 23

44 45 48 46

0

0 0 33 33 31

15 16 18 16 17 12 16 47

58 57 57 53 80

47 45 45 42 45 103

74 83

116 183

117 147

178 231

135 159

81 141

74 82

72 65

128 138

36 18

107 119

149 158

153 162

228 243

190 0

107 112

108 119

98 105

174 184

60 69

144 146 176

233 238 321

355 358 227

463 468 350

305 310 308

203 206 266

136 139 149

53 56 119

280 283 255

59 60 61

182 257 322 321 371 371

233 355 536 537 579 639

228 348 368 367 454 453

313 433 572 573 655 666

293

176

136

273

112

510 520 633 641

181 210 387 387 466 479

282 281 323 325

221 220 248 255

438 435 550 534

148 148 175 172

496 492 499 502 690

746 733 751 755 991

590 581 503 597 853

837 832 840 849 1110

835 791 860 852 lo00

594 579 595 599 773

420 418 422 427 557

325 321 323 329 371

718 705 725 726 964

238 237 240 243 279

55

55

46 41 46

-2 -1 -1 -3 -2 -6 -1

55

At 130 C. These constants are function of temperature. **After ref. 126.

the cornerstone of a whole series of further studies attempting phase characterization, classification and selection. Table 11.10 gives the coefficients of a selection of phases from among the most frequently used. The several sets of coefficients given for Apiezon L and diethylene glycol succinate give an idea of the variability of these phases. References on p. 526.

520

3. The Contribution of Factor Analysis

This powerful statistical method has been applied by Weiner and Howery (112,113) in a series of papers where they proceeded to a careful, detailed analysis of the experimental data of Rohrschneider. This work led them naturally to a discussion of the possible physical meaning of the contributing factors. They concluded that eight factors are required to span the data space. Thus, five coefficients, as used by Rohrschneider (106,107), are insufficient to correctly account for retention data, as this leaves some of the factors not represented, while ten coefficients, as used by McReynolds (108), do seem to bring some redundancy. Also important in this part of their study is the conclusion that nitro-compounds do not have a unique behavior and so are not well suited as polarity probes. They suggested the use of a combination of a nitro and a nitrile group test instead, which would offer some unique information. Unfortunately, there is no single compound which would permit such a test. On the other hand, they confirmed that pyridine and alcohols reveal independent information. The analysis of the chemical significance of the eight factors involved in the prediction of the retention indices allowed the identification of the compound ability to undergo hydrogen bonding and to participate in electron donor-acceptor exchanges as true space factors. Other pertinent parameters are the polarizabilities of both interacting species, solute and stationary phase, and to a lesser extent (i.e. not as “pure” factors now), the dielectric constant, the dipole moment and the heat of vaporization. It is also noteworthy that the gas phase non-ideality, which obviously does not involve any property of the stationary phase, accounts for one of the eight eigenvectors of the data space. This was to be expected, since retention is controlled by partition between the mobile and the stationary phase and depends, to some extent, on the properties of the mobile phase. The importance of this contribution, usually neglected, if not forgotten, by most analysts is somewhat surprising. When dealing with a more restricted set of compounds, Weiner et al. (114) found that the number of eigenvectors of the data space decreases. For example, with alcohols five factors are sufficient to span the data space of saturated alcohols, while a sixth factor is required for unsaturated alcohols. The following physical and chemical factors, which are not mutually independent and do not generate a six-dimensional data space, were found to be significant to some extent: molecular weight and number of carbon atoms, molar refraction, position of the hydroxyl group substitution, boiling temperature, vapor pressure and molar heat of vaporization. Weiner and Parcher (115) have studied more specifically the problem of stationary phase characterization, using factor analysis. It becomes plainly apparent from their work, confirmed by other results (lla), that factor analysis is a most powerful technique for the search of the most significant probes, as well as for the analysis of the influence of the physical and chemical meaning of the parameters involved in solution interactions and in chromatographic retention. Given that enormous potential, it is very unfortunate that nobody, neither an interested

521

industrial analyst nor one of the chemometricians involved in the application of factor analysis to gas chromatography retention data, has ever attempted to reduce the method to practice, in order to achieve a general, reliable scheme of retention data prediction and of stationary phase classification. The question of whether this is due to a lack of understanding of the -7alue of chemometrics on the part of the practitioners and the worth of the practical results they claim could be obtained, on the part of the theorists, or whether this is due to some flaw in the method which is not obvious to us remains unresolved. Maybe, as explained in previous sections of this chapter, the community of real analysts has come unconsciously but definitely to the conclusion that the result would not be worth the trouble associated with the collection of the data required to use it.

4. Classification of Stationary Phases As we have explained above, the sets of Rohrschneider (106,107) or McReynolds (108) coefficients derived from the data published by McReynolds (25) are the most suitable tools for the study and the development of methods of differentiation and classification of the stationary phases. Various approaches have been attempted. Some of the most important are discussed here. The recent publication by Carr et al. (50), of a new set of experimental data, with increased accuracy, may originate a new wave of interest in this problem.

a. Polarity Scales Many arbitrary polarity scales have been suggested in the past. The concept is quite arbitrary, since if there were a polarity scale, the retention increments of all compounds would be simply related to it. This seems to be in contradiction with the extreme complexity of molecular interactions which are difficult to summarize with a single number. According to McReynolds (108), a rough classification could be obtained from an overall polarity scale, defined as the sum of the retention increments of the first five of his ten probe solutes, i.e., benzene, butanol, 2-pentanone, nitropropane and pyridine. Leary et al. (117) used as polarity value the Euclidean distance between the points corresponding to the stationary phase studied and to squalane (i.e., to the origin), in the ten-dimensional space where each dimension is spanned by the retention increment of one of the ten probe solutes. In a later work they reduced that space to a three-dimensional one, using only the retention increments of 1-butanol, l-nitropropane and pyridine (118). Wold and Anderson (119) suggested another definition of the polarity. They took the main eigenvector of the data set, i.e., the direction of largest spread of the retention increments, as reference for polarity and took as a measure of the polarity the distance between the origin and the projection on this main axis of the point representing the phase in the data space. This definition has been supported by McCloskey and Hawkes (120), although they reached slightly different conclusions. These different approaches were compared by Lowry et al. (121), who have shown that they have much in common and lead to very close values. This References on p. 526.

522

agreement should not hide the arbitrary character of this empirical definition of polarity. Molecular interactions are too complex to be characterized by a single number. In a first step, ten probe solutes having widely different molecular structures have been chosen to account for the effects of the different forces involved in these interactions and break down the stationary phase selectivity in terms of individual components. Then the first use of the complex method, using a ten-dimensional plot, is to recombine the different terms in a rather simple way and generate a scalar (one-dimensional) parameter. No doubt much of the information is lost in the process. b. Selectivity Diagram

The first attempt to use a multi-dimensional diagram, representing the different aspects of solute-stationary phase interactions, can be traced to the early work of Brown (68) and to his triangular diagram. Such a diagram could be used to represent stationary phases and illustrate their selectivity, based on the values of the retention increments for butanol, nitropropane and pyridine, for example, although such a diagram has never been suggested, to our knowledge. Lowry et al. (121) have proposed characterizing stationary phases by the projection of their representative point in the McReynolds ten-dimensional space (defined by the values of the retention increments of the ten probe solutes), on the plane defined by the two principal eigenvectors (i.e., the two directions of largest spread of the data). A very similar method was suggested by McCloskey and Hawkes (120). In both cases, each stationary phase is represented by a point in a plane, which permits easy visualization of the results, and especially of the difference between the behavior of different phases. The difficulty with multi-dimensional spaces is their lack of intuitive physical representation. Once a process has been found to represent phases by points in one space or another, a further logical step is to divide the points between clusters of immediate neighbors. Lowry et al. (122) have thus distinguished seven different such clusters of phases. Members of a cluster behave similarly. This selection has some arbitrary character, as the borderlines between clusters are not always quite obvious. It is interesting, however, to observe that among the 226 phases studied, the seven clusters account together for 190 phases, while the 36 others all deviate greatly from TABLE 11.11 List of Unique Phases Zinc stearate Trimer acid Zonyl E-91 Silicone OV-210 Silicone DC LSX-3-0295 Tergitol NPX Stepan DS-60 Siponate DS-10

* After ref. 119.

Zonyl E-7 Epon 1001 Hyprose SP-80 Diglycerol Ethylene glycol phthalate THEED

N,N-Bis(2-cyanoethyl)formamide Silicone QF-1

523

those in the clusters and exhibit some unique selectivity. Among these phases, 12 had been described by Wold and Anderson (119) as having an “abnormal behavior”, while 16 others were found to have “unique retention properties or selectivity”. Their list is given in Table 11.11. The number of these “unique” phases and the unique character of some of them depeqds on the nature of the probe solutes considered for drawing the diagram and on the exact borderlines selected for the seven clusters. The difficulty is to find an appropriate compromise between discrimination and similarity. 5. Selection of Phases

This is the next logical step after having recognized the similarity between many existing phases and having grouped them into clusters. A possible, simple selection would be to take one phase per cluster and to keep the 12, the 16 or the 36 “unique” phases. Even limited to 19, this selection appears to be quite large, however, and we may desire to restrict it further. Although no consensus prevails as yet, indications are that most analysts regularly use fewer than a dozen phases. This is in agreement with the views of Kovats (123). Basing his analysis on a linear combination of the interaction forces, Kovats recommended a minimum number of eight phases, and an optimum number of possibly 12 to 16, in order to cover a wide temperature range. Accordingly, it seems that selecting a group of 10 to 15 phases out of the huge body of 226 phases available, seems to be a realistic goal (75,124). It would be useful to further group these selected phases in clusters, according to their retention properties, to permit the use of other criteria for the choice of the best phase among the suitable cluster. Several processes have been suggested to achieve this aim. a. The Nearest Neighbor

This method has been used by Leary et al. (117), to select 12 stationary phases among the 226 studied by McReynolds (108). The degree of similarity between two phases, A and B, is measured by the distance between their corresponding points in the ten-dimensional space of the retention increments of the probe solutes:

where i stands for the McReynold test solutes. The selection of the phases was made according to the following criteria: each selected phase should be well known and extensively tested, with several reports published in the scientific literature; each one should be readily available, stable over a wide temperature range; and together they should cover an extensive range of polarity. The list of the selected phases is reported in Table 11.12, together with their distance from squalane (the origin). As with any other table of recommended References on p. 526.

524

TABLE 11.12 List of Recommended Stationary Phases Phase

Distance to Squalane

Squalane SE-30 (Dmethylsiloxane) OV-3 (Phenylmethyl-dimethylsiloxane) OV-7 (Phenylmethyl-dimethylsiloxane) DC-710 (Phenylmethylsiloxane) OV-22 (Phenylmethyl-diphenylsiloxane) QF-1 (Trifluoropropyl-methylsiloxane) XE-60 (Cyanomethylsiloxane) Polyethylene glycol 20M DEGA (Diethyleneglycoladipate) DEGS (Diethyleneglycolsuccinate) TCEP (1,2,3-tris(2-cyanoethoxy)propane)

0 100 194 271 377 488 709 821 1052 1259 1612 1885

According to h r y et al. (117).

phases, this list should be regarded merely as a guide to a consideration of retention characteristics against other properties like availability, cost, thermal stability, whose practical importance can never be neglected. Most phases on this list, however, are widely used and could be recommended. It is striking that years of studious investigation of solution thermodynamics and of the retention properties of hundreds of phases and the use of the most subtle techniques of chemometry result in the list given in Table 11.12, which almost duplicates the list of the most quoted phases in the scientific literature or of the stationary phases most often sold (126). Finally, Leary et al. gave for each of the 226 phases studied by McReynold the nearest preferred phase and the distance between them (117). b. Numerical Taxonomy

In an outstanding paper, Massart et al. (125) have discussed the problem of phase selection using the method of numerical taxonomy, which seems particularly well suited to the study of this problem. To characterize the difference between two phases, they use a definition of their distance which is slightly different from equation 16. The retention indices are first normalized, to give the same weight to the contributions of all probe solutes. Numerical taxonomy permits the derivation of a tree describing the closeness between the different phases, somewhat as a genealogical tree describes the closeness between heirs, or a taxonomic tree describes the closeness between species. As an example, Table 11.13 gives the classification of the phases already listed in Tables 11.10 to 11.12, together with their McReynolds constants. The only arbitrary choice is in the number of groups which are considered to build up the tree. The classification gives some clues regarding the proper selection of stationary phases, as well as the strategy to be followed when seeking the achievement of a particular analysis. If attempts at performing a given separation fail to succeed on a

525 TABLE 11.13 McReynolds Constants of a few Phases 1

2

3

4

5

6

7

8

9

10

0

0

0

0

0

0

0

0

0

0

15 44 69

53 86 113

44 81 111

64 124 171

41 88 128

31 55 77

3 39 68

22 46 66

44 84 120

-2 17 35

94 107 160

271 149 188

163 153 191

182 228 283

378 190 253

234 107 133

94 108 152

57 98 132

216 174 228

60 60 99

3 Zinc stearate

61

231

59

98

544

98

50

29

78

33

4 Stephan DS-60 Siponate DS-10

97 99

550 569

303 320

338 344

402 388

440 466

111 114

60 61

418 437

61 63

130 144 146 152

250 233 238 241

320 355 358 366

377 463 468 479

293 305 310 319

235 203 206 208

81 136 139 144

95 53 56 55

295 280 283 291

10 59 60 64

197 204

386 381

258 340

389 493

351 367

281 289

176 203

39 120

293 327

81 94

6 Zonyl E-7

223

359

468

549

465

338

146

137

469

62

7 Epon 1001 Carbowax 20M

284 322

489 536

406 368

539 572

601 510

378 387

291 282

207 221

502 434

187 148

8 Hyprose SP-80 Did ycerol

336 371

742 826

492 560

639 676

727 854

565 608

310 245

227 141

590 724

196 36

9 Ethylene glycol phthalate Diethylene glycol succinate

453

697

602

816

872

560

419

306

699

260

499

751

593

840

860

595

422

323

725

240

10 1.2.3-Tris594 (2-cyanoethoxy)propane N,N'-Bis690 (2-cyanoethy1)formamide

857

759

1031

917

680

509

379

854

269

991

853

1110

loo0

173

557

371

964

279

Group 1 Squalane Silicones SE-30 OV-3 OV-7 2 Trimer acid Silicone DC-710 ov-22

5 Zonyl E-91

QF-1 ov-210 Silicone DC LSX-3-0295 Tergitol NPX Silicone XE-60

certain phase, it is most probable that no better result will be obtained with another phase of the same group. This is not absolutely sure, however, since an increase by a few units of the difference in retention indices of two compounds is all that it takes to turn a nearly impossible separation into a merely difficult one. Finally, we note that among the thirty groups into which Massart et al. (125) broke down the 226 phases studied by McReynolds, 14 of the 16 phases listed in Table 11.11 appear alone in their group, or with only one or two "duplicates". This References on p. 526.

526

is again in agreement with the work of Wold and Anderson (119). These phases should be remembered and their use considered when difficult separations have to be made.

6. Practical Conclusion There is another way to select stationary phases; by using polls. A survey of the sales of these products has been published (126), as a list of the most frequently ordered phases (see Table 11.10). This list is a sort of summary of years of painful struggles, trials, errors and corrections made by thousands of analysts and countless public and private discussions. As such it appears valuable to consider. It is remarkable that this list is nearly identical to the one recommended in a common paper by a group of eight scientists (127) who had previously published some of the most important papers in the field, which are discussed above (115,117-122). The limitations of the validity of the procedures used for the selection of phases has been illustrated by Haken (128) in the case of fatty acid methyl esters. The temperature dependence of the Rohrschneider and McReynolds coefficients should be stressed, as well as the oversimplification of the assumption that additive free energy contributions can be associated with the various intermolecular forces involved in solute-solvent interactions. In practice, we could suggest to perform a series of experiments using phases found in Tables 11.11 or 11.12. When 5 or 10 phases have been tried and the results are still unsatisfactory, results have been acquired which permit the calculation of the coefficients of Rohrschneider (when 5 phases have been used) or McReynolds (after 10 phases have been studied). Then the retention indices of the compounds to be separated can be calculated on the 226 phases, starting by the “unique” phases. Thus, the best phase of the set can be selected, at least in principle. This scheme relies on the assumptions that accurate measurements are made and that the adsorption effects, which can be prevalent with some compounds on certain phases, can be reproduced. If this approach fails, adsorbents or modified adsorbents are worth considering, especially if geometrical isomers are involved (see Chapter 7). For complex mixtures, it is often required to adopt a multiple analysis strategy, combining chemical fractionation, preseparation by liquid chromatography, gas chromatography of selected fractions on several columns and mass spectrometry (130).

LITERATURE CITED (1) D.A. Leathard and B.C. Shurlock, Identification Techniques in Gas Chromatography, Wiley, New

York, NY, 1970. ( 2 ) D.A. Leathard, in Advonces in Chromatography, J.C.Giddings and R.A. Keller Eds., M. Dekker, New York, NY, Vol. 13, 265 (1975). (3) Too many analysts have made this mistake. It would be impossible to list all of them and unfair to pinpoint one of them. (4) M. Goedert and G. Guiochon, Anal. Chem., 45, 1188 (1973).

527 ( 5 ) G.J. Pierotti, C.H. Deal, E.L. Derr and P.E. Porter, J. Amer. Chem. Soc., 78, 2989 (1956). (6) D. Ambrose, A.T. James, A.I.M. Keulemans, E. Kovats, H. Roeck, C. Rouit and F.H. Stross, Pure Appl. Chem., I , 1 (1959). See also in Gas Chromatography 1960, R.P.W. Scott Ed., Butterworths, London, UK, 1960, p. 423. (7) M.B. Evans and J.F. Smith, J. Chromatogr., 6 , 293 (1961). (8) E. sz Kovats, Helv. Chim. Acta, 41, 1915 (1958). (9) M. Goedert and G. Guiochon, Chromatographia, 6 , 39 (1973). (10) M. Goedert and G. Guiochon, J. Chromatogr. Sci., l I , 326 (1973). (11) R. Kaiser, Chromatographia. 3, 383 (1970). (12) A.T. James and A.J.P. Martin, Er. Med. Bull., 10, 170 (1954). (13) A.T. James, J. Chromarogr., 2, 552 (1953). (14) G.P. Cartoni, R.S. Lowrie, C.S.G. Phillips and L.M. Venanzi, in Gas Chromatography 1960, R.P.W. Scott Ed., Butterworths, London, UK, 1960, p. 273. (15) A. Wehrli and E. sz Kovats, Helv. Chim. Ada, 42, 2709 (1959). (16) E. sz Kovats, in Advances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1965, Vol. 1, p. 229. (17) M.V. Budahegyi, E.R. Lombosi, T.S. Lombosi, S.Y. Meszaros, Sz. Nyiredy, G. Tarjan, I. Timar and J.M. Takacs, J. Chrornatogr., 271, 213 (1983). (18) E. Grushka and T.A. Goodwin, Chromatographia, 10, 549 (1977). (19) G. Schomburg, J. Chromatogr., 14, 157 (1964). (20) G. Schomburg, J. Chromatogr., 23, 1 (1966). (21) G. Schomburg, in Advances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1968, Vol. 6, p. 211. (22) L.J. Lorenz and L.B. Rodgers, Anal. Chem., 43, 1593 (1971). (23) V.G. Berezkin and V.N. Returnsky, J. Chromatogr., 292, 9 (1984). (24a)0.E. Schupp and J.S. Lewis, Research and Development, 21(5), 24, May 1970. (24b)0.E. Schupp and J.S. Lewis, Compilation of Retention Data, ASTM Data Series, Publication # DS-25A, ASTM, Philadelphia, PA, 1967. (24c)O.E. Schupp and J.S. Lewis, Gas Chromatographic Data Compilation, First Supplement, ASTM Data Series, Publication # AMD-25A-SI, ASTM, Philadelphia, PA, 1971. (25) W.O. McReynolds, Gas Chromatography Retention Data, Preston Technical Abstract, Evanston, IL, 1966. (26) E.R. Adlard, in Gas Chromatography 1964, A. Goldup Ed., The Institute of Petroleum, London, UK, 1965, p. 348. (27) L.S. Ettre, Anal. Chem., 36, 31A (1964). (28) E.B. Molnar, P. Moritz and J. Takacs, J. Chromatogr., 66, 205 (1972). (29) H.Van den Dool and P. Kratz, J. Chrornatogr., 11, 463 (1963). (30) G. Guiochon, Anal. Chem., 36, 661 (1964). (31) M.R. Moller, Chromatographia, 9, 311 (1976). (32) B. Maume and L. Baron, Bull. SOC.Chim. France, 1962, 1113. (33) C.J.F. Boettcher, F.P. Woodford. E. Boelsma-van Houte and C.M. van Gent, Rec. Trav. Chim. Pays-Bas, 78, 294 (1959). (34) F.C. Woodford and C.M. van Gent, J. Lipid Rex, 1 , 188 (1960). (35) T.K. Miwa, K.L. Mikolajczak, F.R. Earle and LA. Wolff, Anal. Chem, 32, 1239 (1960). (36) W.J.A. VandenHeuvel and E.C. Homing, Eiochim. Eiophys. Acra, 64, 416 (1962). (37) E.C. Homing and W.J.A. VandenHeuvel, J. Amer. Oil Chemists SOC.,41, 102 (1964). (38) W.E. Harris and H.W. Habgood, in Programmed Temperature Gas Chromatography, Wiley, New York, NY, 1966. (39) M. Thizon, P. Valentin, C. Eon and G. Guiochon, Anal. Chem., 48, 1861 (1976). (40) D. Zarazir, P. Chovin and G. Guiochon, Chromatographia, 3, 180 (1970). (41) D.M. Ottenstein, J. Gas Chromatogr., 1(4), 11 (1963). (42) M.B. Evans and J.F. Smith, J. Chromatogr., 30, 325 (1967). (43) V.G. Berezkin, J. Chromatogr., 65, 227 (1972). (44) M.L. Peterson and J. Hirsch, J. Lipid Res., 1 , 132 (1959).

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529 (94) J.E. Dubois and D. Laurent, C.R. Acad Sci., 268A, 405 (1969). (95) J.E. Dubois and J. Chretien, J. Chromafogr. Sci., 12, 811 (1974). (96) J.E. Dubois, Computer Representation and Manipulation of Chemical Information, W.T. Wipke Ed., Wiley, New York, NY, 1974, p. 239. (97) M. Chastrette, G. Lenfant and J.E. Dubois, C.R. Acad. Sci., 265, 602 (1967). (98) G. Lenfant, M. Chastrette and J.E. Dubois, J. Chromatogr. Sci., 9 , 220 (1971). (99) M. Chastrette and G. Lenfant, J. Chromatogr., 68, 19 (1972). (100) M. Chastrette and G. Lenfant, J. Chromafogr., 77, 255 (1973). (101) J. Chretien, C.R. Acad. Sci.. 281C. 151 (1975). (102) L. Sojak, J. Janak and J.A. Rijks, J. Chromatogr., 142, 177 (1977). (103) 2. Krawiec, M.F. Gonnord, G. Guiochon and J.R. Chretien, Anal. Chem., 51, 1655 (1979). (104) C.G. Scott, in Gar Chromatography 1960, R.P.W. Scott Ed., Butterworths, London, UK, 1960, p. 372. (105) D.F. Fritz and E. Kovats, Anal. Chem. 45, 1175 (1973). (106) L. Rohrschneider, J. Chromatogr., 22, 6 (1966). (107) L. Rohrschneider, J. Gar Chromatogr., 6 , 5 (1968). (108) 0. McReynolds, J . Chromatogr. Sci., 8, 685 (1970). (109) J.H. Park and P. Carr, Anal. Chem., 59, 2596 (1987). (110) L. Rohrschneider, Z. Anal. Chem., 170, 256 (1959). (111) L. Rohrschneider, J. Chromatogr., 22, 6 (1966). (112) P.H. Weiner and D.C. Howery, Can. J. Chem., 50, 448 (1972). (113) P.H. Weiner and D.C. Howery, Anal. Chem., 44, 1189 (1972). (114) P.H. Weiner, C.J. Dack and D.C. Howery, J . Chromatogr., 69, 249 (1972). (115) P.H. Weiner and J.F. Parcher, J. Chromatogr. Sci., 10, 612 (1972). (116) P.T. Funke, E.R. Malinowski, D.E. Martire and Z. Pollara, Sep. Sci., 1 , 661 (1966). (117) J.J. Leary, J.B. Justice, S. Tsuge, R.S. Lowry and T.L. Isenhour, J. Chromatogr. Sci, 11, 201 (1973). (118) S.R. Lowry, S. Tsuge, J.J. Leary and T.L. Isenhour, J . Chromatogr. Sci., 12, 124 (1974). (119) S. Wold and K. Anderson, J. Chromatogr., 80, 43 (1973). (120) D.H. McCloskey and S.J. Hawkes, J. Chromatogr. Sci., 13, 1 (1975). (121) S.R. Lowry, H.B. Woodruff and T.L. Isenhour, J. Chromatogr. Sci., 14,129 (1976). (122) S.R. Lowry, G.L. Ritter, H.B. Woodruff and T.L. Isenhour, J. Chromatogr. Sci., 14, 126 (1976). (123) E. sz Kovats, Chimia, 22, 459 (1968). (124) R.S. Henly, J. Chromatogr. Sci., 11, 222 (1973). (125) D.L. Massart, P. Lenders and M. Lauwereys, J. Chromarogr. Sci., 12, 617 (1974). (126) J.R. Mann and T. Preston, J. Chromafogr.Sci., 11, 216 (1973). (127) S. Hawkes, D. Grossman, A. Hartkopf, T. Isenhour, J. Leary, J. Parcher, S. Wold and J. Yancey, J. Chrornatogr. Sci., 13, 117 (1975). (128) J. Haken, J. Chromatogr. Sci., 13, 430 (1975). (129) M.R. Moller, Chromatographia, 9, 311 (1976). (130) J.M. Schmitter, H. Colin, J.L. Excoffier, P. Arpino and G. Guiochon, Anal. Chem., 54, 769 (1982). (131) H.P. Burchfield and E.E. Storrs, Biochemical Applications of Gar Chromatography, Academic Press, New York, NY, 1962. (132) R.H. Kolloff, Anal. Chem., 34, 1840 (1962). (133) E.D. Smith and A.B. Gosnell, Anal. Chem., 34, 646 (1962). (134) W. Kaye, Anal. Chem., 34, 287 (1962). (135) M.E. Kieser and D.J. Sissons, Nature, 185, 529 (1961). (136) C. Weurman and J. Dhont, Nature, 184, 2010 (1959). (137) M. Vilkas and N.A. Abraham, Bull. SOC.Chim. France, 1959, 1651. (138) N.H. Ray, J. Appl. Chem. (London), 4 , 21 (1954). (139) A.T. James, A.J.P. Martin and G.H. Smith, Biochem. J. (London), 52, 238 (1952). (140) E. Kovats, 2.Anal. Chem., 181, 351 (1961). (141) J. Antheaume and G. Guiochon, Bull. SOC.Chim. France, 1965, 298.

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531

CHAPTER 12

QUALITATIVE ANALYSIS Hyphenated Techniques

TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . ............_.. ..................... 1. The Use of Selective Detector Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Determination of Molecular Weight with the Gas Density Balance . . . . . . . . . . . . . . . . . ....................... 2. Use of Selective Detectors . . . . . . . . . . . . . . . . . . . 3. Use of the Human Nose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Use of Insects . . . . . . . . . . ........................................ 11. The Use of On-line Chemical Re ns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Post-Column Reactions . . . . . . . . . . . . . . ...................

.............................. b. Esterification with Boron Trifluoride c. Trimethylsilylation . . . . . . . . . . . . . d. Other Useful Reactions . . . . . . . . .

a. The Ion Source

...............................

.... . .. . .... . .. . . . ........ .

c. The Ion Detector

..................

.............................

.. ....

2. The Various Ionization Meth

a. Electron Impact. . . . . . . . . . . . . . . . . . . . . . . . . . b. Chemical Ionization . . . . . . . . . . . . . . . . ............................

b. The Direct Interface. . . . . . . . . . . . . . . d. The Molecular Separators . . . . . . . . . . . .

............................

4. Data Acquisition and Handling . . . . . . . . . ............................. 5. The Mass Spectrometer as a GC Detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

Parameters Affecting the Response . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....................................... Selectivity . . . . . . . . . Sensitivity . . . . . . . . . ............................... Linearity.. . . . . . . . . . . . .......................... Prediction of the Response ................... . .. .... g. Maintenance and Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. The Coupling of Infrared Spectrophotometry to Gas Chromatography . . . . . . . . . . . . . . . . 1. Principle of Infrared Spectrophotometry . . . . . . . . . . . .......'....'... 2. Fourier Transform Infrared Spectrophotometry . . . . . . . . . . . . . . . . . 3. GC-FTIR Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . ................ 4. Data Acquisition and Handling . . . . . . . . . . . ................ Literaturecited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. b. c. d. e. f.

.

532 533 533 535 536 537 538 538 539 540 540 541 542 542 543 544 545 545 546 541 547 548 549 549 550 551 551 554 554 554 555 555 556 556 556 556 557 558 559 559 560 561

532

INTRODUCTION Chromatography is essentially a separation technique. As demonstrated in the previous chapter (Chapter ll),the detector response supplies very little information regarding the nature of the compounds separated. It is practically impossible in general to identify a compound solely on the basis of the retention data obtained for it, even on a well chosen combination of columns. On the other hand, spectrometric techniques, essentially infrared spectrophotometry, mass spectrometry and nuclear magnetic resonance, afford a huge amount of information regarding the chemical characteristics of the analytes to which they are applied. This information can be related to the composition and structure of the compounds contained in the spectrometer cell, provided these compounds are pure. If a spectrometric method is applied to a mixture, it is difficult, often it is even impossible, to determine whether the spectral features observed are related to one or several components. The combination of chromatography and one or several spectrometric feature appears, therefore, as an extremely powerful combination for the identification of the components of even very complex mixtures. Extremely successful results have been obtained in the combination of mass . spectrometry and gas chromatography, which was the first combination to be developed and used on a large scale. The reason for this preeminence of the GC-MS coupling is explained by the sample size compatibility between the two analytical techniques. The total sample size for a complex mixture is of the order of a few tens of micrograms for an open tubular column, several milligrams for a conventional packed column. It takes a few nanograms to get a mass spectrum with enough clear features to compare with the spectra in a library or to derive clues to the structure of the corresponding compound. It takes a few picograms to obtain a signal in single ion monitoring, i.e., to use the mass spectrometer as a tunable, highly selective detector. These sensitivity thresholds permit the analysis of very dilute traces. Recently, there has been very significant progress in the development of highly sensitive infrared spectrophotometers, using entirely new principles of data acquisition and handling, based on fast Fourier transforms. This has permitted the development of instruments which, although not yet quite as sensitive as the mass spectrometers, can be coupled to gas chromatographic columns for identification purposes, and which supply information which complements that delivered by mass spectrometry in a very useful fashion. Although the most spectacular results in the combination of chromatographic separations and the physical or chemical methods of identification have been obtained with the coupling of gas chromatography and mass spectrometry, other more conventional approaches have been used successfully by analysts. The use of selective detectors, the use of selective chemical reactions, carried out either before or after the separation, have been able to supply valuable information regarding the nature of unknown components. All these methods are reviewed here. It is not the purpose of this book to give a detailed account of the different aspects of these methods, nor an in-depth discus-

533

sion of their problems. There are some dedicated books devoted to GC-MS or to chemical derivatization, and countless review papers. We rather present a discussion of the essential problems encountered in the use of these methods, in relationship with, and from the point of view of chromatography. Obviously, in most instances, a compromise taking into account the limitations and problems of the coupled technique will have to be reached. It is only if we know what we can give and what will be the consequences of trade-offs, that we can achieve satisfactory results.

I. THE USE OF SELECTIVE DETECTOR RESPONSE The simplest approach to the identification of unknown compounds by combining chromatographic separation with the acquisition of selective data, having some relationship with the nature, chemical composition and structure of the unknown, is the proper use of the signal of a selective detector. Surprisingly enough, however, the most informative result, probably because it also contains highly meaningful quantitative information, is given by the gas density detector, which permits the calculation of the molecular weight of an unknown compound, as well as its exact concentration in the analyzed samples. Detectors selective to halogens, nitrogen and phosphorus have also been used. Finally, the human nose can be “coupled” to a chromatographic column and may supply extremely valuable information. 1. Determination of Molecular Weight with the Gas Density Balance The gas density balance (GDB) was invented and has been developed by Martin (1).The model mostly used at present, however, is due to Nerheim (2). The principle and properties of this detector have been described in Chapter 8. It is characterized by the fact that, unlike all other known chromatographic detectors, its relative response factors are predictable from first principles. The first application of this detector to the determination of the molecular weight of an unknown is due to Liberti et al. (3). Several other papers have described this application (4-8). In the early ’seventies, a commercial instrument, the “Mass Chromatograph”, was developed and offered for sale (9-11). Probably because of the insufficient sensitivity of the detector used, which had a detection limit barely below a pg and could not be used with open tubular columns, the venture was unsuccessful. A schematic of the gas circuits in the “Mass Chromatograph” is shown on Figure 12.1. The two sampling valve loops were filled with the same sample. This is not necessary and made the use of this instrument less flexible. The response factor of the GDB (ratio of the amount of unknown compound injected to the peak area) is given by the following relationship (see Chapter 10, Section 11.2):

References on p. 561.

534

.) Figure 12.1. Schematic of the “Mass Chromatograph”. Cgl, Cg2, Inlet of carrier gases 1 and 2, respectively. V1, V2, Sampling valves, filled with the same sample, S, but injecting a sample in each separate gas stream. B1, B2, Gas density balances.

where: - f is the response factor, - d is a constant, function of the detector design and operating parameters, - M, is the molecular weight of the unknown analyte, - Mg is the molecular weight of the carrier gas. The principle of the method is based on the determination of the ratio of the peak areas obtained for the unknown and for a reference compound of known molecular weight, using two different chromatographic circuits and two gas density balances working with different carrier gases. The gases preferred are carbon dioxide and sulfur hexafluoride (4-8). The precision of the determination is about 1%,for molecular weights between 2 and 400 (9-11). A mixture is prepared, containing the sample studied, the unknown, and the reference. Two aliquots of this mixture are injected simultaneously by means of the valves V1 and V2 on the proper column, swept by its own carrier gas, i.e., CO, or SF,. The areas of the four peaks (the peaks of the unknown and the reference compounds on the two chromatograms) are determined. Since the ratios of the amounts of the two compounds (unknown and reference) injected on the columns are the same for both chromatograms, we can write: Qr.1

--Qr.2

QU.1

Qu.2

where:

- Qr., and Qr,, are the amounts of reference compound (molecular weight M,) injected in circuits 1 and 2, respectively,

535

- QU,land Qu.2 are the amounts of unknown compound (molecular weight M u ) injected in circuits 1 and 2, respectively. Using equation 1 for the response factor and the definition of the response factor (Q = f A , see equation 16, Chapter 13), and combining with equation 2, we obtain:

where: - Mg,l and Mg,2 are the molecular weight of the first and second carrier gases used, respectively, - Ar,l and Ar,2 are the peak areas obtained for the reference compound in the first and second chromatograms, respectively, - Au,l and Auq2are the peak areas obtained for the unknown compound in the first and second chromatograms, respectively. Equation 3 can be solved for the unknown, Mu. We obtain: Mu =

m*,lYlP2 - 4 . 2 Y 2 P l YlP2 -Y2P1

(4)

with: Ar,1 Y1 = AU.1

4 , 2

y 2 = z

and:

The precision of the method depends on the difference between the molecular weights of the two carrier gases and on the errors made on the measurements of peak areas.

2. Use of Selective Detectors The use of two detectors at the column exit, most often arranged in parallel because most GC detectors are destructive, is a very common way of collecting information regarding the chemical nature of the components of a mixture. The thermal conductivity detector and the flame ionization detector are most commonly used for the non-selective detector. The electron capture detector (ECD), the flame photometric detector (FPD) and the thermoionic detector (TID) are the most used among selective detectors. The ECD permits the detection of molecules having halogen or sulfur atoms, and of -NO2 groups, but it also gives a strong response to molecules with conjugated aromatic rings and even to those with conjugated double bond systems, especially if References on p. 561.

536 100

ELECTRON CAPTURE

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FLAME

IONIZATION

Figure 12.2. Chromatogram of an extract of garlic, using two parallel detectors. Top trace, electron capture detector. Bottom trace, flame ionization detector. After ref. 30.

a C 4 double bond is involved. The selectivity of the ECD tends to be too broad for this kind of application. The FPD is used to detect molecules carrying either phosphorus or sulfur atoms. The TID can detect molecules with either a phosphorus or a nitrogen atom. The selectivity of these two detectors for these atoms (S,P or N) is excellent, with a response ratio for the derivative and the corresponding hydrocarbon between 10,000 and 1,OOO,OOO. Oaks, Hartmann and Dimick (12,13) have illustrated the use of the ECD in qualitative analysis by the detection of sulfur derivatives in garlic extracts (see Figure 12.2). Schmitter et al. have used a combination of an FID and a TID in the nitrogen mode to study the performance of extraction methods selective for azaarenes (14). Comparison between the two chromatograms, preferably recorded on the same chart, supplies information regarding the presence or absence in the studied mixture of compounds belonging to the chemical families for which the detector used is reputed to be selective. The method should be applied carefully, however, because the selectivity of most detectors is often rather broad. This is especially true of the ECD. 3. Use of the Human Nose

The human nose, especially when properly trained, is an extremely sensitive and selective detector. It has been used for the detection of components of fragrances in various complex samples. Extreme caution must be applied to avoid damaging the precious detector. The column effluent is very dry and can be very hot. It contains sustances which may be highly toxic. The carrier gas stream must be properly cooled before being smelled. Long term exposure of the inner part of the organ to the eluent gas stream should be avoided.

537 FI D

/

He 5 0 m l

1 I

30ml Diameter: ! b i n .

Figure 12.3. Which are the components of a mixture that have an odor? Schematic of a device for letting the analyst smell the column effluent.

Eustache et al. (15) have recommended the following procedure (see Figure 12.3). The column effluent is mixed with an auxiliary stream of pure, cold carrier gas. This stream is then split between the FID and a capillary tube (0.5 mm i.d., 1 m long) which ends in the nose. The proper ratio of flow rates (ca 30% to the FID, 705%to the nose) is adjusted by slightly squeezing the capillary tube. This detection mode has been especially useful for the detection of foul smelling components in the raw materials used for food packaging (16). The most serious drawbacks are experienced with the lack of nose-to-nose reproducibility, some being much more sensitive than others, and with the response time, especially when their use is attempted in connection with open tubular columns. Dull-witted analysts should be avoided. A built-in time delay of a few seconds between the detection of a compound by the FID and its entrance into the nose permits accurate focusing of the nose controller on the detailed processing of the complex set of signals. Acree (56) has recently described a method of identification involving the determination of the periods during which the analyst can detect an odor, and the variation of the length of these periods when the sample is diluted. This method permits the study of the changes of fragrances in food technology. The relationship between olfactory properties and retention data has been studied by Laffort and Patte (57). 4. Use of Insects

The detection of pheromones has been achieved using a system similar to the one shown in Figure 12.3, where the nose is replaced by a glass cage containing an insect belonging to the species studied and of the sex receptive to the pheromone studied. References on p. 561.

538

The insect is watched during the elution of the sample. It becomes highly excited when the band of the pheromone is eluted. Much as the previous one, this detector is very difficult to automate. Its response is very sensitive, but not at all quantitative. It is extremely selective, usually to only a few chemicals, while the nose responds to a much wider range of compounds. Finally, there may be a problem of response time, especially when used with open tubular columns. The elution of the pheromone band may take such a short time that the excitation of the detecting insect may be impossible to observe or will be ascribed wrongly to a later eluted compound. 11. THE USE OF ON-LINE CHEMICAL REACTIONS

The use of selective chemical reactions had been considerably developed in the 'forties to 'sixties, before modem spectrometric instrumentation became available nearly everywhere. During most of the 'sixties, a number of analysts tried to adapt these methods for their use in the identification of compounds separated by gas chromatography. The main source of the difficulties encountered was related to the small amount of material available for the reaction. Most of this work has been abandoned now. Two approaches have been developed: - Post-column reactions, on fractions condensed at column outlet and recovered, - Precolumn reactions, carried out on the sample, prior to injection. Methods of the second kind are still in use. Methods of the first kind are now limited to those reactions carried out in the gas phase in the ionization chamber of a mass spectrometer. There is an extensive literature available on the subject of reactions and derivatizations in gas chromatography (16-21). 1. Post-Column Reactions

,

The carrier gas eluting from the column bubbles through the proper reagent solution. The use of reactions generating colored products may permit sensitive and selective detection. Walsh and Merritt (22) have demonstrated some of the great advantages of the method: simplicity, low cost, sensitivity, rapidity. The carrier gas stream was divided into five streams of approximately the same flow rate, by connecting the outlet tube of the thermal conductivity detector to five hypodermic needles (22). Each needle plunges in a tube containing a reagent solution. This permits the simultaneous use of five different reagents. It is important to keep the gas stream hot as long as possible, to avoid condensation of the analyte vapor in the connecting tubes. A list of reagents giving colored products with compounds belonging to the main chemical functions is given Table 12.1 (22,23). The detection sensitivities sounded extremely good in the early 'sixties. They appear rather poor by present standards. The use of a spectrophotometer would probably improve them by at least one order of magnitude.

539

TABLE 12.1 Functional Group Classification Tests Compound Trpe

Reagent

Olefins Aromatics Alkyl halides Alcohols

HCHO + H,SO, HCHO + H2S04 Alc. AgNO3 K,Cr2O7 + HN03 Ceric nitrate 2,4-DNP Schiff s 2.4-DNP

Aldehydes Ketones

Color for Positive Test Red-wine color Red-wine color White ppt. Blue color Amber color Yellow ppt. Pink color Yellow ppt.

Esters

Ferric hydroxamate

Red color

Amines

Hinsberg Na nitroprusside

Nitriles

Ferric hydroxamatepropylene glycol Na nitroprusside Isatin Lead acetate Na nitroprusside Na nitroprusside Isatin

Orange color Red color, 1 Blue color 2 Red color

Thiols

Sulfides Disulfides

Red color Green color Yellow ppt. Red color Red color Green color

Detection Limit (Pg)

40 20 20 20 100 20 50 20 40

Compounds Tested GH, @H-bC4 c1-c5

1 -c5

C1-C6 c1-c6 cl-c5

(Me ketones) C1-G (acetates)

100 50

DiEt, Diamyl 40 50 100 100 50 50 100

c2-c5 cl-c9 c1-c9 cl-c9

c2-c12 2' -6' c2-c6

Rowan (24) has identified a number of hydrocarbons, paraffins, olefins, naphthenes and aromatics, by combining a series of catalytic reactions and adsorption: hydrogenation or dehydrogenation by a platinum catalyst on alumina, and adsorption of straight chain hydrocarbons on Molecular Sieves 5A. 1-Olefins have been identified in a hydrocarbon mixture by flowing the eluent through a column packed with an organo-aluminum compound, which reacts with 1-olefins (25). Two chromatograms are recorded, one for the untreated eluent, the other for the eluent having flowed across the reagent column. 1-Olefins are identified as corresponding to the missing peaks. 2. he-Column Derivatizations The aim of these methods is to create differences between the chromatograms of the analyzed mixtures before and after a selective treatment, chosen in order to demonstrate the possible presence of certain functional groups in molecules of the sample components. Some peaks disappear after treatment, others appear. Some conclusions may be derived from these changes. They may be difficult to reach in the case of really complex mixtures, when several peaks may appear and disappear, and when it may be difficult to relate them. Further, this binary information (yes, the peak disappears / no, the peak is still here) is difficult to translate in terms of the chemical structure of the unknown compound. References on

p.

561.

540

The reactions most often used in the identification procedures involving this approach are: - the esterification of acids, - the hydrogenation of olefins, - the absorption of olefins, - the absorption of n-paraffins, - the absorption of aldehydes, - the silylation of active hydrogen atoms, - nitration, - cyclization, - the on-line catalytic hydrogenation of the sample. These reactions are described in detail in several books which have been devoted to the topic (19-21). Among these reactions, esterification is the most popular; it is no longer carried out for identification purposes, but rather for the quantitative analysis of fatty acids, because the methyl esters are more volatile and much less polar than the free acids. There are essentially two different approaches in organizing the analytical procedure; on-line or off-line derivatization. The requirements for a suitable on-line reaction are rather severe. The reaction must be semi-quantitative (for qualitative analysis), it must be rapid and should not require complex reagents. Only on-line hydrogenation, as developed by Beroza (26-28) and Thomson et al. (29,30), has been shown to be acceptable. Off-line derivatization is carried out in very small glassware equipment, adapted to handle the minute volumes of sample used in gas chromatography (down to 0.1 mL). Still smaller samples can be treated in the barrel of the sampling syringe as shown by Hoff and Feit (31,32). a. Esterijkation with Diazomethane Diazomethane, CH2N2,is prepared after the method described by De Boer and It is an unstable and Baker (33), from N-methyl-N-nitroso-p-toluenesulfonamide. highly toxic gas, which may explode violently (34,35). It should NEVER be stored NOR prepared in large amounts. However, the danger is much less when it is prepared under a hood, in the flask where it is going to react, in contact with the compound it is going to methylate and which therefore acts as a diazomethane scavenger (36-38). Care should be applied never to achieve a significant concentration of diazomethane and to destroy it completely when the derivatization is complete (see schematics of the apparatus in Figure 12.4). Diazomethane is an ex.cellent methylating agent, reacting rapidly and completely with all acids, fatty acids, aromatic acids, organophosphoric acids, etc. It may also react, albeit more slowly, with reactive hydrogens, such as alcohols or amines, and even with hydrocarbons (39). b. Esterif cation with Boron Trifluoride

This seems to be the most suitable method for the derivatization of carboxylic acids into methyl esters. It uses a solution of boron trifluoride in methanol (14%

541

ll

4 !

I

Figure 12.4. Preparation and use of diazomethane. 1 mL ethanol and 1 mL diethyl ether). a - Reagents (1 g N-methyl-N-nitroso-p-toluenesulfonamide, b - reactor, containing 3 mL solution of potassium hydroxide in ethanol (a%), heated at 60 C. c - Sample to be methylated. d -Solution of HCI, to destroy the diazomethane, when the production is started or when it is not needed.

w/w of BF,), which is now commercially available. For acids having between 8 and 17 carbon atoms, the procedure is very simple. Five mL of the solution are added to 500 mg of the acid mixture. The solution is heated 5 min in a water bath. Then a saturated solution of NaCl is added and the supernatant organic solution is decanted and collected and dried with Na,SO,. The product can be injected directly into the chromatograph. c.

Trimethylsilylation

The replacement of a mobile hydrogen by a -Si(CH,), group can be made easily, using a variety of silanization reagents which are widely available (19-21). Carboxylic acids, alcohols, and amines can be reacted. The reaction is easy to carry out quantitatively, at room temperature, in a test tube. The trimethylsilyl ethers obtained are usually very stable; they are readily eluted on a chromatographic column. Their vapor pressure is much larger than that of the parent compound. Some special reagents are available, which permit the formation of other silyl ethers, related to the classical trimethylsilyl ethers. For example the replacement of a CH, by a CD, results in a derivative for which many peaks of the mass spectrum, but not all, are shifted by three Daltons. The use of dimethylchloromethylsilane or References on p. 561.

542

of other chloro-substituted ethers permits the detection of the derivatives with an electron capture detector.

d. Other Useful Reactions Several other reactions have been and are still used for the rapid, quantitative methylation of various kinds of compounds. - dimethylformamide diacyl acetal (Methyl 8) has been used by McDougall(40) for the methylation of the monobutyl diphosphoric acid and the dibutyl monophosphoric acid, in tributyl phosphate, prior to the injection of the sample in a gas chromatograph. This reagent has also been used for the methylation of fatty acids and amino acids (41,42), - trimethyl( a,a,a-trifluoro-rn-toly1)ammoniumhydroxide (TMTFTH) has been recommended for flash methylation, directly in the sampling port of the gas chromatograph. The reagent and the sample are merely mixed in the syringe barrel, just prior to injection. McGee and Allen (43) and Gerhardt (44) have used this reagent for the rapid methylation of acids extracted with hexane from samples of biological origin. - trimethylanilinium hydroxide (Methelube or TMAH) is a powerful methylating agent of barbituric compounds, related tranquilizers, xanthine bases, phenolic alkaloids, etc. (45). Marlet (46) has successfully used this reagent for the analysis of dibutyl phosphate in tributyl phosphate.

e. On-line Hydrogenation Beroza (26-28) and Thomson et al. (29,30) have suggested a chromatographic procedure for the qualitative analysis of a mixture and the identification of unknown compounds using a combination of chromatographic separations and catalytic reactions. The development of this procedure and its systematic use have been hindered by the rapid spread of the combination GC-MS in the early 'seventies. All functional derivatives studied can be hydrogenated on a platinum catalyst, at a temperature around 250 O C, and the saturated hydrocarbon skeleton is obtained with a very good yield. The procedure involves trapping of the unknown at the exit of a first column, followed by vaporization of the fraction in a hydrogen stream which carries the vapor over the catalyst bed and then on a second column. The catalytic reactor is a 5 cm long column, packed with Chromosorb coated with platinum chloride; heating at 260 O C under a hydrogen stream generates the catalyst. The use of an efficient open tubular column permits the identification of the hydrocarbon, if it is not too complex. The use of a gas density balance could permit the determination of its molecular weight. If the temperature of the catalyst is raised about 30 O C, some degradation of the skeleton takes place and the saturated hydrocarbon appears, having lost the functional carbon atom. If the two hydrocarbons can be identified, the molecular structure and the position of the functional group are known. The functional group

543

can be identified by the analysis of the light gas formed, H,O, NH,, PH,, SH,, HCl, etc. Difficulties would arise with polyfunctional derivatives. Excellent results have been obtained by Beroza and Sarmiento in the identification of pheromones (28) and by Galfre and Guiochon (47) in the analysis of sesquiterpenes. The procedure is long and complex and is not competitive with mass spectrometry. However, it is very attractive for those who do not have access to a mass spectrometer. The reactions involved are simple and straightforward, the identification of saturated hydrocarbons is relatively easy, the retention data of many hydrocarbons are available and they are quite reproducible. The procedure gives successive clues to the molecular structure of the unknown.

111. THE COUPLING OF MASS SPECTROMETRY TO GAS CHROMATOG-

RAPHY As has been made clear in Chapter 11, retention data are totally insufficient to

permit the identification of an unknown compound. Many schemes have been designed in the early days of gas chromatography to at least narrow down the possibilities, but they were relying on the implicit assumption that the analytes had simple molecular structures and were monofunctional. The most potent and promising ones were schemes based on a combination of reactions (pyrolysis or catalytic hydrogenation) and the Rohrschneider-McReynolds identification methods using retention data. Development research on these approaches was progressively abandoned in the early ’seventies and this area of research has essentially dried up, because of the rapid progress of the combination of gas chromatography with on-line mass spectrometry. It should be noted that the development of GC-MS is indeed the ultimate achievement of this general approach at identifying unknown compounds by a combination of selective reactions and the use of retention data. In GC-MS, the first technique separates the components of the mixture and delivers pure substances to the mass spectrometer. The mass spectra obtained contain a large amount of information and are generally sufficient to characterize an unknown and permit its recognition in other mixtures or in other analysis of the same mixtures made with different stationary phases and resulting in changes of the elution order. Furthermore, most features of a mass spectrum can be related to the structure of the molecule. It is possible to derive a number of clues to this structure by a careful examination of these features. In many cases positive identification can be made, either by rationalizing the mass spectrum or by comparison with a library of spectra. Important progress in vacuum technology, electronics and data processing has resulted in the development of a new, hybrid instrument, known as the “GC-MS”. Depending on its owner and/or the circumstances, the GC-MS can be viewed either as a gas chromatograph with a mass spectrometer as a detector, or as a mass spectrometer using a gas chromatograph as the main part of its ion source. In fact this hybrid instrument has many properties of its own. It is the most powerful tool References o n p. 561.

544 544

availableatatpresent presentfor forthe theidentification identificationofofunknowns. unknowns.ItItisisrapid rapidand andaccurate, accurate,very very available sensitive, relatively simple and available almost everywhere. sensitive, relatively simple and available almost everywhere. impossibletotodo dojustice justicetotothe theGC-MS GC-MSininaafew fewpages. pages.ItItisisnot notthe theaim aimofof ItItisisimpossible this section to present a complete description of the instrument design and properthis section to present a complete description of the instrument design and properties,problems problemsand andperformance performancenor norofof its itshuge hugefield fieldofof applications. applications.There Thereisisa a ties, number of books devoted to GC-MS (48-52) where the interested chemist mayfind find number of books devoted to GC-MS (48-52) where the interested chemist may the information needed. We just wish to explain here the reasons for the power the information needed. We just wish to explain here the reasons for the power ofof thistechnique techniqueand anddescribe describeits itsmain mainfeatures. features. this PrincipleofofMM Spectrometry 1.1.Principle aa ss ssSpectrometry

Likeall allspectrometers, spectrometers,the themass massspectrometer spectrometerincludes includesthree threemain mainparts, parts,the theion ion Like source, the ion analyzer and the ion detector. By contrast with other spectrometers, source, the ion analyzer and the ion detector. By contrast with other spectrometers, themass massspectrometer spectrometeranalyzes analyzesions ionsnot notphotons. photons.This Thisintroduces introducesan anadditional additional the variable with which the analyst may play. The speed of photons in vacuum, andfor for variable with which the analyst may play. The speed of photons in vacuum, and most practical purposes in air, is the same for all of them, their energy and most practical purposes in air, is the same for all of them, their energy and b

?r 7-C .-. .-.....-...- ...-._. .-. -.....-...- ..._.

Z'.\

/-

'

Chromatogram

Chromatogram

d

a

d

M

Mass Spectrum

h \-

Figure 12.5. Schematic of a Gas Chromatograph coupled to a Mass Spectrometer.

a - Chromatographic column (packed or open tube). b - Flame ionization detector. c - Interface (here Watson-Biemann separator). d - Vacuum pump. e - Ionization chamber of the mass spectrometer. f - Vacuum pump. g -Magnet. h - Ion collector and electron multiplier. i - Amplifier.

545

frequency are related and there is only one way to separate photons. It is not so for ions. They can be analyzed by speed, mass or energy and there are several different ways to sort out an ion beam, which explains the existence of two classes of mass spectrometers, single and double focussing instruments and of magnetic, quadrupole and time of flight analyzers. A schematic of a GC-MS instrument is shown on Figure 12.5. a. The Ion Source

The ion source generates ions from the sample. A variety of reactions can be used (see pp. 547-548). The ions formed are extracted from the ion source by the repeller, a polarized plate pierced by a pinhole through which they access a channel lined by plates polarized to different voltages. This ion optical system accelerates and focuses the ions on the entrance slit of the ion analyzer. The acceleration voltage is of the order of 3 to 4 kV when the ion analyzer is a magnetic sector, somewhat lower when it is a quadrupole. When high molecular weight fragments have to be analyzed, the voltage must be raised to achieve a sufficient velocity. Depending on the analyte and on the reaction used, a variety of positive and negative ions can be formed. While only positive ions were analyzed by most mass spectrometers until very recently, modern instruments include provision to separate and detect either positive or negative ions. This results from the recent recognition that some very important compounds (usually those which also give a very strong response with the ECD) can capture an electron under favorable circumstances and give a stable negative ion (sometimes after a simple fragmentation). The detection of some trace components of major concern, such as PCB's, PBBs, polychlorodioxins has been achieved at the extraordinarily low concentration level of a fraction of a ppt in various food or environmental samples by GC-MS using negative ions. Although care is taken to communicate the same acceleration to all ions entering the ion optics, the ions entering the analyzer have a finite kinetic energy distribution, hence ions of a given mass have a certain velocity distribution. This results from the energy distribution and the distribution of velocity direction of the ions formed in the source, due to the high energy involved in the ionization reactions. Instruments which directly analyze the ions formed in the source and extracted by the optics have a rather low resolution (i.e., they cannot completely separate ions differing by one Dalton when their mass exceeds 800 to 1,500 Daltons). High resolution mass spectrometry (separation of ions differing by one Dalton with individual masses of several thousand Daltons, determination of molecular weights with an accuracy of a few ppm) is achieved using double focusing instruments. An electrostatic analyzer filters ions and lets into the ion mass analyzer only those which have the same set velocity.

b. The Zon Analyzer Ions of different masses (or rather different m / z , or mass to charge ratios) are analyzed either by a magnetic sector or by a quadrupole. In the former case, the ion References on p. 561.

546

trajectory is bent by a strong perpendicular magnetic field, and only the ions of a gven kinetic moment can cross the exit slit of the analyzer and penetrate into the ion detector. The analysis of ions of different masses is possible provided all ions have the same energy. Any effect resulting in a broadening of the velocity distribution of ions of a given mass will result in a loss of resolution. This is why an electrostatic energy filter is used on high resolution instruments. A progressive variation of the magnetic field changes the mass of the ions which are detected and permits the scanning of the spectrum. The quadrupole filter uses four identical, equidistant metal bars parallel to the ion trajectory (the mechanical constraints are very tight). At any time, all the bars are at the same absolute voltage. Bars which are diagonally opposed have the same polarity. Contiguous bars are at opposed polarities. The voltage applied is the sum of a continuous and a high frequency component. Then, only ions of a given mass have a stable trajectory (which is not linear) and can exit from the slit at the end of the tube. Other ions hit the bars and disappear. To eliminate signals due to the weak X-rays generated in these collisions the ion beam is curved by an electric field before entering the detector. The mass scan is obtained by changing the voltages, while keeping constant the ratio of the constant voltage to the amplitude of the high frequency voltage. The magnetic sector permits an extremely narrow focusing of the ions of a given kinetic moment. Provided the ions of a given mass have the same velocity (hence moment and energy), very high resolution are possible. Technological advances in magnet design have permitted the achievement of sufficiently short scan times (a few seconds for 1,000 Daltons). The mass scan is far from linear, however, but close to logarithmic, which makes mass determination difficult when there are few ions, such as in chemical ionization. The mass range is almost unlimited (as far as GC is concerned). The quadrupole filter gives only low resolution spectra, but the acceptance angle and energy of the ions is wider, so the sensitivity is better. The mass scan can easily be made linear in masses, which is an advantage over magnetic sectors. The mass range of the quadrupole has been extended to about 2,000 which is sufficient in gas chromatography. In both cases, the pressure inside the analyzer is kept very low, below 0.1 ptorr, to avoid ion-molecule collisions. c. The Ion Detector

Two ion detectors are used in GC-MS. The first one is placed on the ion beam at the inlet of the analyzer and collects a small fraction of the ions. The signal is proportional to the total ion current and is a function of the amount of analyte. The second detector is placed at the exit of the analyzer. It is usually a photomultiplier. The signal is a function of the number of ions, of their mass and energy, of their charge and structure and of the amplifying voltage. Usually, one or a very small number of ions can be detected. The time constant of this detector and its ancillary equipment must be very short to follow the change in signal obtained when scanning at a few hundred Daltons per second. The data available to the analyst are the total ion current during the entire chromatographic run and spectra obtained when scanning a predetermined mass

547

range when the total ion current exceeds a certain set threshold. The total ion current is very similar to the signal delivered by a moderately selective detector, such as the FID. It can be used for quantitative analysis, but most often the chromatogram obtained on certain masses is preferred (single ion current). The raw signals of the GC-MS recorded during a moderately complex chromatographic analysis constitute an overwhelming mass of data which exceeds the capability of most analysts. Processing these data and extracting the relevant information is a typical computer task. Because of its complexity, control and audit of the results are an important part of the analyst’s task. It is not the best understood nor the one for which the manufacturers have been the most helpful, in large part because a proper audit would require an understanding of the computer software used, which is proprietary. Calibration and frequent run of authentic samples are required for a suitable assessment of the quality of the analytical results obtained. The computer calculates the mass spectra, i.e. the ion intensity versus fragment mass from the intensity versus time records during mass scanning and stores the spectra acquired during the analysis. It can derive either normalized spectra obtained for the column eluate at any given time or plots of the signal intensity versus time at any given mass (reconstituted single ion currents). Combination of signals acquired on different masses is also possible. Comparison of normalized spectra to those stored in a library considerably facilitates the identification of unknowns. 2. The Various Ionization Methods Used in MS

Many different methods of ionization have been described in mass spectrometry. They deal with the enormously different materials and problems in the study of which the method is involved. GC-MS is rather specialized from this point of view, since the sample is introduced in the ion source as a dilute vapor in a carrier gas. Methods such as field desorption, field ionization, or fast atom bombardment would be of little use and rather difficult to implement. They have been developed to push into the gas phase molecules which are stubbornly nonvolatile. In GC-MS the analyte is already in the gas phase and must merely be kept there, which simply requires proper heating of the sample line. Accordingly, only electron impact and chemical ionization are used in practice. a.

Electron Impact

The eluent enters a low pressure cavity which is crossed by a narrow electron beam. The electrons are generated by a heated metal filament and accelerated by a 10 to 100 V potential. A small magnetic field gives the beam an helicoidal trajectory and increases the probability of collision between a molecule of analyte and an electron. Upon such a collision, organic molecules are ionized (ionization potential, 10 to 12 ev), and part of the electron kinetic energy is transferred to the molecule as internal energy. In many cases, the molecule breaks down into fragments, following one of several different possible pathways. The proportion of fragment ions increases with increasing electron energy (up to about 50 ev) and their average size decreases. References on p. 561.

548

The source temperature is controlled at a temperature high enough to avoid condensation of the low vapor pressure compounds sometimes analyzed by GC. A powerful vacuum pump is required (see subsection on interfaces, pp. 549-553). The pattern of fragmentation ions, i.e., the relative intensity of the different fragments possible, is highly repeatable on a given instrument and reasonably reproducible from an instrument to another one. Such a pattern is called an EI spectrum. They are stored in libraries, containing up to about 30,000 spectra. In most cases ionization reactions are unimolecular and give monocharged ions. A large majority of these ions are positive. In EI negative ions are few, small and usually carry little information. The most important reactions are the simple fragmentations with loss of either a neutral molecule or a neutral free radical, and the rearrangement of the ion followed by the loss of a neutral fragment. Electron impact gives a large number of fragments, the set of which is an almost unique fingerprint of the molecule and permits its identification, either by a proper interpretation of the fragmentation mechanisms, or by a search in a mass spectra library. On the other hand, some molecules, especially the large, bulky, polar ones, are so easily broken that no molecular ion is observed. This complicates their analysis, makes their identification more difficult and increases their detection limit. Other, softer ionization techniques must be used. b. Chemical Ionization

The source contains a plasma at a rather high pressure (0.1 to 2 torr). When the eluent penetrates into the source, the analyte molecules can react and be ionized by electron or proton transfers. These reactions are bimolecular and are efficient only if the source pressure is high enough. The selection of the reagent gas is critical and depends on the type of compounds analyzed. Sometimes the same gas may be used as carrier gas and reagent, at other times not (NH,, CH,NH, or even CH,). A number of ions are derived from the reagent. They may react with the eluites to give proton transfer (fragment M + 1)or proton abstraction (fragment M - l),addition of the whole reagent ion, exchange of a fragment, elimination of a neutral fragment or formation of a negative ion of mass M - 1. Since the reagent ions are in large excess, the reactions of proton transfer and proton abstraction are the most important. CI spectra are much more simple than EI spectra and contain a large proportion of high molecular weight ions. Often the ions M + 1 are dominant. The spectra depend to a large degree on the choice of the reagent gas. The proton affinity increases rapidly from methane to isobutane, to ammonia and to methylamine. Fragmentation ions are still abundant with methane, they are fewer with isobutane and still much fewer with ammonia. The quasi-molecular ions M 1 or M - 1 are abundant and heavier MXH' ions appear, especially with ammonia (M 18). A proper design of the source permits a rapid adjustment of the pressure and the successive collection, on the same chromatographic peak, of an EI and a CI spectrum. The combination of both considerably simplifies the identification of an unknown.

+

+

549

3. GC-MS Interfaces There are some compatibility problems between gas chromatography and mass spectrometry. Basically, the two methods are compatible, because both analyze samples in the gas phase and both handle comparable amounts of material, typically between 1 pg and a few pg. On the other hand, however, they operate under pressures which differ by many orders of magnitude. Furthermore, GC is a dilution method and the compounds of interest are highly diluted in the carrier gas at column outlet. A GC-MS interface is used to solve these problems. a. The Purpose of the GC-MS Interface

The gas at the outlet of a GC column is under a pressure close to atmospheric while the pressure in an MS ion source is more than a million times lower (below 0.001 torr in El). Since the flow rate across a GC column is of the order of 1 mL/min for a conventional open tubular column (i.d., 0.25 mm) and 60 mL/min for a conventional packed column (i.d., 4.5 mm), very large capacity pumps are required to keep the pressure in the ion source and in the analyzer below 0.001 torr torr, respectively. The conductance between the source and the and 1x analyzer is small, because they communicate only through the slit available to the ion beam. Thus, two vacuum pumps will be used, and the higher capacity pump will be connected to the source. The pumping rate in the source must be 12.5 L/sec for each mL/min flow rate at column outlet. If we take into account the losses due to tubings and fittings, a pumping capacity of 200 to 250 L/sec would appear to be sufficient to permit the use of most open tubular columns without creating any problem. A much larger capacity would be required in order to be able to use packed columns. Alternatively, a fraction of the eluate only will be sent to the MS source and the rest vented either directly or through an auxiliary detector. Another problem which arises in the coupling between GC and MS is related to the important extent of the dilution which takes place in a chromatographic column during elution. A small amount of sample is injected. It is eluted as a band of finite width, which depends on the column properties and on the retention. Compared to the concentration of the same component in the analyte, the concentration in the carrier gas at column outlet can be 100 to 1,000 times less. Care should be taken to make sure that the sample injected is large enough, and the column is slightly overloaded for the major components, in order to minimize the consequences of this phenomenon. Since all gases and vapors in the ion source are ionized, there will be an intense emission of the ions characterizing the carrier gas and possibly its impurities. Since the carrier gas is most often helium, sometimes hydrogen, this will not generate important background signals in EI, but an intense carrier gas ion beam may result in noisy spectra and certainly in a very noisy, intense background signal for the total ion current. This is why helium is preferred in GC-MS (hydrogen would be preferred by chromatographers). The ionization potential is set at 20 V when no organic compound is eluted, which is low enough to avoid ionization of the helium References on p. 561.

550

atoms. The decrease in ionization efficiency of the analytes is more than compensated by the enormous reduction in the noise. The contributions of the carrier gas impurities to the spectra may not be negligible. In chromatography, the impurities come essentially from the stationary phase and its slow pyrolysis, often initiated by trace oxygen contained in the carrier gas and leaking into the system by diffusion through the septa. The upper temperature limit of stationary phases is lower in GC-MS than in GC, but this depends much on the nature of the phase and its pyrolysis products. For example, polyolefins decompose by a random process generating a large number of olefins-and resulting in a noisy baseline and noisy spectra. Silicones give only a few well characterized cyclic pyrolysis products, with important signals at only a few masses. Spectra obtained by subtracting for the background are much cleaner with the latter phases than with the former. Ideally, the coupling device or interface should provide for total transfer of the sample components to the ion source, for maximum signal, and no transfer of the carrier gas, to permit the use of low capacity pumps and reduce signal noise. The properties of an interface for GC-MS can thus be summarized as follows: - no loss of analyte, by either condensation, adsorption or reaction; - no contribution to chromatographic band width, resulting in a loss of the resolution provided by the column; - high transfer efficiency for the high molecular weight components of the sample; - the inlet pressure is around atmospheric; - the outlet pressure is a fraction of a Torr; - the transfer efficiency for the low molecular carrier gas is low, providing for some degree of enrichment of the analyte. No interface is completely satisfactory. Several different principles have been studied and developed. The practical solution much depends on whether the column used is an open tubular column or a packed column. b. The Direct Interface

This is the simplest possible interface. A narrow metal or silica tube is connected to the column end and to the ion source. The dimensions of this tube are calculated so that it offers a pneumatic resistance which is appropriate to keep the outlet column pressure near atmospheric when the pressure in the ion source is low vacuum. There is no enrichment in solute concentration, but the transfer yield is total, provided the tube is heated at a temperature close to that of the column. This interface is acceptable only for open tubular columns, otherwise the flow rate is too large and the pressure in the MS exceeds the acceptable limit. It may be difficult to find a tube narrow enough and in many cases the column is directly connected to the ion source. The coupling is thus made as simple as possible. The major drawback of this method is that the GC column is operated with an extremely low outlet pressure, much below atmospheric pressure. The results are not always favorable for the column efficiency. Contradictory results have been reported (58-61). In some cases, the maximum column efficiency is

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hardly changed, while the optimum camer gas velocity increases with decreasing outlet pressure, in agreement with the prediction of Giddings (62). Other authors have reported significant losses in column efficiency when operating them with the outlet under partial vacuum (58). This may seem strange because under such circumstances, the pressure profile in the column, near its outlet, is very steep, so most of the column is operating under the viscous flow regime, at relatively large pressures. In fact it seems that favorable results are obtained if the column is long enough to be operated with an inlet pressure above atmospheric pressure. This requires column lengths exceeding approximately 30 m. c. The Open Split Interface This interface has been developed by Schomburg et al. in the 'seventies (60,63). The outlet of the open tubular column faces the inlet of the connecting tube to the MS source. Both tube ends are surrounded by a sheath of carrier gas arriving through an auxiliary supply. The interface is kept under atmospheric pressure, or any pressure deemed optimum by the analyst, by setting the auxiliary gas flow rate. The excess gas is vented, while a stream of constant flow rate flows to the MS source. The system is self regulating. Originally the connecting tube was 0.15 mm i.d., 1 m long and was made of Pt-Ir alloy. Now it is made of silica and tubings with inner diameters as low as 0.05 mm are available. Their chemical inertness is practically total. This interface provides no enrichment and a transfer yield which is not total. The yield depends on the ratio of the flow rates of the column and the auxiliary supply. Because the flow in the transfer line is viscous, the flow rate depends on the temperature. Usually it is larger than 1.5 mL/min and the transfer yield may be very large. This system is very practical and often adopted.

d. The Molecular Separators Several devices of this type have been described and developed. They have been more or less abandoned because their complexity and some of their drawbacks were not justified in view of the possibilities offered by the open split interface. Ryhage has designed a jet separator, based on the variation of the angle of a molecular beam with the molecular weight of the particles (64). The lighter molecules of the carrier gas diffuse radially faster than the heavier solute molecules. Their beam has a larger cross-section area and hits a diaphragm which prevents their transfer to the next chamber, while the heavier solute molecules go through an orifice in the center of the diaphragm (see Figure 12.6). The yield is between 30 and 70%. It depends very much on the proper construction of the device and especially on the alignment of the beam and the orifice and on the distance between the tip of the jet and the diaphragm. The enrichment can be as large as 50 to 100. The main drawback of the separator is the narrow range of flow rate within which good performance is achieved. References on p. 561.

552 Js,! I

a

I

b

Figure 12.6. Schematic of a two-stage Ryhage separator. a - Vacuum pump. b - Diffusion pump. Distances: S1, 0.15 mm. S2, 0.5 mm. Diameters: dl, 0.10 mm. d2, 0.30 mm. d3, 0.24mm. d4, 0.30 mm.

Watson and Biemann described a simple separator using gas effusion, through very narrow pores (65). The eluate goes through a restrictor to a porous glass tube. The pores are very narrow (cu 1 pm). The tube is placed under vacuum, so that both carrier gas and analytes are pumped across the porous wall and diffuse (see Figure 12.7). The rate of diffusion increases with decreasing molecular weight of the gaseous species. Thus, there is an enrichment and the stream which exits from the tube is richer in organic solutes than the one which enters. The enrichment factor does not exceed 40 but is usually between 4 and 20. The transfer yield is only 20 to 30%. This is one of the major drawbacks of the device. Also the gas flow rate must be optimized within a narrow range, otherwise yield and enrichment factor drop rapidly. Finally, there has been much concern voiced regarding the use of porous glass in contact with more or less sensitive vapors, and the possible catalytic reactions they could experience, although the molecules which enter the porous wall have a low probability to diffuse back and enter the MS source. Llewellyn and Littlejohn have described the use of a silicone membrane as a separator (66). The principle is based on the much larger solubility of organic compounds in silicone rubber than light gases. The diffusion rate of helium is very low, while that of lipophilic compounds is 30 to 100 times larger. The transfer yield is a function of the geometry of the device but also of the nature of the analyte and of the temperature, which makes the use of this system difficult. The upper temperature limit is around 25OoC, which does not permit the analysis of heavy compounds. Finally, the residence time of the analytes in the membrane of silicone rubber is rather long and may contribute markedly to the band broadening. For these reasons, this separator is not much used.

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a

Figure 12.7. Schematic of a Watson-Biemann separator. a - Vacuum pump. b - Porous glass tube (porosity, 1 am). c - Narrow access channel at both ends.

Other separators have been suggested, using semipermeable membranes. A tube of a silver-platinum alloy can be leak-proof for every gas and vapor but hydrogen, and let this gas disappear as if there were a hole. Organic chemists have always been wary of hydrogenation in presence of platinum, so this separator has not been developed. Lipsky, Horvath and McMurray (67,68) have described a very simple separator, using a thin Teflon capillary tube. The tube (cu 2 m long, 0.5 mm o.d., wall thickness 0.12 mm) is placed under vacuum and heated to 280 O C (see Figure 12.8). It is connected at one end to the GC column, at the other to the MS source. The dead volume is very low. The enrichment may be as large as 200, but depends on the nature of the analyte.

Figure 12.8. Schematic of the Lipsky-Horvath separator. a - Vacuum pump. b - Thin wall Teflon tube. c - Metal capillary tube.

References on p. 561.

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4. Data Acquisition and Handing

The amount of data supplied by a GC-MS is enormous and far exceeds the handling capability of a human being. The computer has found there one of its earliest applications in instrumental analysis. Its use makes available an extremely powerful technique in many laboratories which could not afford it otherwise. The data are acquired and processed by the computer which may perform a variety of tasks permitting the selection of the data required and the elimination of time wasted while looking at unnecessary data. The computer first determines when to acquire data. It is usually not necessary to do so when the total ion current is too low or during certain time windows specified by the analyst. When the total ion current exceeds the threshold set, the ionization voltage is raised to 70 V and cyclic scanning is performed, usually at a frequency of 1 Hz. During each scan the computer calculates the mass of each fragment of significant intensity and stores it together with the corresponding intensity. Later it will be possible to use these data to correct for background spectra, to derive normalized spectra, to compare spectra, to calibrate, using standard mixtures, to draw elution profiles on different masses or combination of masses, to compare recorded spectra with those placed in the available library. In the same time the computer is available for diagnosis of the functioning of the mass spectrometer. Books have been published on the use of mass spectra to relate them to the structure of the corresponding compound and use them for identification purposes (69-72). This problem is beyond the scope of the present book. 5. The Mass Spectrometer as a GC Detector

It is interesting to compare the MS to other GC detectors, which we have done by summarizing its principal characteristics and properties, as a detector, using the same framework as for other GC detectors (see Chapter 10). a. Parameters Affecting the Response

There are many parameters influencing the response of the MS, but, when available, this instrument is well controlled and the response is usually very stable. The most important parameters are the nature of the ionization method used, the ionization voltage and the photomultiplier voltage. Computer data acquisition can be made over a much larger range of signal than permitted by the use of chart recorders, which simplifies the selection of this last voltage. The chromatographer is often shocked when he comes to realize the very low ionization yield of the mass spectrometer, i.e., the small number of ions collected by the detector per mole of sample introduced into the source. There are just too many sources of losses (73): - In order to achieve a reasonable precision on the determination of the mass of a fragment, which is the first basic measurement carried out with an MS, it is estimated that, for statistical reasons, the collection of 100 fragment ions of this mass is needed.

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Losses in the analyzer are negligible, but the object and image slits of this ion optical device are rectangular and nearly identical. Their convolution product is triangular. Thus we need 200 ions at the object slit. - The extraction yield of ions from the source to the analyzer is approximately 10%. Thus we need to make 2,000 ions of this fragment in the source. - In order to record a meaningful spectrum, this number applies to the smallest fragment we want to record with precision. Requiring that fragments which have a relative abundance to the base MS peak of 10% be barely detectable as explained above does not seem drastic. This requires that 20,000 base fragments be made during the time this mass is scanned. - The ionization yield varies greatly from one compound to another and depends much on the ionization method used. It can be as high as 1 for electron capture by haloaromatics, under favorable circumstances, and as low as 1X for EI. If we assume an average value of 0.001,this means that 20,000,000 molecules must be present in the source while the spectrum is scanned. Since a scan lasts an average of 1 msec for one mass unit, the mass flow rate to the source, i.e., from the column exit, must be 20 billion molecules per second. - The band characteristics vary widely, depending on the kind of analysis performed, on the nature and retention of the compound considered, on the column performance, etc. Taking average values (column of 160,000 plates, 75 m long, a gas velocity of 25 cm/sec, a 300 Dalton compound, retained with a column capacity factor equal to 4) we obtain a detection limit of 95 pg (73), in excellent agreement with typical specifications for the detection limits of commercial GC-MS instruments. In practice, the detection limit in the scanning mode is difficult to define, since we use a spectrum, i.e., an entire pattern of peaks for the identification of an unknown, and chemical noise may considerably affect the performance of an instrument, and do so to a very different degree for compounds belonging to different families. -

b. Classification The MS is an ionization detector, which transforms a fraction of the eluted sample into ions. It is a destructive detector and it belongs to the group of mass flow detectors. Within limits, its response factor, i.e., the ionization yield, does not depend on the camer gas flow rate. So the peak area on a given mass does not depend on the flow rate either. c. Selectivity

The MS is an extremely selective detector, in so far as it is almost always possible to find a mass for which one compound gives a fragment and another does not. This property has been widely used for the selective detection and quantitative analysis of compounds which are not or are only partially resolved. When used in true single ion monitoring mode (the signal on one or a few selected masses is recorded, References on p. 561.

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without scanning), the sensitivity is very high, possibly one thousand times better than in the scanning mode. At the same time, the GC-MS is a general detector, because all organic compounds have a mass spectrum. d. Sensitivity The detection limits are low, as we have seen above, of the order of 0.1 to 1 ng in the scanning mode, of the order of 100 fg in single ion monitoring. The dynamic linear range is not very large, however. When compounds present in large concentrations are analyzed, it may be necessary to reduce the sample size used or to place a splitter between the column and the MS inlet. The detection limit depends very much on the ionization method used. In chemical ionization there are fewer ions and the yield is much higher for the quasi-molecular ion and the other heavy ions formed. e. Linearity The response of the MS is linear in the low range of sample size. The dynamic linear range is not very large. Saturation problems take place as soon as the ion density becomes significant. This is not a major problem, however. The MS is so complex, expensive and time consuming that GC-MS is used for applications where other detectors cannot be used, mainly for identification purposes and for the quantitation of traces of compounds difficult to separate, isolate or distinguish from closely related species. One important area of application is in the identification and quantitation of drug metabolites. These compounds are almost always present as traces and detector overloading is rarely a problem. Calibration is absolutely necessary for accurate results and a proper standard must be used. Internal standards are preferred.

f. Prediction of the Response Factors It is impossible to predict the absolute response factor for any compound on a given mass, or the relative response of two compounds. The relative response of the detector for two fragments of different masses of the same compound cannot be predicted from first principles, but is quite reproducible from one compound to another. This is the basis of the use of a library of mass spectra for identification purposes. g. Maintenance and Cost

The cost of the detector is well above an order of magnitude larger than the cost of a standard GC. The maintenance is complex and demands a part time specialist.

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IV. THE COUPLING OF INFRARED SPECTROPHOTOMETRY TO GAS CHROMATOGRAPHY Although the coupling of mass spectrometry and gas chromatography has been the first application of combined (or hyphenated (74)) analytical instrumentation techniques and is by far the most widely used, GC-MS cannot solve all identification problems. Difficulties arise because either one of the coupled methods proves insufficient and/or does not meet the requirement of the other one. Sometimes the separation is insufficient. The chromatography can be improved by the use of a longer, more efficient column. This can be done only at the cost of a longer analysis time and a more dilute eluate, i.e., of a less sensitive response. The combination of several columns of widely different retention behavior, using a heart-cutting method for example (see Chapter 9), permits another solution to this problem. Sometimes also the mass spectrometry cannot supply the required information which would permit the identification of the unknown. For example there are several isomers which have similar mass spectra. This situation is not rare with geometrical isomers of derivatives of polyaromatic hydrocarbons having small substituents. The differences between the mass spectra could be sufficient to distinguish between the pure isomers injected carefully with an unsoiled probe in a clean source, in classical MS. They are insufficient to permit the identification of the exact isomer from the spectra obtained in GC-MS, because of the chemical noise which is always observed and limits the precision on the determination of the relative abundance of minor fragments. In a number of other cases it may be difficult to distinguish between the mass spectra of structural isomers and library searches can lead to unsatisfactory or erroneous identifications. This situation is well known from analytical chemists who have long recognized the necessity of using a combination of three spectral techniques for rapid, correct identification of unknowns: mass spectrometry, infrared spectroscopy (IR) and nuclear magnetic resonance (NMR). For a very long time it was considered that infrared spectroscopy was too insensitive to provide satisfactory spectra of unknown compounds purified by gas chromatography, susceptible of permitting their identification. The amount of material which can be injected in a normal packed column was just too small to permit the collection of the amount of the minor components (let alone the trace components) which is required by conventional IR spectrophotometers to provide a useful spectrum. Semipreparative columns were required and devices allowing the collection of condensed fractions in IR cells were described very early on, but until the early 'eighties the minimum sample size required for the recording of a useful IR spectrum decreased more slowly than the maximum sample size allowable in a classical GC column. The rapid spread of open tubular columns seemed to mark a final divorce between IR and GC. The development of a new technique of IR spectroscopy, using interferometry and fast Fourier transform, has suddenly and completely changed the situation (75,76). The amount of product required to obtain a useful IR spectrum has been reduced by several orders of magnitude. Although trace components remain more difficult to handle than with GC-MS, this new References on p. 561.

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technique permits the identification of unknowns with the small amount of material eluted from an open tubular column for the minor components of complex mixtures. 1. Principle of Infrared Spectrophotometry

Molecules of a given compound can absorb only the photons having a certain energy. A plot of the probability of adsorption of a photon versus its wavelength or frequency is a spectrum. The infrared spectrum of a small gaseous molecule is made of a few relatively narrow bands, which can be resolved in series of very narrow rays. The gas phase spectra of large molecules are more complex and the bands more numerous, and they cannot always be resolved. Nevertheless, its IR spectrum is highly characteristic of the molecule. It is exceptional that two compounds have very similar IR spectra, because these spectra contain a large amount of information specific to the molecule, its structure and the distribution of electron density. Its IR spectrum is a fingerprint or a signature of a molecule and may permit its identification, in part because spectral characteristics can be related to features of the molecular structure, in part because large libraries of spectra are available. In the process of absorbing a photon, a molecule increases its internal energy, i.e., its vibration energy. It must also, at the same time, change its rotation energy. The vibration and rotation energies of a molecule, however, are quantized, i.e., they can vary only by fixed, well-defined amounts, the quanta of vibration and rotation energy. A photon can be absorbed only if its energy is equal to the sum of the energies required to increase by one unit one or several of the quantum numbers of vibration and to change one of the quantum numbers of rotation (77). In simple molecules which have few atoms, the patterns of vibration are simple. If the molecule has n atoms, it is necessary to know the 3n coordinates of the n atoms to define exactly its position and structure. Since it has three degrees of freedom of translation (the n atoms together, hence the molecule, can move in the three directions of space) and three degrees of freedom of vibration (the molecule can rotate around any of the three directions in space) it also has 3n - 6 degrees of freedom of vibration. There are as many modes of vibration in which the different atoms in the molecule oscillate simultaneously, in a cooperative fashion, around an average position. These vibration modes are complex and involve many different atoms of the molecule. It is often possible, however, to ascribe many of these modes to the stretching, bending or tilting of some particular bonds of the molecule. The variations from compound to compound of the frequency and intensity of the IR band corresponding to a given bond are then accounted for in terms of the contribution of their environment. This correlation between spectral characteristics and features of the molecular stucture can be used to identify unknowns even when their spectra are not in the library. The spectra of molecules in the gas phase are similar to their spectra in the liquid phase. There are important differences only for small molecules, which are often readily identified by many procedures, including consideration of their retention

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data. For larger molecules which are more difficult to identify, the differences are often small enough to permit the fruitful use of IR spectra scanned from samples in the liquid phase. This permits the use of large libraries. The libraries of IR spectra of vapors are rather limited (ca 10,000 compounds).

2. Fourier Transform Infrared Spectrophotometry The classical design of a spectrophotometer incorporates a source which emits a polychromatic light beam sent to a tunable monochromator, then through the sample to a detector. Changing the setting of the monochromator permits the scan of a spectrum, which is the ratio of the intensities of the light beams received by the detector and sent to the sample, respectively. In FTIR the monochromator is replaced by an interferometer and the light beam passing through the sample cell contains photons of all wavelengths. When the mirror of the interferometer is moved to change the length of one of the optical paths, the detector records a pattern of interference fringes. From this pattern and the similar one recorded with a totally transparent sample, it is possible, by Fourier transform of the data, to derive the spectrum of the sample in the wavelength range where the source emits. Advances in detector material and design, in the design of the sample cell, in the data acquisition, have permitted the construction of commercial equipments which deliver identifiable spectra for injected amounts in the range of 5 to 25 ng for compounds having strong absorption bands (76). It seems possible that advanced equipments permit a reduction of this detection limit by an order of magnitude.

3. GC-FTIR Interface The conventional design at present is the light pipe (75). A straight glass or quartz tube is coated inside by a very smooth gold layer and closed at both ends by an alkali halide window. The eluate enters on the side of the tube at one end and exits at the other end, from where it goes to an FID. The transmittance of the light pipe is of the order of 25%,which is sufficient. The light pipe is typically 1 mm i.d., 10 to 20 cm long. Although the light pipe volume is still large enough to contribute significantly to the band width of the signal, the loss of resolution is now acceptable, in view of the results obtained (a 25 m long, 0.25 mm i.d. open tubular column has a band width equivalent to about 6 cm of column for a non-retained peak (H = 0.125 cm), 30 cm for a retained compound with k’ = 6, see Chapter 4, equations 17, 26 and 27). If the light pipe is 1 mm i.d., the band occupies a volume 4 times larger in cross-section area and these figures must be divided by 4. For obvious optical reasons, the apparent remixing of the eluate over the entire length of the light pipe is total. The use of a scavenger flow could reduce the cell contribution to band broadening, but at the unacceptable price of a considerable reduction in sensitivity. The present light pipes are quite acceptable with large diameter open tubular columns. Alternately, a small amount of argon is added to the helium carrier gas and the column effluent is sent to a very cold surface (12 K) by a narrow jet placed a few References on p. 561.

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IR Source Soursce Interferometer

Paraboloid

Pa Irob

Gas chromatograph

Figure 12.9. Schematics of a GC-FTIR apparatus.

mm from the plate (76). The argon and the vapor are trapped on the surface, while the helium is vented. The plate rotates slowly and passes under a microscope focusing the beam of the FTIR spectrometer. The need of a long light pipe is eliminated and the detection limit decreases to 100-200 pg. A further increase in sensitivity can be obtained by averaging a large number of spectral scans, which can be made by immobilizing the plate on which the chromatogram is now frozen.

4. Data Acquisition and Handling Spectra can be scanned at a frequency of several hertz and recorded. The use of a high scanning frequency has the advantage that several spectra can be averaged, to improve the signal to noise ratio. Also, it becomes possible to compare the composition of the eluate during the front and the tail of a band (75). The software used is very similar to the one developed for GC-MS. It provides for comparison between the recorded spectra and those stored in the library and supplies the lists of best matches with an indication of the quality of the match. Reconstructed chromatograms on a certain frequency could be obtained. Total chromatograms are derived by integration of the spectrum or by combination of the signal obtained in certain frequency ranges. Finally the spectra which have been calculated are stored and can be manipulated. One example of the complementarity of GC-MS and GC-FT'IR is the identification of hydrocarbons: IR spectra of alkanes are very similar while their mass spectra

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are different enough and permit easy identification of many of them. O n the contrary, geometrical isomers of aromatic hydrocarbons, such as xylenes, have very similar mass spectra and cannot be recognized by GC-MS, while GC-FTIR provides an easy identification.

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562 (39) M.C. Simmons,D.B. Richardson and I. Dvoretzky, in Gas Chromatography 1960, R.P.W. Scott Ed., Butterworths, London, UK, 1960, p. 211. (40) C.S. McDougall, Report ORNL/TM 6268. (41) J.P. Thenot, Anal. Letters, 5, 217 (1972). (42) J.P. Thenot and E.C. Homing, Anal. Letters, 5, 519 (1972). (43) J. McGee and K.G. Allen, J. Chromatogr., 100, 35 (1974). (44) K.O. Gerhardt, J. Chromatogr., 143, 335 (1977). (45) E. Brochmann-Hanssen and T.O. Oke, J. Pharm. Sci., 58, 370 (1969). (46) B. Marlet, PhD. Thesis, University Paris XIII, France, 1984. (47) A. Galfre and G. Guiochon, Recherches, 18,13 (1971). (48) W.H. McFadden, Techniques of Combined Gas Chromatography - Mass Spectrometry: Applications in Organic Analysis, Wiley, New York, NY, 1973. (49) J.T. Watson, Introduction to Mass Spectrometry: Biomedical, Environmental and Forensic Applications, Raven Press, New York, NY, 1976. (50) B.J. Gudzinowin, M.J. Gudzinowicz and M.F. Martin, Fundamentals of Integrated G C / M S , Marcel Dekker, New York, NY, 1977. (51) B.S. Middletitch, Practical Mass Spectrometry, a Contemporary Introduction, Plenum Press, New York, NY, 1979. (52) J. M r a e v e , F. Berthou and M.Prost, Mhthodes Chromatographiques Couplhes d la SpectromPtrie de Masse, Masson, Paris, France, 1986. (53) W.H. McFadden, J. Chromatogr. Sci., 17, 2 (1979). (54) M.C. ten Noever de Brauw, J. Chromatogr., 165, 207 (1979). (55) J.R. Chapman, Computers in Mars Spectrometry, Academic Press, New York, NY, 1978. (56) T.E. Acree, see Chem Eng. News, September 28, 1987, p. 21. (57) P. Laffort and F. Patte, J. Chromatogr., 406, 51 (1987). (58) N. Sellier and G. Guiochon, J. Chromatogr. Sci., 8, 147 (1970). (59) C.A. Cramers, G.J. Scherpenzeel and P.A. Leclerq, J. Chromatogr., 203, 207 (1981). (60) D. Henneberg, U. Henrichs and G. Schomburg, J. Chromutogr., 112, 343 (1975). (61) F.W. Hatch and M.E. Parrisch, Anal. Chem., 50, 1164 (1978). (62) J.C. Giddings. Anal. Chem. 36, 741 (1964). (63) D. Henneberg, U. Henrichs and G. Schomburg, J. Chromatogr., 167,139 (1978). (64) R. Ryhage, Anal. Chem, 36, 535 (1964). (65) J.T. Watson and K. Biemann, Anal. Chem., 36, 1135 (1964). (66) P.N. Llewellyn and D.P. Littlejohn, Pittsburgh Conf. Analytical Chemistry and Applied Spectroscopy, 1966. (67) S.R. Lipsky, C.G. Horvath and W.J. McMurray, Anal. Chem., 38, 1585 (1966). (68) S.R. Lipsky, W.J. McMurray and C.G. Horvath, in Gas Chromatography 1966, A.B. Littlewood Ed., The Institute of Petroleum, London, UK, 1967, p. 299. (69) F.W. McLafferty, Mass Spectrometry of Organic Ions, Academic Press, New York, NY, 1963. (70) H.D. Beckey, Field Ionization Mass Spectrometry, Pergaxnon, Oxford, UK, 1971. (71) F.W. McLafferty, Tandem Mass Spectrometry, Wiley, New York, NY, 1983. (72) A. Frigerio and E. Ghisalberti, Mass Spectrometry in Drug Metabolism, Plenum Press, New York, NY. 1977. (73) G. Guiochon and P. Arpino, J. Chromatogr., 271, 13 (1983). (74) T. Hirshfeld, Anal. Chem., 52, 297A (1980). (75) P.R. Griffiths, J.A. de Haseth and L.V. Azarraga, Anal. Chem., 55, 1361A (1983). (76) P.R. Griffiths, S.L. Pentoney Jr., A. Giorgetti and K.H. Shafer, Anal. Chem., 58, 1349A (1986). (77) G. Herzberg, Molecular Spectra and Molecular Structure, Van Nostrand, New York, 1945.

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CHAPTER 13

QUANTITATIVE ANALYSIS BY GAS CHROMATOGRAPHY Basic Problems, Fundamental Relationships, Measurement of the Sample Sue TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Basic Statistics. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Mean and Median . . . . . . . .... ....................... 2. Range of the Measurements . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . 3. Variance and Standard Deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Confidence Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Student Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Repeatability.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Reproducibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . ..... ....... 8. Precision 9. Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. Linear Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Coefficients of the Best Straight Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Confidence Limits for b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Confidence Limits for a Regression Estimate ... . .... .... . . 11. Fundamental Relationship between the Amount of Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Sample Size and Peak Area ................ 2. The Types of Detectors . . . .................................. ................................... a. Concentration Detectors . . . . ........................... b. Mass Flow Detectors . . c. Other Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Measurement of the Sample Size ................................. 1. Repeatability of Syringes . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Gas Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Volatile Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. High Boiling Compounds Dissolved in Light Solvents . . . . . . . . . . . . . . . . . . . . . . . ................. 2. Repeatability of Sampling Valves . . . . a. Gas Sampling Valves . . . .. .... .. . .. . .. b. Liquid Sampling Valves . ............ ..... ... i. Influence of the Air Power Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii. Influence of the Vaporization Temperature .. .... . .... . . .. 3. Precise Determination of the Sample Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. DirectMethod.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

..................................................

Literature Cited

... . . . .. . . . . .. .... ....... ..... . .. ...... . . . . . . .. .... .... . ..

565 565 565 566 566 566 567 567 567 568 569 569 569 570 570 572 572

575 575 575 577 578 578 580 580 582 583 583 585

586

INTRODUCTION Quantitative analysis is the third and final step in the analysis of a mixture by gas chromatography. After having separated the various components of interest in the References on p. 586.

564

mixture and having identified most of them or confirmed their identification, we want to know how much of each is present. As early as 1952, in their first paper on gas chromatography, James and Martin wrote: “We have not striven to reduce the errors below a few percent, though we are of the opinion that the method is essentially a highly accurate one.” (1).Nevertheless, a precision of cu 3% was achieved then on the analysis of fatty acid methyl esters, with an equipment and especially a detector and a data acquisition system with poorer performance than those presently available. The potential precision and accuracy achievable in chromatography have been long and hotly debated. It has been proven again and again that excellent degrees of precision and accuracy can be achieved, but that this requires an adequate control of the various parameters whose interplay determines the reproducibility of chromatographic signals. The most serious difficulty encountered in this field of instrumentation is that mechanical, hydrodynamical or aerodynamical as well as chemical problems play a major role in the overall precision of the chromatographic data. It does not matter that the electronic parts of the instrument work perfectly if the plumbing does not (2). The achievement of a good precision and accuracy in chromatographic analysis requires a mastery of the whole chromatographic process, including sampling, separation, detection and signal handling. Finally, it must be emphasized that good performance in quantitative analysis cannot be obtained without the availability of an adequate sample, which is representative of the product to be analyzed and has been properly handled, without accidental contamination. Off-line sampling operations should be carried out under the supervision of analysts, on-line sampling systems should be designed and operated by them, or, at the very least, analysts should be involved and cooperate in sampling operations as well as in the design of analytical systems. Otherwise, the analyst cannot guarantee that the analytical results obtained are relevant to the plant problems and costly, sterile controversies will ensue with the production department. It is our hard-won experience that most serious difficulties in solving analytical problems or accounting for analytical data originate from faulty sampling. Unfortunately sampling is usually very specific and cannot be discussed on a general basis nor approached from a theoretical standpoint. Some general results and a few examples are reported in Chapter 17. The essential operations the analyst must carry out to perform quantitative analysis by gas chromatography are (i) the measurement of the sample size injected, which is discussed in Section 3 of this Chapter, (ii) the determination of the response factors, which is discussed in Chapter 14 and (iii) the measurement of the peak areas, discussed in Chapter 15. The analyst should also care about the precision and accuracy of these measurements. This topic, very important but too often neglected, is discussed in Chapter 16.

I. BASIC STATISTICS. DEFINITIONS Quantitative analysis requires the use of a few simple statistical tools. The use of more sophisticated methods, collectively known as chemometrics, may be required

565

to give a proper account of a complex set of data (3,4). The use of these methods is beyond the scope of the present book. On the other hand, one single measurement is hardly significant at all: we have no way of knowing how good it is, i.e., how reproducible. In all cases several measurements must be carried out - at least three. An estimate of the true concentration and of the precision of the determination can then be made (5-7). In applying statistics to the study of analytical results, we assume that we return without loss and without pollution the actual sample used for the analysis to the analyzed mixture after each analysis has been completed, so we can, at least in principle, make an infinite number of analyses. The results of this infinite number of analyses are distributed around the true value of the actual concentration, following a normal (Gaussian) distribution, having a certain standard deviation (5,6). The few analyses which have actually been performed are in effect a draw of a few numbers out of that potentially infinite number of measurements. We are trying to find out the best possible estimate of the “true” concentration and of the standard deviation of the distribution. 1. Mean and Median The mean of a series of results is the sum of these results divided by their number ( x = 2 x i / n ) . The mean is also sometimes called the central tendency. The median is the result such that there are as many larger results as smaller ones. The mean is the best estimate we have of the true value. The standard deviation tells us how good this estimate is.

2. Range of the Measurements The range or spread of the measurements is the difference between the largest and the smallest results. It is a very crude indication of the reproducibility of the measurements.

3. Variance and Standard Deviation The variance of the results obtained is:

where the summation is made for all the measurements, x i , where x is the mean of the results, and n , their number. The standard deviation, s, is the square root of the variance. It is the best estimate of the standard deviation of the distribution of the analytical results in our model of analysis. The ratio s / x is called the relative standard deviation, often given in percent, or the coefficient of variation. References on p. 586.

566

A quantitative result is incomplete if it does not include a figure for the absolute or the relative standard deviation of the measurements. Such a number is necessary to assess the reproducibility of any series of measurements and a result does not mean much if we do not know the extent to which it is reproducible. On the other hand it takes a minimum of 3 measurements to calculate a significant standard deviation; 5 or 6 permits a much better estimate.

4. Confidence Limits

Student has shown that we can estimate the range within which we have a certain probability of finding the true value around the mean of the measurements (5,6). There is a probability p of finding the true value, X,within the following range:

where x is the mean of the measurements and s their standard deviation. t( p, n) is the value of the Student function for n measurements and for the confidence level p. Generally a confidence level of 95% is chosen, so the true value has a 0.95 probability (95% chance) to be found in an interval of * s t / f i around the mean of the measurements. It is in that sense that x is an estimate of the true value. The determination of the standard deviation also permits an estimate of the probable range within which the true value can be found. As can be seen from equation 2, the range, or the precision of the estimate of the true value, decreases with increasing number of the measurements in the series. The value of t( p , n ) also decreases with increasing number of measurements, especially between a few and about 10. The precision of analytical determinations can be markedly increased (i.e., the confidence limit is reduced by a factor 2.5 to 3) by increasing the number of measurements from 2-3 to about 10. If the precision is not yet considered as sufficient with 10 measurements, it is probably better to search for the sources of errors, identify the most important of them and strive to reduce its influence, rather than to carry out the large number of measurements which would be necessary to reduce the confidence limit using the unchanged experimental setup. 5. Student Function As explained above, the Student function permits an estimate of the range within which we have a certain probability of finding the true value of an unknown, when we have the mean and standard deviation of a series of measurements of that unknown. The values of the Student function can be found in many publications dealing with statistics, quantitative measurements, and in handbooks. For the sake of convenience the values corresponding to the most useful cases ( n between 3 and 10, confidence levels of 90%,95% and 99%)are given in Table 13.1.

6. Repeatability

This is the standard deviation of measurements obtained by the same analyst, working with the same equipment, in the same laboratory, using the same experi-

567

TABLE 13.1 Student Function, t Number of Observations

Probability Level

90%

95%

99%

3 4 5 6 8 10 21

2.920 2.353 2.132 2.015 1.895 1.833 1.725

4.303 3.182 2.176 2.571 2.365 2.262 2.086

9.925 5.841 4.604 4.032 3.500 3.250 2.845

mental procedure. It characterizes the ability of an individual to reproduce his own results, while working in a familiar setting, with his own tools and methodology. This is by no means an estimate of the quality of a measurement. Estimates of the true value of an unknown from repeatability data can be highly misleading since no provision for systematic errors is included. 7. Reproducibility This is the standard deviation of measurements obtained by different analysts, using different equipments, in different laboratories, but following the same procedure. Each analyst uses his own tools, in his own personal way, and follows the common written procedure as he understands it. Significant variations are sometimes encountered, quite unexpectedly. There are several intermediates between the repeatability and the reproducibility as described in the two previous paragraphs, for example the standard deviation of measurements achieved by different analysts, using different apparatus, in the same laboratory. In this case, chances are that the actual procedures followed are much closer than when the analysts belong to different nations. Round robin analyses are very instructive, as they reveal most often that most laboratories produce highly reproducible results, but that these results are unexpectedly far from each other, i.e., that the determinate errors are much larger than the random ones, which are often easier to spot and control than most determinate errors.

8. Precision The ability to reproduce your own measurements (including the reproduction of determinate errors!), is characterized by the repeatability or the reproducibility, i.e., by the standard deviation of the measurements camed out on a standard. 9. Accuracy

Accuracy is the difference between the mean of the measurements and the true value. It is usually unknown and inaccessible, which makes the determination of the accuracy of analytical methods the Holy Grail of quantitative analysis. Round robin References on p. 586.

568

analysis and computer simulation of quantitative measurements provide the only possible approaches to this problem. Round robins are complex to organize, expensive and time consuming for the participants and quite threatening for the ego of the analysts involved, which may explain why there are so few reported in the literature. Computer simulations are easier and potentially much less harmful, but they are also much more limited in their scope. A detailed model of the experimental process is required and only determinate sources of errors which have been identified can be studied. By definition these sources are by far the least dangerous, since they are already known. Data acquisition and data handling procedures, and noise contributions are the easiest and most convenient sources of error to study in this way (see Chapter 16). 10. Linear Regression

Linear regression is the most common form of regression analysis. An instrument is calibrated with a series of standard samples. A graph is constructed by drawing a line through the calibration points. This line may be a curve or a straight line. The regression is said to be linear if the relationship between the signal measured (response) and the experimental factors whose effect on the response is to be determined is linear with respect to the coefficients. Thus, for example the Knox equation (see Chapter 4):

B

H = - + A u ” ~ + CU u

(3)

which is not linear with respect to u, is linear with respect to A , B and C . The determination of the best values of the constants A, B and C which account for a set of experimental measurements, i.e., fitting the experimental results ( H ,u ) to equation 3, is a linear regression. Detectors are often selected and designed so as to be linear (see Chapter lo), because calculations are easier, but it does not have to be so, and the recent advent of powerful microcomputers in laboratories permits the easy use of more complex response functions. Linear response are frequent, however, and it is useful to know how to calculate the parameters of the straight line which best fits a set of data points, using the least squares method. A detailed treatment of the problem is found in the literature (7). It is not our aim to demonstrate or even discuss in this book the equations used. We wish merely to recall them, because they are useful. The data being presented as a set of data points ( x i , y i ) , it is convenient for further calculations to determine the values of the following expressions: 2 1 2 X U 2 = Z ( x , - x * ) = E x ? - -(Ex,) n 2 1 2 W = Z ( y , - y * ) =zy+ --(ZY,)

1 Z U V = Z ( x , - x * ) ( y , - y * ) = E x , y , - -Xx,Ey, n

569

a. Coefficients of the Best Straight Line

The equation of the straight line which best represents the data is:

y=ax+b

(7)

and the best estimates of the coefficients a and b are:

b=

Bxiyi - nx*y* ~x,?-nx*’

ZUV

=-

X J ~

1

a = - ( X y i - bXxi) n

(9)

where x* and y * are the average values of xi and yi, i.e., Z x i / n and X y , / n , respectively. In this procedure, the sum of the squares of the deviations parallel to the y-axis is minimized. The values of the xi’s are regarded as fixed. The standards should be very carefully prepared, so that the errors on the xi’s are negligible. The problem of significant errors occurring in both dimensions has been discussed by York (8).

b. Confidence Limits for b It often happens that the slope of a regression is compared to the value predicted by theory, or to the value obtained in a previous series of experiments. It is important to have an estimate of the confidence limits for b. It can be shown (7) that the variance about the regression is given by: 2 0Y.X

-

-

Z V 2 - b2ZU2 n-2

The variance of the regression coefficient b, i.e., the standard deviation of b, is given by:

The confidence limits for b are determined in the conventional way, as the product of the standard deviation for b by the Student function for n - 2 degrees of freedom, corresponding to the confidence level required. c, Confidence Limits for a Regression Estimate

In practice the analyst goes to the troubles of preparing authentic samples of accurately known composition, collecting n sets of data points and determining the regression coefficients only in order to be able to estimate, from further measureReferences on p. 586.

570

ments, what is the composition of an unknown sample. It is important to calculate the confidence level of the concentration thus obtained. The variance of an x k value (Le., a concentration here) which has been determined from the results of m measurements of the signal is given by (7):

- m is the number of independent, successive determinations of the signal y, corresponding to the analyzed sample. Too frequently rn is equal to 1. is the average of the m values of yk obtained. - x k is the concentration of the compound studied in the new sample analyzed. It is derived from y k using the coefficients of the regression and solving equation 7 for x k . - n is the total number of calibration points measured. - y * is the average of the values of the signal obtained during the calibration (i.e., y * is the same as in equations 8 and 9). - b is given by equation 8 (slope of the regression). - XU2 is given by equation 4. - by,, is given by equation 10. The confidence limits on the estimate are obtained by multiplying the standard deviation derived from equation 12 by the Student function for the degree of freedom n - 2 and corresponding to the required confidence level (7). We note that the standard deviation of the estimate of the true concentration of the unknown increases rapidly with increasing difference y k - y *. This means that the uncertainty on the estimate of a regression is lowest near the center of the set of calibration points and that extrapolation is dangerous.

11. FUNDAMENTAL RELATIONSHIP BETWEEN A COMPOUND IN A SAMPLE A N D ITS PEAK SIZE

THE AMOUNT OF

There are two data elements derived directly from the chromatogram (see Chapter 1) which can be related to the amount of a compound present in the analyzed sample: the peak height and the peak area. As we explain later, in Chapter 15, in almost all cases the peak area is used. It is important to discuss the basic relationship between the chromatographic parameters of an analysis, the sample size and the peak area.

1. Sample Size and Peak Area The peak area is the integral of the detector signal during a certain period of time. Ideally the integration should be carried out from the elution of the inert peak

571

to infinity. This is not very realistic and chromatography theory shows that the concentration of a compound in the carrier gas is different from zero only during a rather short period of time, a few peak standard deviations before and after the elution of the peak maximum. Experiments confirm this prediction. The only exceptions pertain to conditions which are best avoided in quantitative analysis (strongly tailing peaks). Accordingly, integration of the signal corresponding to each peak is carried out during a short period of time, when the signal is above a certain threshold, defined either as an absolute level, often by reference to the base line noise, or as a ratio to the band maximum (see Chapter 16). Whereas the peak area is the integral of the detector signal as a function of time, the amount of compound eluted is the integral of its concentration in the carrier gas as a function of the volume of carrier gas. Since one of these two integrals is a function of time and the other a function of volume, the relationship between them will require the involvement of the carrier gas flow rate, for the sake of homogeneity of the equations. Thus, two parameters will be required to relate the peak area and the amount of the corresponding compound which has been injected with the original sample: the carrier gas flow rate and the response factor, which relates the detector signal to the amount of compound present in the detector at any given time. There are two main types of detectors, those whose response is proportional to the concentration of the analyte in the carrier gas, at the column exit (concentration detectors) and those whose response is proportional to the mass flow rate of analyte to the detector (mass flow detectors). For a few detectors, like the electron capture detector for example, the response factor itself is a function of the carrier gas flow rate, which obfuscates the issue. Finally a word of caution is in order. The response factor, i.e.. the proportionality coefficient between the detector signal measured and recorded during the analysis and the chemical event, either the analyte concentration or its mass flow at the outlet of the column, can be expressed in two very similar ways: y

= FC

(or dm/dt)

or :

C (or dm/dt)

=fr

Obviously:

f = 1/F In the following, equation 13b will be used as the definition for the response factors, since the aim of quantitative analysis is to determine the concentration or the amount of a given analyte in a sample, while the experimental data to which the analyst has direct access is the peak area. References on p. 586.

572

We want to emphasize, however, that the two definitions (equations 13a and 13b) are used in a very loose way in the literature, in the description of procedures or in technical booklets. Sometimes the two definitions are used within the same publication, without any clear indication of the one which applies to any given set of data. Similarly it is not always clearly indicated whether the response factors refer to the number of moles, to the weight or to the volume of the corresponding compound. The use of response factors taken from the literature is already dangerous, since the response mechanism of most detectors is not always completely elucidated and the response factor may depend on the value of some unspecified parameter. Care should be taken to use the proper values with the proper set of units. 2. The Types of Detectors

There are detectors whose response is proportional to the concentration of the analyte in the carrier gas (such as the thermal conductivity detector and the ultrasonic detector) and there are those whose response is proportional to the mass flow rate of analyte to the detector cell (such as the flame ionization detector and the mass spectrometer). Other more complex detectors are those which are not linear (such as the flame photometric detector in the sulfur mode or the UV absorption photometer) and those whose response depends on the carrier gas flow rate (such as the electron capture detector). We discuss here the peak area-amount of analyte relationship for these detectors (9). a. Concentration Detectors

A concentration detector is non-destructive. The signal is proportional to the concentration of the analyte in the carrier gas, inside the detector cell. If the camer gas flow is abruptly interrupted the detector signal remains constant until the flow resumes. If a gas stream with a constant concentration of analyte is passed through the detector the signal is constant, proportional to the concentration used, and independent of the carrier gas flow rate, at least as long as the convection does not appreciably perturb the response mechanism (9,lO). The relationship between the detector signal and the concentration is written (see equation 13b):

Integration of this relationship during the elution of the peak corresponding to an analyte gives:

If the response factor is constant, independent of the time, of the flow rate, and of other parameters which can change during the course of an analysis, the RHS of

513

equation 14 is equal to the product of the (constant) response factor by the peak area, as measured on the chart of the recorder or as calculated by a digital integrator. As explained above, the sample size (in mole or weight units) is equal to the integral of the concentration as a function of the volume of carrier gas swept through the detector cell. Thus:

/C$

dV= fA

If the carrier gas flow rate, F,, is constant during the analysis, it can be withdrawn from the integral and becomes a factor in the LHS of equation 15. Since the integral of the concentration as a function of the carrier gas volume is equal to the amount, m ,of analyte, we have: m = fAF,

The peak area observed for a given amount of analyte is inversely proportional to the carrier gas flow rate, since the slower the flow rate, the longer the analyte stays in the detector. The peak height can be derived from the general equation relating the height of a Gaussian distribution to the characteristics of the peak (see Chapter 1, equation 39):

c,=

m f i -

I/,G

Combination with equation 13b gives the peak height, h:

h is proportional to the sample size and to the square root of the plate number and inversely proportional to the response factor and to the retention volume (10). For a given column, this volume is a function of temperature only. At or around the optimum flow rate, where N is maximum, the peak height will not vary for small changes in the flow rate. However, it will be seriously affected by temperature fluctuations, which explains conflicting observations regarding the reproducibility of peak height measurements, as reported in the early literature. b. Mass Flow Detectors A mass flow detector is destructive: usually the analyte molecules are reacted and transformed into ions which are collected and counted. Instead of being a voltage, as with most concentration detectors, the primary signal of a mass flow detector is usually the intensity of a current (the electronics associated with the detector often References on p. 586.

514

transform that current into a voltage). The signal is proportional to the mass flow rate of analyte swept by the carrier gas into the detector cell. If the carrier gas flow is abruptly interrupted, the detector signal falls rapidly to zero and remains at this value until the flow resumes. The variation of the signal when flow is stopped and resumed follows an exponential profile, with a time constant equal to the detector response time. If a gas stream with a constant concentration of analyte is passed through the detector, the sighal is proportional to the concentration used, but also to the carrier gas flow rate. In fact it is proportional to the mass flow rate of the analyte (9). The relationship between the detector signal and the mass flow rate is written (see equation 13b): dm =fr dt Integration of this relationship during the elution of the peak corresponding to an analyte gives: /dm

=

jfrdt

The LHS of equation 14b is the analyte amount while the RHS is the product of the response factor by the peak area. Thus: m=fA

( W

With a mass flow detector the peak area observed for a constant amount of analyte is independent of the flow rate, which certainly reduces the extent of errors in quantitative determinations. On the other hand, the peak height is a function of the carrier gas flow rate. Since the band width increases constantly with decreasing flow rate while the area remains constant, the peak height must decrease. Trace analysis will be easier at large carrier gas flow rate, since there is less time for diffusion and dilution of the analyte in the carrier gas. One must, however, avoid an excessive flow rate which would cause a significant increase of the signal noise and eventually modify the response mechanism. c. Other Detectors The response of these detectors is more complex, because in principle they are not linear (e.g. the flame photometric detector in the sulfur mode or absorption photometric detectors), or because the response factors depend on the carrier gas flow rate. In this last case the use of an auxiliary stream of scavenger gas could bring the detector back into one of the two main categories previously described. These detectors must be carefully controlled. It is especially important to keep the carrier gas flow rate constant or at least to maintain the total flow rate of gas through the detector constant.

575

111. MEASUREMENT OF THE SAMPLE SIZE

Because of the large number of parameters affecting the precision of chromatographic measurements, and also because of the difficulty in measuring with accuracy the small sample sizes which a chromatographic column may accommodate, relative determinations are greatly preferred to absolute ones. Accordingly, the exact determination of the amount injected is not required. This amount must be known approximately, however, so that excessive sample size and the resulting detector and/or column overload may be avoided. It must be reproduced properly so that the various settings of the instrument, especially the amplifier ranges remain the same. This ensures the best possible level of repeatability of the measurements. Finally, it is not sufficient to achieve a good repeatability of the total sample amount. The amount of each component of the sample aliquot injected in the chromatograph must be proportional to its concentration in the original sample. There should be no selectivity or preferential loss in the sampling system. These losses are sometimes hghly irreproducible and cannot be accounted for in the calibration.

1. Repeatability of Syringes Of all the tools available to the chromatographer, the syringe is the most popular and the one which has changed little since its inception, in the late 'fifties. Syringes are available in all sizes, from 0.5 or 1 pL for liquid samples to 50 mL or more for gas samples. Several designs are used. For very small samples, the needle is the actual syringe cylinder and the plunger is a wire sliding inside the needle. The glass barrel is just the housing of the metering device. For larger samples, a more traditional design is used. Then the volume of the needle may have to be taken into account in calculating the volume of sample actually injected into the chromatograph. The reproducibility of injections made with a syringe much depends on the syringe capacity and on the fraction of the total capacity which is injected. For example, in an industrial laboratory, the repeatability (5 determinations) of a 1 pL injection made with a 5 pL syringe is 5% while the repeatability of a 0.1 pL injection made with a 1 pL syringe is 10%. The repeatability also depends on the nature of the compounds analyzed: gases, low boiling point or high boiling point liquids. If the last compounds do not afford major difficulties, it is not always easy to carry out quantitative analysis of gases or liquids with a high vapor pressure, for which special care must be taken during sample introduction. a. Gas Analyses

Syringe injection of gas mixtures for quantitative analysis is certainly not a recommended procedure. It should be used only to speed up the work in the case of References o n p. 586.

576

T

c

E 8 I

Figure 13.1. Injection of volatile liquids with a syringe. a, rubber cube. b, sampling port septum.

qualitative analysis or of semi-quantitative analysis. Diffusion of air into the syringe or of the mixture components to the atmosphere via either end of the syringe is difficult to avoid. The use of a thin film of lubricant (oil, vaseline or even water) between the piston and the cylinder permits an almost tight seal, but also promotes selective losses by dissolution or adsorption and may result in memory effects. The syringe needle may be temporarily closed by sticking it into a small piece of thick rubber or in a septum, the tip of the needle resting in the middle of the rubber mass. As shown in Figure 13.1, sampling or injection can be carried out with minimum exchange of gas with the atmosphere by tightly pressing the rubber piece against a septum, and pushing the needle tip across the rubber piece. The most serious difficulty encountered in the use of syringes for the introduction of gas samples into a gas chromatograph results, however, from the large pressure difference between the gas inside the syringe barrel, which is at atmospheric pressure, and the carrier gas at the column inlet. The column back pressure for gas analysis is usually of the order of a few atmospheres. The sudden increase of pressure inside the syringe barrel could break a large syringe, if it is too large. It certainly results in a strong compression of the sample, with intense convection currents, due to the rapid mixing of the sample with the carrier gas surging into the syringe barrel. Leaks may take place. The entire process is not greatly reproducible, and it is an important source of errors. For these reasons, gas sampling valves should be preferred whenever possible.

517

6. Volatile Compounds A similar procedure (see Section 1II.l.a above), using capped syringes, can be used with volatile liquid samples, to avoid losses by vaporization. Furthermore, the syringe can be weighed after filling and after injection, for a more exact determination of the sample size. In this case, however, the entire content of the syringe should be injected, to avoid systematic errors due to partial vaporization of the non-injected fraction of the sample. A very interesting device (see Figure 13.2) has been described by Borba de Oliveira (11) which permits the accurate injection of samples of volatile liquids, assuming the original sample is available in rather large amount (e.g., routine analysis of gasoline and related products, solvents, etc.). A small cell is screwed onto the chromatograph injection port, in place of the septum cover nut. A second septum is fastened to the cell, in the axis of the first septum. The cell can be filled, under pressure if needed, with the sample or the sample can flow across the cell. A syringe can be used to grab an aliquot sample and inject it into the chromatograph, as easily as with a normal liquid. This device is very practical and can be used to inject liquid samples of LPGs, butadiene or vinyl chloride (b.p. - 13.9 O C).

Figure 13.2. Injection of a sample of a volatile liquid with a liquid syringe. A, filling of the syringe.

B, injection of the sample in the sampling port. (after ref. 11).

References on p. 586.

578 n

/

sample

solvent

Figure 13.3. Procedure for achieving reproducible injections of high boiling point liquid samples diluted in a light solvent.

c. High Boiling Compounds Dissolved in Light Solvents

This is a most difficult operation. To ensure complete vaporization of the heavy compounds, the injection port is heated to a high temperature, where their vapor pressure is important. The almost instantaneous vaporization of the solvent which takes place in the needle under such conditions cools it and leaves a deposit of heavy compounds. Injection is incomplete and results in a determinate error. This can be demonstrated by filling the syringe with a pure, heavier solvent, immediately after the incorrect injection has taken place and making a second injection. A significant memory effect is observed. In such a case, the best solution is found in the use of a heavier solvent. Should this be impossible, a small amount of pure solvent is pumped into the syringe prior to the sample (see Figure 13.3). This solvent flushes the sample and the residual out of the syringe needle during the injection. It is always prudent to check that the whole sample has indeed been injected, by filling the syringe with an appropriate solvent after an injection has been made and carrying out a second injection, to determine the amount of residual, if any. 2. Repeatability of Sampling Valves

Sampling valves usually give much better results than syringes for routine analysis, especially in the case of gases. The better reproducibility obtained for gas than for liquid samples is due to the fact that the relative contribution of the total volume of the mobile parts of the sampling device to the total volume injected is much smaller with gas valves than with syringes (12). a. Gas Sampling Valves

These valves are designed to inject samples of dry gases or vapors, i.e., samples containing no mist or clouds of liquid particles in equilibrium with the vapor of the sample. The mass of sample injected depends on the sampling loop volume, on the pressure and the temperature of the loop. The volume is constant, except for the small fluctuations of the volume of the mobile parts. The temperature of the valve should be controlled, especially when the chromatograph is not in the laboratory (process control analysis, GC analysis carried out close to a pilot unit, etc.). To maintain a constant sample pressure and to achieve good repeatability, the

579

I I

atm

Figure 13.4. Injection of gas sample. The gas sample in the valve loop is brought to atmospheric pressure shortly before injection.

easiest method is to make sure that the pressure in the valve is atmospheric. For this purpose, the stream of analyte flowing through the valve is interrupted briefly, immediately prior to injection. Usually, this stream is wasted to atmosphere, after passing through a certain length of tubing, in order to avoid back diffusion of air to the loop (see Figure 13.4). The duration of this interruption period depends on the length and diameter of the waste line. For example, for a 1 mm i.d., 4 or 5 m long line, 20 to 30 seconds are required. Back diffusion of air into the line takes place TABLE 13.2 Repeatability of the Sampling Sizes Obtained with Valves Volumes Larger than 1 mL Gas Rotary Valves with External Loop Sliding Valves with External Loop Membrane Valves with External Loop

Standard Deviation 0.2 to 0.3% 0.2 to 0.3% 1%

Volumes Smaller than 100 pL

Standard Deviation

Gas

Rotary Valves with Internal Volume (10.5 pL) Sliding Valves with Internal Volume (1 pL)

0.3 to 0.6%

Piston Valves with Toroidal Volume (1pL) Piston Valves with Longitudinal Cavity (0.7pL) Sliding Valves for Pulsed Injection (0.7 pL)

0.5 to 0.6%

Liquids

0.3 to 0.6%

0.5 to 1%

0.3 to 0.5%

Gas sample: C2H4. Liquid sample: CC14. For all gas sampling valves: equilibration time with atmospheric pressure: 20 seconds. The repeatability achieved for valve injection is of the same order of magnitude as the error of measurement on the peak area. References on p. 586.

580

and could result in a pollution of the sample for longer equilibration times. If the sample pressure is below atmospheric, a special protection must be arranged. A 100 mL volume tank (e.g., a tube, 2.5 cm i.d., 20 cm long) is placed at the end of the line (see Figure 13.4). It protects the sample from pollution by the air stream coming up the line when the air ejector or membrane pump which draws up the sample is stopped to permit pressure equilibration. Data in Table 13.2 give the repeatability achieved with different sampling valves having a wide range of sample volume. Such repeatabilities can be observed over a relatively long period of time. For instance, a commercial rotary valve with a 1.2 mL loop has carried out 270,000 injections, without maintenance (i.e., 1 year for an on-line analysis repeated every 2 minutes). b. Liquid Sampling Valves

In most cases, the sample delivered by a liquid sampling valve is small. The most popular design is a cylindrical piston, with a toroidal groove, sliding between “O’-rings (or similar rings with a diamond cross section) and transferring a volume of approximately 1 pL between the analyte stream and the carrier gas stream. These valves almost always are automatic. They are actuated by compressed air supplied through electro-pneumatic valves and controlled either directly by the operator or by the chromatograph, as is the case with on-line process control apparatus. The reason for preferring automatic valves is that the repeatability of the sampling depends greatly on the operating conditions. This is illustrated by the data reported in Tables 13.3 and 13.4, and on Figures 13.5 and 13.6 and dealing with the injection of pure carbon tetrachloride. i. Influence of the Air Power Pressure The influence of major fluctuations of the pressure of the compressed air actuating the valves is illustrated by a series of experiments reported in Table 13.3. TABLE 13.3 Influence of the Pressure of the Servo-Control Air on the Repeatability of a Liquid Sampling Valve Sample No.

3168 5184 5760

Peak Area

Peak Height

A

0

A%

H

2655 2676 2679

9(0.3%) 8 (0.3%) 9(0.3%)

o.8

15.76

o.l

13.90 14.40

0

0.15 0.30 0.10

A’R,

Servo-Control Pressure

13.4

:;;I

3*5

4 atm

A , H: Mean of the last 10 previous results. 0 : Absolute (and relative) standard deviations of the 10 previous results. A%: Percentage difference between the means. Peak areas measured by computer. Sample: pure carbon tetrachloride flowing continuously through the sampling loop and cooled by an air stream. Volume: 1 pL. Vaporization chamber normally at 12OoC. Cycle time: 270 sec (loop rinsing: 240 sec, injection: 30 sec). Standard pressure of compressed air: 6 atm. Thermal conductivity detector. Flow-through, parallel, Gow-Mac “Pretzel” cells. Current: 250 mA. Carrier gas: helium. Flow rate: 3 L/hour.

581

TABLE 13.4 Influence of the Vaporization Temperature on the Repeatability of a Liquid Sampling Valve Sample No.

A

Peak Area U

AW

H

Peak Height U

Temp.

4608 5412 5760 6048 6336 6624 7876 8064

2875 2835 2939 2899 2910 2882 2896 2896

3(0.1%) 3 (0.1%) 4 (0.11) 4(0.1%) 7 (0.2%) 5 (0.2%) 3 (0.1%) 6 (0.2%)

1.4 3.5 1.4 0.4 1.0

16.16 17.78 12.55 18.34 17.99

0.5 0.0

23.90 22.20 22.22

0.10 0.03 0.01 0.07 0.20 0.02 0.04 0.03

A% 9 41 31

5o1'9 15

o'2

("C)

105 105 95 105 105 120 105 105

A, H: Mean of the last 10 previous results. u : Average (and relative) standard deviation of the 10

previous results. A%: Percentage difference between the two means. Same experimental conditions as for Table 13.3.

When the air pressure changes from 6 to 3 atm, the peak area changes by less than 1%(see Table 13.3) while the peak height changes by more than 10% (see Figure 13.5 and Table 13.3). The actual volume of sample transferred to the carrier gas stream changes very little, but the injection function, or profile of the input zone of analyte to the column is altered by a decrease in air pressure which slows down the movement of the piston. Especially noteworthy is the long-term stability of the valve, illustrated by the high degree of repeatability of the peak area between the 3,168th and the 5,760th injections. The tests were stopped after the 13,000th injection took place without any malfunction. No maintenance was necessary during the course of the tests.

Figure 13.5. Automatic injection of liquid samples. Influence of the servo-air pressure of the air actuator (see Table 13.3). References on p. 586.

582

-

Figure 13.6. Automatic injection of liquid samples. Influence of the temperature of the vaporization chamber (see Table 13.4). A, 120 O C, peaks have a conventional profile. B, 95OC, the peaks have a hump and are about half as high as the peaks obtained at 12OoC (see electronic chart recorder sensitivity).

ii. Influence of the Vaporization Temperature

The influence of the temperature of the hot section of the valve was studied under the same conditions as in the previous section (see Table 13.4 and Figure 13.6). The influence of the temperature is still more spectacular than that of the pressure. A moderate decrease in the temperature results in a change of the peak area of less than 1%.A strong decrease, to an unacceptably low value may result in a change of the area by 3.5%. Under the same conditions, the change in peak height may exceed 50%(see Table 13.4 and Figure 13.6). Furthermore, the peak shape is drastically affected. Spurious shoulders take place, attesting to too slow a vaporization of the sample. For the achievement of a satisfactory band profile, flash vaporization of the sample must take place. In conclusion, we observe that the repeatability and reliability of the peak area is much better than that of the peak height. The peak height depends much more on the experimental conditions than the peak area. Accordingly, the use of the " bar-graph" method for recording chromatographic data on the quantitative composition of samples, a method still widely used in process control, is very dangerous and prone to generate very serious errors. In the bar-graph records, all peaks are represented by bars of equal widths and of height proportional to the maximum signal. This method should be replaced by methods based on the determination of peak areas: the bar height should rather be proportional to the peak area. Finally, the systematic determination of the peak height for a standard of known concentration can be used profitably for the periodic assessment of the proper

583

behavior of the chromatographic equipment and particularly for the detection of any malfunction of the injection system (see Chapter 17, Section 111.6).

3. Precise Determination of the Sample Volume Only the acidimetric method can be recommended for the precise and accurate determination of the volume of sample actually delivered by a gas or liquid sampling valve, in the whole range of volume used, from about 1 pL to several mL (13). The other methods that have been suggested are either too dangerous, such as all methods using mercury, or too restricted in their range of applicability, such as the method suggested by Janak (14), using nitrogen as standard gas, carbon dioxide as carrier gas and a solution of potassium hydroxide to absorb the CO,; this method is valid only with gas sampling valves having a sample volume in excess of 1 mL. a. Direct Method

In the acidimetric method the sample loop is filled with a standard acid solution, by flushing the sample line (see Figure 13.7). The volume transferred to a stream of distilled water flushing the carrier gas line is collected and titrated (13). An acetic

Figure 13.7. Calibration of the loop volume of sampling valve by acidimetry. Principle (see ref. 13).

References on p. 586.

584

Figure 13.8. Calibration of the loop volume of a sampling valve by acidimetry. Example (13).

TABLE 13.5 Calibration of Sampling Valves by Acidimetry Valve Type

Mean Volume (mL)

to

Precision (I)

1.8600

0.0094

0.51

1.2797

0.004

0.31

0.3970

0.0003

0.10

0.2345

0.0017

0.70

1.3420

0.009

0.6

0.9220

0.0058

0.63

0.4560

0.0044

0.96

Volumes larger than 0.1 mL Rotary Valve External Loop Sliding Valve External Loop Sliding Valve External Loop Membrane Valve External Loop Volumes smaller than 1pL Rotary Valve Internal Loop Sliding Valve Internal Loop Sliding Valve Internal Loop

Mean volume is the average of 10 measurements. r is the Student function (95% confidence level). Precision is the confidence interval on the mean.

585

acid solution is used and it is titrated by sodium hydroxide (see Figure 13.8). We have called this method of measuring the volume of sample loops the Peyron method. The flow in the sample and carrier gas lines should take place in the direction opposed to gravity, to facilitate the elimic?.tion of air bubbles, which could result in systematic errors. A good precision is achieved if the lines are flushed for about 20 to 30 seconds between each valve operation. When the sample loop volume exceeds ca 100 pL, the titration is carried out directly on the acid aliquot collected in each injection. A normal solution of acetic acid is used and it is titrated with 0.1 N sodium hydroxide. When the sample loop volume is smaller than 100 pL, a number of “injections” of a 1 N acid solution are performed and the titration is done with 0.02 N sodium hydroxide. For 1pL valves a large number of injections has to be performed and an automatic system is used. The precision is improved by retitrating the sodium hydroxide solution used against an acetic acid solution at the time of the measurements. Data reported in Table 13.5 illustrate the precision of the results achieved. It is between 0.1 and 0.5% with large loops (volume larger than ca 100 pL) and between 0.5 and 1% for very small valve loops (volumes smaller than 1pL). The procedure must be repeated whenever the valve is dismantled for cleaning or for any other reason.

b. Comparison The acidimetric method works only with valves operated at room temperature. In gas chromatography, however, sampling is often carried out at high temperatures. Because of the complex design of sampling valves, incorporating many parts made of various materials, it is impossible to predict the change in the valve volume which will take place when the valve temperature changes. A calibration is possible, by comparison. A previously calibrated valve is placed on-line with the valve to be calibrated (see Figure 13.9). The former valve is at room temperature. The latter valve is placed in the oven of the chromatograph, at the temperature at which it will eventually be used. The two valves are selected so that their volumes are similar. A sample of a pure gas can be injected by either valve. The peak area is measured by electronic integration. The ratio of the valve volumes is equal to the ratio of the peak areas. For better precision, a series of injections are made with the two valves. Good precision can be achieved if the flow rate and the purge time of the standard gas in the two valves are kept as close as possible, as well as the time alloted for pressure equilibration, between the moment when the standard gas flow is interrupted and the time when the injection is actually performed. The recommended values are 3 L/hour for the standard gas flow rate, 90 seconds for flushing the valve sample lines and 30 seconds to reach atmospheric pressure in the sample loop. For volumes larger than about 100 pL, we prefer to use nitrogen as a standard gas and to perform detection with a thermal conductivity detector, using helium or References on p. 586.

586

Figure 13.9. Determination of the temperature correction on the loop volume of a sampling valve (comparison method). V1, standard valve, at room temperature. V2, valve to be calibrated at higher temperature.

hydrogen as carrier gas. For smaller volumes, we prefer to use ethylene as the standard gas, a flame ionization detector and nitrogen as carrier gas. LITERATURE CITED (1) A.T. James and A.J.P. Martin, Biochem J.. 50,679 (1952). (2) G. Guiochon, M. Goedert and L. Jacob, in Gas Chromatography 1970,R. Stock Ed.,The Institute of Petroleum, London, UK, 1971,p. 160. (3) D.L. Massart, A. Dijkstra and L. Kaufman, Evaluation and Optimization of Luboratoiy Methoh and Analytical Procedures, Elsevier, Amsterdam, NL, 1978. (4) R.A. Day Jr. and A.L. Underwood, Quantitatiue Analysis, 5th Edition, Prentice-Hall, Englewood Cliffs, NJ, 1986,Ch. 2. ( 5 ) J. Philippe, Les Methodes Statistiques en Pharmacie et en Chimie, Masson, Paris, France, 1967. (6) M.R, Spiegel, Statisrics, McGraw-Hill, New York, NY, 1961. (7) D.G. Peters, J.M. Hayes and G.M. Hieftje, Chemical Separations and Measurements. Theory and Practice of Analytical Chemistry, W.B.Saunders, New York, NY, 1974,pp. 29-37. ( 8 ) D. York, Can. J. Phys., 44,1079 (1966). (9) I. Halasz, Anal. Chem, 36,1428(1964). (10) G. Guiochon, J. Chromatogr., 14, 378 (1964). (11) D. Borba de Oliveira, J. Gas Chromatogr., 6,230 (1968). (12) M.Goedert and G. Guiochon, J. Gas Chromatogr., 7, 323 (1969). (13) C.L. Guillemin, J. Vermont, P.Juston, P. Ferradini, A. Artur and A. Peyron, J. Chromatogr. Sci., 9, 155 (1971). (14) J. Jan&, Mikrochim Act@ 1956, 1038.

587

CHAPTER 14

QUANTITATIVE ANALYSIS BY GAS CHROMATOGRAPHY Response Factors. Determination. Accuracy and Precision TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Determination of the Response Factors with Conventional Methods . . . . . . . . . . . . . . . . . . 1. Gases and Volatile Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Gas Mixtures Prepared From Partial Pressures ............................. b. Exponential Dilution Flask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Volatile Liquid Samples ............................................... a. NormalMixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b.TraceAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Diffusion Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d . PermeationTubes ....................... .......................... 3. Calibration of Liquid Samples ........................................... 4. Calibration of Solid Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Determination of the Response Factors with the Gas Density Balance . . . . . . . . . . . . . . . . . 1. Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Thermal Conductivity Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b . Flame Ionization Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Linearity of the Stream Splitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. CalibrationProcedure ................................................ 4. Advantages of the Gas Density Balance .................................... 5 . Practical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I11. Stability and Reproducibility of the Response Factors............................. 1. Influence of the Chromatographic System .................................. 2. Influence of the Characteristics of a Thermal Conductivity Detector . . . . . . . . . . . . . . . . a. GeometryoftheDetector ............................................ b. Nature of the Detector Wires ......................................... c. Temperature of the Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Temperature of the Detector Block ..................................... e. Long-Term Stability of the Response Factors .............................. 3. Influence of the Characteristics of a Flame Ionization Detector . . . . . . . . . . . . . . . . . . . a. Geometry of the Detector ............................................ b . Flame Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c Nature of the Carrier Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Comparison between Experimental and Calculated Response Factors . . . . . . . . . . . . . Literaturecited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

587 589 589 590 591 595 595 596 598

600 601 601 601 602 602 603 604 605 607 608 609 612 613 613 615 616 620 621 621 623 624 625 625 626

INTRODUCTION As we have shown in the previous chapter (Chapter 13). the determination of the amount of a certain compound in the sample injected in gas chromatography requires the measurement of the peak area and a knowledge of the response factor of this compound. It is much easier to carry out relative measurements than absolute ones. as the latter would require the determination of the exact amount of References on p. 626.

588

sample injected, which requires special calibration (see Chapter 13, Section 111.3) and introduces another source of error. As used in this section, the response factor is defined as the proportionality coefficient between the peak area, A , and the amount of the corresponding compound, Q.Thus.

Accordingly, the relative response factor of compound 2 with respect to compound 1 (compound 1 standard) will be. f 2 =f 2 / 1 Q2 Ai E

fl

Qi

A,

In principle, fZl1 depends only on the nature of the compounds 1 and 2 and on the detector used. There are, however, a number of chromatographic parameters which may affect the value of the relative response factor, for example because they alter the elution yield (ratio of eluted amount of a compound to the injected amount; normally 100!%,the yield may be much lower in some cases) or because they interfere with the proper operation of the integrator (see Chapter 15, Sections I1 and 111). The most important reasons why relative response factors may change with chromatographic conditions are as follows: - At injection. Pyrolysis of the analyte or the standard, adsorption on tars or activated charcoal formed in the sampling port or other reactions may take place. The extent of losses depends on the nature of the walls of the injection port, on their cleanliness and on the temperature of the sampling system. - During separation. firolysis in the column, reactions with the stationary phase or with the column support may take place. Adsorption on the column support has been reported (1). The extent of the losses depend on the nature of the support (which has often to be treated) and sometimes even on the nature of the column walls. - At detection. Pyrolysis may take place in the detector cell. Change in the operating conditions of the detector may affect the response of the analyte and the standard differently. - During signal processing. Changes in retention time and efficiency result in changes in the relative times when the thresholds for starting and stopping integration are met. Thus, if the relative retention of the analyte and the standard change widely, it is possible that the ratio of the peak areas measured becomes different. The analyst must remain alert to all these sources of errors at all times. Validation of response factors must be carried out at all stages of quantitative analysis, as well as periodically. There are analytical conditions which are perfectly suitable for a reasonable separation and for qualitative analysis but which lead to unacceptable quantitative results. In this chapter we discuss the determination of the response factors, their stability, repeatability and accuracy. The problems encountered in the determination of the peak area are discussed in Chapter 15.

589

I. DETERMINATION OF THE RESPONSE FACTORS WITH CONVENTIONAL METHODS In principle, these methods rely on the preparation of authentic mixtures of known composition, their injection under proper chromatographic conditions and the measurement of the signals obtained. There are an extremely large number of methods described for the preparation of such mixtures, as well as many discussions of the problems encountered and the pitfalls to avoid. The reader is referred to these sources and particularly to the publications by Barratt (2) and Nelson (3). We shall discuss here only the methods and procedures which we have experimented with and found useful and well adapted to the solution of the problems of quantitative analysis. They permit a satisfactory solution of most of the problems encountered in practice. Absolute calibrations require the determination of the amount of compound injected and of the slope of plots of the peak area versus the sample size in the range of linear response of the detector. Calibration of the detector in a range where it is not linear is possible, in principle, as long as the response is repeatable (4). The interpolation of the response curve may be difficult to do and the variable response factor may be more difficult to use. If a non-linear response is used, the integration procedure must take it into account. It is the product of the signal by the variable response factor which must be integrated, so that the number obtained will be really proportional to the amount of compound eluted. The widespread availability of microcomputers, which can readily perform that kind of calculations, should relieve us of the fetishism for linearity that physical and analytical chemists have exhibited over the last century. Relative calibration requires the determination of the detector response for binary mixtures of known composition of the analyte and a standard i.e., of the ratio of the areas of the two peaks, for a number of mixtures of different composition. Generally, the standard will be the same for a whole series of analytes. This is tantamount to the measurement of the ratios of the slopes of the straight lines discussed in the previous paragraph, when the peak area is plotted versus the amount of pure compound injected, for compounds 2, 3, etc., n, and for compound 1, the standard. Relative calibrations can also be carried out in the domain of non-linear response of the detector. Handling these data requires a microcomputer and software which is not yet generally available. In the range of normal concentrations, somewhat arbitrarily defined as 1 to 99%, static calibration methods are used. Calibration mixtures are prepared separately and sometimes conserved for a while. For small concentrations and certainly for trace analysis, dynamic methods are preferred. They involve the preparation of a stream of gas containing the trace component(s) at a known concentration and flowing through the sampling valve. The most important dynamic methods are the exponential dilution method, the diffusion method and the permeation tube method. 1. Gases and Volatile Compounds

The most common methods used for the calibration of gases or very volatile compounds is the preparation of pressurized mixtures in cylinders or the use of the References on p. 626.

590

exponential dilution flask, which pennits the ready generation of a stream of gas with one or a few analytes at a concentration which decreases with passing time, following an exponential decay that is easy to adjust. a. Gas Mixtures Prepared From Partial Pressures

Calibration mixtures may be purchased from different suppliers or prepared in the laboratory, provided some suitable, simple instrumentation is available. The advantages of purchasing calibrated gas mixtures are the safety (these mixtures must be pressurized to avoid contamination by air), especially if dangerous, toxic or flammable gases or vapors are used, the convenience, rapidity and cost, if small amounts of mixtures are used and only a few calibrations are performed. If mixtures are to be prepared in the laboratory some equipment is necessary, especially a gas line with valve manifolds, to which cylinders can be connected, a vacuum pump, a mercury manometer or a precision pressure gauge which can measure pressures above and below atmospheric pressure and a sampling valve. Absolute calibrations could be carried out directly by introducing the analyte of interest into the gas line connected to the sampling loop under increasing pressures, and carrying out the analysis. The difficulty of this method results from the great difficulty in achieving proper tightness of the line and avoiding dilution by the carrier gas or contamination by air. The preparation of cylinders or tanks of calibrated gases and vapors is described on Figure 14.1. Cylinders of the pure gases required are connected to the gas line through the valve manifold. The cylinder, R, which will contain the final mixture is carefully emptied by the vacuum pump, with valves V and V, (Figure 14.1) open. In some cases it may be necessary to bake the cylinder walls. Then V is closed, Va is open and through the pressure controller, D, the first gas is introduced in the cylinder until a certain pressure, Pa,of this gas is reached in the cylinder. Valves V,, and then V, are closed. The gas line is emptied with the vacuum pump. The same procedure is used to introduce a certain pressure P b of the compound B, the total pressure in R being Pa + P b . A mixture of several gases can be prepared in the cylinder R, this way. Provided that the final pressure does not exceed a few atmospheres and that the temperature be kept really constant during the operation, the volume concentration of the mixture is derived from the ideal gas law: Pn c,, = -

(3) pt where P,, is the partial pressure of compound n and P, the total pressure. The use of a liquid chromatography valve, much tighter than most gas chromatography valves, permits the dilution of a gas or a gas mixture. The trace component is introduced in the gas line connected to the sample loop of the LC valve (see Figure 14.1B). Then the diluent gas is introduced, at a much larger pressure. The concentration of the trace component, in ppm (v/v) is given by:

591

Figure 14.1. Preparation of standard mixtures of gases for calibration. A, for normal concentrations. B, for trace components.

where u is the sample loop volume, V the cylinder volume and PA the pressure (in atm) of the gas A in the cylinder. Caution should be applied when using this method, in order to avoid accidents and also to ensure that the gas mixture prepared in the sample loop and the rest of the gas line is homogeneous. Although the diffusion coefficients of gases are rather large, that may require some time.

b. Exponential Dilution Flask This method is extremely well suited to the calibration of trace components in gases. First described by Lovelock (5), then discussed by other authors (6-8), it has been widely used for the study of the response of highly sensitive detectors, such as the flame ionization detector or the electron capture detector. A flask, preferably a glass flask (but Lovelock used a large building, a barn lined with a plastic sheet (9) for some ultra-trace calibrations), is swept by a steady stream of an inert dilution gas, often the carrier gas used, which then passes through the sample loop of the sampling valve of the chromatograph (see Figure 14.2). The flask contains a little fan, driven from outside by a magnetic stirrer, to keep the gas content homogeneous. A known amount of gas or vapor is introduced with a syringe References on p. 626.

592

S

Figure 14.2. Exponential dilution flask. A, trace calibration. B, use to study the range of linear response of a detector. S, sample; g, diluent gas; V, sample injection valve.

inside the flask. The concentration of the gas or vapor in the outlet stream is given by:

c = c, e-D'/V

(4)

where C, is the initial concentration of the injected gas or vapor (amount injected divided by the flask volume), C is the concentration in the outlet gas stream at time t , D is the flow rate of scavenger gas, Y is the volume of the flask and t is the time elapsed since injection of the gas sample in the flask. The flask volume is measured by weighing the flask empty and filled with water. In practice, a 250 mL flask is used, with a gas flow rate set between 40 and 50 mL/min. . Samples of the effluent from the flask are analyzed periodically. A plot of the logarithm of the peak area versus the time is a straight line (see Figure 14.3). Deviations from the theoretical response are often observed, depending on the concentration range, the nature of the compounds analyzed and the detector used. The most common source of deviation, especially at low concentrations, is the adsorption of the trace components on the flask wall, the fittings or the fan and their slow release. Deviations up to 15% can be observed at low concentrations. The results of the experimental plot, not those of the theoretical calculation (equation 4) should always be used. It is better to inject the smallest possible amount of calibrated compound as required for the first measurement (the largest concentration achieved), and, if necessary, to repeat the operation with different sample sizes. The use of the part of the calibration curve which deviates from the straight line is dangerous and is not advised. As long as the reason for this deviation has not been found it could also be attributed to an unexpected detector behavior, or to some leak in the device. Neither the extrapolated straight line nor the experimental response curve can be used as long as the actual composition of the outlet stream is not known.

593

Figure 14.3. Exponential dilution flask. Calibration curve in the vpm range.

ct

Figure 14.4. Exponential dilution flask. Determination of the dynamic linear range of a detector.

References on p. 626.

594

TCD

5:128

5:32

I

GDB

Figure 14.5. Exponential dilution flask. Determination of the dynamic linear range of a TCD and a GDB. H cm

Figure 14.6. Exponential dilution flask. Dynamic linear range for peak height, with the TCD and the GDB operating simultaneously, in parallel. Camer gas, argon.

595

TABLE 14.1 Use of an Exponential Dilution Flask for the Determination of the Dynamic Linear Range of Two Detectors Time (fin) 0 2 4 6 8 10 12 14 16 18 20 22

Calculated Concentration

Peak Height (GDB)

100 77.44 58.54 43.6 32.92 24.99 18.29 13.53 10.36 7.62 5.48 4.26

16.4 12.7 9.6 7.2 5.4 4.1 3.0 2.2 1.7 1.3 0.9 0.7

Sample: nitrogen. Volume: 1.11 mL. Split ratio 1/1, i.e., 0.555 mL for each detector. Carrier and diluent gases: argon. Concentration in % (v/v). Peak height in cm. Detectors: TCD and GDB. See Figure 14.6.

An especially valuable application of the exponential dilution method is the rapid determination of the dynamic linear range of a detector. The flask is filled with the pure gas and the stream of scavenger is started when the first analysis is made. A simple modification of the gas line is made (see Figure 14.2, B). Figures 14.4 to 14.6 and Table 14.1 illustrate this application in the case of the thermal conductivity detector and the gas density balance. 2. Volatile Liquid Samples

Calibration of mixtures of compounds which have boiling points close to ambient temperature (C, hydrocarbons, Freons, vinyl chloride, etc.) is more difficult than that of gases or higher boiling liquids. The problems and the solutions are different depending on the range of concentrations considered. a. Normal Mixtures

The two main steps to consider are the preparation of the calibration mixture and its injection. The preparation of calibration mixtures is made by weighing in a metallic bottle of small capacity (a few liters) the required amounts of the compounds desired. The most abundant components of the mixture are introduced first, to reduce as far as possible the error due to the saturation of the vapor phase and to the loss of introduced compound to this gas phase (Henry’s law). The injection of the sample must be made in such a way that the aliquot introduced into the chromatograph is representative of the composition of the liquid References on p. 626.

596

Figure 14.7. Injection of a representative sample of a liquid mixture of several volatile or very volatile compounds. V1, stop valve. V2, metering valve. E, heat exchanger, packed with glass or steel beads. V3 sampling valve. cg, carrier gas.

phase and not of the gas phase in equilibrium with the liquid phase, as this vapor has a very different composition. Either a liquid sample is injected with a pressurized liquid valve, or a stream of the liquid is continuously vaporized in totality, and the vapor stream passed through the gas sampling valve. The composition of the vapor phase is then identical to that of the liquid stream, but no separation must take place in the flash vaporizer, where any kind of distillation should be carefully avoided. Careful thermal insulation of the vapor line, up to a point downstream of the sampling valve may sometimes be necessary. Figure 14.7 illustrates the principle of the method. The validity of the method is demonstrated by the results obtained during calibration of the thermal conductivity detector using the gas density balance (see Table 14.5, Section 3.2). A binary mixture of Freons prepared in a sufficient amount to eliminate the influence of the weighing errors is continuously vaporized by injection in a short heated tube packed with metal beads. The vapor stream (ca 10 L/hour) is analyzed with a gas density balance. The ratio of the peak areas corresponds exactly to the ratio of the mass concentrations. b. Trace Analysis A very small amount of a volatile compound B is introduced in a metallic bottle, under vacuum. The bottle is then filled by the diluent, which is most often a volatile compound, sometimes a gas. The diluent may be pure or a mixture. Figure 14.8 shows how these operations can be performed. The tube c, terminated by a septum, is soldered to the gas sample bottle, R. A connecting tube b, which serves also as a nut holding the septum tight against the end of part c, permits the

597

septum

a

b

C

Figure 14.8. Preparation of a standard mixture containing a small amount of an impurity diluted in a very volatile liquid matrix. 1: b + c, introduction of the internal standard with a syringe into the empty bottle, R . 2: a + b + c, transfer of the volatile compound from the first tank ( A ) to the second one ( R ) .

connection to the bottle A containing the diluent gas or the high vapor pressure liquid. The tube a, is connected at one end to the bottle of diluent gas or vapor, at the other to a strong syringe needle with a side hole. Using a microsyringe, weighed before and after the operation, a small amount of compound B is injected into the empty bottle R, under vacuum, using attachments b and c (Figure 14.8). The cylinder A is then connected to the bottle R by pushing the syringe needle through the septum. After opening valve V, (see Figure 14.1), a certain amount of diluent is introduced into the bottle R, until the desired pressure is reached. If needed, a large amount of liquid may be transferred by cooling bottle R to a temperature lower than that of bottle A. The concentration of B is given by:

where m ( A ) and m ( B ) are the respective weights of compounds A and B introduced in the bottle R. The injection of the mixture requires the use of the same precautions and the same methods as in the previous case. References on p. 626.

598

c. Diffurion

Cells

The use of the diffusion cell permits the preparation of a steady stream of inert gas containing a constant, small, adjustable concentration of a volatile liquid. In the original device described by Desty et al. (10) for the study of the response of the flame ionization detector, a capillary tube contains the liquid under study. A stream of gas passes at constant flow rate above the top of the capillary tube, carrying away the vapor which diffuses out of the tube (see Figure 14.9). The diffusion mass flux, or mass flow rate, S, of sample is given by:

where X is a constant function of the temperature (vapor pressure of the compound used), p is the density of the liquid at the temperature of the experiment, A is the cross-sectional area of the capillary tube, and 1 is the vertical distance between the top of the tube and the meniscus of the liquid. The concentration of the gas stream

5 cm scale

Figure 14.9. Preparation of a stream of gas containing a trace amount of the vapor of a volatile liquid (see

ref. 10).

599

is given by the ratio of the diffusion flux of analyte (g/sec or mL/sec) by the gas flow rate (mL/sec). The main difficulty encountered in the use of this device is that the distance I is not constant. It varies with time, following a quadratic law (10):

I’ = at

(6b)

and the constant a is determined from a plot of the square of the distance I versus time. The composition of the gas stream generated by this device is not constant and periodic determinations are required. On the other hand, the variation in the composition covers a much narrower range than the exponential flask, so the method is not very practical. It has been improved by others (11-14) and applied to the solution of various problems of calibration, especially in trace analysis. The improvement consists in the use of a little flask at the bottom of the capillary tube, containing the liquid used for the calibration. The capillary tube connects this flask, where the vapor pressure of the compound is constant, to the tube where passes the scavenger gas flow. Accordingly, the vertical mass flow of analyte by diffusion does not depend on time. For a tube of given length and cross-sectional area, it depends only on the vapor pressure of the analyte, i.e., on the temperature (12). The mass flow rate of solute is given by:

g)

s = - DoPoMA T ln(1RT~I

(7)

where Do is the NTP diffusion coefficient of the solute in the carrier gas, Po is the atmospheric pressure, M is the solute molecular weight, A is the cross-sectional area of the tube and I its length, To is the normal temperature (273 K), R is the ideal gas constant, T is the temperature of the liquid during the experiment, p o is the vapor pressure of the solute at temperature T and P is the total pressure in the apparatus. The validity of equation 7 has been verified experimentally (12,13). The composition of the gas stream generated by this diffusion cell can be adjusted in a large range by changing the scavenger gas flow rate and the temperature of the diffusion cell (13). TABLE 14.2 Calibration of a Diffusion Cell Measure No.

I (cm)

12

1

5.20 5.39 5.90 6.06 6.61

21.04 29.05 34.81 36.12 44.49

2 3 4 5

A12

(cm2

2.01 1.17

9.68 11.45

(SS)

cm2/sec) (see equation 6b)

0 21600 82800 100800 18oooO

0.932 0.938 0.961 0.969

t

u

a average: 0.950X Capillary tube: 2 mm id., 68 mm length. Temperature: 60 C.

References on p. 626.

TABLE 14.3 Adjustment of the Water Content of a Gas Stream with a Diffusion Cell I

S

Concentration (ppm, v/v), at different Flow Rates

(cm)

(pg/sec)

40L/h

36 L/h

18 L/h

9 L/h

4.5 L/h

3.5 3.6 3.7 3.8 3.9 4.0

0.431 0.419 0.408 0.397 0.387 0.377

52.5 51 50 48.5 47 46

58 57 55.5 54 52.5 51

117 114 111 108 105 102

233 228 222 216 210 204

466 455 443 431 420 408

Capillary tube, i.d. 2 mm; length 6.8 cm. Temperature: 60 C. S1= apA/2I (pg/sec) (see equation 6). S2 = S1/180 (pmole/sec). S3 = 24.400 S2 (ml/sec).

Tables 14.2 (determination of a ) and 14.3 (determination of S,equation 6) show results obtained with a diffusion cell for the preparation of gas streams of known concentration in water vapor. d. Permeation Tubes

This more recent, very practical dynamic method permits the preparation of extremely dilute gas streams. It is based on the permeation of gases or vapors across polymer tubings (15). A liquefied gas or a volatile liquid contained in a closed polymer tubing diffuses slowly across the wall. The mass flux of diffused material is constant. For a given tube it depends only on its temperature. For a given tubing material it depends on the length, cross section and thickness of the particular tube used. The products most often selected are Teflon (polytetrafluoroethylene),Nylon (polyamide) and Mylar (polyester). Lucero (16) has derived an equation which relates the mass flux, S, of analyte diffusing across the tube wall to the tube characteristics and to the vapor pressure of the analyte:

where L is the tube length, R iand R, its inner and outer radii, respectively, X , is the permeability coefficient of the wall material, E the energy of activation for the diffusion of the gas or vapor across the polymer, R is the ideal gas constant and T the absolute temperature, Pi and Po the partial pressure of the analyte inside (vapor pressure) and outside (usually negligible) the tube, respectively. In practice the mass flow rate of analyte is determined by weighing the tube as a function of time, usually over very long periods, because S is very small (17-19). Frequent recalibration of these tubes is required for compounds which can react, for example vinyl chloride polymerizes slowly in diffusion tubes.

601

Devices incorporating a precalibrated permeation tube, a flow rate controller and a temperature controller are commercially available. They can be connected directly to a sampling valve. Temperature equilibration often requires long periods of patience (20), up to several hours. These devices are used for the calibration of chromatographs used in air pollution monitoring, of portable chromatographs and of on-line process control chromatographs.

3. Calibration of Liquid Samples The preparation of calibration mixtures of liquids by weighmg is a traditional procedure which affords no difficulty. When the boiling point is below 100°C, however, it is better to be careful and avoid possible selective losses of the most volatile components by cooling the calibration mixtures at temperatures close to 0 O C, or by using vials with a sealed rubber cap, with a Teflon lining.

4. Calibration of Solid Samples Although sampling systems for solids have been described and some models are available (21), the only practical method of calibration for solids consists in weighmg a determined amount and dissolving it in the appropriate amount of solvent. Too light a solvent must be avoided.

LI. DETERMINATION OF THE RESPONSE FACTORS WITH THE GAS DENSITY BALANCE As discussed in Chapter 10, the gas density balance has the unique property of a response which exactly follows the prediction derived from a simple model of its behavior and which can be calculated from the detector characteristics. In fact the absolute response cannot be calculated but the relative response of two compounds can, which is all that we need for calibration in gas chromatography, as is discussed above. The response of the detector is proportional to the ratio:

MS f= Ms-Mg

(9)

where M, and Mg are the molecular weights of the analyte and the carrier gas, respectively. The response is zero when the analyte and the carrier gas have the same molecular weights. On the other hand, the gas density balance has a rather large detection limit (it is not very sensitive, see Chapter 10) and a rather large dynamic linear range (cu 10,000). Accordingly, the best possible uses of the properties of this detector in quantitative analysis are: - either in the preparation and control of standard mixtures used for the calibration References on p. 626.

602

of other detectors; a suitable sample size will be chosen to inject a sufficient amount of analyte to permit accurate measurements (22,23), - or as a calibration detector, for the direct determination of relative response factors (22-25). The first use is obvious and does not require a specific procedure. The gas density balance is used as a regular detector on the chromatograph, with a slightly wider column than usual and a sampling valve permitting the injection of rather large samples. The following discussion is specifically dedicated to the second type of application, the direct determination of the relative response factors of a new detector. 1. Experimental Setup

The detector used in this application is the Gow-Mac gas density balance Model 373, the characteristics of which have been described in Chapter 10. There are two possible schematics for the experimental setup. The two detectors can be placed in series (26) or in parallel (22-25). Because the principle of the gas density balance (GDB) requires the use of a rather large flow of reference gas (see Chapter lo), this detector should be placed second on the line, otherwise the calibrated detector will malfunction or its response factors may be significantly changed by the high gas velocity in its cell. This is not possible with the flame ionization detector (FID) nor with the flame photometric detector (FPD). It would be possible with the thermal conductivity detector (TCD) or even with the electron capture detector (ECD) when the yield of the reaction is low. The range of concentrations which can be conveniently measured with an ECD and a GDB are so widely different that this last application would not make much sense anyway. Furthermore, the first detector, the one to be calibrated, is going to operate at a pressure significantly higher than atmospheric, because of the large flow rates required by proper operation of the GDB and of the narrow tubings of this detector. Although the thermal conductivity of gases do not change with increasing pressure between 0.5 and 5 atm, one can fear that some modification of the response of the calibrated detector may take place, since the TCD may respond also to changes in gas density. For these reasons we prefer to operate the GDB in parallel to the detector to calibrate. For this purpose we use the schematic shown on Figure 14.10. The GDB is placed in the oven of the chromatograph containing the detector to calibrate. A split is placed between the column and the normal detector and connected to the GDB. Different T-splits are used, so the GDB can receive from 1/2 to 29/30 of the column effluent. The gas tubings and electric wirings of the GDB are independent of those of the chromatograph. No permanent modification is made to the chromatograph and the GDB is taken off as soon as the calibration has been performed. a. Thermal Conductivity Detector A “T” fitting (Swagelock 1/16 inch or Car10 Erba, 1 mm) is connected to the column end. The sides of the T are connected to each detector by a 30 cm long, 0.25

603

U

I

I

I

e

l

-

I

carrier g a t

1

1

I

column

I @

I

I

I

I I

I

I

I

I

U

make-upgaa

I

carrlar g a g

-

I I

U

column 1

I

I I

I

113 B DG raference , . B.

I

I

I

I L

Figure 14.10. The use of the gas density balance as a calibration detector. A, with a thermal conductivity detector. B, with a flame ionization detector. The figures on the two branches of the column effluent give the relative importance of the flow rates of these gas streams.

mm i.d. tube. This provides a splitting ratio close to 1/1 (see next section). To avoid interferences the three gas lines, the carrier gas flow, the TCD and the GDB reference flows are independent, including their pressure controllers (see Figure 14.10A). The carrier gas flow rate is adjusted so that the flow rate through the calibrated detector (TCD) is equal to the flow rate which will be used in the quantitative analyses to be carried out later. This means that the carrier gas flow rate will be about double the one normally used with this column; the inlet pressure will be larger, the analysis time shorter, the peaks narrower and the column efficiency somewhat reduced, but still sufficient since only simple separations are required during calibration. This should not much affect the performance of the data acquisition system. 6. Flame Ionization Detector A similar “T” fitting is used but a splitting ratio much different from unity is desired, since the FID is much more sensitive than the GDB (see Figure 14.10B). A ratio of 1/30 or 1/50 is obtained by connecting the GDB to a 10 cm long tubing References on p. 626.

604

and the FID to a 300 or 500 cm long tubing, both 0.25 mm i.d. (see next section for a discussion of the linearity of this splitter). The different gas streams are designed to be independent of each other. In addition to the normal gas lines of the GDB (reference and column eluent) and the FID (hydrogen, oxygen and column eluent) a stream of make-up gas is necessary to bring to the FID the same flow rate of carrier gas it will receive in normal operation. Failure to do so may result in large changes of the relative response factors in some cases. If the FID receives an independent stream of make-up gas in normal operation, the flow rate of that gas will be adjusted to compensate for carrier gas lost to the GDB. 2. Linearity of the Stream Splitter

The validity of the use of a GDB in parallel to the detector to calibrate depends on the linearity of the splitter. Splitters enjoy a poor reputation in gas chromatography because they have been mainly used and investigated in connection with the injection of the minute samples required by open tubular columns (see Chapter 8, Section 5.1). In such a case, however, the splitter operates on a gas mixture which is not homogeneous, since to reduce the dead volume contribution the splitter is placed immediately downstream of the vaporizer. It is most probable that the sample is not completely vaporized in many cases when poor linearity has been observed. The gas stream is certainly not homogeneous. The use of a splitter in the present case is markedly different. The splitter operates at the end of a long chromatographic column. If satisfactory results are obtained and quantitative analysis is considered, the mixture of carrier gas and analyte vapor at the column outlet must be really homogeneous. Furthermore, for a variety of reasons dealing with the method, calibration of relative responses is made with standards which have retention times and vapor pressures which are not markedly different. Accordingly, we may anticipate a much more satisfactory performance of our splitters, the ratio of which is not very different from unity, than has been observed in quantitative analysis with open tubular columns. TABLE 14.4 Study of the Linear Behavior of the GDB Splitter split Ratio 1/3

Propane Benzene

FID GDB FID GDB

1/10

Area Ratio

A (%)

0.998

o.8R,

A (%)

Ratio

1.006

1.027

Area

0.2%

OH8 1.001

0.3%

1.027

0.5%

A: Relative difference between the two area ratios.

1/30

1/15 Area Ratio

iz 0.998 o.999

(W)

A (56)

Area Ratio

A

0.1%

1.007 1.009

0.2%

0.1%

*.081

0.4%

605

a 2

1

t

f Figure 14.11. Procedure for the determination of the relative response factors of a detector, using the GDB.

A demonstration of the linearity of the splitters used can be obtained by successively injecting samples of different sizes of a given, pure compound. If the splitter is linear, the ratio of the peak areas for two successive injections should be identical on each detector, since each detector must receive the same fraction of the amount injected and the response factor remains the same on each detector. This of course is valid only in the linear range of the detector responses. Data to that effect are reported in Table 14.4 for different splitters, with ratios between 1/3 and 1/30.

3. Calibration Procedure This procedure is illustrated in Figure 14.11. Samples of compounds 1 and 2, of suitable sizes, are injected successively on the chromatograph and the areas of the peaks obtained are determined. Let Al,, Alx, A , , the areas obtained for compounds 1 and 2, on the GDB (B) and on the detecto; to calibrate (X),respectively. We want to derive the relative response factor of compounds 1 and 2 on detector x , i.e., fi,/fi,. The ratio of the amounts m1 and m 2 of compounds 1 and 2 eluted through the GDB is given by (see Chapter 13, equation 3c):

References on p. 626.

606

where f,, and f i b are the response factors of the GDB for compounds 1 and 2, respectively (see equation 9 for the value of these factors), MI, M2 and Mg are the molecular weights of compounds 1, 2 and the carrier gas, respectively. The ratio of the amounts of compounds 1 and 2 eluted through the detector x is the same as the ratio m2/ml, since the splitter is linear. Thus, we have:

and:

In other words, the relative response factor, f2/1, of the two compounds on the detector x , to calibrate, is given by the product of the ratio of the amounts of compound 1 and 2 introduced in the detector x , m 2 / m l , multiplied by the ratio of the peak areas, A , / A 2 (see equations 1, 2 and 11 above). The ratio of peak areas is determined directly, while the ratio of the amounts introduced in the detector x is the same as the ratio of the amounts of analytes introduced in the GDB, which can be calculated from the ratio of the peak areas on this detector and the relative response factor on the GDB, predicted accurately by equation 24 in Chapter 10. The situation is very similar to the classical calibration, where a mixture of known composition is injected in the chromatograph, and the relative response factor is derived from the ratio of the peak areas and the concentration ratio of the binary mixture. In this latter case we have:

where C, and C2 are the concentrations of compounds 1 and 2 in the calibration mixture, respectively. The major difference is that, with the present calibration method, no mixture is actually made. The use of the GDB permits the determination of the concentration ratio C2/C,, of the "virtual" mixture (see equation 12), while the peak area ratio, A,T/A2r, is given by the calibrated detector. From the properties of the "virtual" mixture used, several of the major advantages of the method are derived. The relative response factors, f2,1, given by this method are weight factors, i.e., the amounts of compounds 1 and 2 used are given in mass units.

607

4. Advantages of the Gas Density Balance

The comparison between the performance, the problems and the difficulties of the classical calibration method and the method using the GDB for direct calibration leads to the following conclusions, essentially a list of the advantages offered by the GDB. The GDB Method -

The Classical Method

Purity of Standard Compounds:

Any technical product, even mixtures resulting directly from a chemical reaction, can be used for calibration, without purification, provided the compound(s) for which calibration is carried out is (are) separated on the column, under the conditions selected.

Pure products, often difficult to find and expensive, are absolutely necessary for a precise and accurate calibration.

The accuracy of the relative response factors obtained does not depend on the purity of the reagents used.

The accuracy of the relative response factors obtained depends directly on the purity of the products used.

-

Standard Mixture:

It is not necessary to prepare a standard mixture. The method works by using virtual mixtures between the pure compounds separated by the column. Thus, it is possible to determine easily the relative response factor of a solid with regard to a gas. -

Exceptional Cases:

It is easy to determine the relative response factors for all kind of compounds, isomers, isotopes, toxic compounds, aggressive compounds, as long as they do not react with the column. -

It is absolutely necessary to prepare one or several standard mixtures. Difficult problems may arise with compounds which are poorly miscible. Direct calibration of a solid with respect to a gas is nearly impossible. Several intermediate mixtures are requested.

Relative response factors cannot be determined for compounds which cannot be separated (isomers, isotopes) or which cannot be handled safely in the laboratory.

Precision and Accuracy of the Determination:

The precision is similar for all response factors, since they are obtained directly, whatever the two compounds involved.

The precision depends on the number of intermediate mixtures which must be prepared (e.g. in the case of nonmiscible compounds). References oh p. 626.

608

The Classical Method The GDB Method The precision depends on only two The precision depends on four parameters: parameters: -The precision of the peak area - The precision of the composition of the standard mixture, determination, - The deviation from linearity of the - The accuracy of the transfer of the detector response. standard mixture to the analyzer, - The precision of the peak area determination, - The deviation from linearity of the detector response. The relative response factors obtained Irreversible adsorption or decomposiare independent of possible irreversible tion reactions lead to systematic errors adsorption or of other phenomena tak- on the relative response factors. ing place inside the chromatographic column.

- Conclusion: A method which is simple, fast, pre- A method which is rather complex and cise, accurate and relatively inexpen- slow. It is less precise and accurate sive. than the GDB method and much more expensive. 5. Practical Considerations

The analyst has a choice between several procedures for the determination of the relative response factors: - The injection of reaction mixtures, coming directly from the laboratory, the pilot plant or the plant itself. The only requirement is that the compound(s) for which the calibration is desired be well resolved from all other components of the mixture. More reproducible results are obtained if the chromatographic analysis is carried out in isothermal conditions than in temperature programming. With a reaction mixture the elution of the last compounds could be accelerated by using a backflush or a column switching system, especially if calibration is not required for these components (see Chapter 9). - The injection of synthetic mixtures. The quantitative composition of these mixtures does not have to be known, as discussed above, only the nature of the compounds and the elution order. Figures 14.12 and 14.13 show the use of this method for the calibration of a TCD and a FID, respectively, with a GDB. -The successive injection of pure samples of the standard and of each of the compounds for which calibration is required. A series of injections permits the rapid determination of the average and standard deviation of the relative response factors. Figure 14.14 shows an application of the method. Table 14.5 summarizes the data obtained. Two digital integrators or a dual channel integrator, using BASIC programs, are helpful for a direct calculation of the response factors.

609

F114

I 12 F 11

ir

m

d TCD

GDB

Figure 14.12. Chromatograms obtained simultaneously for the same sample of a mixture of fluorochloroalkanes, with the TCD (left) and the GDB (right). F12,CCI,F,; F,14rC,CI,F4; Fl13,C,C13F3.

An order of magnitude of the savings made possible by the use of this method can be derived from the following example. In 1958 the determination of the response factors (16 replicate measurements for each factor) of the 19 chloroalkanes in C l and C2 with respect to ethylene took us several months, using the conventional method without integrator and calculator. More recently, the GDB method permitted the same determination in 2 days. Examples of relative response factors obtained with a GDB are given in Tables 14.6 to 14.16 and 14.19 to 14.23. 111. STABILITY AND REPRODUCIBILITY OF THE RESPONSE FACTORS

The problems of the precision and accuracy of the chromatographic measurements are discussed later, in Chapter 16. The problem we are dealing with here is the long-term stability of response factors and the influence of the design and implementation of the chromatographic instrument and system on the value of the response factors. In other words, how often is it necessary to repeat the calibration procedure with a given instrument (long-term stability of the response factors)? and to what extent can we use the same factors when the equipment is modified, by References on p. 626.

610 FI D

GDB

4

U

HZ 21Ih

# 4

split ratio 1

to 50

l-7

column 5.1 I/h He

He

Figure 14.13. Chromatograms obtained simultaneously for tk same sampl of a mixture of chlorohydrocarbons, with the GDB (right) and the FID (left). 1, Vinylidene chloride, CHCI=CHCl. 2, Chloroform. 3, Carbon tetrachloride. 4, Trichloroethylene. 5, 1,1,2-Trichloroethane.6, Perchloroethylene.

replacing the column, the injection system or the detector, by a device of the same type? In principle, the response factors should depend only on the compounds studied and on the operating parameters of the detector. The detector characteristics may drift, however, and changes in the chromatographic system or in other parts of the instrumentation may indirectly affect the detector response. This is more prone to happen with the conventional calibration methods than when the gas density

611

TCD

GDB

Figure 14.14. Calibration of a TCD with the GDB. Chromatograms obtained for four consecutive injections of compound 1 (acrolein), followed by four consecutive injections of compound 2 (benzene). Trace of the GDB (left) and TCD (right). See Table 14.5.

TABLE 14.5 Calibration of a TCD with a GDB Area of Ethylene Peaks

Area of Acrolein Peaks:

TCD 46464

GDB 910

TCD 45274

GDB 890

TCD 43597

GDB 870

TCD 43930

GDB 815

GDB TCD

1071 31642

1.664

1.658

1.633

1.636

GDB TCD

974 28758

1.665

1.659

1.634

1.637

GDB TCD

1328 39008

1.674

1.667

1.642

1.646

GDB TCD

1320 38976

1.665

1.659

1.634

1.637

Relative response factor, acrolein/C,H, = 1.651. Relative standard deviation: 0.8846.Confidence interval at the 9546 confidence level: *0.4646. TCD: Gow-Mac Pretzel. Semi-diffusion cells. Measuring cells in series. Filaments: WX. Current: 220 mA. Temperature 150 C.Carrier gas: H1, 3.6 L/h. References on p. 626.

612

balance detector is used, since it operates directly on the column eluent. Calibration is very time consuming and expensive and should be limited as much as possible. Thus, an assessment of these phenomena and of their influence on the relative response factors becomes necessary. The analyst must be able to find out under what conditions the relative response factors are constant and to which extent the optimization of the experimental conditions may minimize the fluctuations or drift of response factors. 1. Influence of the Chromatographic System

The most important sources of influence of the chromatographic equipment and system on the quantitative responses are the possible reactions of pyrolysis or catalytic decomposition which may be experienced by some analytes in the sampling system, especially if it is very hot, or in the column, when the support has not been properly deactivated. The extent to which these phenomena take place may be most easily studied using the GDB as described in the previous section. A calibration mixture is injected into the chromatograph. If the composition of this mixture as derived from the peak areas measured with the GDB is the same as the known composition of the injected mixture, the chromatograph is chemically inert and does not modify the composition of this kind of mixture. If a significant variation is observed, the origin of the change can be located as follows. The same procedure is repeated after adjusting the temperature of the sampling system, replacing the sampling system, the sampling port or its insert by a similar part made of a different material. A change in the composition measured for the mixture under study demonstrates that the sampling system is implicated in the composition changes. The problem can usually be fixed by the replacement of the faulty part. If the injection system only is responsible, the problem can usually be fixed rapidly. The possible influence of the column on the composition of the eluent can be assessed by using the GDB as a calibration detector. A second column, identical to the first one, is placed on-line with the detector to calibrate, after the splitter (see Figure 14.15). The pneumatic resistances are adjusted to restore the splitting ratio to the proper value. If the relative response factors determined in the conventional way (see Figure 14.10) are different from those measured with the new setting, it means that the composition of the analyzed mixture is selectively altered during its elution. Although it has almost always been possible to find conditions under which the analytes do not react and and are not destroyed, even partially, during the chromatographic analysis, the possibility of this phenomenon should always be investigated by the analyst when considering the quantitation of a new type of mixture. Another test of the integrity of the eluted mixture can be obtained by using two identical GDBs, instead of a GDB and a regular detector in a setting similar to the one shown on Figure 14.15, and measuring the relative response factors which should now be identical to the ratios of the factors given by equation 9 for the two compounds.

613

Column A 1

J

D

B

I

-

Figure 14.15. Study of the influence of on-column reaction or adsorption on the response factors.

In all these experiments it should be born in mind that the repeatability of the determination of response factors with a GDB does not exceed approximately 2%. Only changes in composition corresponding to larger variations are significant.

2. Influence of the Characteristics of a Thermal Conductivity Detector Because of the rapidity with which a large number of precise data can be acquired, the systematic use of the GDB permits the detailed investigation of the parameters which determine the response of detectors. For the thermal conductivity detector (TCD), we have studied the influence of the geometrical design of the detector cells, of the nature and temperature of the wires and of the temperature of the cell block. As discussed in the following, only the geometrical design was found to have a significant influence on the relative response factors. In this work we have essentially used chlorinated alkanes with 1 and 2 carbon atoms. There are simple relationships between the response factors of closely related compounds and their molecular weight (24). For example, the plot of the relative response factors of the four chloromethanes versus their molecular weight or the number of their chlorine atoms is a straight line (cf. Figure 14.16). These relationships can be used in the study of the influence of the detector parameters on its response. The influence of a number of detector parameters on the detector response factors is illustrated in Tables 14.6 to 14.16. It is also discussed in Section 111, Chapter 10. a. Geometry of the Detector

Results in Figure 14.16 show that for different detector designs (TCD) there are different relative response factors. The slope of the straight line obtained for the plot of the response factors of chloromethanes versus their molecular weight is lower for flow-through cells than it is for semi-diffusion cells and it is lower for measuring cells in series than for cells in parallel. The steeper straight line (semi-diffusion, cells References on p. 626.

614 ?------A

3-

2-

MW b

0

50

100

150

200

Figure 14.16. Plot of response factors of chlorinated hydrocarbons on a TCD versus the molecular weight. A. Two semi-diffusion cells, in parallel. B + C. Two semi-diffusion cells, in series. D. Two flow-through cells, in parallel. E.Two flow-through cells, in series.

in parallel, detector A) is 18% steeper than the shallower one (flow through, cells in series, detector E). Detectors of the D-type give smaller relative response factors than detectors of the A-type, which were very popular at the beginning of gas chromatography (25). The analyst should carefully refrain from using relative response factors published in the literature without sufficient detail regarding the design and the operating conditions of the detector. Values of relative response factors are given in Tables 14.6 to 14.16,for a number of compounds. They are to be used only under the same operating conditions. Values in Tables 14.9 to 14.13,14.15 to 14.17 and 14.19 correspond to semi-diffusion cells placed in series (see Figure 14.16, B + C). Values in Table 14.14 correspond to flow-through cells placed in series (see Figure 14.16,E) and values in Table 14.18 to flow-through cells placed in parallel on the effluent stream (see Figure 14.16,D). From table to table the temperature, the flow rate and the compounds differ. The only difference between the experimental conditions under which the response factors in Tables 14.13 and 14.14 were measured is the nature and design of the detector; carrier gas, flow rate, temperature, wires and bridge current were the same.

615

TABLE 14.6 Weight Relative Response Factors for the Thermal Conductivity Detector Reference: Air = 1 C2H4

SH2

so2 N2

M

f

a/f

28.05 34.08 64.07 28.013

0.93 1.10 1.81 0.94

2 1.4 1.6 3

(W

Semi-diffusion cells, measuring cells in series (Pretzel Gow-Mac, Fractomatic TC Carlo Erba). Filaments: 4 x WX; current: 250 mA; temperature: 80 O C; carrier gas: hydrogen; flow rate: 3 L/h. TABLE 14.7 Weight Relative Response Factors for the Thermal Conductivity Detector Reference: C2H4= 1

M

f

a/f (W)

H2O Acetaldehyde Acetone Acrolein Acetic acid Propionic acid Acrylic acid

18.02 44.05 58.08 56.06 60.05 74.08 72.06

0.78 1.375 1.64 1.65 1.77 2.025 1.98

0.9 0.9 0.9 0.9 1.1 1.4 1.65

Semi-diffusion cells, measuring cells in series (Pretzel Cow-Mac, Fractomatic TC Carlo Erba). Filaments: 4 x WX; current: 220 mA; temperature: 150°C; carrier gas: hydrogen; flow rate: 3.6 L/h.

TABLE 14.8 Weight Relative Response Factors for the Thermal Conductivity Detector Reference: C2H4= 1

M

f

u/f (46)

Air Vinyl chloride H2O Vinyl acetate

29.02 62.50 18.016 86.09

1.11 1.57 0.895 1.085

1.3 2.2 2.6 2.4

Semi-diffusion cells, measuring cells in series (Pretzel Gow-Mac, Fractomatic TC Carlo Erba). Filaments: 4 x WX; current: 250 mA; temperature: 140 C; carrier gas: hydrogen; flow rate: 3 L/h.

b. Nature of the Detector Wires Measurements were carried out with different filaments, in order to study the influence of the nature of the wire metal. A TCD, with semi-diffusion measuring cells in series (Pretzel Model, Gow-Mac) was used as detector and a GDB as a calibration detector. This combination permits the determination of response factors that are independent from the column used. Data in Table 14.17 and Figure 14.17 report the response factor of trichlorol,l,l-ethane relative to ethylene, carried out under these conditions. It is seen that the variation of the response factor with the nature of the wire is not significant. Values in Tables 14.6 to 14.16 were obtained with tungsten wires (WX from Gow-Mac). References on p. 626.

616 TABLE 14.9 Weight Relative Response Factors for the Thermal Conductivity Detector Reference: C2H4= 1 Ethane Propane Propylene Butane I-Butene cis-2-Butene trans-2-Butene Isobutane Isobutene Oxygen Nitrogen Carbon monoxide Carbon dioxide

M

f

30.07 44.09 42.08 58.12 56.10 56.10 56.10 58.12 56.10 31.999 28.013 28.01 44.01

1.02 1.24 1.22 1.43 1.33 1.40 1.40 1.77 1.465 1.37 1.14 1.15 1.55

a/f (W) 2 1.4 0.9 0.7 2.25 0.3 0.5 0.1 0.7 1.7

1.2 0.5 0.95

Semi-diffusion cells, measuring cells in series (Pretzel Gow-Mac, Fractomatic TC Carlo Erba). Filaments: 4WX; current: 220 mA; temperature: 65OC; carrier gas: hydrogen; flow rate: 3.6 L/h. TABLE 14.10 Weight Relative Response Factors for the Thermal Conductivity Detector

-

Reference: C,H, 1 Methyl chloride Methylene chloride Chloroform Carbon tetrachloride Ethyl chloride 1,l -Dichloroethane 1,2-Dichloroethane 1JJ-Trichloroethane 1,1,2-Trichloroethane

1,1.1,2-Tetrachloroethane 1,1,2,2-Tetrachloroethane Pentachloroethane Hexachloroethane Vinyl chloride Vinylidene chloride 1,2-Dichloroethylene cistram-

Trichloroethylene Perchloroethylene

M

f

50.49 84.93 119.38 153.82 64.52 98.96 98.96 133.41 133.41 167.85 167.85 202.30 236.74 62.50 96.95

1.51 2.15 2.77 3.17 1.805 2.38 2.31 2.725 2.79 3.45 3.40 3.88 4.315 1.765 2.34

o/f 1.2 1.3 2.2 1.2 2.2 2.6 0.8 1.4 3.8 2.4 1.4 1.2 3.8 1.2 2.6

96.95 96.95 131.39 165.83

2.33 2.32 2.84 3.30

0.8 1.2 2 1.2

(W

Semi-diffusion cells, measuring cells in series (Pretzel Gow-Mac, Fractomatic TC Carlo Erba). Filaments: 4WX; current: 250 mA; temperature: 200 O C; Carrier gas: hydrogen; flow rate: 3 L/h.

c. Temperature of the Wires

The same system and wires were also used in a study of the influence of the wire temperature on the relative response factors. The data reported in Table 14.17 and

617 TABLE 14.11 Weight Relative Response Factors for the Thermal Conductivity Detector Reference: C2HI = 1 Methyl chloride Methylene chloride Chloroform Carbon tetrachloride Ethyl chloride 1,l-Dichloroethane 1,2-Dichloroethane l,l,l-Trichloroethane 1,l ,2-Trichloroethane

1,1,1,2-Tetrachloroethane 1,1,2,2-Tetrachloroethane Pentachloroethane Hexachloroethane Vinyl chloride Vinylidene chloride 1,2-Dichloroethylene cistransTrichloroethylene Perchloroethylene

M

f

a/f 6)

50.49 84.93 119.38 153.82 64.52 98.96 98.96 133.41 133.41 167.85 167.85 202.30 236.74 62.50 96.95

1.45 1.90 2.41 2.95 1.60 2.01 2.24 2.31 2.14 3.24 3.30 3.87 4.63 1.57 2.05

0.8 1.6 3.2 2 1.8 1.4 3.6 2.8 1 1.8 1.2 2 0.8 1 2

96.95 96.95 131.39 165.83

2.30 2.08 2.53 3.0

1.8 2.8 1.6 2

Flow-through cells, measuring cells in series (Bendix PGC). Filaments: 4xWX; current: 250 mA; temperature: 200 O C; carrier gas: hydrogen; flow rate: 3 L/h.

Figure 14.17 show that the wire current, i.e. the wire temperature does not control the response factors. For currents between 100 and 250 mA the response factors remain unchanged. At 300 mA there is a slight increase of the relative response factor of trichloro-l,l,l-ethane, which may correspond to the onset of thermal degradation of the chlorinated compound. TABLE 14.12 Weight Relative Response Factors for the Thermal Conductivity Detector Reference: C2H4 =1 Air

M

f

a/f (W

28.96 16.04 30.07 58.12 64.07 34.08 44.01 60.07 76.13 18.02

1.08 0.72 1.13 1.48 1.84 1.14 1.49 1.70 1.76 0.85

1.8 1 1.8 1.3 1.6 0.9 1.3 1.2 3.4 4

Semi-diffusion cells, measuring cells in series (Pretzel Gow-Mac, Fractomatic TC Carlo Erba). Filaments: 4 X WX; current: 220 mA; temperature: 130 C; carrier gas: helium; flow rate: 3 L/h. References on p. 626.

618

TABLE 14.13 Weight Relative Response Factors for the Thermal Conductivity Detector

-

Reference: C2H4 1 H2O Acetaldehyde Methanol Ethanol n-Propanol Isopropanol n-Butanol Isobutanol rerr-Bu tanol Methyl acetate Ethyl acetate Acetic acid Formic acid Propionic acid Methoxy-2-ethanol Ethylene glycol p-DioTane 3-Methyl-1,2-dioxolane

M

f

o/f

18 44 32 46 60 60 74 74 74 74 88 60 46 74 76 62 88 88

0.81 1.30 1.07 1.32 1.59 1.53 1.80 1.72 1.79 1.75 1.87 1.52 1.34 1.64 1.85 1.62 2.17 2.05

0.9 2.3 0.9 1.1 3.6 2.2 0.9 0.25 0.9 0.9 1.5 1.3 1.3 1.9 1 1.2 2.3 10

Semi-diffusion cells. measuring cells in series (Pretzel Gow-Mac, Fractomatic TC Carlo Erba). Filaments: 4 x WX; current: 250 mA; temperature: 145OC; carrier gas: helium; flow rate: 3 L/h.

TABLE 14.14 Weight Relative Response Factors for the Thermal Conductivity Detector Reference: C2H4= 1 1,fButadiene Styrene ~

M

f

o/f (%)

54.09 104.14

1.70 2.54

0.5 0.9

Semi-diffusion cells, measuring cells in series (Pretzel Gow-Mac, Fractomatic TC Carlo Erba). Filaments: 4 x WX; current: 250 mA; temperature: 150 C; carrier gas: helium; flow rate: 1.5 L/h.

TABLE 14.15 Weight Relative Response Factors for the Thermal Conductivity Detector Reference: C2H4 = 1 Methanol Ethanol n-Propanol Isopropanol Acetone Methyl ethyl ketone Methyl isobutyl ketone Diethyl ether Methyl acetate Ethyl acetate

M

f

o/f (W)

32.04 46.07 60.09 60.09 58.08 72.10 100.16 74.12 74.08 88.10

0.98 1.34 1.56 1.59 1.535 1.72 2.01 1.73 1.80 1.92

1.8 0.7 1.1 1.1 0.6 1.6 1.1 1 1 1

Flow-throughcells, measuring cells in parallel (Fractovap Model GT, Carlo Erba). Filaments: 4 X WX; current: 250 mA; temperature: 125OC; carrier gas: helium; flow rate: 3 L/h.

619 TABLE 14.16 Weight Relative Response Factors for the Thermal Conductivity Detector Reference: C,H, = 1 Hydrogen Oxygen Nitrogen Methane Ethane Carbon monoxide Carbon dioxide Propane n-Butane Isobutane

M

f

2.016 31.99 28.02 16.04 30.07 28.01 44.01 44.09 58.12 58.12

0.0116 1.95 2.18 0.40 0.92 2.22 4.0 1.62 2.58 2.47

o/f ($1 0.3 0.4 0.5 0.4 0.4 0.4 0.9 0.5 1.6 0.8

Semi-diffusion cells, measuring cells in series (Pretzel Gow-Mac, Fractomatic TC, Carlo Erba). Fdaments: 4xWX;current: 110 mA; Temperature: 100OC; carrier gas: argon; flow rate: 3 L/h.

The relative standard deviation of the whole series of measurements of the response factors (Table 14.17) is 1.2%,which confirms the negligible influence of the nature and temperature of the wire on the relative response factors. The same conclusion can be derived from the observation that changes in the carrier gas flow rate do not bring about any significant variation of these response factors. The change in the response factor of tetrachloroethylene relative to dichloro-1,Zethane when the carrier gas (hydrogen) flow rate increases from 2 to 5 L/hour is less than 0.7% at constant bridge current and detector temperature. Most values in Tables 14.6 to 14.15 were obtained with bridge currents of 220 and 250 mA. Only in Table 14.16, the bridge current is 110 mA but the carrier gas is argon, which has a much lower heat conductivity. With this gas the bridge current should be lower. TABLE 14.17 Influence of the Nature and Temperature of the Wires on the Response Factor Nature of the Wires

Current of the Wheatstone Bridge 100 150 200

f (average) 250

300

W

2.70

2.69

2.67

2.69

2.73

wx

2.78

2.16

2.73

2.74

2.83

2.79

2.78

2.78

2.83

2.72

2.77

2.65

2.82

w2x AU !(average) (0)

2.74 2.76 (0.97%)

2.74 (1.59%)

2.74 (1.79%)

of a TCD

2.71 (1.93%)

(0)

2.70 (0.77%) 2.77 (1.40%) 2.79 (0.88%) 2.74 (2.24%)

2.80 (1.70%)

Relative response of trichloro-l,l,l-ethane with respect to ethylene (w/w).

f average: 2.75; relative standard deviation: 1.17%. References on p. 626.

620 f

C # J C ~ ~ / CI ~H 2 75 ~ 4 %117

3.0-

8

N

"

I

100

I

150

I

I

I

200

250

300

mA

*

Figure 14.17. Influence of the nature and temperature of the wires of a TCD on the response factor of 1,1,1-trichloroethane relative to ethylene.

d. Temperature of the Detector Block

The results reported in Table 14.18 show a variation of the response factor of tetrachloroethylene relative to dichloro-1,2-ethane less than 0.9% when the block temperature is increased from 130 to 200 O C. This factor does not seem to contribute significantly. The only difference between the experimental conditions under which the tabulated data were obtained is the block temperature for the following groups of Tables: Tables 14.6, 14.8, 14.10 (carrier gas: hydrogen, flow rate: 3 L/hour, bridge current: 250 mA); Tables 14.7 and 14.9 (camer gas: hydrogen, flow rate: 3.6 L/hour, bridge current: 220 mA). TABLE 14.18 Influence of the Temperature of the Detector Block on the Response Factor of a TCD Temperature

Response Factor

("C) 130 150 180 200

1.417 1.398 1.405 1.387

f (average)

1.401 (0.9%)

(0)

Response factor of perchloroethylenerelative to dichloro-1,2-ethane. TCD: semi-diffusion cells. Measuring cells in series. Current: 250 mA. Carrier gas: H,,3 L/h.

621

e. Long-Term Stability of the Response Factors The response factors of all chloromethanes and chloroethanes relative to ethylene have been determined a first time, then, after extensive use of the chromatograph followed by a total overhaul, taking it apart and putting it together again, they have been determined a second time, six months later. The coefficient of variations did not exceed 25%.This means that TCD’s should be calibrated carefully once. Then an infrequent check (once every six months or a year) of the response factors for a few selected compounds would be sufficient, as long as no major change is made in the detector setting. The use of any column which tends to modify relative response factors should be avoided. Similarly, relative response factors determined with a given detector can be used with another one of the same type. It is recommended, however, to check that the correct values are obtained with a few compounds. 3. Influence of the Characteristicsof a Flame Ionization Detector In the case of the flame ionization detector (FID), we have investigated the influence on the response factor of the geometry of the detector, the nature of the TABLE 14.19 Weight Relative Response Factors for the Flame Ionization Detector Reference: Freon 12 = 1

M

f

o/f

Freon-11 CFCl Freon-12 CF,CI, Freon-21 CHFCI, Freon-22 CHF,CI Carbon tetrachloride

137.4 120.8 102.93 86.5 153.84

1.49 1 0.73 0.86 0.625

0.6

0.5 0.5 0.9

Two parallel plate electrodes (Fractomatic FID from Carlo Erba). Flow rates: camer gas (nitrogen) 3 L/h; hydrogen: 2 L/h; air: 15 L/h. TABLE 14.20 Weight Relative Response Factors for the Flame Ionization Detector Reference: C,H, = 1 Acetic acid Propionic acid Acrylic acid Methacrylic acid Maleic anhydride Acetaldehyde Propionaldehyde Acrolein Methacrolein Furan

M

f

60.054 74.087 72.065 86.092 98.060 44.054 58.080 56.065 70.092 68.076

4.43 2.765 2.78 2.15 3.55 3.70 2.20 2.01 1.65 1.765

a/f

(W

2

0.5 2.4 2.4 3 2 2 0.6 1.7 0.7

Two parallel plate electrodes (Fractomatic FID from Carlo Erba). Flow rates: carrier gas (nitrogen) 1 L/h; hydrogen: 0.9 L/h; air: 6 L/h. References on p. 626.

622

TABLE 14.21 Weight Relative Response Factors for the Flame Ionization Detector Reference: G H , = 1 Propane Propylene n-Butane lsobutane I-Butene Isobutene cis-2-Butene trans-2-Butene 1,3-Butadiene

M

f

o/f

44.097 42.081 58.124 58.124 56.108 56.108 56.108 56.108 54.092

1.16 1.115 1.14 1.14 1.18 1.12 1.11 1.145 1.09

1.5 1.1 0.7 1 2 1.3 1.8 2 1.2

(41)

Two parallel plate electrodes (Fractomatic FID from Carlo Erba). Flow rates: carrier gas (nitrogen) 1 L/h; hydrogen: 0.9 L/h; air: 6 L/h. TABLE 14.22 Weight Relative Response Factors for the Flame Ionization Detector Reference: GH, = 1 Diethyl ether Methyl bromide Ethyl bromide Ethyl acetate Methyl bromoacetate Ethyl bromoacetate Ethyl chloroacetate Ethyl ethoxyacetate Chloroacetyl chloride Bromoacetyl chloride Bromoacetyl bromide Bromoacetic acid Chloroacetic acid Ethyl alcohol

M

f

o/f

74.12 94.95 108.98 88.10 153 167.01 122.55 132 112.95 157.41 201.87 138.96 94.50 46.07

1.80 6.62 3.84 2.57 6.85 4.73 3.41 2.62 8.77 11.06 14.64 11 10.50 2.20

2.2 1.4 2 1.7 2.4 2.5 2 1.2 0.8 0.5 1.3 1.5 1.1 1.5

,

Two parallel plate electrodes (Fractomatic model GT from Carlo Erba). Flow rates: carrier gas (nitrogen) 3 L/h; hydrogen: 2 L/h; air: 15 L/h. TABLE 14.23 Weight Relative Response Factors for the Flame Ionization Detector Reference: C6H6= 1 Toluene Ethylbenzene Styrene Isopropylbenzene Propylbenzene Methyl chloride Methylene chloride Chloroform Carbon tetrachloride Tetrahydrofuran Cyclohexane Cyclohexene

M

f

92.13 106.16 104.14 120.19 120.19 50.49 84.94 119.39 153.84 72.12 84.16 70.14

1.05 1.08 1.03 1.02 1.025 4.77 9.13 14.35 20.64 1.87 1.12 0.98

o/f (I) 1.8 1.7 0.8 1.4 1.1 1.8 0.9 1.4 0.8 1.7 2 2

Polarized jet (Fractovap model 2400 from Carlo Erba). Flow rates: carrier gas (nitrogen) 1 L/h; hydrogen: 2 L/h; air: 15 L/h.

623

1I f

FID

HC HC ar/C,H,

f

I I

t

Chlorinated HC/C6H6

I

I

.

I

I I

‘2’6 I

20

I

40

I

I

60

t

80

1

I

100

I

1

120

I

140

MW 160

Figure 14.18. Influence of the geometrical design of a FID on the relative response factors of various compounds: chlorinated and aromatic hydrocarbons, etc. Plot of response factors relative to benzene versus molecular weight. + , polarized jet. 11, parallel collecting electrodes.

carrier gas and the flame temperature. The same method, involving the use of the GDB as just described, has been used. Response factors measured under various sets of experimental conditions are reported in Tables 14.19 to 14.23. a. Geometty of the Detector

Two basic designs are widely used for the FID (see Chapter 10):

- a grounded jet, with two parallel electrodes, placed symmetrically by respect to the flame (see data in Tables 14.19 to 14.22). a positively polarized jet, with a negatively polarized collecting electrode (see data in Table 14.23). Novak et al. have shown that the relative response factors obtained with these two types of detector may be very different (27). They also claimed that the second type of detector, with a polarized jet, gives more reproducible quantitative results than those of the first type, because the influence of the distance between the collecting electrodes is much larger with parallel electrodes. These results are in agreement with our data reported on Figure 14.18, where the relative response factors of hydrocarbons and chlorohydrocarbons are plotted versus the molecular weight (28). For each group of compounds and each detector type, the plot is a straight line. There is no predicting the response with the parallel -

References on p. 626.

624

plate detector knowing the response with the polarized jet detector. For example, with alkanes and aromatic hydrocarbons the parallel plate detector gives larger response factors than the polarized jet FID; with chloromethanes the opposite is true; with chloroethanes, the responses are almost identical. Accordingly, the value of the response factors, absolute as well as relative, depends on the detector with which they are measured and it is impossible to use response factors which have been determined with other instruments and are published in the literature without complete documentation. The use of the GDB permits a rapid calibration of all FIDs and their recalibration when some detail of their design is changed. b. Flame Temperature

The flame temperature depends essentially on the jet dimensions and the hydrogen flow rate. The influence of this flow rate has been one of the first parameters of the FID to be studied. Work by Ettre (29,30),Ongkiehong (31), Desty et al. (32), Halasz (33) has shown significant variations of the response factors with the hydrogen flow rates. Hainova et al. have reported variations.in excess of 15 to 20% for the relative response factors of oxygen derivatives (34). Extreme caution is required when quantitative measurements have to be carried out using response factors found in the literature. It has been shown rather recently that with a hot flame, obtained with a large hydrogen flow rate and by using oxygen instead of air, the chemi-ionization effect is markedly decreased and that the response factors for chloroalkanes and for the corresponding alkane are almost the same (35,36).This would permit the achievement of quantitative analysis of mixtures of chloroalkanes and alkanes without previous calibration, provided the flame gas flow rates be properly optimized. The effect of the hydrogen flow rate on the relative response factor of trichlorol,l,l-ethane and trichloroethylene (w/w) has been studied (28). The results are reported on Figure 14.19.The response factor is equal to 1.0 for flow rates between f

C2HJC13/ C2HClj

4

Figure 14.19. Influence of the hydrogen flow rate on the response factor of l,l,l-trichloroethane relative

to trichloroethylene.

625

1 and 2 L/hour. A decrease of the flow rate down to 0.6 L/hour reduces the response factor to 0.85, while an increase up to 4 L/hour reduces it only slightly, to 0.97. For a flow rate between 1.1 and 1.5 L/hour there is almost no influence from moderate changes of the flow rate on the response factor. c. Nature of the Carrier Gas

The influence of the nature and flow rate of the carrier gas on the response factors seems to be less important than the influence of the hydrogen flow rate. It is obvious, however, that there should be some effect, through changes in the flame temperature, as well as because of the larger dilution of the ions formed. Some results have been reported. Hainova et al. (34) have shown that the response factor increases with increasing carrier gas flow rate. An attempt to assess the influence of the nature of the carrier gas by relating the response factor to the gas thermal conductivity has not been successful (28). d. Comparison between Experimental and Calculated Response Factors As explained above, it is dangerous to use response factors found in the literature. Too many factors control the detector response and their influence is poorly known at best. The direct determination of the factors needed is a much TABLE 14.24 Comparison between Response Factors Sternberg Compound CH3Cl CH2C12 CHCI, CCI 4 C2HC1, C6H6

C6H5CI Styrene c6 H 5 cZ

5

Furane THF CH3C02H C, H5C02H C, H 3 C 4 H CH,CHO CH,CHCHO

M 50.49 84.93 119.38 153.82 131.40 78.00 112.50 104.14 106.16 68.07 72.00 60.00 74.00 72.00 44.00 56.06

Eff C No. 0.88 0.76 0.64 0.52 2.15 6 6 8 8 2.85 3 1 2 1.9 1 1.9

for FID Measured by Calibration and Calculated after Eff No. eq. c

Stemberg factor

FID factor

A

1.359 0.698 0.418 0.263 1.276

4.41 8.59 14.34 22.75 4.7 1 1.44 1 1.02 1.83 1.84 4.61 2.84 2.91 3.38 2.26

4.77 9.13 14.35 20.64 5.18 1 1.42 1.03 1.08 1.76 1.87 4.96 2.97 3.06 3.28 2.01

8 6 0 9 10

4.16 6 5.877 3.26 3.25 1.3 2.1 2.05 1.77 2.64

(W)

1.5 3 6 4 1 7 4 5 3 11

* Response factors relative to benzene. Eff C No. is the effective number of carbon atoms; Eff No. Eq. C is the effective number of equivalent carbon atoms. See Chapter 10, Section IV.7.1, for the development of the Sternberg calculation. References on p. 626.

626

safer proposition. These reservations extend to the use of the Sternberg method of prediction of response factors (37), which should be used only when a quantitative result is urgently needed or when calibration is extremely difficult, costly or dangerous to carry out. The method suggested by Sternberg et al. to predict response factors makes use of calibration results obtained long ago, with old FID models, for various test compounds (37). It permits the prediction of the response factors using a system of increment contributions (see Chapter 10, Section IV.7). The advantage of the method is the exclusive use of atomic contributions. The drawbacks are that it daes not take the molecular structure into account, nor the polarisability, and it is somewhat inaccurate. Data in Table 14.24 permit a comparison between the relative response factors measured by calibration with a GDB, for a number of compounds belonging to various chemical groups, and those calculated by the Sternberg method, for the same type of detector (polarized jet). Differences between the two sets of results may be as large as 15 to 20%. It would probably be useful to revisit the principle of the method and carry out a more accurate determination of the Sternberg increments, as Clementi et al. have done for heterocyclic compounds (38). LITERATURE CITED (1) C.S.G. Phillips, in Gus Chromatography 1970, R. Stock Ed., The Institute of Petroleum, London, UK, 1971,p. 1. (2) R.S. Barratt, Analyst, 106, 817 (1981). (3) G.O. Nelson, Controlled Test Atmospheres, Principles and Techniques, Ann Arbor Science Publishers, Ann Arbor, MI, 1971. (4) J.L. Excoffier and G. Guiochon, Chromutographiu, 15. 543 (1982). (5) J.E. Lovelock, in Gas Chromatography 1960, R.P.W. Scott Ed., Butterworths, London, UK, 1960,p. 26. (6) I.A. Follis and R.P.W. Scott, J. Chromatogr., 11, 1 (1963). (7) H.P. Williams and J.D. Wmefordner, J. Gas Chromatogr., 4, 271 (1966). (8) J.J. Ritter and N.K. Adams, Anal. Chem. 48, 612 (1976). (9) J.E. Lovelock and A.J. Watson, J. Chromatogr., 158, 123 (1978). (10) D.H. Desty, C.J. Geach and A. Goldup, in Gar Chromatography 1960, R.P.W. Scott Ed., Butterworths, London, UK, 1960,p. 46. (11) A. Goldup and M.T. Westaway, Anal. Chem., 38, 1657 (1966). (12) J.M. McKelvey and H.E. Hoescher, Anal. Chem., 29. 123 (1957). (13) P. Devaux and G. Guiochon, Bull. Soc. Chim France, 1967, 1404. (14) A.C. Savitsky and S . Siggia, Anal. Chem., 44, 1712 (1972). (15) A.E. OKeefe and G.C. Ortman, Anal. Chem., 38, 760 (1966). (16) D.P. Lucero, Anal. Chem.. 43, 1744 (1971). (17) I. Demaio, Instrument. Technol., 19, 37 (1966). (18) R.N. Dietz, E.A. Cote and J.D. Smith, Anal. Chem., 46, 315 (1974). (19)'H.J. van de Wiel, J.W. Uiterwijk and T.A. Regts, in Studies in Enuironmental Science, 2. Air Pollution Reference. Merhoh and Systems, Elsevier, Amsterdam, The Netherlands, 1978. (20) F.J. Debbrecht and E.M. Neel, in Calibration in Air Monitoring, 7, ASTM Special Technical Publication 598, Philadelphia, PA, 1976,p. 55. (21) L.M. Carson and K.L. Uglum, J. Gas Chromutogr., 3, 208 (1965). (22) C.L. Guillemin, F.Auriaurt and P. Blaise, Z. Anal. Chem., 227, 260 (1967).

627 (23) (24) (25) (26) (27) (28) (29) (30)

(31) (32) (33) (34) (35) (36) (37) (38)

C.L. Guillemin, F. Auricourt and J. Vermont, Chromutographia, 1, 357 (1968). C.L. Guillemin, F. Auricourt, J. Du Crest and J. Vermont, J. Chromatogr. Sci., 7,493 (1969). J. Vermont and C. Guillemin, A n d Chem., 45, 775 (1973). E.F. Barry and D.M. Rosie, J. Chromatogr., 103, 180 (1975). J. Novak, P. Bocek, L. Keprt and J. Janalr, J. Chromutogr., 51, 385 (1970). C.L. Guillemin and J. Vermont, unpublished data. L.S. Ettre and N. Claudy, Chem. Can., 12, 34 (1960). L.S. Ettre, J. Chromutogr., 8, 525 (1962). L. Ongluehong, in Gas Chromatography 1960, R.P.W. Scott Ed., Buttenvorths, London, UK, 1960, p. 7. D.H. Desty, C.J. Geach and A. Goldup, in Gas Chromatography 1960, R.P.W. Scott Ed., Butterworths, London, UK,1960,p. 46. I. Halasz and N. Schneider, in Gas Chromatography, N. Brenner, J.E. Callen and M.D. Weiss Eds., Academic Press, New York, NY, 1962, p. 287. 0. Hainova, P. Bocek, J. Novak and J. Janak, J. Gas Chromatogr., 4 , 401 (1967). A.E. Karagozler and C.F. Simpson, J. Chromatogr., 150, 329 (1978). T.A. Gough, M.A. Pringuer and C.J. Woollam, J. Chromutogr., 150, 533 (1978). J.C. Sternberg, W.S. Gallaway and D.T.L.Jones, in Gas Chromatography, N. Brenner, J.E. Callen and M.D. Weiss Eds., Academic Press, New York, NY, 1962, p. 231. S. Clementi, G. Savelli and M. Vergoni, Chromatographia, 5, 413 (1972).

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629

CHAPTER 15

QUANTITATIVE ANALYSIS BY GAS CHROMATOGRAPHY Measurement of Peak Area and Derivation of Sample Composition TABLE OF CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . ............................. I. Measurement of the Peak Area by Manual n... . . . . . . . . . . . . . . . . . . . . 1. Area of the Triangle Made by the Base Line and the Inflexion Tangents . . . . . . . . . . . . . 2. Product of the Peak Height by the Width at Half-Height ........................ 3. The Condal-Bosch Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Measurement of the Peak Area by Semi-Automatic Methods .................. ................................ 1. Electromechanical Integrators 2. Electronic Integrators . . . . . . . . . . . . . . . . . . . . . . . .

629 633 633

635 635

................................. 3. 4. 5. 6.

Acquisition Frequency . . . . ....................................... Noise Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............... Peak Detection . . . . . . . . . . . Peak Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

................................

8. Conclusion . . . . . . IV. Area Allocation for Part

................ ved Peaks . . . . . . . .

641 642

645

a. Manual Calculations . . . . . . . . . . . . . . . . . . . . . . . . . .

............................... V. Analytical Procedures for the Determination of the Composition of the Sample . . . . . . . . . . 1. Internal Normalization of Peak Areas . . . . . . . . . . . ................ 2. Internal Normalization of Corrected Peak Areas . . . . 3. Standard Additions . . . . . . . . . ............................. 4. Internal Standard ................. 5. External Standard . . . . . . . . . . . . . . . . . . . . . . . . . 6. Deferred Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Choice of Numerical Units Literature Cited . .

........

649 650 651 652 653 655

................

INTRODUCTION Quantitative analysis can, in principle, be carried out on the basis of either peak height or peak area. As we have seen in Chapter 13, however, the repeatability of peak area is much better than that of peak height. The effect of column temperature on peak area is negligible, while it is very important on peak height since the References on p. 658.

630

retention time and the band width increase rapidly with decreasing temperature (see Chapter 3). The influence of the fluctuations of the experimental parameters which control the way the injection is carried out is much stronger on the peak height than on the peak area (see Chapter 13, Tables 13.3 and 13.4). Throughout this chapter, we assume that the response of the detector is linear. It is the implicit assumption made when relating the peak area to the amount of the corresponding component in the sample. It is extremely difficult to work with a non-linear detector, unless extensive absolute calibration is made, and a response function derived empirically (1). Then a computer is required, in practice, to derive a corrected response proportional to the concentration or to the mass flow of compound in the detector. This response can then be integrated and handled as described below. Petitclerc and Guiochon (2) have shown that for a deviation of 1% from linearity in the detector response, the relative error made in the calculation of the peak area is approximately 0.7%. Deviation of the detector response from linearity may result in very significant determinate errors. In so far as the detector response is linear, the peak area is measured by integration. This procedure has long been carried out manually; it still is done this way in a surprisingly large number of cases and this is why we shall first review the manual methods. Various electronic techniques permit the automatic derivation of the peak area. Whatever the method used, the main problems are similar: when and on what basis should we decide to start and stop the integration process? how is the base line interpolated under the peaks? how is the area calculated? how is the area of a group of incompletely resolved peaks allocated between its independent components? These problems are thoroughly discussed here. The solutions chosen by equipment manufacturers and software designers should be understood by analysts, at least in their broad outlines, as well as the constraints within which engineers and programmers must work, because these solutions have serious consequences on the accuracy and precision of our measurements. The precision which can be expected from the different methods of peak area measurements discussed in this chapter are summarized in Table 15.1. These are TABLE 15.1 Expected Precision of Peak Area Measurements Method of measurement used Triangulation: Inflexion tangents Height X half-width Condal-Bosch Cut and weigh Planimetry Electromechanical integrators Digital integrators Computers

Expected precision

f 4% f 2.5%

f 2% f 1.7%

f 4% f 4% f 3% f0.556

631

average results, which can be expected in normal situations. Careful selection of experimental conditions and of equipment settings, together with great attention to detail may permit an improvement. Operation around the limit of performance, in trace analysis for example, yields considerably degraded results.

I. MEASUREMENT OF THE PEAK AREA BY MANUAL INTEGRATION In principle the manual methods of integration should be more accurate than the automatic ones, since the analyst is directly involved in the critical decisions which have to be made in all cases, regarding the integration thresholds and the area allocation. The criteria available are not easily quantifiable, however, and much room is left for intuition and experience, while precision is only moderate. Furthermore these procedures are long and terribly boring, so the task is usually entrusted to the less qualified members of the team, which nullifies the main advantage presented by the procedures. The use of interactive software is certainly a much more effective method of using the skill and experience of an analyst by presenting him with facts and relevant questions and showing him in real time the consequences of his decisions. The use of the manual methods of integration has been reviewed by Ball, Hams and Habgood (3,4). They have also presented a classical discussion of the precision of these methods and of the various parameters that control it. The simple plate theory of chromatography predicts a Poisson distribution for the band profile, but with the efficiency currently achieved in gas chromatography, it is not possible to distinguish between a Poisson and a Gaussian profile (5-7). In

Wr 40

I

,-----.-I

Figure 15.1. Characteristics of a Gaussian profile. References on p. 658.

632

fact the profile of chromatographic peaks is often quite different from a Gaussian profile, but this remains a good approximation for most discussions on the handling of chromatographic signals. The profile of a Gaussian band is:

where A is the peak area, (I its standard deviation and maximum value of the signal is:

1,

the retention time. The

so the peak area is related to the peak height and its standard deviation by: A

=HUG

(3)

Several manual methods of integration make use of this relationship. A Gaussian

I\

Figure 15.2. Measurement of peak area by triangulation.a. Area of the triangle made with the base line and the inflexion tangents. b. Product of the peak height by the width at half-height. c. Condal-Bosch method. Case of an unsymmetric peak.

633

profile is represented on Figure 15.1 where are given its main characteristics. The different manual methods discussed here are illustrated on Figure 15.2. 1. Area of the Triangle Made by the Base Line and the Inflexion Tangents If the resolution between the peak considered and its neighbors is sufficient, the peak area can be estimated from the area of the triangle formed by the base line and the two inflexion tangents (see Figure 15.2a). It is easy, by differentiation of equation 1, to show that the equations of the inflexion tangents in the reference system of the center of the Gaussian curve are:

As a consequence, the width of the triangle formed by the two inflexion tangents is equal to 40 and its height is:

de The area of the triangle is: 4uH' A'= --4Hu 2 6

By comparing equations 3 and 6 we obtain: A ' =-=4A

0.968 A

&

(7)

In theory the approximation is excellent. The error of 3.2% can be corrected easily if needed (it is a systematic error), but this is not necessary since relative peak areas are always used and the correction cancels out. In practice, however, the drawing of the inflexion tangent is rather inexact. Small errors on the correct placement of the tangents may result in large errors on the determination of the peak area. The error can be minimized by selecting a chart speed such that the slope of the inflexion tangents is about 45". Further discussion on the accuracy and precision of the method is presented in Chapter 16, Section I.2.a.

2. Product of the Peak Height by the Width at Half-Height The peak area is estimated as the product of the peak height by its width at halfheight (see Figure 15.2b). From equation 1 it is easy to derive that the width at halfheight is given by: w,,* = U

J

r

n

References on p. 658.

634

Accordingly the approximation for the peak area is: = Hw,,, = H

A”

a d m

(9)

The approximation is slightly less satisfactory than the previous one, but quite acceptable since the area ratio is unchanged, and the band profiles are not Gaussian anyway. 3. The Condal-Bosch Method This method is considered to be more accurate for the manual determination of the area of unsymmetrical peaks than the previous two methods. It is based on the use of the peak widths at 15 and 85% of the peak height, W,, and w.5,respectively (8), as illustrated on Figure 15.2~.The area is approximated by:

From equation 1 we derive that:

Accordingly: A”’

= 2.518

A”’

= 1.OO5 A

aH

(13) (14)

The Condal-Bosch estimate is 0.5% accurate for a Gaussian peak. This estimate is much more accurate than those supplied by the other methods for unsymmetrical peaks. This is an important property because calibration procedures do rely on the constancy of the ratio between the actual peak area and the estimated one. If the peak is unsymmetrical it is quite probable that its shape will change with sample size and with other column operating parameters.

4. Cutting the Peak and Weighing the Piece of Paper

I ! I I

The peak is cut with scissors, while attempting to follow its contour closely. A square of comparable area is also cut and the two pieces of paper are weighed. The main inconvenience of the method, besides the time spent in the operation, is that the chromatogram is destroyed. This can be remedied by making photocopies of the chromatograms, using good, homogeneous, heavy paper, and cutting them.

635

This is a very accurate method provided it is used with a highly homogeneous paper and that great care is taken that the water content of the paper remains constant. The cut paper should be kept for a certain time in an oven, at constant temperature and humidity. 5. Planimetry

The planimeter is an instrument composed of a lever, a little wheel and a pin. The analyst must carefully follow the profile of the peak and the interpolated base line, previously drawn with a pencil on the chromatogram, with the pin, which moves the lever. The movement of the lever makes the wheel turn and a counter records the number of turns and the fraction of turn the wheel has rotated during the travel around the peak. This number is proportional to the peak area. The proportionality coefficient is obtained by calibration, by measuring the area of a square of known base. This method is tedious and very slow. The precision depends very much on the ability of the operator to carefully follow a thin continuous line. It is comparable to the precision obtained when using the product of the height by the width at half height.

11. MEASUREMENT OF THE PEAK AREA BY SEMI-AUTOMATIC METHODS

The sequence of operations leading to the derivation of the peak area is performed automatically by an electric or electronic device. Depending on the degree of sophistication of the device, the control of the analyst is more or less indirect. It is real, though, because many of the parameters which determine the results of the integration are under his control. The recent progress made in the miniaturization of computers has permitted the development of very complex integrators which can follow a base line drift and compensate for it, detect a peak, interpolate the base line under the peak, calculate an exact integral of the detector signal, determine the retention time and sometimes the peak efficiency, and allocate the area of partly unresolved peaks in different ways, depending on the choice of the analyst. This last operation is the most critical and most controversial. Less advanced systems are still in operation in many laboratories and will also be discussed. 1. Electromechanical Integrators

The deflection of the recorder pen, or the position of the potentiometer of an electronic chart recorder, controls the rotation speed of a cylinder which in turn controls the position of a second pen. This pen draws the time integral of the signal on the side of the chart. The width of this second record is usually narrow (about 2 References o n p. 658.

636

inches) and the direction of the pen movement changes each time it hits the margin. Determination of the peak integral requires the analyst (i) to decide what are the times when the peak begins and ends, (ii) what are the corresponding positions of the integral signal and (iii) to calculate the distance between these two positions. This is a rather long and tedious procedure, to be repeated for each peak. It is not very accurate either, nor is the mechanical integrator itself. It is not surprising that these integrators have now almost disappeared. They certainly belong now to science and technology museums, not to analytical laboratories. 2. Electronic Integrators

Early electronic integrators were entirely wired systems, with no operational flexibility and no memory, carrying out on-line integration. Their parameters had to be adjusted analogically, by turning potentiometers or commuting resistors. Drift of characteristics could be a major problem. The modem electronic integrators use digital electronics. There is a whole range of devices with increasing level of performance between those which just mimic the simple on-line electronic integrators and those which make full use of the capability of modem microprocessors. Accordingly, it is somewhat arbitrary to separate them into two classes, but it is very convenient. Electronic integrators have no memory or possibly remember only the last few data points, but they carry out their calculations on the fly and cannot refer to previous events (nor store signals and wait for further events) in order to make decisions regarding the area allocation. Microprocessor integrators can. Depending on the sophistication of the microprocessor, the amount of memory incorporated in the hardware and the number of subroutines included in the software by the manufacturer, they can offer very different levels of sophistication in their handling of the data, some not entirely necessary, but the basic distinction remains whether or not they are able to take decisions based on past events kept in memory and to include logical operations in the decision process. Electronic integrators carry out calculations “on the fly”, which are most often limited to the derivation of retention times at peak maximum and of peak areas (9-11). The signal is digitized, usually by a voltage to frequency converter (VFC), and the number of pulses reaching a counter is a measure of the peak area. Accordingly, a peak sensor and a base line corrector are needed. Before the VFC, a circuit determines the derivative of the signal and compares it to a threshold, sometimes adjustable by the analyst as a function of the base line noise experienced. As long as the signal derivative is lower than the threshold the integrator detects base line and constantly updates for the detector base line level (i.e., corrects for what is taken by the instrument, rightly or wrongly, to be a base line drift). When the derivative exceeds the threshold level, a peak is detected and a voltage equal to the difference between the detector signal and the last base line update is sent to the VFC. The pulses are counted until the signal derivative exceeds another threshold, negative this time, which indicates the end of the peak (i.e., the absolute value of the negative signal derivative becomes smaller than the theshold for peak end). The area count is memorized.

631

Similarly, the retention time is determined by comparing the signal derivative to a certain threshold, very small but negative to avoid spurious detection of small peaks. This comparison starts as soon as the peak has been detected. The electronic integrator will usually supply two area counts for partially resolved peaks which are separated by a valley without return to the base line. This procedure of area allocation is often used, without real justification, because it is available. It is a dangerous practice because it supplies numbers which look precise but are not accurate. Marshall and Hulbert (12) have shown that this procedure is erroneous whenever the two peaks are different in size, i.e., practically always. An analysis bulletin is printed at the end of the analysis, recognized by the integrator when it receives a clock signal. This bulletin includes the retention times and areas of each peak detected. Most integrators may also calculate the percentage area of each peak, if needed. It is even possible to introduce response factors, but it is difficult for the integrator to deal with unexpected or missing peaks. The principles used for the electronic integrator result in a number of errors which must be understood if they are to supply accurate results. They have been the focus of a classical study by Baumann and Tao (11). Since the pulses delivered by the VFC are counted only during the time when the absolute value of the signal derivative is large enough, the two wings at the beginning and the end of the peak

Figure 15.3. Illustration of the measurement problems encountered with an “on-the-fly’’ electronic integrator. The areas lost are depicted in black. A. Losses at both ends, dues to delays in starting and stopping integration. B. Loss due to base line drift correction (fast corrector). C. Loss due to base line drift correction (slow corrector). D. Error due to base line drift during the elution of the peak (the base line corrector is inoperative).

References on p. 658.

638

are lost (see Figure 15.3A): the peak is either not yet recognized as such (the derivative is positive but too small) or its derivative is negative and too close to zero, so it is considered as finished by the peak sensor. Furthermore, if the integrator has an automatic base line drift corrector, the base line value of the signal is up-dated during the time the peak elution has begun but is not yet detected. In other words, the integrator does not sense that the peak is starting and assigns the increase in detector signal to a base line drift, for which it corrects automatically. Thus, a rectangle on the base of the peak is also lost, due to the excessive base line correction made (see Figure 15.3B). This systematic error can be reduced by adjusting the speed at which the base line drift is corrected. Especially if the detector is stable, the correction can be slow, reducing the area lost (see Figure 15.3C).Depending on the conditions under which the analysis is performed, different compromises between the systematic errors due to an excessive base line correction (Figure 15.3B) and the lack of it will be selected. Finally, if there is no base line correction during the elution of a peak while the base line drifts, serious errors take place, especially in trace analysis, at the maximum detector sensitivity (see Figure 15.3D). Since the electronic integrator detects peaks after the level of the signal derivative, it may happen that spurious peaks and spikes are detected on a noisy base line. These results are often easy to discount, but this is rather inconvenient. 111. MEASUREMENT OF THE PEAK AREA BY COMPUTER INTEGRATION Since the early days chromatographers knew that all the calculations required to translate the detector signal into numbers representing the composition of the analyzed sample should be done with a computer (13). The problem was to gain access to the machine. The first works were performed using time-shared mainframes (14-16), large minicomputers (17) or dedicated calculators with limited performance (18J9). Later on the developments of digital electronics brought generations of more and more sophisticated computers which were also smaller and smaller and less and less expensive. Now the whole system of A/D converter, interface, microcomputer and dedicated software has become affordable by almost all laboratories performing quantitative analysis. The same instrument is used as a recorder, an integrator and a calculator. It combines a memory which can store the chromatographic data and a set of programs which process it and can reprocess it if needed, and which may include routines provided by the manufacturer and routines written by the user. The main differences between the various instruments are in the degree of sophistication in the computer/analyst interaction that is allowed and in the complexity of the models used and of the calculations that can be performed. Using these data stations the analyst can perform, rapidly and with ease, what he used to do painstakingly, with pencil, ruler, French curve and eraser: draw the base line, calculate the peak areas, allocate areas to incompletely resolved peaks, and use response factors to derive sample composition (20-26).

639

Basically, the different functions of the interface and data station are (27,28): A/D conversion of the signal, and transfer to the computer memory, noise filtering, determination of the base line, by interpolation, derivation of the area under each peak, using different algorithms depending on the degree of resolution between the peaks, - derivation of the retention time, - identification of the different components of the mixture, - calculation of the concentration of each identified component, using its response factor, - printing an analytical report. These functions are discussed below in some detail. For further information the reader is referred to recent discussions on the design of interfaces for liquid chromatography (29-35). Most of the material there can be applied directly to data acquisition in gas chromatography. -

1. A/D Conversion

The output of a detector or detector “amplifier” is a voltage (e.g., with the FID the amplifier, which is rather an impedance transformer, delivers a voltage which is proportional to the current between the two electrodes). This voltage is an analog signal and must be converted into a series of digital numbers, the only kind of data the computer can handle. There should be a minimum of information lost during this conversion, so the accuracy and speed of the A/D converter should be matched to those of the detector. The frequency of the data conversion should be such that 3 data points are acquired during a time equal to the response time of the detector. The noise is minimized if the signal is integrated during the entire period separating the acquisition of two successive data points. There is a further advantage in selecting a frequency of data acquisition which is an exact divisor of the mains frequency (i.e., in the USA 60, 30, 20, 15, 12, 10, etc., Hz); this permits a strong rejection of the noise at the mains frequency, which is often an important component of the total noise. Designing electronic circuits for detectors which have a low signal noise in the frequency range below 30 Hz has been one of the unknown but critical contributions of the equipment industry to the progress of quantitative gas chromatographic analysis using fast open tubular columns. The accuracy of the conversion depends on the size of the outlet number used by the converter. This number is in binary format. Each position in the number is a bit and the number of bits determines the size of the word and the accuracy of the conversion. This size varies between 8 and 16, depending on the converter used. For example a 12-bit number permits the writing of decimal numbers between 0 and 4095. The smallest change in signal that can be reported is 1/4095, i.e., 0.028. This is precise enough in most cases, provided the range can be automatically adjusted (see below). An %bit word gives a precision of 1/255 or 0.48, equivalent to that of a chart recorder, barely satisfactory. A 16-bit word affords a precision of ca 15 ppm, which is rarely necessary. Because the signal of a GC detector varies over a very References on p. 658.

wide range it is necessary, however, to perform a scaling operation before the conversion, to ensure that the same precision is achieved with both small and large signals. This is achieved by an autoranging amplifier which automatically adjusts the amplification factor so that the outlet voltage remains within certain limits. The amplifier gain as well as the signal are recorded by the computer, using two words. There are four different types of A/D converters, the sample and hold successive approximation converters (SHC), the single slope converters (SSC), the dual slope converters (DSC), and the voltage to frequency converters (VFC). The first and last types are the most used in chromatographic applications, due to the fast rate of measurement they permit. The SHC holds the signal constant and compares it to a variable voltage which it generates, until they are equal. The VFC uses the signal to charge the capacitor of an RC oscillator whose frequency is proportional to the input voltage. These converters are more sensitive to noise than the SSC and DSC, which are integrating converters, but they are faster, which is the reason why they are preferred. DSC are more accurate than the other ones but cannot operate faster than ca 20 Hz. 2. Transfer of Data

The transfer of the digital signal obtained, often referred to as “the raw data”, is made using either serial or parallel transmission. The raw data are often in ASCII format, sometimes in binary format, rarely in another format. Analysts who want to have access to the raw data for further processing by personal software should demand equipment storing these data in ASCII or at least binary format, in files accessible to their own software. This will save them much trouble and time. Unfortunately, in 1987 this requirement is still not always easy to satisfy, nor well understood by some vendors providing computers, interfaces and software. Transmission is made by 8-bit words. If the word is longer, it is handled accordingly, cut into 8-bit fragments which are transferred one at a time by the interface and processed together by the computer. The A/D converter usually has a parallel output which must be transformed into a serial one for transmission with an RS 232 protocol. This is based on transient voltages, a voltage below - 3 V represents a “1” bit, a voltage higher than 3 V a “0” bit. Standard “handshaking” protocols permit control of the transmission and ascertain that the data have been sent and received. Most computers accept data through an RS 232 port, since it is the transmission method used for the connection of printers or modems to microcomputers. Some error detection and correction protocols may be used. Advances in the field of data telecommunication, including the recent development of high speed modems, permit the safe transmission of data at speeds which remain rather slow (2400/4800 bauds) over long distances (accross the country, or from building to building, on a’ phone line with a 2400 baud modem). Null modems (i.e., the mere cable connection of two RS 232 ports) permit data transmission over distances not exceeding 15 m. The parallel mode permits a much faster transfer of data. The 8 bits of an octet are transmitted simultaneously on the corresponding wires of a special cable called a

+

641

“bus”. This bus connects different peripherals, each of which has its own address. The procedure of transmission is strictly codified and controlled by the computer, using other wires on the bus. The most popular standard of parallel data transmission is the IEEE 488 standard. When properly implemented it is very easy to use. It permits very fast transmissions, at speeds exceeding several hundred thousand bauds. It is sensitive to noise and transmission cannot be made over distances exceeding ca 15 m.

3. Acquisition Frequency This frequency should be chosen as a compromise between the effects of too large an acquisition frequency - an increase in the base line noise, and an excessive requirement for data storage space - and the effects of too low an acquisition frequency - the loss of information. Independently of these effects, an upper limit is also set by the characteristics of the hardware used. According to the Shannon rule, the frequency of data acquisition must be at least double the highest frequency component of interest in the input signal. A high level of noise rejection is achieved if the sampling frequency is a multiple of the mains frequency. Finally, it has been shown that a minimum sampling frequency corresponding to the acquisition of 5 data points per standard deviation is required to afford an exact description of a chromatographic signal (36,37). A quantitative discussion of the consequences of the Shannon rule and of other considerations shows that the acquisition frequency, v,, and the sampling period, t,, should fulfill the following conditions: ’

t, c m

(16)

where v, is the cut-off frequency of the measurement system, which has to be larger than the largest frequency to be transmitted, and 7 is the detector-amplifier time constant. The total amount of data points to be acquired during an analysis can be estimated from the analysis time, t,, and the acquisition frequency, IT, to be equal to t , X f , . As was shown by Schmauch and Dinerstein (38), the acquisition frequency should be about 10 data points per standard deviation for a Gaussian peak. The total number of data points required is thus: P=lO-t R a

If the acquisition frequency during the analysis is going to be constant, the standard deviation of the narrowest peak should be introduced in equation 17. This corresponds to the non-retained peak and, from the definition of the column efficiency, we obtain a total number of data points equal to:

References on p. 658.

642

If we can change the acquisition frequency during the analysis, and if we assume the efficiency of the column to be constant, we obtain a smaller number of data points:

+

P = 1 0 f i j r R $ = lo@ ln(1 k’) fm

The value given by equation 19 is much smaller than the one resulting from equation 18. For example, for a conventional packed column, having 5,000 plates, if a range of k’ up to 7 is recorded, 5,600 data points are required in the first case, 1,470 in the second case. The amount of useful information is the same in both cases, however. If the k’ range recorded increases and the column is more efficient, the difference becomes much larger (i.e., for a 100,000 plate column, if data acquisition is made over a range of k’ from 0 to 10, the number of data points are 35,000 and 7,600, respectively). In cases when large amounts of data have to be acquired on a computer and stored, it may be very economical to be able to use an acquisition frequency which decreases during the course of the analysis. Thus, it is important to select a frequency of data acquisition which permits a correct estimate of the peak area and retention time, but which is not too large, in order to avoid the storage of excessively large amounts of data. 4. Noise Filtering

An analog filter is sometimes used on the detector signal, to reduce the noise of the signal sent to the A/D converter. Although useful in certain cases, this method may considerably increase the effective detector time constant, without the analyst being aware of it. In fact the analog filter modifies the peak profile, which appears as the convolution product of the original profile by an exponential. It must be emphasized that any noise filtering appears as a convolution operation which smoothes both the data, the desired effect, and the band profile, an undesirable side effect. In most cases it is much more effective to proceed to noise filtering on the digital signal. The number crunching capability of the computer is to be used here. Numerical filtering can be carried out in the time or the frequency domains, or in both, successively. Filtering in the time domain includes data point bunching, smoothing and correlations. A first step in filtering noisy data is in the bunching of successive data points. The extent of bunching depends on the characteristics of the data acquisition hardware, e.g., if signal integration is carried out by a VFC or an SHC for too short a fraction of the time, it may be very effective to perform signal acquisition at a high frequency rate and to bunch a number of successive data points together. For example, if the data acquisition is carried out at 60 Hz but the peak width is 5 seconds, so that a frequency of 4 Hz would be sufficient, data can be bunched by 12 or 15, which improves the signal-to-noise ratio by a factor 3.5 to 4. The bunching

643

rate can be changed along the chromatogram, since the band width tends to increase linearly with the retention time. This permits a very effective filtering procedure, since early peaks require high data acquisition frequency but usually have large signal-to-noise ratio, while late peaks require a much lower acquisition frequency but more noise rejection. Furthermore bunching permits compressing the data file without losing useful information, while using a constant acquisition frequency, which requires a much simpler system. A further filtering is achieved by convolution with a rectangular function or by curve fitting on a polynomial. In the first case, the n first points are each multiplied by an appropriate coefficient and summed. This yields the first “average” data point. The first data point is then dropped from the set while a new one is added at the other end of the set and the procedure is repeated to obtain the second average data point, and so forth until the last point is used. This process replaces the N data points collected by N - n + 1 averaged points. Another method involves fitting the first n points on a pth degree polynomial and adjusting the parameters of the polynomial to minimize the sum of the square of the residuals (least squares fit). The data point at ( n - 1)/2 is replaced by the value of the polynomial at that point. Then the first point is dropped, a new point included in the set and the procedure is repeated with the new set. Details regarding these procedures are given in the classical paper by Savitsky and Golay (39) and in other publications on fast digital filtering (1,40). Correlation techniques, based on the fact that the signal is predictable while the noise is not, have been used to enhance the signal-to-noise ratio and to perform trace analysis (41). Although the feasibility of this approach has been demonstrated (42), it does not seem that many applications have yet been reported. Working in the frequency domain permits a more straightforward approach to the rejection of noise. Noise frequencies appear clearly on the Fourier transform of the signal. Convolution in the time domain becomes a multiplication in the frequency domain, which greatly simplifies the operation. The signal can be filtered in the frequency domain by multiplication by the proper function (filter) or by cancelling the unwanted part of the Fourier transform and properly interpolating the remaining curve to replace the suppressed part. The advent of fast Fourier transform (FFT) algorithms permits the rapid transformation of a signal into its Fourier transform, the fast filtering of the signal in the frequency domain and the speedy return of the signal to the time domain. Spikes, high frequency noise, or spurious signals may easily be eliminated (1). Obviously, these operations can be carried out properly only in an interactive computer / analyst mode. 5. Peak Detection

The processed signal is used by the data handling algorithms. The peak can be detected by one of many different methods or combination of methods, signal or first derivative threshold (43), adapted filter (44),pseudo-derivative threshold (l), etc. The difficulties encountered in the design of the proper sequence of instructions to a computer-controlled data handling system have been discussed in detail by References on p. 658.

644

Baumann et al. (45). This work is still relevant, although the hardware has evolved and improved considerably since then. The advantage of the pseudo-derivative of the signal results from its proportionality to the peak height, independently of the band width, and is somewhat similar to that of data point bunching. Thus detection of strongly-retained peaks is much improved. Similarly the effect of signal noise is reduced (1). 6. Peak Integration

The algorithms used for integration of the signal during the time window corresponding to the peak elution are described in detail in the technical literature supplied by manufacturers. They include the means to determine the base line by interpolation under the peak of the base line recorded before and after the peak, the correction for base line drift which is implicit in this definition of the base line determination, the reincorporation of the areas of the two little wings, before and after the peak, which is easy to do since the computer keeps the smoothed signal in its memory, and the calculation of the peak area. Difficulties arise from the fact that many of these algorithms have been written by computer analysts or by electronic engineers with little chromatographic skill. The analyst should avoid any program which does not show clearly what the algorithm has been doing. This is especially important for (i) base line determination, (ii) the extrapolation of solvent band profile and (iii) the allocation of the area of partially resolved bands. The use of certain algorithms generates serious systematic errors. This is not easy to recognize and is almost impossible to correct for. The problem is made more critical by the fact that these programs are long and costly to write, with the result that manufacturers do not want to communicate the source code to their customers, who have little possibility to understand them anyway. This is a very important and nagging problem, with major legal aspects in the fields of regulatory, clinical and forensic analysis. As far as possible simple integrators with a limited set of compiled instructions should be avoided altogether. Preference should be given to systems which provide the possibility to store the “raw data” and/or the smoothed, filtered, averaged data and to replay them with a different set of instructions or parameters for the peak detection and integration. The optimum set of instructions can then be determined without the need to analyze a number of identical samples, which saves time and effort. At the same time, these programs supply more information on what they are doing and some changes in the set of instructions and parameters may permit a better understanding of the results of the base line interpolation. The possibility of importing the raw data file on a microcomputer, of processing it following different algorithms, of analyzing the chromatogram in an interactive mode, and of comparing it with chromatograms obtained with previous, similar samples offers new insights to the analyst regarding the composition of his sample and the behavior of his instrument. The availability of the raw data file in the memory of the computer also permits, if needed, more advanced treatments of the peak profile than is permitted by the use

645

Figure 15.4. Microprocessor integration. The profile is kept in the memory and the contributions of the two wings, at both sides of the peak, can be reincorporated.

of empirical functions (46,47). It certainly permits a more accurate determination of the peak area than electronic integrators, since the computer may look back when a peak has been detected and include previous data points in this calculation (see Figure 15.4).

7.Other Operations The determination of the retention time can be made from the smoothed signal profile. If a high precision is not required, the retention time will be the time when the largest value of the signal is recorded (after base line correction). If a higher precision is desired, the values of the signal exceeding cu 85% of the maximum signal can be fitted on to a parabola. The parameters of the parabola give the retention time and a better approximation to the true maximum signal. The identification of the eluted peaks may be carried out by asking the computer to search in a table for the compounds which have a retention time within a certain window. Comparison between the times in the table and the measured retention times provides a means to identify the eluted compounds, to recognize those which are missing and to flag the peaks which do not correspond to one of the expected compounds. Once the peaks have been identified, their response factors can be found in the table and the computer can calculate the corresponding concentrations. The computer may now print an analytical bulletin, with a chromatogram incorporating the events such as peak detection, peak maximum, area allocation, base line, actuation of valves, etc., and a table giving the retention times of the peaks detected, their name and their concentration in the analyzed mixture. When an analytical result is found to be out of specifications, the report can be printed with a different format or on another printer to draw immediate attention for proper action. Advanced computer programs now suggest to the analyst default values during the preparation of a new method, i.e., the setting of an integration program dedicated to a specific analysis. This possibility is both an extremely convenient References on p. 658.

646 0.01

U 'la

'

0.1

1

10

190

rnV

Figure 15.5. Plot of the relative indeterminate error (rsd) made on the measurement of peak areas as a

function of the solute concentration. a. Manual determination of peak area, from the product of peak height by width at half height, early 'sixties. b. First computers, early 'seventies. c. Computer integrator, early 'eighties.

help, which will save considerable time to the discriminative analyst, and a temble danger to the unsophisticated user. Computers never make mistakes (or exceedingly rarely). Humans who program them do. Accepting default values during the first stage of a method development permits the rapid obtention of preliminary results. The work of the computer must be checked, however, to ascertain to the analyst's satisfaction that serious errors in the determination of peak areas are not made. It is rare that some optimization of the parameters of the integration is not required. 8. Conclusion Each progressive step in the methods used for handling the chromatographic data and deriving the sample composition from the variation of the detector signal during the analysis has resulted in an improvement of the precision achieved (48). Figure 15.5 compares the precision obtained using three different methods: the triangulation by the product of the peak height by the width at half height (1960), the early computers (1970) and the new generation of microcomputers and software (1980). The improvement has been remarkable, especially at concentrations below 0.5%.

IV.AREA ALLOCATION FOR PARTIALLY RESOLVED PEAKS In many cases the analyst has to deal with incompletely resolved chromatograms. It should be emphasized that deriving quantitative information on the composition

641

of a mixture from such a chromatogram is poor analytical practice, unless the unresolved peaks are those of compounds with no importance for the analysis. The accuracy of the data obtained from unresolved chromatograms is always markedly lower than the accuracy of measurements made on well resolved peaks. There are several reasons, the combination of which explains the validity of this general statement. First, peaks are almost never Gaussian. Each peak has a different shape. Deconvolution requires that the proper profile be used for each of the peaks involved. Furthermore, the profile for a mixed band is rarely the sum of the profiles that would be recorded for each of the component peaks if the same amount of each pure compound were injected successively. There are two independent reasons for this nonlinear behavior. First, the detector responses are not additive. For example, the thermal conductivities of vapors are not additive, even at low concentrations. Secondly, the column is overloaded more often than is generally recognized. The band shape depends on the concentration of the two compounds, simultaneously (49). Although all these effects are relatively small when low sample amounts are used, they combine to create a significant systematic error which would be difficult to correct for, but is usually not even identified. Peak deconvolution itself, even in a linear case, introduces an additional error, which we investigate here in more detail. It is related to the difficulties encountered in allocating its proper share of the total area to each component of the interference band. Of course, the magnitude of all these errors depends strongly on the degree of resolution between the peaks to be quantitized. If this resolution is 1.0, although we consider that good quantitative analysis requires a resolution close to 1.5, the error will still be acceptable, unless the relative concentration of the two compounds involved exceeds one order of magnitude (see Chapter 1, Figure 1.6). If the resolution is lower than 0.5, the situation may prevent one from obtaining anything better than a crude order of magnitude for the relative concentration.

1. Two Compounds with a Moderate Relative Concentration The two peaks interfere because the resolution between them is low. If no better column, either a longer one or one using another stationary phase, is available, some results may be obtained by measuring the areas of the two peaks. The common area is allocated following different methods which are easier to implement when a microprocessor is available. a. Manual Calculations

There are two main cases: if the trough of the valley between the two peaks is lower than the half height of the smaller peak (see Figure 15.6A), it still is possible to carry out normal triangulation by the product of the peak height and its width at half height. The result is in error, however, because the interference between the two peaks increases their half-width. Their height also is increased, but to a lesser extent. There is no

-

References on p. 658.

648

A

I

C

D

Figure 15.6. Peak area allocation in the case. of partly resolved peaks. A. Triangulation. The valley trough is below the half peak height. Triangulation is often carried out as for total separation, although the widths at half height are too large. Integrators use the vertical from the minimum of the valley to allocate the two areas (see figure). B. Triangulation. The valley trough is above the half height. Areas are allocated by the vertical going through the valley minimum.C. Deep valley. The base line is forced through the minimum of the valley. D. Peak of a trace component on the tail of a solvent peak. Interpolation of the major component peak profile.

suitable correction. So both the relative area of the two compounds and their absolute areas are in error. - if the trough between the valleys is higher than the half height of the taller peak, the method suggested by Pecsok (50) and by Brace (51) is used. A straight line is drawn perpendicular to the base line. If the inflexion tangents can be drawn with a reasonable accuracy, the perpendicular goes through the intersection of these two tangents (see Figure 15.6B). If not, the straight line goes through the lowest point of the valley between the peaks. Each peak receives the total area of the composite band on its side of this perpendicular line. Marshall and Hulpert (12) have shown that this procedure always results in an underestimation of the size of the smaller peak. The error is already 1%when the valley height is 20%of the smaller peak height. The error is only slightly affected by the size of the larger peak. It increases with decreasing resolution. Another procedure advocated in the early days of gas chromatography involves

649

TABLE 15.2 Precision of Peak Area Determination as a Function of the Resolution and of the Relative Concentration of the Two Compounds Concentration of Compound # 1 (in %) 15.84 30.36

Resolution between the two compounds 2.0

0.7 13.58 (- 16.6%) 27.91 (- 8.8%) 48.60 ( - 3.1%) 69.20 (- 0.8%) 82.41 (0.2%)

15.75

15.78

15.44

( - 0.6%)

( - 0.4%)

( - 2.6%)

30.36

30.21 (- 0.5%) 49.13 (- 0.8%) 69.47 (-0.4%) 82.47 (0.25%)

30.05 (-1.0%) 49.70 (- 0.9%) 69.26 ( - 0.7%) 82.20 ( - 0.1%)

50.13 69.74

(0%) 82.27

1.o

15.84

(0%) 69.74

1.6

(0%) (0%) 50.13

1.7

82.21

(0%)

29.59 ( - 2.6%)

49.06 (- 2.2%) 68.76 ( - 1.4%) 81.66 (-0.75%)

Composition of a binary mixture derived from actual peak area determination. The figure in parentheses is the relative error on the concentration of the first compound.

cutting the compound band and determining its area by weighing it. The total area is then shared between the two compounds in proportion to the ratio of the heights of their peaks. b. Automatic Processing

Originally the manufacturers of electronic integrators tried to design them so they could reconstruct peaks using a Gaussian profile (52-55). For reasons explained in the previous section this attempt was doomed to failure: peak profiles are almost never Gaussian. Most electronic integrators use now the perpendicular to the base line going through the bottom of the valley to allocate the areas in a binary composite band (56,57). When the resolution is large enough (i-e., larger than about l S ) , it is also possible to force the base line to go through the bottom of the valley (see Figure 15.6C), but this results in a bias, the area being systematically too small for both peaks. The procedure is not recommended when the resolution is lower than 1.5. The accuracy of the determination of the relative concentration of two peaks depends on the resolution if it is not large enough. The data in Table 15.2 illustrate this dependence. Samples of five binary mixtures of the same components, with different relative concentrations between (16/84) and (82/18), have been injected on different columns on which the resolution of the peaks of the two compounds varies from 2.0 to 0.7. In this case the error made in the concentration of the first eluted compound is almost always negative. The systematic error is lower than 1% when the resolution exceeds 1.0, it is between 2 and 3% for values of the resolution around 1.0 and may exceed 10%for a resolution of 0.7 (see Table 15.2). The following error has been observed with one of the softwares commonly used in 1987. A binary mixture (composition ca 1/3) is used for calibration. The References on p. 658.

650

resolution between the two peaks is around 0.8. When samples of increasing sizes are injected, it is observed that the area ratio, which should remain constant, experiences an abrupt jump for a certain size. This corresponds to a change in the area allocation procedure used by the software. At low sample sizes, the base line is forced through the minimum of the valley trough (see Figure 15.6C). At large sample sizes, peak areas are allocated after the vertical through the minimum of the valley trough (see Figure 15.6B). Even with a linear column and a linear detector, there is no reason for these two area ratios to be equal. 2. Two Compounds with a Very Large Relative Concentration

Peaks tend to tail, even with properly deactivated supports or column walls. This tailing may be due to injection or vaporization problems but most probably results from overloading of the column with the main compound of the mixture under analysis. If the major compound is eluted second, the situation is very similar to the one described previously, because the tailing of the minor compound does not create any problem in the determination of the two areas. If the major compound is eluted first, however, as in the case of trace analysis when a solvent is used, the peak of the minor component appears on the tail of the major one (see Figure 15.6D), as a bump on a much wider profile. In such a case, the use of the perpendicular to the base line would obviously result in an enormous error. One of two methods can be used. The “base line” for the trace component is either the tangent to the profile of the major peak at the intersection between the major peak profile and the vertical of the minor peak maximum (see Figure 15.6D), or the profile of the major peak is reconstructed by fitting the data points before and after the minor peak on an exponential decay. In both cases serious errors are introduced. Depending on the type of detector used, the response factor of a minor compound eluted on the tail of a major one may vary widely. In any case it is absolutely necessary to carry out a special calibration with standard mixtures, in the same composition range as the one where the determinations are going to be made. Assuming that the response factors will remain the same for peaks eluted under the conditions depicted on Figure 15.6D as they are when calibration is performed on pure samples, with the gas density balance method, could result in extremely large errors. V. ANALYTICAL PROCEDURES FOR THE DETERMINATION OF THE COMPOSITION OF THE SAMPLE Once the areas of the peaks of the different components of the mixture analyzed have been calculated, the composition of the mixture must be derived. In theory, it could be sufficient to determine the absolute response factor of each component of the mixture to calculate what amount of it has been injected, i.e., was contained in the aliquot of the sample which has been analyzed. Unfortunately, the reproducibil-

651

ity of absolute determinations in gas chromatography is not very good. Although it has improved considerably over the last 25 years, and the reproducibility of the sample injection can be excellent (see Tables 13.1 to 13.4), detector response factors tend to drift on a day-to-day operation, while relative response factors are much more stable. Since calibration is very tedious, complex and expensive, it is better to use relative response factors. The determination of the concentrations of the components of the mixture analyzed requires the selection of a proper procedure. To a great extent the choice of the procedure will depend on the accuracy desired. Almost always, because of the difficulties encountered in the reproduction of sample sizes, procedures which use relative peak area and relative response factors will be used rather than those using absolute areas and absolute response factors. Most of these procedures have been discussed in detail by Novak (58). Throughout the following the concentrations are given in 5% (w/w). 1. Internal Normalization of Peak Areas The concentration of component j is given by:

c,= A , + A , +A, ... +A,, x 100

(20)

where A,, A,, .., A,, are the areas of the peaks of the various components of the mixture. This method assumes first that all components of the mixture are eluted off the column. This can be so, in the normal case, but if an accident takes place the procedure will not alert the analyst. Suppose that a gasoline sample from a storage tank is analyzed. If this procedure is adopted, accidental pollution of the gasoline tank by gas oil will most probably go undetected, since the components of gas oil are normally not eluted from the column used to analyze gasoline. Certainly the column will start drifting and poor chromatograms will be obtained after a while. If this is the only warning, however, millions of gallons of a product completely out of specifications can be shipped before the analyst finds out. This is not an imaginary example. Such an accident really took place somewhere, years ago. The analyst involved now teaches gas chromatography at a local university. Another unrealistic assumption made in this procedure is that all the components of the mixture have the same response factor. This is an exceptional situation, which happens with optical isomers and, to a limited extent, for saturated hydrocarbons with a flame ionization detector. With a thermal conductivity detector and if gases having a large thermal conductivity such as hydrogen or helium are used, internal normalization of peak areas, without any calibration correction, will result in systematic errors in one direction or the other which rarely exceed 15%. With a flame ionization detector, if compounds which are closely related chemically are analyzed, the error may be markedly smaller. This is especially true for saturated hydrocarbons. In other cases the error can be very large. References on p. 658.

652

Although approximate, this procedure which does not require previous calibration may be very useful, for example in following the progress of a reaction or in studying the development of a new process. In these latter cases, the relative variations of the relative concentrations may contain most of the useful information requested. In most cases, however, the accuracy of the simple internal normalization procedure is very poor and other methods are preferred.

2. Internal Normalization of Corrected Peak Areas A similar calculation is performed, now using the corrected peak areas, which take into account the relative response factors of the detector for the different components of the mixture analyzed. The concentration of the j t h component is given by:

c.= J

fi

XAj f , x A l + f 2 X A , + ...+f, XA,

x 100

where fl, f2, ... f, are the relative response factors of the different components of the mixture which are eluted. The method can be applied only (i) if all the components of the mixture are eluted from the column, (ii) if they are all identified and (iii) if their relative response factors have been properly determined. Most computer software is designed to apply this procedure when required. 3. Standard Additions

This procedure is used for the analysis of one or two components in a more complex mixture. Known amounts of the analyte(s) to be quantitized are added to aliquots of the original sample. Similar amounts of the original sample and of the spiked samples are analyzed under the same conditions. The amounts of the aliquot of the mixture and of the component added must be known accurately and the dilution effect must be taken into account, for example by measuring the area of the peak of another component of the mixture. The concentration of the j t h component is given by:

where Q j is the concentration increase of compound j ( Q j = m j / ( m j + m,), where mj is the mass of compound j added to the aliquot, and m , the mass of compound j already present in the same amount of the mixture, A j and AS are the areas of the peaks of compound j before and after the addition, respectively,

653

A, and A: are the areas of the peaks of another component of the mixture, taken as a reference, before and after the addition, respectively. The denominator of equation 22 is the increase of the area of the peak of the component j due to the addition, while A : / A , is the dilution factor.

4. Internal Standard This procedure involves the addition to an aliquot of the analyzed mixture of a known amount of a reference compound which does not exist in the original sample. If the reference, or standard, compound is also the reference used for the calibration of the detector, the relative response factors for all the components of the mixture are known and the concentration of the j t h component of the mixture is given by: c,=C,,Xf..

A-

x' A ,

where C,,is the concentration of the internal standard in the sample injected to the chromatograph, i.e., mls/(m,,+ m s ) , where m,, is the mass of internal standard added to a mass m, of original sample, f//,. is the relative response factor of compound j (internal standard reference), and A, and A,, are the peak areas of the compound j and the internal standard, respectively. The internal standard must be well resolved from the different components of the analyzed mixture. Furthermore it must fulfill the following requirements: - the response factor of the internal standard should be of the same order of magnitude as that of the compounds which are analyzed; - the retention time of the internal standard must be reasonably close to those of the compounds analyzed. The internal standard must be well resolved from all the components of the mixture, but should not be eluted much before or much after those compounds which are quantitized. This wiIl ensure that the error made on the determination of the peak area of the internal standard is comparable to the error made on the measurement of the areas of the peaks of these components; - the concentration of the internal standard in the sample analyzed by chromatography should be of the same order of magnitude as that of the compounds for the analysis of which it is used. It is not unusual to add a solution of several internal standards, with rather widely different concentrations and retention times, to a complex sample. In contrast to what was noted for the previously described internal normalization procedures, when an internal standard is used it is not necessary that all the components of the mixture analyzed be eluted from the column for the achievement of a successful, accurate analysis, as long as all the compounds of interest are eluted with well shaped peaks.

5. External Standard After the requisite number of samples of the unknown have been analyzed, alternating with these samples, a known amount of a pure or dilute standard, or a References on p. 658.

654

mixture of known composition, is injected a certain number of times. As explained above it is necessary to repeat any analysis at least twice, preferably three or four times, to make sure nothing has gone wrong in the procedure. Thus, the external standard procedure involves the analysis of a series of samples of known amounts of the unknown mixture and of a reference mixture (which can be a single compound, pure or diluted in a solvent). The standard is called external because, in contrast to what takes place in the internal standard or standard addition procedures, the standard is separate from the mixture, it is not added to it. Accordingly, the precision of the procedure depends on the reproducibility of the sample sizes. In the early days of gas chromatographic analysis, this repeatability was pretty poor for liquids, so the procedure was applied only to the analysis of gas mixtures. It is particularly well suited to gas analysis, since it is not necessary to prepare standard mixtures, unless trace analyses have to be camed out. With modem liquid injection valves, actuated by compressed air, the reproducibility of the injected volume is typically between 0.1 and 0.5% (see Tables 13.1 to 13.4). The external standard procedure may now be considered in a number of cases of practical importance. It is very convenient for the analysis of effluent streams, the composition of which changes only slightly, since it is then possible to prepare standards of known composition which can be used as reference. If the standard is a pure compound (possibly diluted in a solvent), the determination of the relative concentrations of the various components is made from their respective peak areas and relative response factors to the standard. The concentration of the jth component is: A.

c, = cesxfj/esx 2 Aes where C,, is the concentration of the external standard, &s, the relative response factor of compound j by respect to the external standard, A j and A,, the areas of the peaks of compound j in the chromatogram of the unknown and of the external standard in the chromatogram of the reference material. C, is obtained in the same units as Ces.However, if w/w concentrations are required it is necessary to determine the density of the unknown sample, which may be difficult. Due to the variable mixing volume, the density of a mixture is not accurately calculated from the composition and the density of the individual components. If the standard is a mixture of known composition, preferably similar to that of the unknown, the areas of the peaks corresponding to the same compound are compared and the concentration of the j t h component is:

where cj, is the concentration of compound j in the standard mixture, and A j and

655

Aj, the areas of the peaks of j in the chromatograms of the unknown and of the standard, respectively. Although the sample size does not appear explicitly in this equation, it should be the same for the two samples (unknown and standard), otherwise the area ratio will change, resulting in a systematic error in the concentrations.

6. Deferred Standard This procedure is especially useful in process control analysis, for which it has been developed by Guillemin (59), or in other applications of routine analysis. The standard is not incorporated in the analyzed mixture, as with the internal standard procedure; it is not injected after the analysis of the unknown mixture has been carried out, in a different sequence, as with the external standard procedure. With the deferred standard procedure, a pure compound (the standard) is injected during the analysis of the unknown mixture, but not at the same time. The time of the second injection is chosen so that the standard elutes well resolved from all the components of the mixture, somewhere in the middle of the chromatogram, hence the name of deferred standard. The standard can be any compound, even a non-retained gas. Using a gas as a deferred standard has the particular advantage of emphasizing the control of the proper behavior of the pneumatic system of the chromatograph. It has the disadvantage of giving no information on the possible drift of the column properties, due for example to slow liquid phase bleeding. This last phenomenon is easier to detect, however, than malfunctions of the chromatograph itself; this can be done for example by following the drift of the retention times of the components of the mixture analyzed. Its consequences are less harmful on a short-term basis for the accuracy of the analytical results. The injection valve used for the standard can be the same valve as used for the injection of the sample (an %port valve, for example, with two sample loops), or a different one. The essential function of the deferred standard is the control of the proper functioning of the chromatograph. The peak area of the deferred standard should remain constant within a small fraction of 1%if the equipment works properly. Any larger change in its area can be ascribed to a change in the characteristics of the chromatograph and should be construed as a warning that the response of the detector is no longer reliable. The deferred standard can also be used as an internal standard for quantitative analysis. In such a case equation 24 in the section above (external standard) applies to the determination of the concentration of the j t h component of the sample. The concentration of the j t h component of the mixture is then given by:

where c d , and A d , are the concentration of the deferred standard and its peak area, References on p. 658.

656

respectively. C,, is equal to 100%if the deferred standard is injected pure, with the same sampling loop as the analyte. Otherwise, it is equal to the product of the concentration of the deferred standard in the standard mixture used, multiplied by the ratio of the sampling loop volumes. It is advantageous in this case to determine the relative response factor of the analytes to be quantitized by respect to the compound used as deferred standard. The use of the gas density balance for the determination of relative response factors permits that, without difficulty, even if the deferred standard is a non-retained gas which would be difficult to mix accurately with a liquid, if the conventional calibration procedures were used. The attractive features and advantages of the deferred standard are further illustrated in Chapter 17. 7. Quantitative Analysis of Unknown or Unavailable Components

The calibration procedures are possible only with compounds that have been identified and are available at a sufficient degree of purity. As shown in Chapter 14, the use of the gas density balance permits an accurate calibration with impure samples or even complex mixtures. When a gas density balance is not available, internal normalization becomes the only choice, with all its drawbacks. An attractive alternative has been suggested by Janik (60-62). It requires that the following conditions be satisfied: - All the components of the mixtures used for calibration are eluted from the column selected for the calibration procedure. -The detector response is linear for all components in the sample sizes and concentration ranges used. - All the components of the mixtures used are resolved. - At least as many mixtures as there are components are available. These mixtures are independent, i.e., the concentration of the various components are unrelated. A known amount of a standard is added to an aliquot of each mixture. These mixtures are then analyzed. From the peak areas of the chromatograms we derive the following relationship for each mixture j : n

k,ASj+

i=l

k i A i j= mSj+ mi

where m is a mass, k a response factor and A a peak area. The indices s, j , i refer to the standard, the mixture j and the component i of the mixture. Equation 26 states that the sample weight ( m S j )added to the weight of the aliquot ( m i ) is equal to the sum of the products of the response factor ( k , for the standard, k i for component i ) by the peak area ( A s j for the standard, A i j for component i). We may also write, since the weight of standard is equal to k,ASj:

657

If we have as many as, or more mixtures than we have components, we have as many as, or more equations than we have unknowns in this system of linear equations. The numerical solution can be easily obtained, provided the compositions of the mixtures are independent. This method has been used for the determination of the concentration of peroxides or other unstable, dangerous compounds at trace levels in various mixtures of industrial origins. 8. Choice of Numerical Units Concentrations can be reported in a variety of units. The most important in practice are weight by weight, volume by volume, weight by volume, mole by mole, mole by volume (molarity). The choice is often a matter of preference and/or local culture and traditions. It is of paramount importance, however, to be consistent, and the proper selection of units should be double checked, as a matter of policy. TABLE 15.3 Results of the Quantitative Analysis of a Standard Mixture of Chlorinated Hydrocarbons made with Three Different Detectors Column: stainless steel, 4 mm ~4 m. Packed with Spherosil83 m2/g coated with 5% polyethylene glycol 400. Temperature: 85OC. Carrier gas: hydrogen for GDB and TCD, nitrogen for FID. Sample flask refrigerated and closed with a rubber stopper. Syringe injection. Response factors obtained with the GDB. Concentrations derived by internal normalization of the corrected areas. Peak areas measured by computer. Compound

b.p. ( C) Composition of the mixture (in weight %) Std * withGDB Dif

1.1-Dichloroethane 57.3 80.1 Benzene Trichloroethylene 87.0 1,2-Dichloroethane 83.5 Tetrachloroethylene 121.O

19.33 16.22 20.80 16.05 27.60

19.07 16.07 20.84 15.93 28.09

**

-1.3 -0.9 0.2 -0.7 1.8

withTCD Dif 18.93 15.87 21.23 15.95 28.02

**

-2.1 -2.2 2.1 -0.6 1.5

with FID Dif 19.16 16.03 21.00 15.84 27.97

**

-0.9 -1.2 1.o 1.3 1.3

Composition of the standard mixture calibrated for this comparison.

** Relative difference (W)with the composition of the standard mixture. TABLE 15.4 Quantitative Analysis of a Fluorochloroalkane Mixture Composition in w/w. Column: 4 mmX6 m, Packed with Chromosorb P, coated with 10.1%Voltalef (Plastugil). Temperature 52OC. Helium 3 L/hour. Sampling by continuous vaporization of a liquid mixture prepared by weighmg (cn 1 kg) in a metal tank (see Section 2). Area measured by triangulation. Concentration derived by internal normalization of peak areas. Compound

b.p. ( C)

CC1,F (F11) C,CI2F4 (F114)

23.77 3.55

CC12F2 (F12) C,Cl,F4 (F114)

- 29.79 3.55

GDB

Difference

Standard mixture 42.30 57.70

42.53 57.47

0.54 - 0.40

47.14 52.86

46.72 53.28

- 0.90 0.80

(W)

References on p. 658.

658

TABLE 15.5 Quantitative Analysis of a Mixture of Organic Acids Teflon column,4 mmX6 m, packed with Chromosorb 102, coated with 3% Carbowax 20M. Temperature: 12OoC; carrier gas: hydrogen, 3.6 L/hour Calibration of response factors with GDB. Peak area measured with integrator-computer. Concentration derived by internal normalization of corrected peak areas. The lower precision achieved with pure acids is due to their chemical aggressivity. Standard mixture

TCD

Undiluted mixture of the acids Acetic acid 118.5 141.6 Acrylic acid

40.0 60.0

41.52 58.47

- 3.80

Diluted aqueous solution Acetic acid 118.5 Acrylic acid 141.6

40.0 60.0

40.46 59.54

- 1.15 0.77

Compound

b.p. ( O C)

Difference

(W 2.55

Composition in weight/weight.

The report of concentrations as weight by weight requires the knowledge or the determination of the densities of the standard and the compounds analyzed. In the case of a major component of a mixture, the density of that compound may be taken as being equal to the density of the sample, to a first approximation. If densities are not accessible, relative response factors should be converted to a more suitable unit, and the results converted accordingly. Tables 15.3 to 15.5 illustrate the level of accuracy that can be expected when the techniques described previously are applied to the solution of industrial problems requiring quantitative analysis and exhibiting serious difficulties, for different reasons, such as sampling of volatile compounds, analysis of reactive compounds, etc.

LITERATURE CITED (1) J.L. Excoffier and G. Guiochon, Chromatographia, 15, 543 (1982). (2) T. Petitclerc and G. Guiochon, Chromatographia, 7, 10 (1974). (3) D.L. Ball, W.E. Harris and H.W. Habgood, J. Gas Chromarogr., 5, 613 (1967). (4) D.L. Ball, W.E. Harris and H.W. Habgood, Anal. Chem, 40, 129 (1968). (5) A. Klinkenberg and F.Sjenitzer, Chem. Eng. Sci., 5, 258 (1956). (6) A.S. Said, A.Z.Ch.E. J., 2, 477 (1956). (7) A.I.M. Keulemans, Gas Chromatography, Reinhold, New York, NY, 1959, p. 124. (8) L. Condal-Bosch, J. Chem Ed., 41, A235 (1964). (9) J.G. Karohl, J. Gas Chromarogr., 5,627 (1967). (10) J.T. Shank and H.E. Persinger, J. Chromatogr., 5, 631 (1967). (11) F. Baumann and F. Tao, J. Gas Chromatogr.. 5, 621 (1967). (12) R.C. Marshall and K. Hulbert, Chromatographia, 2, 32 (1969). (13) R.D. McCullough, J. Gas Chromatogr., 5, 635 (1967). (14) G. Schomburg and E. Ziegler, Chromatographia, 5. 96 (1972). (15) N. Guichard and G. Sicart, Chromatographia, 5, 83 (1972). (16) J.M. Gill and J. Henselman, Chromatographia, 5, 108 (1972).

659 (17) D.R. Deans, J. Chromatogr. Sci., 9, 729 (1971). (18) L.L. Hegedus and E.E. Petersen, J. Chromatogr. Sci., 9, 551 (1971). (19) H.W. Jackson, J. Chromatogr. Sci., 9, 706 (1971). (20) J.M. Gill, J. Chromatogr. Sci., 7, 731 (1969). (21) J.M. Gill, J. Chromatogr. Sci., 10, l(1972). (22) G.D. Dupre, J.M. Gill and J.R. Hubbard, Amer. Lab., 2, 39 (1970). (23) G. Paterson, Analytical Aduances, Hewlett-Packard, 1970. (24) E. Herlicska, A.C. Brown and J. Hendrickson, Amer. Lab., 3(5), 29 (1971). (25) J.D. Hettinger, J.R. Hubbard, J.M. Gill and L.A. Miller, J. Chromatogr. Sci., 9, 710 (1969). (26) D.G. Gillen, Chromatography Reviews - Spectra-Physics, 5, 1 (1979). (27) J.D. Wilson and C.A.J. McInnes, J. Chromatogr., 19, 486 (1965). (28) H.M. McNair and W.M. Cooke, J. Chromutogr. Sci., 10, 27 (1972). (29) C.E. Reese, J. Chromatogr. Sci., 18, 201 (1980). (30) E.F.G. Woerlee and J.C. Mol, J. Chromatogr. Sci., 18, 258 (1980). (31) H.A. Ashworth and R.L. Augustine, Reu. Sci. Instrum., 52, 105 (1981). (32) P.M. Lyne and K.F. Scott, J. Chromarogr. Sci., 19, 547 (1981). (33) S.L.Smith and C.E. Wilson, Anal. Chem., 54, 1439 (1982). (34) H.G. Matthews, Int. h b . , June 1982, p. 60. (35) J.G. Liscouski, Anal. Chem., 54, 849A (1982). (36) S.P. Cram and S . Cheder, Anal. Chem., 43, 1922 (1971). (37) M. Goedert and G. Guiochon, Chromatographiu, 6, 76 (1973). (38) L.J. Schmauch and R.A. Dinerstein, Anal. Chem., 32, 343 (1960). (39) A. Savitsky and M.J.E. Golay, Anal. Chem., 36, 1627 (1964). (40) T.R. Edwards and R.D. Knight, Instrument and Control Systems, September 1974, p. 73. (41) R. Annino, in Aduances in Chromatography, J.C. Giddings, E. Grushka, J. Cazes and P. Brown Eds., M. Dekker, New York, NY, 1977, Vol. 15, p. 33. (42) R. Annino, M.F. Gonnord and G. Guiochon, Anal. Chem., 51, 379 (1979). (43) C.E. Reese, J . Chromatogr. Sci., 18, 249 (1980). (44)M.H.J. van kjswick, Chromatographiu, 7, 491 (1974). (45) F. Baumann, A.C. Brown and M.B. Mitchell, J. Chrornatogr. Sci., 8, 20 (1970). (46) F. Dondi, A. Betti, G. Blo and C. Bighi, Anal. Chem., 53, 496 (1981). (47) A. Jaulmes, C. Vidal-Madjar, M. Gaspar and G. Guiochon, J. Phys. Chem., 88,5385 (1984). (48) T.A. Gough and E.A. Walker, J. Chromutogr., 45, 14 (1969). (49) S. Ghodbane and G. Guiochon, J. Chromatogr., 440, 9 (1988). (50) R.L. Pecsok, Principles and Practice of Gar Chromatography, Wiley, New York, NY, 1959. (51) R.O. Brace, Beckman Instruments Review, Fullerton, CA, 1959. (52) D.W. Grant and G.A. Vaughan, J. Appl. Chem. (London), 10,181 (1960). (53) Y. Mori, J. Chromatogr., 66, 9 (1972). (54) Y. Mori, J. Chromatogr., 70, 31 (1972). (55) T.F. Schatzki, J. Chromutogr. Sci., 11, 597 (1973). (56) J.C. Bartlet and D.M. Smith, Can. J. Chem., 38, 2057 (1960). (57) K. Kishimoto, H. Miyauchi and S . Musha, J. Chromatogr. Sci., 10, 220 (1972). (58) J. Novak, in Aduances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1974, Vol. 11, p. 1. (59) C.L. Guillemin, Instrum. Technol., 4 , 43 (1975). (60) A. Janik, J . Chromatogr., 54, 321 (1971). (61) A. Janik and J. Hetper, J . Chromatogr., 54, 327 (1971). (62) A. Janik, J. Chromatogr., 69, 231 (1972).

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CHAPTER 16

QUANTITATIVE ANALYSIS BY GAS CHROMATOGRAPHY Sources of Errors, Accuracy and Precision of ChromatographicMeasurements TABLE OF CONTENTS Introduction ............................ 1. Sources of Errors in Chromatographic Measurements . . . . . . . . . . . . . , . . . . . . . . . . . . . . 1. Measurement of Peak Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. From the Recorder Chart . . . . . . . . . . . . . . . . . . . . . . . . . . , . b. From the Data Acquired with a Computer . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2. Measurement of Peak Area . . . . a. From the Recorder Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. With an Electronic Integrator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. From the Data Acquired with a Computer . . . . . . . . . . . . . . . . . . . . . . . . . 3. Peak Height or Peak Area? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , , . , 4. Measurement of Sample Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. The General Problem of Instrumental Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Pressure and Flow Rate Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Relationship between the Fluctuations of Pressure and Flow Rate and the Precision on Peak Area for Class I Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Relationship between the Fluctuations of Pressure and Flow Rate and the Precision on Peak Area for Class I1 Detectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.................................................. ................

.................................................... VI. Other Sources of Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1. Measurement of Sample Size . . . . . . . . 2. Representativity of the Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI1. Global Precision of Chromatographic Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature Cited . . . . .... .. . ...................... 3. OtherDetectors

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INTRODUCTION

Quantitative analysis by GC is based on the determination of parameters of the chromatogram related to the amount of the corresponding component of the injected sample. All sources of errors in the determination of these parameters as well as all sources of fluctuations in the quantitative relationship between the amount of the compound and its peak size will contribute to the analytical error. GC techniques are very sensitive and can be made very precise and accurate over a large range of concentrations (see Figure 15.5). In the first paper published on gas chromatography (l), James and Martin, dealing in part with the quantitative determination of small amounts of formic to dodecanoic acids in lipid materials, References on p. 687.

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achieved a reproducibility of a few percent. Analysis of free fatty acids was not, and still is not, the easiest GC analysis. They emphasized, even at that time, that GC is potentially a very accurate method of analysis. It so happened that in the vast majority of cases a precision of two or three percent is considered to be satisfactory and little effort has been made to improve on that performance level. It should be pointed out first that any analytical technique can give quantitative information only on the sample used to carry out the determinations. Obviously, this sample must be representative. Sampling techniques are by no mean easy. Further operations, such as grinding, dissolution, extraction, derivatization, etc., may alter the sample composition. Their effects must be carefully examined (2). Some of the problems encountered in dealing with samples have been discussed above in Chapters 13 to 15 or are examined in the next chapter, but by and large the sampling problems are outside the scope of the present book. It is disappointing to observe that in spite of the large amount of literature published regarding the quantitative applications of GC, the problems of the origin of errors have been generally dealt with most superficially, except in a small minority of cases (3). A large number of papers report on the quantitation of a certain group of compounds in a certain type of matrices. No serious attempt is made at identifying the sources of errors, and certainly not at reducing the most important of them (4-7). In the best cases only are meaningful statistical results, such as the standard deviation for more than 3 determinations, included in the results. Errors are still regarded by many as a plague, not a topic worthy of scientific discussions. The general interest of these papers is limited for the aim of the present discussion. A second group of papers deal with the performance of detectors and the quantitative relationships between the value of the different parameters which control the behavior of the detector and its response for a selected group of compounds. Although the information supplied here is important and relevant to the topic of quantitative analysis, it is rather unusual to find a discussion on the sources of error in the quantitative applications of the detector, on the influence of the fluctuations of the detector parameters on the reproducibility of its response nor on the extent of control required in order to achieve a certain level of precision. The precision of quantitative analysis is, however, directly related to the stability of the instruments used for the determinations which are required and of the experimental conditions within which they are used. We discuss here some of these relationships, essentially the influence of the noise and of the characteristics of the data acquisition hardware, the iqfluence of the fluctuations of the carrier gas flow rate and pressure and of the detector temperature. A detailed discussion of the precision of the measurements made with a thermal conductivity detector and a flame ionization detector follows, as examples of application.

I. SOURCES OF ERRORS IN CHROMATOGRAPHIC MEASUREMENTS The errors of measurements are essentially related to the influence of the parameters of the data acquisition system: (i) the frequency of data acquisition, (ii)

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the time constant of the detector and the amplifier, (iii) the threshold for peak detection and (iv) the value of the signal to noise ratio. The influence of these parameters can be studied most conveniently by computer simulation. It is cautious, however, to verify the validity of the conclusions achieved by some suitable experiments. 1. Measurement of Peak Height The determination of the peak height can be carried out either from the paper chart where the chromatogram has been recorded or from the data file acquired with a computer. Although there is rarely a suitable subroutine for this determination in most software packages available, it can easily be implemented, at least if the software used accepts the incorporation of new subprograms, because it is a simple operation. The determination involves two steps. First, the base line, B, under the peak is drawn or otherwise determined. Then the height of the peak, h, is measured from this base line. Both steps introduce an error, characterized by the standard deviations on B and h, respectively. These errors depend on the way the measurement is carried out, on the paper chart or directly from the detector signal.

a. From the Recorder Chart Systematic determinations have been carried out by Ball, Harris and Habgood (8) on peaks of various shapes and sizes, drawn on sheets of paper, reproduced by photocopy and given to a large number of operators. They observed that the standard deviations on the two steps are both approximately 0.01 cm and the standard deviation on the peak height is 0.014 cm, if the base line is not too noisy. The absolute standard deviation being rather constant, the relative standard deviation, hence the repeatability is inversely proportional to the peak height. This conclusion is independent of the peak shape. Thus, in order to achieve a precision of 0.1% on the determination of the peak height, the peak should be taller than 14 cm. In other words, to achieve the maximum precision by this method, all peaks should be between one half and one full scale deflexion high, which demands that the analyst plays with the signal attenuation knob during the entire analysis and has some prior knowledge of results to come. In a similar but less systematic study, Janak et al. have found the absolute standard deviation on the peak height to be 0.02 cm (9). Other authors have reported similar figures (10). The direct error of measurement on the recorder chart adds up to the error due to the recording process itself. The rated accuracy of a recorder is the limit which errors will not exceed when the instrument is used under proper conditions (llJ2). For most recorders currently available for GC, this accuracy is between 0.15 and 0.4% of full scale. Unfortunately departure from the rated, proper operating conditions may severely alter this accuracy. Overdamping of the measuring circuit References on p. 687.

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by too large a source resistance, or overloading of the recorder amplifier by a noisy signal, even if this noise has a high frequency and is later filtered out, will result in an increased dead band and ib errors greatly exceeding the rated accuracy of the device. Finally, changes in the water content of the paper readily follow changes in the weather and especially the humidity. Dimensional stability of the paper may be questioned, although we are not aware of any detailed study of the implication of this remark. Thus, it appears that it is difficult in practice to carry out measurements of peak heights from a recorder chart with a repeatability better than ca 0.5%. This requires that careful attention be paid to proper scaling of the signal which should occupy more than half the chart width. b. From the Data Acquired with a Computer

The computer can easily determine the largest signal value acquired. This is not the peak maximum, however, for several reasons. The signal is noisy around the maximum, as well as on the base line. Furthermore, even if adjusted to zero at the beginning of the analysis, the base line may drift during the elution of the peak. The base line must first be interpolated under the peak. This is done by averaging the signal over a certain period of time before and after the peak considered, provided no other compound is eluted then. A period equal to two or three standard deviations is convenient. This may be difficult to determine between any two peaks during the course of a GC analysis. Then the base line is sampled before the elution of the first component of the mixture and after the elution of the last one. The two base line sequences are used to draw the base line under the peak and 'the peak profile is derived by subtraction of the interpolated base line from the signal. The longer the time over which the signal is interpolated, the larger the probable error. In spite of the wonderful qualities of modern software, this operation of deriving the proper base line during the analysis is better achieved, at least for complex analyses, by an analyst - computer interactive procedure. As we have mentioned above, the maximum signal does not give the best estimate of the peak maximum, because it may be tainted by the effect of a high noise fluctuation. A better method is to collect a certain number of values of the signal around the maximum signal and to fit them to an appropriate equation. This requires a very simple program and a small amount of calculation, so it is most easily implemented on a microcomputer. In practice, we operate as follows (13). Once the signal maximum has been identified, all data points which correspond to a value of the signal larger than 0.73 times the signal maximum are fitted to a parabolic equation, using a least-squares fit algorithm. This permits an excellent approximation of the parabola superosculatory to the peak profile at the peak maximum (i.e., the parabola which has the same maximum and the same curvature as the peak considered). From the parameters of the parabola an estimate of the retention time and of the peak maximum are derived, which are the best that can be obtained from the set of data obtained. The reason to take the points which are higher than 0.73*h, where h is the maximum signal, is that it corresponds to a

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distance from the peak maximum of 0.8*a. Since the Gaussian function can be expanded in a power series as: e-I2/* = 1- t 2 / 2 + t4/8 - .. . it is easy to see that at t = 0.8 the difference between the parabola and the Gaussian profile is less than 5%. A narrower sequence would give a smaller difference but also fewer points, which would result in a less precise determination of the coefficients of the regression. Depending on the specific application, a different compromise can be made. The influence of the density of points of measurements, of the signal to noise ratio, of the width of the sequence used for the least square fit, and of the degree of its eccentricity on the reproducibility and bias in the determination of the retention times has been studied in detail (13). Both computer simulation and the acquisition of actual experimental data have been used in this study. The influence of these parameters on the precision and accuracy of the measurement of the peak height have not been studied, however, and we know of no other study which could throw more light on this topic. The conclusions of this work are that a density of 10 data points per standard deviation is sufficient to achieve a bias on the retention time less than 2 X lop4 (0.02%). A density of 50 points per standard deviation would allow a bias no less than 1 x (0.002%). The sequence of data points selected for the least squares fit is obviously not centered on the true value and at low values of the signal to noise ratio its center may be some distance away. The result of the least squares fit procedure is biased. The bias does not exceed 18, however, except possibly in exceptional conditions, at low values of the signal to noise ratio. The reproducibility of the peak height determination is inversely proportional to the signal to noise ratio. 2. Measurement of Peak Area

The peak area may be measured directly from the chromatogram recorded on a paper chart, with an electronic integrator or calculated from the file of data points acquired by a computer. We discuss only briefly the nature and value of the errors made in the first case (measurements from paper chart). The reader is referred for more detail to the papers published on this topic by Ball, Harris and Habgood, which are classics (14-16). a. From the Recorder Chart

Ball, Harris and Habgood have examined in great detail the experimental procedures involved in the four most popular methods of manual integration, (i) the product of peak height by the width at a given fraction of the peak height, (ii) the area of the triangle formed by the base line and the two inflexion tangents, (iii) the weighing of the peak cut from a copy of the chromatogram with scissors and (iv) References on p. 687.

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planimetry (14-16). They determined the different steps involved in each procedure and studied, theoretically and experimentally, the sources of errors and their contribution.

P

Figure 16.1. Errors made in measuring the peak area using the product of the peak height by its width at half height. Schematic diagram for a Gaussian peak illustrating the errors associated with the four basic operations. After Ball,Harris and Habgood (8). 1. The error A B associated with the placement of the base line. 2. The error A h associated with the measurement of the peak height from the presumed base line. 3. The error Ay associated with the positioning of the measuring ruler parallel to the base line, at the presumed half height, for the peak width measurement. 4. The error Aw associated with the measurement of the distance between the two sides of the peak, at the position of the ruler. The inserts show the detail of each step and illustrate how the different errors compound together. For example, insert 3 refers to the positioning of the ruler to measure the peak width at half height. From the presumed base line, a distance h / 2 is measured and it is attempted to place the ruler at this intermediate height. An error has already been made on the true position of the base line, however, as well as on the value of the true peak height. The intermediate line which is actually drawn will not be placed where it was attempted to put it. Furthermore, the line along which the measuring scale of the ruler will be placed to measure the band width will differ from the line actually drawn. The different contributions to Ay are shown as two error bands of different widths around the presumed base line (first insert 3) and the attempted line at half width (second insert 3). (Reproduced from Analytical Chemistry,40,130 (1968) by permission of the copyright owner.)

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For example, in the first method there are four successive steps, (i) locating the base line, (ii) measuring the peak height, (iii) positioning the intermediate height and (iv) measuring the peak width (see Figure 16.1). The two first steps have already been discussed in the previous Section I.l.a, devoted to the determination of peak height. Each step introduces an error which influences all further steps (14,15). Theoretical analysis of the different contributions shows that the relative standard deviation on the peak area is given by: (2) where AB, Ay, A h and A w are the standard deviations of the positioning of the base line and of the intermediate height (0.5 * h), of the peak height and of the peak width, respectively (9). A statistical study of the measurements carried out by a group of operators on peaks of different sizes and shapes has shown an excellent agreement between the

Figure 16.2. Errors made on the measurement of peak areas, using different manual methods (15). Comparison between the relative errors made as a function of peak shape for the following techniques: a. Product of the peak height by the width at half height. b. Area of the triangle made by the base line and the inflexion tangents. c. Cutting the peak and weighing the piece of paper. d. Planhetry. (Reproduced from Journal of Gus Chromurogruphy, 5, 615 (1967) by permission of Preston Publications.)

References o n p. 687.

668 TABLE 16.1 Comparison between the Repeatability of Peak Areas measured by Different Methods of Integration Method of integration

Ref. (17)

Ref. (18)

Our work

Triangle area:base h e and inflexion tangents Product of peak height by width at half height Condal-Bosch method Product of peak height by base width Product of peak height by retention time Cut and weigh” Planimetry Peak height Electromechanical integrators Electronic digital integrators Computers

4% 2.5%

1-2.7% 0.8-2%

4% 2.5% 2%

1.7%

1.1-2.9% 0.4-1% -

‘I

4%

1.75% 4%

0.25-0.9% 0.4%

0.1-0.4%

4% 3% 0.5%

experimental results and those predicted by equation 2. The values of the standard deviations corresponding to the first three contributions are practically independent of the peak shape. They are worth, respectively, 0.010 cm (B), 0.012 cm ( h ) and 0.020 cm ( y ) . Aw increases from approximately 0.008 cm for sharp peaks to large values for wide peaks (14). The maximum precision of about 0.5% is achieved for peaks higher than 10 cm and between 3 and 5 cm wide. The recorder sensitivity and chart speed should be chosen carefully for maximum precision. Similar studies have been carried out for the three other manual methods of integration (14-16). The precision achieved is comparable, except for the second method (area of the triangle made with the base line and the two inflexion tangents), which is less good, because of the great difficulty of estimating the position of the inflexion tangents. The perimeter methods (“cut and weigh” and planimetry) are better than the product of the width at half height by the peak height for the determination of the areas of unsymmetrical peaks (see Figure 16.2). These results are in substantial agreement with those published by Gill et al. (17) who obtained the values reported in Table 16.1 for the relative standard deviation of the measurements. Similar results have been obtained by Bocek et al. (9) and by Grant and Clarke (18); they too are reported in Table 16.1. b, With an Electronic Integrator As we discussed in Chapter 15, Section 1.2, the difference between electronic integrators and integrating computers is in the lack of any significant amount of memory for the former. Lacking the ability to refer to immediate past events, the electronic integrator has to make immediate decision regarding the nature of the phenomena it observes and cannot correct later for the consequences of an incorrect or tardy decision. Thus, when the signal first derivative is positive but lower than the threshold value for peak detection, the integrator, which has no way of knowing a peak is coming, behaves as if for a base line drift and corrects for it (19). When,

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later, a peak is detected because the first derivative exceeds the threshold, it is too late to include the part of the profile area lost, corresponding to early eluted molecules and to return to the proper value of the base line (19). As a consequence the electronic integrator introduces systematic errors which are difficult to correct for. Their importance depends on the peak shape. The error is very small for early eluted, narrow peaks and becomes quite large for shallow, wide, late eluted bands. Baumann et al. have discussed the difficulties in defining the automatic sequence of operations followed by an automatic integrator (20). More generally, the errors introduced by an electronic integrator are the following: (i) non-linearity of the voltage/frequency conversion, (ii) error in the position of the reference signal (base line), (iii) incorrect count of the pulse number, (iv) errors in the decision to start or stop the integration. The first error is usually small, the linearity of the voltage/ frequency converters (VFC) is specified to be 0.1%.It is difficult to check that figure properIy: one would have to integrate a constant voltage signal for a certain period of time and plot the ratio of the signal area to the signal voltage as a function of the logarithm of the signal voltage. It is difficult to achieve such measurements with a precision much better than 0.01%, as would be required to check the linearity of the VFC. To deliver a signal truly proportional to the analyte concentration when this compound is eluted, the converter zero is constantly adjusted by a feed-back system which corrects for possible base drift between peaks. During the time elapsed between the actual beginning of the peak elution and its detection the system overcorrects, for what it wrongly takes to be a base line drift. An entire area strip along the base line is lost. For this reason, the analyst should strive to stabilize his equipment and should adjust the base line drift correction rate to the minimum compatible with the quality of his base line. Similarly, the detector noise should be reduced as much as possible, without using an RC filter on the signal line, which may dramatically increase the detector response time and result in sluggish response, tailing peaks, loss of resolution and other types of errors. A compromise has to be chosen in the setting of the peak sensor threshold, between a low value, which will improve the quality of the detection of late eluting, wide peaks and a high value which eliminates false detection due to high noise fluctuations. Baumann and Tao have studied the errors introduced by electronic integrators and reported that it is not difficult to find experimental conditions for which the integration error is smaller than 1 8 , but it is extremely difficult to reduce this error below about 0.2%(19). These results are in excellent agreement with those of Gill et al. (17) and of Grant and Clarke (18), reported in Table 16.1. c. From the Data Acquired with a Computer

There are two possibilities for the data handling: it is carried out either on-line or off-line. In the first case the program has access to the stored data and can use them to correct for the consequences of its later decisions. Furthermore, in the latter case, the analyst can participate in the process, in an interactive mode. The computer References on p. 687.

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rapidly makes the calculations required and supplies the results in tabular form and/or the chromatogram with the base line and the border lines of the area allocation made to each peak. The entire chromatogram, or expanded sections of it, can be displayed on the computer monitor. The analyst may accept the computer suggestions or demand further calculations corresponding to other decisions, overruling the computer. The repeatability of the measurements and the bias depend on the frequency of data acquisition, on the peak detection threshold and on the signal to noise ratio. The influence of these different factors has been studied in detail, experimentally and by computer simulation, by Goedert and Guiochon (21-24). If the density of data points is too low, the repeatability of the measurement is poor and the bias large (21,25). These phenomena result from the lack of repeatability of the shift between the time of the peak maximum and the time when the nearest data point is acquired. When the acquisition frequency is increased, the repeatability improves rapidly and the bias stabilizes at a value depending on the width of the integration window. The magnitude of the error made at low density of data points depends on the asymmetry of the peak. The phenomenon hardly affects the area of Gaussian peaks. It becomes important for tailing peaks. When an accuracy between 1%and 0.1%is looked for, a density of data points of about 10 points per standard deviation is sufficient. If an accuracy of 0.01% or better is looked for, higher densities of data points may be necessary (25). As is explained above, in Chapter 15, Section I11 on data processing, the signal is first smoothed by either fitting an nth degree polynomial or by convolution with a numerical filter. Peak detection is then made after the value of the derivative or of the pseudo-derivative (26). The pseudo-derivative is the derivative on an adjusted time scale, taking into account the fact that band width increases with increasing retention time. Computer simulation shows that the bias on the peak area is approximately equal to the ratio of the signal at both ends of the integration time window to the peak maximum (22). If the signal does not have the same value at the two ends of the time window, the larger value is taken. Accordingly, when the required accuracy is increased, the time window has to be enlarged to encompass all the time range where the relative value of the signal exceeds the corresponding threshold. For unsymmetrical peaks it may be impossible to do data acquisition and processing in the extremely wide time window required for an accuracy of 0.01%, for example. This would in most cases require unrealistic values of the resolution and an enormous analysis time (21,22,25). The residual bias, due essentially to the impossibility of carrying out the integration in a wide enough time window, even in the ideal case when there is no noise and the resolution is large enough, disappears in practice, because the signal noise generates a larger random error (22). A study on the influence of the signal to noise ratio (i.e., the ratio of the maximum peak height to four times the standard deviation of the noise) has been made on Gaussian profiles (22). The results show that the repeatability of ten measurements is inversely proportional to the signal to noise ratio in a range of 0.5 to 10,OOO for this ratio. The confidence interval on the mean of ten measurements is approximately 0.15 times the signal to noise ratio. The bias on the mean of a series

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of ten measurements decreases at first with increasing signal to noise ratio, then levels off at a value which is approximately equal to 0.5 times the value of the signal at the end of the integration window. To achieve this result, a segment of base line about three times the standard deviation of the Gaussian peak must be recorded before and after the peak. The noise superimposed on the signal had no low frequency component, i.e., there was no base line drift on the time scale of either the peak width or the retention time. This corresponds to the conditions of a stable detector signal, as is most often encountered in routine analysis, but is somewhat optimistic in many practical cases when only small series of similar samples are analyzed quantitatively under the same experimental conditions. Furthermore, it is exceptional that the same analysis is repeated 10 times. Most often even careful analysts rarely repeat the same analysis more than 3 times. Thus, in practice the repeatability of an analysis will be of the order of 0.5 to 1 times the signal to noise ratio (22). While the reproducibility of the peak area determination is almost totally independent of the width of the integration window, the bias decreases in proportion to the value of the signal at the end of the window, i.e., as exp( - t 2 / 2 ) . where t is half the width of the window, in peak standard deviation unit. As a consequence, the width of the integration window should be adjusted as a function of the signal to noise ratio. Integration limits corresponding to values of the signal equal to 0.01, 0.001 and 0.0001 times the peak maximum, are quite acceptable for Gaussian peaks corresponding to signal to noise ratios of 20,200 and 10,000, respectively. Since the precision of the measurements increases steadily with decreasing signal to noise ratio, but since it is often impossible to increase the signal without overloading the column and spoiling the resolution between some components, that is if the column has been wisely selected, the analyst should strive to reduce the detector noise as much as is reasonably possible. For that purpose the time constant of the amplifier should be carefully adjusted. The effect of the time constant is to reduce the noise by convoluting the signal with an exponential function having the same time constant. The peak area of this convolute is the same as the area of the signal (27), but the retention time is increased and the peak becomes unsymmetrical. The time to end the integration is increased and less well defined. The signal to noise ratio is decreased, so is the peak efficiency and the resolution. The quality of the analysis is degraded. To minimize these negative effects, the time constant should be smaller than 1/20 of the base width of the peak. Efforts to reduce the signal noise should be made rather in selecting a high quality system and in operating and maintaining it properly. In practical applications, an excellent repeatability is usually observed (see Table 16.1), much better than the one achieved with other methods of integration, which explains the popularity of computer or programmable digital integrators. In the case of complex chromatograms it becomes more difficult to determine the position of the base line as the distance between successive peaks decreases. Sometimes the base line under two peaks has to be assigned as indicated on Figure 15.3C.As a result, systematic errors increase. In spite of many attempts, peak References on

D. 687.

612

deconvolution when the degree of resolution between successive peaks is smaller than 0.7 to 1.0 has not been successful (28). In large part this is due to the fact that the behavior of chromatographic columns and detectors is not linear to the degree required for achieving a good precision with the deconvolution methods used. The profile obtained is not merely the sum of the profiles which would be obtained if each component of the mixture were injected separately, in the same amount as is in the sample studied (see Chapter 5). In such a case, the deconvolution based on linear behavior fails.

3. Peak Height or Peak Area? There is little practical choice for those who have to work with a data system purchased from a manufacturer, as all available softwares are based on the use of peak area. The controversy between the use of peak height or peak area for the determination of the composition of a mixture was settled in the very early 'sixties in favor of peak areas and has never been seriously revisited ever since. There are many results that tend to show that peak height is often more precise than peak area (29). On the other hand, peak area tends to be more accurate. The choice, if it were made on purely rational reasons for each analysis would probably favor peak height in a significant minority of cases. On a general basis it can be said that peak heights are more sensitive than peak areas to the fluctuations of most experimental conditions, especially the column temperature, the column efficiency, the amount of stationary phase, the sample injection profile (see Chapter 13, Section III.2.b above, on the discussion of the reproducibility of valve injection), and the carrier gas flow rate for class I1 detectors (see Chapter 13, Section II.2.a and next section). Also the peak height does not increase in proportion to the sample size if the column is overloaded, whereas the peak area does, at least as long as the detector is not overloaded. The dynamic linear range may be narrower when peak height is used (9). Finally, since the maximum analyte concentration in the elution profile depends on the band width, the peak height depends on the retention time and the column efficiency. Thus, the response factors cannot be used independently of the specific conditions of the analysis for the derivation of a quantitative estimate of the concentration of a component in a mixture. In other words, when using peak height to determine the composition of samples, the analyst has to spend a large fraction of the time doing calibration. On the other hand, for class I detectors the peak area decreases in proportion to the inverse of the flow rate, while the peak height is proportional to the square root of the plate number and vanes very little around the optimum flow rate. These properties of the peak height are certainly important drawbacks for use in quantitative analysis, but less than they were in the early 'sixties. Modem gas chromatographs are much better controlled than were their cousins of 25 years ago. In many cases the degree of control achieved with routine analyzers is such that peak height would be more precise than peak area. Analyses would be cheaper to perform, since simpler equipment and shorter computer time are required, although calibration would be needed more often.

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This position is in agreement with the conclusions of several authors who observed that, with careful and suitable control of their equipment, they obtained a better precision from peak height measurements than from peak areas (4,5,10,29,30). The profound drawback of peak height measurements at present is the lack of suitable equipment or computer software for its automatic determination during an analysis.

4. Measurement of Sample Size The repeatability of sampling systems has been discussed above, Chapter 13, Section 111. It improves from syringe to sampling valves to automatic sampling valves which must be prefered any time an accurate analysis is required. With syringes the absolute standard deviation of the sample volume delivered has been estimated to be around 0.04 pL for sample volumes between 1 and 10 pL (9). A similar result was cited by King and Dupre (31) who give a repeatability of 5% at the 95% confidence level in the range 0.1 to 3 UL (i.e. a standard deviation around 0.002 to 0.06 pL). Kaiser (5) also reports similar results, while noting that automatic syringe injection devices perform better. Grant and Clarke (18) have observed that the relative standard deviation of the ratio between the areas of two compounds of similar vapor pressure injected with a syringe is 0.2 to 0.98, while for compounds of widely different vapor pressure values of 0.7 to 1.6% have been measured. For gas sampling valves the accuracy of the calibration is around 0.1% but the repeatability is better (5). If the gas pressure inside the sample loop is properly controlled, a repeatability of 0.03%of the sample size can be achieved (30). The performance of liquid sampling valves is not as good, but repeatability of 0.3 to 0.5% can be achieved with automatic valves (see Chapter 13, Table 13.1).

11. THE GENERAL PROBLEM OF INSTRUMENTAL ERRORS

The stability of the gas chromatograph and especially of the detector is a critical factor in achieving repeatable measurements (3). The response factor has been treated so far as a physicochemical constant. In fact, the response factor is a function of the value of a number of parameters which together determine the detector response. These parameters are kept more or less stable, depending on the quality of the instrument used and on the care with which it is maintained and set up by the analyst. The fluctuations of the detector operation and ambient parameters result in an error which can be calculated if we know the relationship between the response factor and these parameters and the range of their fluctuations (30). We discuss these relationships here, first from a general viewpoint, then in more detail for the better known detectors, the TCD and the FID. Fluctuations of the detector response factor originate in fluctuations of the parameters which may take place either during an analysis, and affect the area of one or several peaks or the relative area of an analyte and the internal standard, for example, or from one analysis to the next one in a series. Some of these fluctuations, References on p. 687.

614

but not all of them, are also at the root of the base line noise or drift. The effect of short-term fluctuations is cancelled out in the determination of the area of one single peak, if the period of these fluctuations is small compared to the width of the analyte peak. The effect of long-term fluctuations can be cancelled by the use of relative peak areas, if their period is large compared to the difference between the retention times of the analyte and the standard. Fluctuations that take place over a period of between a few seconds (a few tenths of a second when open tubular columns are used) and several minutes to an hour are often the most dangerous. When a function of several variables x, y, z , such as a response factor or a peak area, is determined, any error or fluctuation in the variables or parameters results in an error in the function. Generally the following relationship holds between the standard deviations S,, of the function measured and S,, S,, S, of the (more or less stable) parameters:

The partial differentials, af/ax, af/ay, af/az are known as the error propagation coefficients (30). Systematic measurements of the effects of fluctuations of ambient parameters can be made from the variation of peak areas which result from a small but significant change (ca 10 to 20 times the observed noise or fluctuation level) of each parameter, successively (30). This method has been applied both to the TCD (30) and the FID (32), giving results which can be used to determine the specifications of instruments of a given precision. In principle the effect of fluctuations of the ambient parameters could also be studied by using a method similar to the one described by Johnson and Stross (33), and applied to the analysis of base line fluctuations. This time, a mixture of carrier gas and analyte vapor of known composition would be passed through the detector. Such a method has not yet been investigated, as far as we are informed. Instrumental errors have received little systematic attention in the scientific literature. The purely empirical work of pruning the sources of fluctuations of detector response and striving to reduce them is not very glamorous, but is very demanding. Until the recent incorporation of microprocessors in analytical instruments, the errors introduced by the measurement of the response itself were the determining contribution to the precision of analytical results (24). They still are sometimes. But instrumental fluctuations have now become an important contribution to the precision of analysis and a proper use of sensors, computers and statistical analysis should permit a great improvement in the quality of data obtained by gas chromatography. This requires, however, a profound understanding of the behavior of the detector used. In what follows we discuss the influence of pressure, flow rate and temperature on the detector response, then the special cases of the two most important detectors, the TCD and the FID are reviewed.

675

111.

PRESSURE A N D FLOW RATE STABILITY

The existence of two different classes of detectors and their specific properties have been discussed previously (see Chapter 10, Section 1.1 and Chapter 13, Section 11.2). The first class contains the detectors which respond to variations of the solute concentration in the column effluent (34,35). The peak areas are inversely proportional to the gas flow rate. The peak heights are proportional to the square root of the column efficiency and accordingly remain rather insensitive to flow rate fluctuations around the optimum value, corresponding to maximum column efficiency (see Chapter 4). The detectors of the second class respond to changes in the mass flow of solute to the detector cell. The peak area is independent of the flow rate, while the peak height increases with increasing flow velocity. From the relationships between peak area, carrier gas flow rate, inlet and outlet pressure, it is possible to derive specifications regarding the required stability of the flow rate or pressures. These specifications will be different for the two classes of detectors.

1. Relationship between the Fluctuations of Pressure and Flow Rate and the Precision on Peak Area for Class I Detectors The peak area is the integral of the concentration of analyte in the eluent versus time (see Chapter 10, Section 1.1). The mass of analyte is the integral of its concentration versus volume of eluent. Accordingly, for a class I detector, the response of which is proportional to the concentration of the analyte in the detector cell at all times, the peak area, A, is given by: A = -Fm

DO

(4)

where F is the response factor for the analyte, m its mass in the injected sample and Do the carrier gas flow rate in the detector. The outlet flow rate is related to the outlet flow velocity and the inlet and outlet pressures, Piand Po,respectively (see Chapter 2, section I) by:

where S is the cross section area of the column volume available to the gas phase, k the column permeability, 17 the carrier gas viscosity and L the column length. The outlet flow rate is a function of the inlet and outlet pressures. In practice, however, it is rare that the inlet and outlet pressures of the column are controlled separately. In fact it has been shown that it would not be good technical practice, because the specifications on the control of each pressure would be too drastic, References on p. 687.

676

especially if the pressure drop along the column is small or moderate (37). Controlling the pressure drop, Pi - Po, and the outlet pressure separately is theoretically more sound. It is also experimentally easier: pressure controllers operate by reference to some reference pressure, generally the atmospheric pressure. When this is not stable enough, they have to be referred to vacuum (36,37). If we let: p = Pi - Po

(6)

equation 5 becomes:

Combination of equations 4 and 7 gives the relationship between the peak area, the inlet pressure and the pressure drop:

Differentiation by respect to Po and p, the pressure differential, gives the two error propagation coefficients (37): dA -

4FmqL

Po(p+Po)

dP

Sk

[P(P+2PO)l2

(9)

-dA' --4FmqL 1 dPo sk (p+2PJ2 or:

dA

-=--

A

2p dPo p + 2P0 Po

The relative random error made on the determination of the peak area with a Class I detector is the sum of two terms, one proportional to the relative fluctuations of the pressure drop and the other proportional to the relative fluctuations of the outlet pressure. The two error propagation coefficients are given by equations 11 and 12. respectively. Typical numerical values are reported in Table 16.2. For a very small value of the pressure drop the propagation coefficients are -1 and 0, respectively. For very large pressure drops they are equal to - 2 and 2, respectively. Since in most cases the outlet pressure is not controlled but is set equal to the

677

TABLE 16.2 Error Propagation Coefficients of the Outlet Pressure and the Pressure Drop for the Peak Area Outlet pressure,

p=1.2

p=lS

p=2.0

p=3.0

p=5.0

p=7.0

p=10.0

PO

1 atm

EPC(p) EPC(Po)

-1.375 0.750

-1.429 0.857

-1.500 1.OOO

-1.600 1.200

-1.714 1.429

-1.778 1.556

-1.833 1,667

0.5 atm

EPC(p) EPC(Po)

-1.545 1.091

-1.600 1.200

-1.667 1.333

-1.750 1.500

-1.833 1.667

-1.875 1.750

-1.909 1.818

1.2 atm

EPC( p ) EPC(Po)

- 1.333 0.667

- 1.385 0.769

- 1.455

- 1.556 1.111

- 1.676 1.351

- 1.745 1.489

- 1.806 1.613

0.909

EPC(p), EPC(Po) stand for the error propagation coefficients of p and Po, respectively. p is the pressure drop, Pi - Po. Pi and Po are the inlet and outlet pressures, respectively.

atmospheric pressure, the precision of the analysis cannot be better than the stability of the local weather. Accordingly, errors of 0.2 to 0.5% due to fluctuations of the atmospheric pressure are difficult to avoid when using a concentration sensitive detector (Class I). 2. Relationship between the Fluctuations of Pressure and Flow Rate and the Precision on Peak Area for Class I1 Detectors With a mass flow detector the peak area is the integral of the mass flow rate of analyte to the detector by respect to time. Thus: A=Fm

In this case the peak area is independent of the flow rate and there is no error contribution due to pressure fluctuations, whether pressure drop or outlet pressure. This is why the measurement of peak areas from signals supplied by Class I1 detectors (such as the flame ionization detector) is more precise than from signals supplied by Class I detectors (such as the thermal conductivity detector).

3. Specifications Knowing the error propagation coefficients it is possible to derive the figure required for the pressure stability, depending on the error that is considered to be acceptable (30). Obviously, the pressure fluctuations should not account for more than half the final error, since other experimental parameters, such as those controlling the detector response, will also contribute to the error by their fluctuations and since there is always a contribution to the error from the measurement process itself. It seems reasonable to require that the contribution of the fluctuations of each pressure (i.e., pressure drop and outlet pressure) to the variance of the measurements be lower than 1/9 of the acceptable total variance, which means that the References on p. 687.

678 TABLE 16.3 Specificationsfor the Pressure Control of a Chromatograph using a Class I Detector Precision level

Pressure hop

Outlet pressure

1% 0.1% 0.01%

0.6%

0.06% 0.006%

0.5% 0.05% 0.005%

The fluctuations of each pressure contribute to 1/9 of the total variance, Le., are worth 1/3 of the total standard deviation (cf. Table 16.2, Po= 1 atm, p = 5.0 atm).

standard deviation of the relative pressure fluctuation will be such that the corresponding fluctuation of the peak area will be 1/3 the accepted relative standard deviation of the measurements. The reason for this is that there are other sources of error, for which some provision should be made. In carrying out the calculations for the specifications for a class I detector, we have taken the error propagation coefficient corresponding to the largest pressure drop which is used in practice, 5 atm. The results are reported in Table 16.3. They show that with Class I detectors it may be necessary to control the outlet column pressure to achieve precise determinations (30).

IV.TEMPERATURE STABILITY From equations 1 and 13 we see that the peak area can be influenced by temperature fluctuations only if the response factor of the detector is temperature dependent or, for Class I detectors only, if the column flow rate depends on temperature. The viscosity of gases is a function of temperature (see Chapter 2). Accordingly, the derivation of equation 8 by respect to temperature gives the error propagation coefficient of the peak area for the temperature:

For a Class I1 detector a similar equation is obtained, which does not contain the second term of the RHS of equation 14. This term is equal to 0.8dT/T (see Chapter 2), where T is the column temperature. The first term of the RHS of equation 14 depends on the detector temperature. It will usually be much larger than the second term, so the temperature dependence of the response factor of Class I and I1 detectors will be very comparable and essentially determined by the thermal stability of the detector itself. The requirement for constant retention times in isothermal analysis imposes such drastic specifications for the temperature control of the column that no significant flow rate fluctuations will result from a change in carrier gas viscosity with temperature.

679

The situation is different in temperature programming. The carrier gas viscosity changes greatly during the analysis. Any fluctuation in the program rate results in a lack of reproducibility of the flow rate profile, hence in fluctuations of peak area and retention time. This probably explains why quantitative analyses are less precise in temperature programming than in isothermal conditions.

V. STABILITY OF THE DETECTOR PARAMETERS The behavior of each detector used for quantitative analysis should be studied in detail. Obviously, the nature and importance of the dependence of the response factor of a detector on the ambient parameters is a function of the detector principle. For each principle, however, different implementations may result in very different quantitative relationships between response factor and ambient parameters. Finally, it is not rare to see detectors made by the same manufacturer which exhibit slightly different behavior.

1. Thermal Conductivity Detector The error propagation coefficients for the TCD can be determined experirnentally as explained above, by changing slightly the set value of the parameters and measuring the induced change in the response (30). They can also be calculated from the equation derived by Littlewood (38) for the response factor (see Chapter 10). The results obtained by the two methods are only in fair agreement, due to the approximate character of the theoretical equation, its validity being restricted to the use of a light carrier gas (H, or He), of a detector cell receiving the analyte vapor only by diffusion, not by convection, and of a moderate sensor temperature. Finally, the theoretical equation includes two constants which are impossible to derive a priori and which may in fact turn out to depend to some extent on some of the ambient parameters. They are the average collision diameters of the carrier gas and analyte, and the geometrical constant of the detector cell. The experimental parameters which determine the response of the TCD are (i) the temperature of the detector, (ii) the gas flow rate in the detector, and (iii) the bridge current or voltage. In addition the response of the detector depends on (iv) the temperature of the column (since the TCD belongs to the Class I of detectors), (v) the inlet and outlet pressures (which determine the actual flow rate through the detector), (vi) the ambient temperature (which has an indirect effect on the stability of the pressure or flow rate controllers, on the heat leak of the ovens, and on the performance of electronic components) and, for a gas sample, (vii) the temperature and pressure of the sample loop. The error propagation coefficients for peak height and peak area have been calculated and discussed (30). The values are reported in Table 16.4. A comparison between the values predicted and measured with a Gow-Mac TCD are reported in Table 16.5. The agreement is very good. The only significant discrepancy is observed with the propagation coefficient for the bridge current, which has been References on p. 687.

680 TABLE 16.4 Error Propagation Coefficients for a Thermal Conductivity Detector P i , Inlet pressure, Po, Outlet pressure. a, /3, Coefficients in the expansion of the resistance versus temperature relationship, R = Ro(l + ar + j3t2). k', Column capacity factor. A H , Heat of solution of the vapor in the stationary phase. Peak area Inlet pressure* Outlet pressure*

Peak height

2 Pi'

***

Pi' - P,' -2Pj

***

Pi' - P,'

Sample pressure (gas)*

1

- 0.8 -

Column temperature*

T

/3

Detector temperature**

0.4

a~~

Sample temperature (gas)** Bridge emf*

-1/T

- 1/T

3

3

Coefficient for relative variations of the peak size.

** Coefficient for absolute variations of the peak size.

*** Depends on the camer gas flow rate compared to the optimum flow rate. TABLE 16.5 Comparison between Measured and Predicted Values of the Error Propagation Coefficients of a TCD Peak area Temperature Inlet pressure Oulet pressure Bridge emf Flow rate Sample pressure

Peak height

Theoretical

Experimental

- 1.8 -4.3 1.86 3.0 - 1.0 1.o

- 1.3 - 4.7 1.8 3.5 - 1.0 1.o

Experimental conditions: k' P,= 1.5 bar; /i = 0.5.

= 1.0;

Theoretical 3.3

- 2.1 0.9 3.0 - 0.5 1.o

T = 330 K (57O C); Po =1.1 bar. a = 4.5 X

Experimental 3.6 - 1.5 0.11 3.5 -0.33 1.o A H = 4 kcal/mole;

TABLE 16.6 Specificationsfor a Precise Thermal Conductivity Detector Total error at the 95% confidence level Range of fluctuations of Inlet pressure (%) Outlet pressure (4;) Sample size (%) Temperature ( O C) Bridge current (I) Error of measurement (%)

1%

0.1%

0.01%

0.1 0.2 0.4 0.9 0.15 0.4

0.01 0.02 0.04 0.09 0.015 0.04

0.001 0.002 0.004 0.009 0.0015 0.004

measured larger than predicted. These results are in agreement with those obtained by Clarke and Grant (32). These results can be used to derive specifications for the design of an instrument capable of achieving any given level of repeatability, above about 1/10,000. Better precision would be possible, but additiocd problems may appear which have not been identified and discussed as yet. Some results are given in Table 16.6, assuming that all parameters may contribute equally to the error. Some trade-offs are possible, but they are limited, because of the variance addition rule. It can be observed from the data in Table 16.6 that the outlet pressure has a very important effect on the precision of the results of quantitative analysis by gas chromatography. Its control should be given some importance, in contrast to current practice. Goedert and Guiochon (30) have conclusively shown that it is possible to achieve quantitative results with an excellent precision by using carefully built equipment, incorporating excellent control of all parameters, including the outlet pressure. They found a concentration of nitrogen in air of 78.1 f 0.3% (at the 95% confidence level) from peak area measurements and 78.0 f 0.15% from peak height. These values are in excellent agreement with that obtained by volumetric analysis (78.1 f 0.1%). The lower precision obtained with peak area may be explained in part by the use of a very early model of electronic integrator. Using a similar method, Jecko and Raynaud (10) have achieved the analysis of blast furnace gases with a relative standard deviation of 0.1% for nitrogen (54%)and for carbon monoxide (27%).The relative standard deviation was 0.2% for carbon dioxide (19%) and 1%for hydrogen (5%). Helium was used as carrier gas, hence the small signal for hydrogen. Sanford et al. (39) have built a process gas chromatograph incorporating high quality temperature and pressure controls to analyze light hydrocarbon mixtures. For 16 replicate analyses of the same mixture, carried out over a two-day period, the relative standard deviation was between 0.05% and 0.1% for the major components (concentration larger than ca 15%), and 1%for the minor components having a concentration around 1%.For 40 replicates of the analysis of another reference mixture, carried out at random during a seven-month period, the relative standard deviation was 0.4% for the major components and 1%for the minor ones. These results demonstrate that good control of the ambient parameters of a TCD, and probably of other detectors as well, allows the achievement of high quality measurements.

2. Flame Ionization Detector No theoretical study similar to the one carried out with the TCD can be made for the FID, for the lack of a theoretical equation predicting the response factor and relating this factor to the ambient parameters of the detector, such as the pressure inside the cell, the flame temperature, etc. Although the reaction leading to the formation of the charge carriers has probably been identified by Sternberg et al. (40), its kinetics is still largely unknown. Furthermore, the collection of small amounts of ions such as those formed during References on p. 687.

682

the combustion of tiny samples of hydrocarbons is difficult. The design and implementation of electronic amplifiers for the very low currents taking place at large impedence such as those collected in an FID are made very difficult by the requirement of a small time constant. A number of phenomena described in the literature, such as the S-shape response of a FID described by Bruderreck et al. (41), may probably be ascribed to the nonlinear behavior of certain types of amplifiers or of splitter-type injection devices. Improved amplifiers have permitted the achievement of dynamic linear ranges exceeding 1 million. The change of amplifier range during the course of an analysis and especially during the elution of a compound should be avoided, however, unless the calibration factors relate to the specific ranges used (18). Widely different figures have been published by different authors regarding the polarization voltage of the detector and its effect on the response factor or the dynamic linear range. This is largely due to the fact that only the electrical field created between the collecting electrodes is relevant. Data published by Bruderreck et al. (41) show that with a polarization voltage of 225 V, i.e., an electric field of 400 V/cm, the detector response is linear within 1%up to a sample mass flow rate of 3 X lo-’ g/s (I= 12 nA, linear dynamic range about 100,000). With a 10 GO input resistance, such a current results in a 120 V voltage drop. Even if a good electrode design still permits a total ion collection, it is not surprising that deviation from linearity appears for higher currents, unless a lower input resistance be used. Ultimately a space charge appears and the ion collection yield decreases. A current of 10 nA,however, corresponds to a small amount of hydrocarbon, about 3 pg for a typical conventional packed column peak (e.g., t,=250 s, peak width 20 s, N = 2,500 plates). Hence, the FID is linear only for small sample sizes (or for strongly retained peaks), and a splitter injection device will often be necessary for precise quantitative analysis of large samples. Alternately, dilution of the sample is possible, if needed, in a solvent which gives almost no signal with the FID, such as C!$, CH3CN, H,O, etc. In addition to the collection voltage, the FID response depends also on the flow rates of hydrogen, oxygen or air and carrier gas, and on its temperature. The absolute responses but also the relative response factors vary when these parameters change, the variations of the latter being large for compounds of different chemical structure. This dependence has been studied in detail and thoroughly discussed by Grant and Clarke (18) in a paper which is a landmark in the area of quantitative analysis. The absolute response of the FID for a given compound is maximum for a certain value of the flow rates of the carrier gas (helium or nitrogen) and of the hydrogen. These two “local optimum” flow rates are related and there is a set of flow rates giving an absolute extremum. The derivation of this set can be considerably helped by the use of a “Simplex” process, such as the one implemented in the “Instrumentune-up” program (42). The flow rates of hydrogen and carrier gas giving the largest response factor are somewhat different for each compound analyzed, so the relative response factors depend to some extent on the flow rates (see Chapter 14, Section 3.2). Around the optimum values, the variation is mod-

683

erate, however, about 4% for the response of n-propanol relative to ethylbenzene (18). Accordingly, the gas flow rate settings of a FID should never be adjusted between the time of calibration and the time of analysis. Otherwise the detector should be recalibrated. This explains why it is wise to have two sets of valves for each gas line, a stop valve and a metering valve. At a given setting of hydrogen and carrier gas flow rates, the detector response increases at first with increasing air or oxygen flow rate, but rapidly levels off and reaches a plateau. The air flow rate should be set at a value on this plateau. The curvature of the surface representing the response factor plotted against the hydrogen and the carrier gas flow rates increases with decreasing oxygen flow rate. The combination of these effects of the flow rates of the various gases fed to a FID explains why the response factors, absolute as well as relative, will vary for a given compound from detector to detector, even for apparently minor changes in the design. Small variations in detector temperature hardly affect the precision of area ratios, but may drastically change the absolute areas obtained, so procedures using such area ratios or relative response factors should be preferred. In temperature programming, the detector temperature should be carefully kept constant, independent from the column temperature. The variation of the column oven temperature should not interfere either with the carrier gas flow rate, and a mass flow rate controller must be used for optimum performance. Otherwise, the flow rate decreases by 0.45% for a temperature increase of l 0 C (see Chapter 2). In temperature programming, with a mass flow rate controller, the volume flow rate of carrier gas at column temperature increases with increasing temperature, due to gas expansion, but this has minimal effect on the detector response if the detector temperature is kept constant. It has been shown by Blu et al. that the response of the FID varies with increasing pressure, going through a maximum around 5-7 atm (43). In order to be able to achieve a precision better than about 1%on the absolute peak area, it will become necessary to control the pressure in the detector cell. From the data reported by Grant and Clarke (18), it is possible to derive the specifications for a detector with a repeatability of 196, assuming that all sources of error contribute equally to the total error. These values are given in Table 16.7. It should be understood that, although the trends illustrated by these data are valid for TABLE 16.7 Specifications for a FID* ~

Parameter

Maximum fluctuation allowed

FID temperature Carrier gas flow rate** Hydrogen flow rate** Air flow rate** Polarization voltage Column temperature

2OC 2% 1.5% 1.5% 1v 2OC

Precision: 1%. See ref. 18.

** The detector is supposed to be operated under optimum hydrogen and carrier gas flow rates. References on p. 687.

684

about all FIDs, the exact values reported in this table apply only to the detector studied by Grant and Clarke (18). 3. Other Detectors Very few studies dealing with the sources of error in quantitative analysis using another detector have been made.

V1. OTHER SOURCES OF ERRORS 1. Measurement of Sample Sue These sources of error have been discussed in detail in Chapter 13. It is not necessary to discuss them again here. The conclusion of this chapter was that the sample size can be measured with an accuracy of about 0.5% and a precision between 0.1 and 0.2% with sampling valves. The errors may be 3 to 10 times larger with syringes.

2. Representativity of the Sample Although they are not properly classified as contribution to the measurement errors, the phenomena which cause discrimination in the sample, i.e., enrichment of certain compounds compared to others in the mixture which is actually eluted of the column, are the sources of major systematic and random errors. Of major concern to the analyst is the behavior of splitting injection systems for open tubular columns (see Chapter 8, Section IV.1).

VII. GLOBAL PRECISION OF CHROMATOGRAPHIC MEASUREMENTS A combination of the methods described in Chapters 13 to 16 permits the achievement of a repeatability of gas chromatographic measurements of the composition of mixtures which is normally between 1 and 2%. Better results can be achieved sometimes, in favorable conditions, especially if well designed and maintained equipments are used in temperature controlled rooms, with computer data acquisition and handling. When the results are less satisfactory, it is probable that either the equipment has some problems requiring maintenance or that the sample contains some component(s) which are lost in a nonreproducible way, by pyrolysis, adsorption or selective vaporization during sampling and injection. Poor precision can be observed also when pushing the technique to its limits, e.g., in trace analysis, in the analysis of highly corrosive or reactive materials or of compounds with a very low vapor pressure, requiring columns temperature in excess of CLI 250 O C. The methods which are recommended to achieve the best performance in quantitative analysis are:

685

- The determination of the sample loop volumes by acidimetry; the average precision is about 0.58, - The determination of relative response factors with the gas density balance; the average precision is 1.38, - The calculation of peak areas with a computer or a digital integrator using a programmable microprocessor; the average precision is 0.55%. The fundamental equations relating the amount of a compound eluted after the injection of a sample in which it is present, and its concentration to the response factors and the peak areas are:

m, = f , A j and (in the case when the internal standard method is used, see Chapter 15, equation 23):

In both cases, the study of error propagation shows that the variance of the result is the sum of the variances of each of the parameters involved (see Chapter 13, Section I), hence the standard deviation of the measured sample amount is given by: a,,, =

/m-

while the standard deviation of the concentration is:

where a is a standard deviation and the indices m , C, f and A refer to the amount of component of interest, its concentration, its response factor and its peak area, respectively. Cis refers to the internal standard; the standard deviation on the concentration of the internal standard is estimated to 0.5%. The numerical result is that the precision on the amount is 1.4%,while that on the concentration is about 1.6%. The difference is small, almost negligible. Relative determinations are preferred to absolute ones, in spite of a comparable precision and a somewhat greater complexity, because they carry a built-in correction for a number of determinate errors. TABLE 16.8 Analysis of Blast Furnace Gas (10)

Concentration (%) Relative standard deviation (%)

N2

co

COZ

H2

54 0.09

27 0.10

19 0.22

5. 1.oo

Carrier gas: helium. References on p. 687.

686

TABLE 16.9 Analysis of Light Hydrocarbons (39) Component

16 Consecutiveanalyses of a vapor sample

co CH4 c2 H6

+ c2

4

COZ C3H8 C3H6

iso-C4Hl0 n-C4H10

neo-C, HI, iso-C4H, +l-C4H, rrans-2-C4H8 cis-2-C4H8 1,3-C4H, cs +

RSD *

40 Analyses from March to September

Mean concentr. (mole W )

Mean concentr. (mole %)

RSD *

(%)

0.06 4.25 0.71 5.51 0.05 3.04 1.12 6.02 0.59 20.95 22.18 17.14 16.52 1.86

50 0.75 1.4 0.4 20 0.3 1 0.16 2 0.1 0.05 0.06 0.12 1.1

0.06 0.07 0.01 0.02 0.02 3.97 1.12 8.1 0.82 24.74 23.46 23.09 14.35 0.17

50 70 100 100 50 2 1 0.4 1.5 0.3 0.25 0.5 0.4 50

The analysis is made using three columns. A total of 44 program instructions are required to operate the valves, auto-zero, stream selection, peak gating, attenuation and read-out.

TABLE 16.10 Analysis of Nitrogen in Air (30) Series No.

Concentration of nitrogen from peak area (46)

from peak height (%)

2 3 4 5

78.03 78.08 78.12 78.10

77.90 77.99 78.05 78.02

Average Standard deviation

78.07 0.050

77.99 0.055

Tables 16.8 to 16.10 demonstrate the accuracy and precision that can be achieved in routine quantitative analysis carried out in an industrial laboratory. The results reported correspond to samples offering different levels and natures of challenges to the analyst (sampling of volatile mixtures, analysis of reactive compounds, etc.). In a number of cases, the errors reported are less than the value predicted above. This is due to a rather conservative estimate of the error contributions in equations 17 and 18.

687

LITERATURE CITED A.T. James and A.J.P. Martin, Biochem J., 50,679 (1952). E.A. Hauser, in Principles of Sample Handling and Sampling System Design for Process Analysis, Instrument Society of America, Pittsburgh, PA, 1972. G. Guiochon, M. Goedert and L. Jacob, in Gas Chromatography 1970, R. Stock Ed., The Institute of Petroleum, London, UK, 1971, p. 160. A.F. Williams and W.J. Murray, Talanta, 10, 937 (1963). R. Kaiser, Methodes Phys. Anal., 5, 357 (1969). R. Kaiser, Gas Chromatography, Vol. I K Quantitative Analysis, Buttenvorths, London, UK, 1963. R. Kaiser, Chromatographia, 4 , 479 (1971). D.L. Ball, W.E. Harris and H.W. Habgood, Anal. Chem., 40,129 (1968). P. Bocek, J. Novak and J. Janak, J. Chromatogr., 42, l(1969). G. Jecko and B. Reynaud, Reu. Metal., 64, 681 (1967). H.L. Daneman and D.E. Ross, Gar Chromatography Institute Technical Symposium, Canisius College, Buflalo, N Y , 1960. P. Hay, Chromatographia, 1 , 268, 347 and 423 (1968). M. Goedert and G. Guiochon, Chromatographia, 6, 116 (1973). D.L. Ball, W.E. Hanis and H.W. Habgood, Separ. Sci., 2, 81 (1967). D.L. Ball, W.E. Hams and H.W. Habgood, J. Gas Chromatogr., 5, 613 (1967). D.L. Ball, W.E. Hams and H.W. Habgood, Anal. Chem., 40, 1113 (1968). J.M. Gill, F. Bauman and F. Tao, Previews and Reviews, Varian Aerograph, August 1967. D.W. Grant and A. Clarke, Anal. Chem., 43, 1951 (1971). F. Baumann and F. Tao, J. Gar Chromatogr., 5, 621 (1967). F. Baumann, A.C. Brown and M.B. Mitchell, J. Chomatogr. Sci., 8, 20 (1970). M. Goedert and G. Guiochon, Chromatographia, 6 , 116 (1973). M. Goedert and G. Guiochon, J. Chromatogr. Sci., 11, 326 (1973). M. Goedert and G. Guiochon, Chromatographia, 6 , 76 (1973). M. Goedert and G. Guiochon, Chim. Anal., 53, 214 (1971). S.P. Cram and S . Cheder, Anal. Chem., 43, 1922 (1971). J.L. Excoffier and G. Guiochon, Chromatographia, IS, 543 (1982). L.J. Schmauch and R.A. Dinerstein, Anal. Chem, 32, 343 (1960). A.H. Anderson, T.C. Gibb and A.B. Littlewood, J. Chromatogr. Sci., 8, 640 (1970). D.R. Deans, Chromatographia, 1 , 187 (1968). M. Goedert and G. Guiochon, J. Chromatogr. Sci., 7, 323 (1969). W.H. King and G.D. Dupre, Anal. Chem., 41, 1936 (1969). A. Clarke and D.W. Grant, in Gas Chromatography 1970, R. Stock Ed., The Institute of Petroleum, London, UK, 1971, p. 189. H.W. Johnson and F.H. Stross, Anal. Chem., 31, 1206 (1959). I. Halasz, Anal. Chem., 36, 1428 (1964). G . Guiochon, J. Chromatogr., 14, 378 (1964). M. Goedert and G. Guiochon, Anal. Chem., 45,1188 (1973). M. Goedert and G. Guiochon, Anal. Chem.. 42, 962 (1970). A.B. Littlewood, Gas Chromatography, Principles, Techniques, and Applications, Academic Press, New York, NY, 1970. R.A. Sanford, M.I. Miller and B.O. Agers, Analytical Instruments, Plenum Press, New York, NY, 1965, p. 87. J.C. Sternberg, W.S. Gallaway and D.T.L. Jones, in Gas Chromatography, N. Brenner, J.E. Callen and M.D. Weiss Eds., Academic Press, New York, NY, 1962, p. 231. H. Bruderreck, W. Schneider and I. Halasz, Anal. Chem, 36, 461 (1964). S.N. Deming and S.L. Morgan, InstrumenTune-up, Elsevier Scientific Software, Amsterdam, NL, 1983. G. Blu, F. Lazarre and G. Guiochon, Anal. Chem., 45, 1375 (1973).

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689

CHAPTER 1 7

APPLICATIONS TO PROCESS CONTROL ANALYSIS

TABLE OF CONTENTS Introduction

...........................

1. The Analytical Unit

..............

..................

b. The Pneumatic System

..........................

..........................

..............

690 691 692

2. The Control Unit

I I. Methodology . . . . . . . . 1. Selection of the Expe 2. Determination of the

................................ an Analysis

.............

......

4. Selection of the Deferred Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................... 5. Calibration ..................... 6. Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Sample Probe with a Lateral Slit . . . . . . . . . . . . . . . . . . . . . . . . .......... c. Long Distance Transfer of the Sample .................... .......... d. Sample Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......... 7. Location of the Analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Start-up of the Analyzer . . . . . . . ................................... 9. Maintenance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .............. 111. The Deferred Standard Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Present Status of Process Control Gas Chro y ........................ a. Reliability ..................... ......................... b. Credibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Response Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........... .............................. d. Maintenance . . . . . . . . . . . . . . . . e. Conclusion . . . . . . . .................................. 2. Definition of the Deferr rd . . . . . . . . . . . . . . . . 3. Implementation of the Deferred St 4. Alarm Function of the Deferred St ................ a. PrimaryAlarm.. ........................ ................ b. SecondaryAlarm . . . . . . . . . . . . ............................... 5. Calibration Function of the Deferred Standard . . . . . . . . . . . . . . . . . .......... 6. Predictive Maintenance with the Deferred Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . ............... 7. Advantages of the Deferred Standard . . . . . . . . . . . . . . . . . . . 8. Applications of the Deferred Standard Functions . . . . . . . . . . ............... 9. Integration of the Analyzer in the Workshop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................... 10. Conclusion . . . . . . . . . . . . . . . . . . . IV. Examples of On-Line Industrial Analyses . ............................... 1. Analysis of Hydrogen in a Catalytic Reforming Process . . . . . . . . . . . . . . . . . . . 2. Synthesis of Vinyl Chloride ...................... ................... a. Experimental Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. ColumnLifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

694 694

696 696 696 697 698 699 701 702 702 702 703 704 704 705 705

708 708 709 713 713 713 714 716 716 718 718 720 720 720

690

c. Gascircuit ..................................................... d. LkferredStandard ................................................ e. Calibration ..................................................... f. SampleLine ..................................................... g. Results ........................................................ 3. Analysis of the Gas Evolved During a Chloration Process ....................... 4. Analysis of Gaseous Ammonia. ......................................... 5. Synthesisof Phthalic Anhydride. ........................................ 6. Analysis of Recycled Styrene ........................................... 7. Airborne Pollution Analysis in a Polymerization Plant ......................... 8. Analysis of Chloral .................................................. 9. On-Line Control of a DichlorodifluoromethaneProcess ........................ 10. Conclusion ....................................................... Literature Cited ..........................................................

720 721 722 722 723 725 727 730 731 732 r135 736 738 739

INTRODUCTION

Once the qualitative composition of the analyte has been elucidated, the separation scheme has been determined and the calibration completed, routine quantitative analysis may be performed. This may be done either in the laboratory or in the plant, using a process control analyzer. In both cases, the requirements of proper production control have major consequences on the implementation of the analysis. They are more drastic in the case of process control analysis. This last chapter deals essentially with the problems encountered when designing and operating an on-line chromatographic analysis. The methodology and part of the procedures may also be applied to routine laboratory analyses. Process control chromatographic analysis is very popular and extremely useful in petroleum refineries, petrochemical plants and most plants manufacturing fine chemicals, where it has been used for nearly 30 years. It has been discussed in detail in general papers dealing with industrial analyzers (1-4), in specialized papers (5-15) and in a few fundamental papers dealing with the specific problems of on-line gas chromatography, notably those of Pine (16), McWilliam (17) and Martin (18).

I. DESCRIPTION OF AN ON-LINE PROCESS GAS CHROMATOGRAPH

Unlike laboratory gas chromatographs, which are usually integrated as a single unit, process control gas chromatographs are made of three different modules (see Figure 17.1): - the analytical unit, located at the plant site, - the control unit, and - the recording unit, or data display unit. These last two units are located in the control room.

691

I Electrleal

I

HoUilnp

I

I I

I

AU

I *

Thermoil.1

I I

PneumaIIc

I

nousing

I

cu

-

RU

I

-

-

-1

Field mounted

I

I

Control room mounted

Figure 17.1. Schematic of an on-line process gas chromatograph. AU, analytical unit (with its three modules, oven, pneumatic circuit and electrical and electronic compartment). CU, control unit. RU, recording or display unit.

1. The Analytical Unit

The analytical unit incorporates the gas chromatograph proper, but with a design which is very different from that of a conventional laboratory instrument. It includes: - the temperature controlled oven, including the injection, the separation and the detection systems, - the pneumatic system, - the electronics. a. The Oven

The oven contains the sampling system (for gas or liquid samples), the column(s), the switching valves and an explosion-proof model of the detector. The oven is designed to easily accommodate several columns and valves and its size permits easy access to them for maintenance. The oven is designed to operate isothermally. It can be simple, well insulated, with a rather large thermal inertia. It does not usually include a fan or blower. This simplifies maintenance, but requires a very homogeneous thermal insulation of the walls to limit the temperature gradient in the oven. The standard temperature range extends from 50 to 250 O C. Temperature control at lower temperatures, between 0 and 5OoC,requires the use of a vortex fed with compressed air. Columns have too short a lifetime above 250 O C to justify the use of such temperatures. Temperature programming has not been successfully implemented in process control analysis, because of a lack of reliability and an excessive complexity requiring too much maintenance. It is difficult to achieve exactly the same temperature at the beginning of each cycle, which prevents the achievement of the required References on p. 739.

692

level of repeatability, and the stationary phase does not tolerate frequent thermal shocks, which reduce the column lifetime. b. The Pneumatic System

An automatic gas chromatograph requires several sources of gases at controlled pressure: main carrier gas stream, auxiliary carrier gas, e.g., for rapid backpurging, hydrogen and air for the flame ionization detector, servo-air delivery to the solenoid valves which actuate the switching and sampling valves. In process control analysis, pressure control is adequate. Since temperature programming is not used and flow rate programming is too sophisticared, flow rate control is superfluous. c. The Electronics

This explosion-proof unit contains the various electrical and electronic circuits required for the temperature control of the oven (power supply to heat the oven, temperature sensor and control device), the temperature control of the sampling valve, the operation of the detector (power supply, bridge (TCD), electrometer (FID), impedance transformer, etc.), and the commands of the solenoid valves. 2. The Control Unit

The purpose of this unit is to program the cycle of operations during one analysis and its indefinite repetition. Its sends continuous voltages or pulses to the different subunits, usually solenoid valves, but also detector controls, at predetermined times, to order appropriate action. The design of this unit has changed considerably since the construction of the first process gas chromatographs. Originally electromechanical (rotary cams or disks actuating microswitches, punched tapes read by photoelectric cells, etc.), it incorporated more and more electronic circuits, then digital electronic boards. Now, the control unit is organized around a microcomputer. It is easily programmable, more reliable and much faster. Progress in this area as well as in the design of fast gas chromatographic columns permit the achievement of very fast analysis in process control, if needed. The control unit permits the achievement of the proper analytical cycle: automatic zero of the detector base line, connection of the sampling valve to the appropriate sampling line, filling of the sample loop, sampling, column commutation, injection of a deferred standard, adjustment of the detector signal for proper, on-scale display, integration of the detector signal corresponding to the key components of the mixture, and injection of a calibration mixture when needed. Finally, the control unit calculates the composition of the sample and sends the analysis report to the display unit and to a central computer for further decision in the closed loop control, if required, and possibly for archiving. A new task is progressively implemented on the control unit: the self-control of the analyzer (see below).

693

3. The Data Display Originally a potentiometric recorder, the display unit is increasingly replaced by a monitor. The chromatogram is displayed as such or in a condensed format, the base line segments between successive peaks not being recorded, or as a bar graph, or as a trend recording, each peak being represented by a point corresponding to its maximum height (see Figure 17.2). The development of large computers as the heart of the control room permits the use of sophsticated programs resulting in more informative displays, making the task of the operators easier. For example, the computer may determine and display the difference between the current analysis and the previous one(s), illustrating trends, or between the current analysis and a typical or standard analysis, showing the difference between the composition of the product and the ideal specifications. It may as well display an OK message as long as the product is within the specifications and warn the operator when an adverse trend is developing. The basic requirement here is to avoid the display of useless information, resulting in an overloading of the mind of the operator. Gas chromatography easily produces a large amount of information, most of which is irrelevant as long as the plant works correctly .

1

I

1

2

1

2

1

1

1

1

2

1

3

i

3

L 1

1

1

2

1

3

1

4

1

1

2

3

4

5

Figure 17.2. Schematic of the different modes of display of chromatographic data. 1 . Regular chromatograms, too complex for the plant operators. 2, Condensed chromatograms, still too complex. 3, Bar graph record of each peak. 4, Trend lines, displaying only the summit of each peak.

References o n p. 139.

694

11. METHODOLOGY

The proper implementation of an industrial analysis requires the prior completion of a certain number of tasks. These tasks are to be carried out under the joint responsibility of the chromatographer (department of analysis) and his colleagues in the department of plant control. Close cooperation between members of the two groups is required for the achievement of satisfactory performance. These tasks are listed in the order of increasing involvement of the regulation people (and decreasing involvement of the chromatographer). - Study of the conditions permitting a proper separation of the key components of the sample. - Determination of the column lifetime. - Design and operation of a column system permitting a satisfactory analysis (including column commutation if needed). - Selection of the deferred standard and of the proper time for its injection. - Quantitative calibration. Determination of the response factors of the components of the analyte relative to the deferred standard, or preparation of the required calibration mixtures or purchase of these mixtures. - Determination of the best method for the sampling of the product stream to be analyzed. - Check that the process control gas chromatograph works under laboratory conditions. - Start-up of the process gas chromatograph in the plant. - Maintenance evaluation. Writing the maintenance manual and the final report. 1. Selection of the Experimental Conditions for an Analysis

This first step requires the identification of all the components of the analyte, those whch are normally present as well as those which may appear in the case of some expectable malfunctions of the plant unit. This is usually an easy task, the process and the feed being known. Then a column or a column system permitting a resolution of the key components, whose concentration in the plant effluent has to be determined must be found (see Chapters 6, 7 and 8). The separation must be performed under constant temperature, but several column commutations may be performed. 2. Determination of the Column Lifetime A process control gas chromatograph works continuously, 24 hours per day,

often more than 350 days per year. It performs several analyses per hour, i.e., 20,000 analyses per year or more. It must work with little maintenance and no failure. The selection of the stationary phase cannot be made on its selectivity alone, however important this characteristic is. The column lifetime is a very important feature. It should be at least many months, if possible more than a year. A standard 1,000 hour test should be performed to assess the column lifetime. A

695 TABLE 17.1 Results of a 1000 hour test of a stationary phase* Over the 1000 hours of the test, a maximum deviation of 3% has been observed for absolute retention times, and a maximum change of 0.7% of the relative retention. The 3% fluctuation is probably explained more by fluctuation of parameters of the chromatograph than by a change of the properties of the stationary phase. Since the test is positive, the stationary phase may be used in process gas chromatography. Time

Absolute retention time

(h)

CCI,

240 336 432 552 600 840 936 1104

16.2 16.4 16.4 16.45 16.10 16.55 16.10 16.10

Change (%)

+ 1.20 0 + 0.30 -2.10 + 2.80 - 2.70

0

Change

('RC6H6/'RcCI,)

C6H6

27.3 27.6 27.8 27.9 27.3 27.95 27.15 27.3

Relative reten tion

+ 1.10 + 0.70

+ 0.35 -2.15

+ 2.40 - 2.90 +0.55

1.685 1.683 1.695 1.696 1.695 1.688 1.686 1.695

1,2,3,4,5,6-Hexakis(2-cyano)ethoxyhexane, 10% on 75 m2/g silica (Spherosil).

couple of components of the studied mixture are selected and they are injected periodically on the column, which is kept at the constant, selected temperature, in a process gas chromatograph. Their uncorrected retention times and their resolution are measured and plotted as a function of time, over at least 1,000 hours. The drift should be less than the experimental error (3% on the retention times). Table 17.1 shows typical results obtained for this test. The stationary phase used is 1,2,3,4,5,6-hexakis(2-cyano)ethoxyhexane,coated on silica. Experience shows that a column which passes t h s test has a lifetime of at least several months, often exceeding one year. Since it is imperative that columns used in process control analysis pass the 1,000 hour test, there will be cases where the selected column is not the one which offers the best separation of the mixture or the largest resolution of its components, i.e., the shortest analysis time. This type of compromise is frequent in industrial applications.

3. Design of the Switching Valve System The basic operations have been discussed in Chapter 9. Most process control analyses use a combination of several such operations. All industrial analyses must involve at least a back-purging step, as described by Villalobos et al. as early as 1961 (19), in order to eliminate the heavy components of the mixture analyzed, and avoid the base line drifts which would eventually appear and would interfere in an unpredictable way with quantitative analysis. In most cases, with conventional process control gas chromatographs using packed columns, the backpurging operation is carried out using valves on-line with the column (20,21), not the Deans method (see Chapter 9, Sections IV.1 and IV.2), References on p. 739.

696

in spite of the better performance obtained with the latter method, its better suitability to the requirements of process control analysis and the lesser maintenance which is required for the valves used in the Deans implementation. It is interesting to observe, however, that the situation is very different for the instruments using open tubular columns. They are still very few, and we are certainly at the development stage. But all process control gas chromatographs which will operate with open tubular columns will certainly use the Deans method of column switching. The times at which the bands pass through the various valves are easily calculated using the values reported in Tables 9.3-9.6. 4. Selection of the Deferred Standard

This is discussed in more detail in the following sections. 5. Calibration

Calibration problems are discussed in Chapter 14. Conventional methods as well as the deferred standard approach are described and compared. Specific problems of quantitative analysis encountered in process control analysis have been discussed by different authors. Villalobos (22-24) dealt with the selection of the detector; Turner and Crum (25) with calibration methods and the pitfalls to avoid. Smith et al. (26) discussed the specifications for the achievement of a high degree of precision, and Villalobos and Turner (27) compared the use of peak height and peak area. When the gas density balance is used for calibration, it is placed temporarily in the oven, so that the relative response factors may be determined under the exact same experimental conditions that will be used later for the industrial analysis. 6. Sampling

Sampling requires extremely careful attention. Each case requires specific, tailored solutions (28-32). The accuracy of the analytical results much depends on the representativity of the sample. Laboratory simulation of a sample line is almost always doomed to failure and should not be attempted, except as a topic of research. One of the major reasons for this observation is found in the extreme difficulties encountered in scaling up or down the behavior of a system which depends on non-linear phenomena, such as molecular diffusion. Sample lines, sample pretreatment, and sample representativity should be studied at scale 1, in the plant. There are, however, some simple rules to follow (33). The sampling system must: - Deliver a representative sample of the plant stream. - Make the sample compatible with its introduction in the gas chromatograph (e.g., cool it, warm it, compress it, decompress it, etc.). There should be no change in composition of the sample, however, or minor and easily accounted for (e.g., filtering out suspended particulates).

691

- Deliver the sample with small delay and very little mixing. - Recycle to the plant or send to waste the excess sample, to maintain constant flow in the sample line. - Require little maintenance or none at all. The reliability of the results supplied by an on-line analyzer depends very much on the care taken to design and build a suitable sample line.

a.

Procedures

The various operations applied to the sample before introduction into the chromatographic columns are: Operation

Technical solutions

Sampling

Various types of probes Selection of material Backflush of the sample line

Adjustment of temperature

Condensers Coolers Heaters (steam or electric)

Adjustment of pressure

Pressure controllers Compressors Pumps

Sample treatment

Filters, separators Scrubbers, vaporizers Chemical treatment

Adjustment of flow rate

Flow rate controller

Flow meters Valves Utilities

Tubings, unions, valves Materials Steam, water, servo-air

Safety

Fire proofing Explosion proofing Various protections

For obvious reasons, the selection of the sampling point in the plant should be decided by common agreement among all the interested parties: plant manager, chemical engineers, control specialists and analysts. The sampling probe should be located at a place where the sample is representative of the process, and preferably in a place where the stream is highly turbulent. Sometimes a primary loop has to be installed to ensure a short response time for the sampling system. Finally the probe should be designed so that its maintenance and its cleaning are easy. Often industrial streams contain a wide range of components, from gases to tars. Some of these components may condense somewhere in the probe and plug it. Various technical solutions have been described and used. They are not always completely satisfactory. References on p. 739.

698

Figure 17.3. Schematic of the lateral slit probe for sampling a stream containing tars.

b. Sample Probe with a Lateral Slit

In most cases, a concentric probe is used. When the stream to be sampled contains tars or sticky suspended particles, a different probe is used. A small cylindrical tube, with its axis perpendicular to the direction of the stream, is introduced across the effluent tubing. This probe is closed at its end, but open along a slit parallel to its axis. The probe is oriented so that the slit is placed in the direction opposed to the incoming stream (see Figure 17.3). The impinging tar particles tend to stick on the sides of the probe and few of them may penetrate through the slit into the probe, because of their inertia and of the turbulent eddies inside the stream. A periodic backflush of the probe by a suitable gas or liquid, by steam or by a solvent may also help in keeping it clean and unplugged (see Figure 17.4).

c.g.

Figure 17.4. Principle of the method used to clean the sampling line with a dry gas or a steam jet. a. Probe. b, Filter. c, Valve permitting isolation of the sample loop, to let it reach the atmospheric pressure. d. Sampling valve. e, Stop valve, giving access to a stream of dry gas or steam, to periodically clean the sampling line.

699 c. Long Distance Transfer of the Sample

This original idea was tried first by Konrad (34) in 1960. It has permitted a satisfactory solution to very difficult sampling problems, resulting in a considerable reduction of maintenance problems. The idea is to shorten the sampling line whde increasing the length of the transfer line, by placing the sample valve of the gas chromatograph close to the stream to be analyzed, far from the gas chromatograph (35). A schematic is given in Figure 17.5, where the classical solution (sampling valve in the gas chromatograph) is compared to this original approach (sampling valve close to the plant stream). The transfer line is now reduced to a few tens of centimeters (a couple of feet) and can easily be purged automatically after each injection. The price to pay is in the considerably longer transfer line. It results in long injection times but surprisingly not in the injection of wide, diffused bands of sample into the gas chromatograph. The band width is increased and the resolution diminished. Longer, more efficient columns must be used and the detection limits are lugher. Selective adsorption of some components may take place on the wall of the transfer line. A compromise is acheved by using 1 mm i.d. stainless steel or Teflon tubing. The transfer line is heated electrically, or with steam flowing through a concentric tube. The temperature required is lower than it would be for a comparable sampling line, however. Figure 17.6 shows two chromatograms obtained for the same plant stream containing ethylene, ethyl chloride and vinyl chloride. In the first chromatogram a

Figure 17.5. Principle of the long transfer line. A. Conventional technique. The sampling line is long, the transfer line short. The sample is brought to the gas chromatograph. B. Long transfer line. The sampling line is as short as possible. The gas chromatograph inlet is brought close to the process.

References on p. 739.

700

15 min

Figure 17.6. Example of application of a long transfer line. Analysis of a mixture of ethylene (l), chloroethane(2) and vinyl chloride (3) (see Section IV.2). A, Sampling valve close to the column inlet. B, Sample injected at 38 m from the gas chromatograph.

normal injection is made. In the second one the sampling valve is placed 38 m away from the gas chromatograph. Comparison between the two chromatograms shows a very long delay but very little band broadening, demonstrating the rapid radial diffusion in the 1 mm i.d. transfer tubing. We have found that very long transfer lines may be used and have been unable to determine an upper limit to the length which may reasonably be used in practice. Figure 17.7 shows an analysis of air on a Molecular Sieve 5A column. The use of a 50 m long transfer line does not result in a significant increase of the band width. Note that the volume of the line (1 mm i.d., 50 m long) is 40 mL. The 4a band width of such a tube ( O K with k’ = 0, see p. 105) at the appropriate flow rate (ca 5-10 mL/min) is about 0.4 mL. This is quite a reasonable sample volume for a conventional column and is at least 7 times smaller than the band width of an unretained zone. The most spectacular applications of this method we are aware of are in the

701 Long distance sample valve

Figure 17.7. Comparison between the width of an air peak injected just at column inlet (top), at the inlet of a 50 m long transfer line (middle) and at the inlet of a 140 m long transfer line (bottom).

analysis of the effluents of steam cracking units or of Claus process units, concerning the determination of H,S and SO,. d. Sample Treatment

Compatibility between the sample and the analyzer may need some adjustment of the characteristics of the sample, such as its temperature, pressure, flow rate, water content or some chemical treatment. The composition of the sample should not be altered, but, obviously, in these last two cases this is impossible. The change should be at least predictable. Although some preliminary work can be done in the laboratory, the study of the performance of the sample treatment devices can be carried out usefully only on site. Simulation in the laboratory does not afford a solution which can be trusted and merely amounts to a waste of time, energy and money.

702

7. Location of the Analyzer The analytical unit of the process control chromatograph should ideally be located rather near the sampling point. Also, it should be housed in a protected cabin, where fluctuations in ambient conditions during the day and over the seasons are minimized, to ensure a good repeatability of the analytical results. When a plant requires the use of several chromatographs on the same site, a compromise becomes necessary, as for obvious economical reasons it is preferred to locate them in the same cabin, minimizing the costs of investment (electrical cables, cabin, sources of carrier gas, auxiliary gases, steam, servo-air, etc.) and functioning (air conditioning, etc.). The use of long transfer lines becomes a very useful and economical solution (see above).

8. Start-up of the Analyzer It is important that this critical operation be carried out by a team representing the analysts and the control department. They will have to write detailed instructions for proper start-up and stopping procedures of the instrument, for the determination and control of the optimum chromatographic conditions and for the operation and maintenance of the sampling line. 9. Maintenance Evaluation Maintenance evaluation can be done only after the instrument has been working in the plant for a certain time. It is always observed that the failure frequency decreases steadily with increasing time, after the first start-up. The frequency of calibration depends on the process controlled and the specifications, i.e., the importance in having accurate results. It can be daily or weekly. The use of microcomputers in the control unit permits tying the calibration to the occurrence of certain events, such as an analytical result out of specification, or a rapid variation in the concentration of a certain compound. The systematic use of the deferred standard and the proper assessment of its results permit serious economies on the maintenance by helping in scheduling preventive maintenance operations. Maintenance can be drastically reduced by observing some simple rules discovered through long term experience. For example, it is strongly recommended to systematically dry all the gases used in a process control gas chromatograph. Each gas line includes two drying cartridges, packed with a suitable adsorbent and a switching valve, permitting the regeneration of one while the other is operating. Water vapor in the carrier gas results in a slow hydrolysis of many stationary phases and in a slow decrease in the performance of nearly all columns. The response of the TCD varies with the composition of the carrier gas, including its water content. The response of the FID depends to some extent on the water content of the gases fed to it. Villalobos (36) has shown that the concentration of water in the gas delivered by a pressurized cylinder varies considerably with time, increasing steadily with decreasing pressure in the cylinder. As an example, if the pressure inside the cylinder

703

-

I

I 400

I

I

I

I

I

I

I

a m

I

1200 1600 2000 Cylinder pressure, psi

800

F;gure 17.8. Plot of the carrier gas water content versus the pressure in the cylinder. After ref. 36.

is 150 atm, and the water content is 150 ppm, the water content of the gas stream rises to 8,150 ppm when the pressure has decreased to 2 atm. Figure 17.8 shows a plot of the water content of the gas stream as a function of the pressure inside the cylinder (36). 111. THE DEFERRED STANDARD CONCEPT

Designed by Guillemin in 1965, the deferred standard concept aims at controlling the process gas chromatograph itself. It was originally implemented in the on-line control of a unit for the synthesis of vinyl chloride. Since the first publication in 1971 (37), the deferred standard concept has gained wide acceptance in the field of process control analysis and of high precision analysis (38). Despite the recognized capability of the process gas chromatograph and a proven record of reliability, it is always considered suspicious by plant technical management, chemical engineers and even instrumentation engineers when it is incorporated in a closed loop control. Because most of them do not fully understand the operation of what seems to them a rather sophisticated piece of equipment, because the instrument gives results periodically, not continuously and its status at a given time is difficult to figure out by the non-specialist, its results are immediately questioned as soon as they point to another answer than the gut feelings of the plant operators. In order to be acceptable for the use in a closed loop control, an industrial sensor must meet the following fundamental criteria: - Reliability, or high probability that the results are accurate, or long mean time between failures. - Credibility, or confidence in the accuracy of the results. - Continuous response. - Low maintenance cost. References on p. 739.

704

We discuss the present level of performance of the process gas chromatograph with regard to these criteria. 1. Present Status of Process Control Gas Chromatography

The process gas chromatograph marginally satisfies the basic requirements of control engineers for its incorporation in a closed loop control. On the other hand, it readily supplies information that no other sensor can. Something must be done to improve the confidence in its results. a. Reliability

Experience has demonstrated that the process gas chromatograph is indeed a very reliable instrument. The problem, however, is that it is very difficult to demonstrate to the satisfaction of the plant manager that the gas chromatograph is working reliably at a given instant, when confidence in unexpected results is vital for the soundness of impending decisions, to be taken for the operation of the plant; decisions which, if unwisely made, may cost huge amounts of money to the company and put the said manager in serious trouble. When the analyzer shows that the composition of the plant stream changes, one wants to be sure that this result is real and not a consequence of a faulty analyzer or a malfunctioning sample line. In conventional instruments the proof that the analyzer is working soundly can be obtained by injecting a calibration mixture, usually once, in difficult cases several times. The complete loss of information on the process behavior during the time necessary to process these calibration samples may be unacceptable in certain circumstances, however, especially when the gas chromatograph is included in a closed control loop. This situation generates justified fear and anxiety in the mind of the plant managers and needless hostility towards the chromatographic sorcerers. 6. Credibility

Confidence in the analytical results of the process gas chromatograph requires a satisfactory answer to the following conditions: - Accurate calibration mixtures must be constantly available. - The analytical results obtained for calibration mixtures must be in agreement with their known composition. - The sample must be representative of the analyzed stream. - The detector must be linear and reliable. The method lacks credibility especially when it is not possible to prepare accurate calibration mixtures, for example in the case of mixtures of ethylene and hydrochloric acid, gases which can coexist at low concentration in a plant effluent, but react in a metal bottle.

705

c. Response Time The gas chromatograph is a sequential analyzer. Its response is periodic. Much time and effort has been spent in trying to design chromatographic methods supplying continuous responses, for example by deconvolution of the signal obtained with a pulsed input. Results have not justified the implementation of these methods in industrial practice. Chromatographic analyses are fast. In practice they can be performed in a time sufficiently short for the response to be considered to be semi-continuous, i.e., in most cases it is not very difficult to achieve an analysis time which is about three times shorter than the response time of the controlled unit in the plant. Still faster analyses can be performed, permitting a statistical study of the data.

d. Maintenance Routine, preventive maintenance is typically performed on the control instruments in almost every plant. Scheduled replacement of parts such as sampling and switching valves, columns, etc., is systematically performed at a frequency chosen arbitrarily, often as a function of the importance of the analysis performed. This frequency has not changed while the quality of the parts has improved markedly. Calibration are also performed at constant frequency. Such preventive maintenance is very costly. e. Conclusion This review shows that the conventional process gas chromatograph is not yet really a true process monitor, but a highly sophisticated analyzer. This justifies the frustrations of the plant managers and unit operators. who expect the same kind of reliability and service from a gas chromatograph as they are used to obtain from temperature sensors or infrared absorption analyzers. The implementation of the deferred standard, together with the use of microcomputers permits a definitive solution to this problem.

2. Definition of the Deferred Standard A second injection is performed during each analytical cycle (37-42). This injection is made a constant time after the injection of the sample. The second injection is of a pure compound, a gas or a liquid, chosen to be cheap, stable and easy to elute with a symmetrical peak. The delay between the two injections is chosen so that the peak of the deferred standard is eluted well resolved from all the components of the analyzed mixture. The deferred standard doubles conveniently as the reference compound for quantitative analysis, i.e., it replaces the internal standard (see Chapter 15). Figure 17.9 dramatically illustrates the major advantage of the deferred standard. It is immediately obvious that the gas chromatograph is working fine and the process is going wrong. References on p. 739.

106 WHiCH ONE

I

I

I

I

I

iS WRONG: THE P G C

I

I

1

-+

THE PC

7

is

I

I

I

I

-+

2

OK

-

I

I

I

I

;-sequence

OR THE PROCESS 7

3

+

A

THE PROCESS

4

-I

[is WRONG

!

I

4-

i i

c4-

‘ 2

I

Figure 17.9. Illustration of the main application of the deferred standard: “What is going wrong, my nice process or your cursed machine?” (After ref. 42.) A, There is no deferred standard. The answer requires at least one analysis of a calibration mixture. B, The peak of the deferred standard is perfectly stable, the process is drifting, corrective action has to and may be taken immediately: as soon as frame 2, as a matter of fact.

The deferred standard has three functions in process control analysis: an alarm function, informing the operator of the status of the chromatograph, good or bad. It is a self-control function. - a calibration function, permitting ready achievement of accurate results. - a maintenance need function, quickly alerting the operator to the advisability of early service, before anything has gone wrong in the analytical results supplied by the instrument. Together, these functions permit the transformation of the process gas chromatograph into a true industrial sensor (43), as we show in the following four sections. -

3. Implementation of the Deferred Standard In order to minimize the difficulty in placing its band between the peaks of the components of the sample, the deferred standard is preferably a gas with a very small retention, eluted near or at the gas hold-up time. Air and nitrogen are most often used with the TCD and ethylene with the FID. Two different procedures may be used to inject the deferred standard: - a second sampling valve can be introduced in the gas line, upstream of the regular sampling valve, to prevent its accidental or progressive pollution by components of the sample. The standard is then pure and the volume of standard injected is selected to provide a peak having the proper size, depending whether one is interested in trace or main component analysis. - a single sampling valve is used, which alternately injects the sample and the standard. Since the volume injected is the same for both standard and sample, it may be necessary to use as standard a gas diluted in the carrier gas, or preferably in nitrogen, which has the same molecular weight and density and very similar physico-chemical characteristics as ethylene. As a consequence, the mixture of N,

t

DS ( g a s )

S

(liquid)

0

Figure 17.10. Schematic of different possible implementation of the deferred standard. a, One injection valve for the sample, another one for the standard, preferably placed upstream. b, The same valve is used for the sample and the standard. c, The deferred standard is a gas and the sample a liquid. atm indicates that the pressure in the gas loop is brought to atmospheric before the injection is carried out.

References on p. 739.

708

and C,H, behaves as nearly ideal and there is no need for compressibility correction when the mixture is prepared in a compressed gas cylinder. Also the mixture remains homogeneous after long periods of storage in poor weather conditions, another precious property for its use as deferred standard, since the cylinder must not be replaced often, but must supply a gas of constant composition. Various possible combinations are illustrated in Figure 17.10. 4. Alarm Function of the Deferred Standard This is illustrated in Figure 17.9. Figure 17.9A shows the result of four consecutive analyses of a process stream. It is not possible to immediately answer the critical question: “What is wrong, the process or the cursed chromatograph?” A calibration would be necessary to make sure the chromatograph is working properly. This would require at least the time of one sequence, which would be lost before proper action be taken. In Figure 17.9B it is now immediately obvious that the gas chromatograph is working fine but that either the sampling line, or the process is going wrong, since the repeatability of the deferred standard peak is excellent. In fact the second analysis should alert the operator and the third trigger some corrective action. The deferred standard does not check the proper functioning of the sampling line, through which it does not pass. It flows only through the transfer line. In the case when the chromatograph malfunctions, the deferred standard peak size would fluctuate, alerting the operator to its failure and the need for urgent maintenance, an alert which would be triggered as early as the failure appears. Thus the deferred standard is a constant, on-line check of the gas chromatograph. Its availability makes the gas chromatograph much more reliable and trustworthy. In the early implementations, the height of the deferred standard peak was determined and served as a visual basis for decisions by the operator. Things have improved. The area of the peak is measured during each analysis, by the microcomputer used for signal integration (see Chapter 15). The program available to the microcomputer permits a detailed analysis of the characteristics of the peak of the deferred standard, supplying useful information regarding a possible malfunction. Those are called the primary and secondary alarm functions. a. Primary Alarm

The repeatability of the area of the peak of the deferred standard is a measure of the reliability of the results of the process gas chromatograph. If the area of the deferred standard peak is within the range of experimental error, indicated to the microcomputer of the control unit from previous measurements, the gas chromatograph is considered as operative and reliable. The analytical report determined by the control unit of the gas chromatograph is accepted by the plant computer which takes proper action to keep the process working. If the area supplied to the computer is off limits an alarm is triggered, while the computer shifts to the proper alternate subroutine available to it, in order to

709

safeguard the process, the products and if possible continue operation without the information on the composition of the plant stream normally supplied by the gas chromatograph. b. Secondary Alarm

During each analysis the microcomputer of the control unit of the gas chromatograph measures the following characteristics of the peak of the deferred standard: its retention time, its height and its area. This permits the early detection of potential sources of trouble, while the area of the peak is still within the specifications for satisfactory results. The algorithm of the secondary alarm detection is summarized in Figure 17.11. The deferred standard is identified from its elution time, measured from the begmning of the analytical sequence, i.e., from the injection of the sample, not from its own injection. If no peak is observed during the proper time window an alarm, S a m p l e ,injection

DS

injection

Alarm : detection

Calculations carried out

1

?=*

Alarm : injection

Alarm :Separation

Displayed

messages

-

Alarm

D S not found

(END

)

Figure 17.11. Schematic of the algorithm used for the alarm functions of the deferred standard (44).

References on p. 739.

710

I

L T N

I

I

4 I I

Figure 17.12. Alarm function of the deferred standard. Definition of the parameters measured for the standard peak (44).

with a message: “Deferred standard not found” is issued. The gas chromatograph is declared inoperative. If the standard is found, its peak area is determined. The peak area is a function of the amount injected and the values of the experimental parameters determining the detector response. Over the years, the reliability of the sampling valves has proven to be excellent, much better than that of the detectors. If the area is off specifications, it is most probably due to a variation of the bridge current, of the detector temperature or of the flow rate for a TCD, a variation of the flame temperature, i.e. of the flow rates of air or hydrogen for a FID. An alarm with a message “Detection error” is issued and the gas chromatograph is declared inoperative. If the area is within the preset limits the concentrations of the various components are derived from the area of their peaks, the area of the standard peak and the relative response factors. The results are accepted by the plant computer. Then the microcomputer calculates the height of the deferred standard peak. Important variations of the peak height are sometimes observed, up to 50%, when the peak area changes by a few percent or less (see Chapter 13). They are due to faulty injection, such as a drop in the temperature of the vaporizer or in the pressure of the servo-air of the pneumatic sampling valve. Finally, fluctuations of the carrier gas flow rate cause changes in the retention times. Since the deferred standard has been identified, the pneumatic system is operating satisfactorily. Early signs of wear or other malfunction may result in short term, small fluctuations. Erratic fluctuations of the column temperature will have the same effect. These fluctuations may be detected by measuring the time interval between two closely eluted peaks (see Figure 17.12).

711 LI S T

1 0 ! " D E F C F ~ R E D S T A N D A R D - RLRRI! t C A L I B F U N C T I O N S " : 2 0 IN P u T "a H A L Y s I s ' I , i i 1 1 3 8 I N P U T " P I C D S " t DS: I N P U T "COI~C 9S ",Cd 4 0 I H P L I T "MAX S D S S h : I k i P U T " H I E ! S DS 'I, 5 1 50 I N P U T " M A X H D S ",Hh: I N P U T " M I N h DS " d H 1 6 0 I N P U T " I l A X T D S " I Tts: I S P U T " M I N T 35 ' ' 3 T 1

!

.'I

7B s0 90 I00 110 120 150 140 150

160 178 180 196 288 218 228 230 240 250 3 50 360 37B

180 399 4 0@ 4 18 420

438 440 458 468 4:a 488 499 508

514 528 530 680

610 620 638 640 650 2688 2885 2098 2891

3826 4858

I N P U T "REF P I C 'I: P 4 I N P U T " H A X T H ".Nh: i N P U T " H I N T N ",N1 1=1 I N P I J T ' P I C Y o 'I: X r C I ) I F R X 3 C > 1 6 THEN 1 5 8 I N P U T " R F 'I, F i ( 1 ) I H P l J T "NAME "; N o ( 1 ) I=I+~: G O T O 10a ! " E N D O F D I A L O G ": t i p = I - l : END: !! I F P S T C D S > > = T h O F P S T < D S > C = T l T H E N 1 7 8 E L S E 208 !! G R R P H :5e,25e. I: !I ! " ALARM D s N O T FOUND": G O T O c e e !"tlRtlE No WEIGHT X " : ! FOR 1 = 1 70 N F

Ci(l)-Cd*Fi:I)+~PSRCXi/~S~C~S~~ ! S5.E13 N o < I > ; $18.3 X i ( I > ; T A B ; B CiCI) NEXT !! T N=PST ( D S ) - P S T < PR) -IF P S R < D S > > = S h O R P S R C D S > < = S l T H E N S = 0 E L S E S = 4 I F P S A < D S > > = H h OF( P S R < D S ) C = H l T H E N H = B E L S E H = 2 I F T H > = N h CR T N < = N 1 T H E N T r i = 0 ELSE T n = l ! " S - " : S: T 4 8 2 8 " H = " : ti; T R E 4 a " T h = " ; TN; T A B 6 D " T r i = " : T r i ! " P S R < DS 1 = " P 5R ( D 5 > ;" P C f i C D S > = " P SR < D S > ! " P S T < D S ) = " P S T C DS > ;" P S T ( PR > = " P S T < PR > Al=S+H+Tri !: P L O T o GRAPH 35a,a50,1: !: O H ~ i + : G G T O 4 6 0 , 4 7 8 . 4 8 8 . 498.508. 518, 5 2 8 , 5 3 0 ALARM i i i i c c t i ~ n - S e p a r a t i o r i - D e t ~ c ~ i o i iG"E:T 0 600 ALRRM I n j e c t i o n D e t P c t i o 11 " : G 0 T 0 6 @ 8 ALRFH S e p a r a t i o n - D e t e c t i o n " : G O T O 688 !" Plerm 3etectiori": GOT0 6 8 8 !TAR3"0 K R t t e f I t i a fi: I r i i e c t io 11 -S e P a r a t i o r i ' I : GOTO 6 00 !TRB3"0 K R t t e n t i o r i : I i i J e c t i o r i " : G O T C 688 !TRB3"0 K A t t eri 1. i ori i S e P a r a t i o n " : 0 0 T O 6 8 8 !TRB3"O K CJOOD WORKING O R G E R " : GOTO 680 R E S T O R E 620: F O R 1.1 TO 7 : R E A D X , V , Z GRAPH X , ' t , Z : N E X T : !L: E C H O 1 D R - A 0,388, 5 8 8 , 3 8 e , 0,5 8 8 , 9 5 0 , 0, 950,0,0,;m8 D A T A 0 . 4 9 5 , I, 3 0 8 . ~ 9 5 , ~ P L O T AUTO END S=YC3U0: K=RC38a: I N P U T " L I N E 7'' L: L I S T C L ) 1=2Y+ZPEEK(PEEK#C3AZ*S): F O R T = S TO S t 6 4 I F C C > 1 3 THE14 I = I + l : C = P E E K I AND # i F : P O K E T , C N E X T : POKE K , S , 9 8 5 : END D = D T : I F D C T 1 T H E N D = T l A L W A V S I F M t i = B T H E N 5208 P O K E O C 2 C D . 0 : D I S P : GGTO 1 6 0 : E N D

-

I.

u,

Figure 17.13. BASIC program used to implement the alarm function of the deferred standard on a

programmable integrator (44). The instruction "RUN" initializes the program. The operator is asked the reference of the analysis, the peak rank of the deferred standard, its concentration, the rank and name of each peak, the response factor relative to the standard, the upper and lower limits for the area, height and retention time of the standard and for the distance to the next peak, TN. An example is given in Section 111.8 and Figure 17.14. References on p. 739.

712

TABLE 17.2 Alarm Function of the Deferred Standard Failure Diagnosis (44) TDS

0 1

S

H

TN

Actions

-

Alarm “DS not found”. Calculations are not made. Good working order - Concentrations are calculated with the DS used as standard. Good working order Calculations are made. Caution, “injection function”. G o d working order Calculations are made. Caution, “injection, separation functions”. Good working order - Calculations are made. Caution, “separation function”. Alarm - Calculations are not made. Failure on detection and injection systems. Alarm Calculations are not made. Failure on detection and separation system. Alarm Calculations are not made. Failure on detection and injection systems. Alarm Calculations are not made. Failure on detection, injection, and separation systems.

-

1 1 1

-

The diagnosis of the process gas chromatograph is carried out after each analysis, combining the results of all these measurements. A warning message is issued if the deferred standard peak is identified and has the proper area but its height or its distance to a close neighbor are out of specifications. Figure 17.11 and Table 17.2 explain the various combinations possible. A BASIC program (44),written for a Spectra-Physics4100 integrator, is given in Figure 17.13. This integrator was used to simulate a process gas chromatograph control unit in the laboratory. The determination of other characteristics of the deferred standard peak, such as its width at half height, its efficiency, its asymmetry, the resolution with a closely eluted peak permit more refined diagnosis of beginning malfunctions, before they have any serious effect. This, in turn, allows a more effective and cheaper maintenance, by avoiding a number of preventive maintenance steps. An example of application of these functions of the deferred standard is given later, Section 111.8. As with any other automatic system, the deferred standard is not a perfect zero-risk solution. The excellent reliability of microcomputers and of gas sampling valves, however, permits the achievement of an extremely high degree of performance. The method has been accepted by many industrial analysts in a large number of companies. The deferred standard gives an indisputable test of the chromatograph and gives total credibility to analytical results which would otherwise be hotly disputed between analysts and plant engineers. The use of the deferred standard restores confidence between these partners in the operation of the plant.

713

5. Calibration Function of the Deferred Standard This results from a combination of the properties of the deferred standard already described and the use of the gas density balance as a calibration detector (see Chapter 14). This detector permits 2 rapid determination of relative response factors for any compound, using any reference standard. The deferred standard is the ideal reference for quantitative analysis. The use of thz deferred standard as a reference for quantitative analysis, with calibration using the GDB, permits the total elimination of the use of calibration mixtures which are costly and impractical. As a consequence, more frequent calibrations are possible, more accurate results are obtained and the process gas chromatograph credibility is further enhanced. 6. Predictive Maintenance with the Deferred Standard As explained above (Section 111.4), the use of the deferred standard permits more predictive maintenance and less preventive maintenance, resulting in a better reliability of the analytical results and a lower cost. As long as the test results, retention time of the standard, peak area, peak height, retention time difference, and peak width, are within the specifications, it is unnecessary to change parts, to recalibrate the detector or to proceed to other maintenance actions. The drift of one of the secondary parameters out of specifications does not require stopping the chromatograph. Some corrective actions may often be taken and it is possible to delay the required maintenance until a more favorable time. The alarm function of the deferred standard permits savings on the operator time and the cost of calibration gas mixtures. The calibration function of the standard permits additional savings on the preparation or purchase of calibration mixtures which are no longer necessary. The down time of a conventional process gas chromatograph is approximately 150 hours per year. With the use of the deferred standard we have been able to decrease it to approximately 50 hours per year. This reduction and the savings just mentioned combine to make the implementation of the method a very profitable investment. In the worst case, the cost of implementation would be: - a second sampling valve. - the pressure release in the sample loop, to atmospheric, using a solenoid valve (see Chapter 13). - the operation of these valves by the control unit. - one cylinder per year of either air or ethylene.

7. Advantages of the Deferred Standard

The only competition to the deferred standard method is the internal standard method. The automatic preparation of the sample to be injected is extremely costly, however, much more complicated than the injection of a pure compound. In order References on p. 739.

714

TABLE 17.3 Comparison between Internal Standard and Deferred Standard Internal standard Principle

Deferred standard

Needs addition of known amount of Does not need any addition of coma very pure compound in the mix- ponent. Injection of pure standard is ture to be analyzed. deferred by respect to sample injection. No retention time constraint. Deferred injection allows choice of any gas or liquid compound (air, N,, ethylene, benzene etc.). May or may not be a component of analyte.

Choice

Standard must have a retention time different from all the components of the mixture analyzed. ID is almost always a Liquid.

Apparatus

Needs automatic preparation by ad- Needs 2 additional valves. The DS ding known amounts of IS and sam- does not increase the response time ple and mixing. Increases the re- of the analytical system. sponse time of the analytical system.

Cost of standard

Depends on the compound selected Consumption of one bottle of air, as internal standard. N, or ethylene during one year of operation.

Cost of apparatus

Coefficient 10 (10 times more than Coefficient 1. DS).

to meet the accuracy requirements, it needs a very carefully prepared mixture of sample and standard, which may be nearly impossible with difficult samples. Table 17.3 contains a comparison between the main features of the two methods. The self-control of the analyzer can be performed to some extent by placing pressure and temperature sensors in critical locations of the instrument. The development of microcomputers and of data acquisition techniques certainly permits the use of enough sensors to be able to recognize malfunctions and issue the proper alarms. The system becomes very complex and expensive. By contrast, the deferred standard is a global test, which integrates all the effects of the chromatograph parts on a peak, from injection to detection, and which addresses the reproducibility of the very phenomena that are used to perform the required analysis. Furthermore, a fine analysis of the standard peak shape proves very suitable for troubleshooting investigations, while remaining simple and inexpensive. 8. Applications of the Deferred Standard Functions The analysis of air (oxygen and nitrogen) was performed as a test. One of the great advantages of this sample is that the result is well known in advance, so bias can be determined as well as experimental errors, and it is difficult not to grab a representative sample.

715 NAME

NO

WEIGHT '1s

02

1. 2.

24.2

N2

s= 4 . PSR(DS1- 118960, PST(DSl= 216.

4

77. 8 9 HE 2. P S A I D S I ; 11168. P S T I P R I E 110.

TN-

OK

INJECT

106.

T n = 1.

GOOD

WORKING ORDER

T I M E 1 8 13 : 1 8 : 2 5

A 1 1 0 .

F

N -

L

DS

184.

NAME

NO

WEIGHT %

02 N2

1. 2.

24.18 77.9

s- 4 . PSR I D S ) - 119114. P S T I D S I = 217.

n. 2 . PSAlDSl=

TN = 107.

GOOD

-2

110.

1

DS

N2

NAME

NO

02 N2

1. 2

119135. 217.

4

4 -w

F

5. 4 . PSRIDSI-

WORKING ORDER

TIME 18 1 3 : 2 8 : 5 1

*

PST I D S ) ,

Tn=l.

11170. 6 6 7

PsTiPn)= 110.

OK

INJECT

144.

N2

.

w

217.

WEIGHT . I .

24.19 77.9

H . 2. PSAIDSI PST I P R I

I

4

TN;

107.

T"=

1

11176. 110.

OK

I

GOOD

W O R K I N G ORDER

Figure 17.14. Example of implementation of the deferred standard. Analysis of air: oxygen (1) and nitrogen (2). Standard, nitrogen (3).

716

TABLE 17.4 Quantitative Analysis of Air by Different Methods Theoretical

Concentrationof oxygen in air (average of 10 analyses)

composition of the air

1 Internal normalization of areas 0,(W) 24.48 f 0.80% volume: 1.12 ml

Oxygen + argon 24.27%weight

2 Deferred standard 1 valve S and DS 0 2

($1

24.41 f 0.40% volume: 1.12 ml

3 Deferred standard 2 valves S and DS 0 2

(%)

24.17 & 0.57% volumes: Vol. S : 1.385 ml Vol. DS: 0.264 ml

Peak areas are measured with a computing integrator. Same experimental conditions for the 3 analyses. Elapsed time at atmospheric pressure prior to injection: 30 seconds.

The analysis was performed with the following experimental conditions: Column: i.d., 4 mm. Length: 2 m. Stationary phase: Molecular Sieve 5A, 26/29 mesh. Temperature: 72.5 O C. Carrier gas: helium, 3 L/hour. Detector: TCD,two parallel, direct passage cells, current: 250 mA. Sampling: two different procedures were used successively, with two sampling valves (see Figure 17.10a) and with one single valve (see Figure 17.10b). Pressure released to atmosphere during 30 seconds prior to injection. The threshold limits for the various characteristics of the deferred standard peak (nitrogen) were: peak area 1%;peak height 3%; elution time of the standard 2%; time between the two nitrogen peaks 25%. Table 17.4 gives the results of the quantitative analysis for the two injection modes. Figure 17.14 illustrates the analytical results and shows simplified analytical reports and messages regarding the status of the instrument. 9. Integration of the Analyzer in the Workshop

This task is carried out by the control and regulation department, with the help of the analysts. During its accomplishment, the deferred standard gives precious information regarding the status of the gas chromatograph and the origin of the troubles encountered. It permits a rapid check-up of the entire system, and the separation of problem sources between the three main types: those associated with the gas chromatograph, with the sample line and with the process. 10. Conclusion

Recent development in process control analysis by gas chromatography has focused along the following lines: adoption of the deferred standard and implementation of its different functions, incorporation of powerful microcomputers and sophisticated software, use of faster columns and column systems to accelerate the

717

analysis. The process gas chromatograph has become an industrial sensor, as shown by a comparison between the criteria detailed above (see Section 111) and the solution now adopted: Criteria

Technical Solutions

Reliability

Primary and secondary alarm functions of the deferred standard

Credibility

Calibration function of the deferred standard Fast analysis, permitting an estimate of the precision by averaging the results of several analyses, thus enhancing the credibility

Continuous response

Fast analysis permits a quasi-continuous response

Low maintenance cost

Predictive maintenance function of deferred standard

It should be emphasized at this point that, although the use of fast packed columns can be contemplated on conventional process control gas chromatographs without any significant modification of the analytical unit, this is not true of the short columns made available by modified gas-solid chromatography nor of open tubular columns. For these columns, which could permit analysis times within a minute or so, the entire design of the analytical unit has to be rethought. Work is in progress in this area in several companies, but no system of proven design and performance has yet been described. All control units should use a microcomputer. These devices have performance levels, in terms of speed, memory capacity and reliability that well exceed the requirements of the fastest, most complex gas chromatograph we can imagine. Its main tasks should certainly be the programming of the analysis (injection of sample and deferred standard, valve switching, zero base line, etc.) and the acquisition and handling of the detector signal (calculation of the deferred standard peak characteristics, integration of the sample component peak areas and calculation of the concentrations of these compounds in the monitored stream). But the tasks of the microcomputer should also include the control of the analytical unit (from the characteristics of the peak of the deferred standard) and the preparation of the analytical report for the display unit and the central plant computer. Because the power of the available microcomputers so much exceeds the needs of the process gas chromatograph, the question arises whether it is better to use a dedicated control unit for each process gas chromatograph, or one single control unit for a number of gas chromatographs. There is no general answer. It depends whether safety or cost is considered to be the most important factor. With a dedicated control unit, each process gas chromatograph is autonomous. If one control unit is used for several gas chromatographs, important savings are made, but if it fails, the information supplied by all the chromatographs it controls will be lost. It is certainly unwise to use the central plant computer to control all the gas chromatographs in the plant. This idea, which originated before the appearance of References on p. 739.

718

microcomputers, has proved utopian and dangerous. It has been abandoned. It could be conceivable to have fewer control units than gas chromatographs and to interconnect them, so that if control unit a, which normally works for the gas chromatographs A, B and C, fails, control unit p will take charge of the gas chromatographs A and B and control unit y of the gas chromatograph C (in addition to the gas chromatographs control units p and y already control normally).

IV. EXAMPLES OF ON-LINE INDUSTRIAL ANALYSES We present here several applications, which have been selected from real problems, in order to illustrate the various techniques and concepts presented in the first part of this chapter and emphasize their usefulness, or to describe the serious difficulties encountered by the analyst working in this challenging field, together with the special constraints of process control analysis: reliability, precision, rapidity and low maintenance cost. 1. Analysis of Hydrogen in a Catalytic Reforming Process The hydrogen concentration in these units, which produce high octane gasolines, is high, between 70 and 90%; the rest of the gas contains all hydrocarbons up to hexanes. It is important for a long catalyst life to accurately control the hydrogen concentration. The determination by the analyzer of the hydrogen concentration must be made with an absolute accuracy of 0.4%, i.e., with a relative accuracy on this concentration of 0.5%. Two methods have been tried by Follain (45): - a direct method uses a thermal conductivity detector, with argon as carrier gas, and compares the area of the hydrogen peak to the area of the peak of a deferred hydrogen standard. - an indirect method uses a flame ionization detector to measure the total amount of hydrocarbons in the sample, using methane as a deferred standard, and calculates the concentration of hydrogen by difference. The use of the TCD, whose response depends on the carrier gas flow rate and on the block temperature, and is not linear under the experimental conditions which have to be used, does not allow the required accuracy. On the other hand, the response of the FID is less sensitive to the fluctuations of experimental parameters, is more closely linear, and permits the achievement of an absolute error on the total amount of hydrocarbons which is the same as the absolute error made by the first method on the hydrogen concentration. The relative error of the hydrogen concentration derived by the second method is thus four times smaller. The second method demands, however, that all hydrocarbons be eluted from the column and that an accurate calibration be made. The hydrocarbons must be resolved because their relative responses are too different to permit the use of a single response factor for all of them. Both conditions have been satisfied, the second one because of the use of the deferred standard method (45). A mixture of

719

7

L

Figure 17.15. Quantitative analysis of hydrocarbons in the effluent of a catalytic reforming process. After Follain (45). Column and experimental conditions, see text. 1, Methane. 2, Ethane. 3, Propane. 4, Isobutane. 5, n-Butane. 6, Isopentane. 7, n-Pentane. 8.2.2-Dimethylbutane. 9, 2-Methylpentane. 10, 3-Methylpentane. 11, n-Hexane. 12, Methylcyclopentane. 13, Benzene. 14,Isoheptane. 15, Isoheptane. 16, Isoheptane. 17, Deferred standard (methane).

hydrogen (90%) and methane (10%)is used and response factors of hydrocarbons relative to methane have been determined. Figure 17.15 shows the typical chromatogram obtained during this analysis, TABLE 17.6 Hydrogen Analysis by Direct* and Indirect** Methods (45) Theoretical composition

Hydrogen Methane Ethane Propane Isobutane n-Butane

79.45 i-0.5 10.70 5.40 2.89 0.53 1.02

Indirect method** (average of 10 runs) vol. % 79.805 f0.15 10.66 f0.07 5.20 f0.06 2.86 f0.045 0.494 f 0.02 0.994 f 0.04

Direct method* (average of 10 runs) vol. % 82.01 f 0.635

TCD, H, as deferred standard. methane as deferred standard (10% CH, in hydrogen). Concentration of H, equals to the balance of the total concentration of hydrocarbons.

** FID,

References on p. 739.

720

exhibiting complete resolution between the mixture components and with the deferred standard. The column used is 6 m long, 1/8 inch i.d.; it is packed with Chromosorb P, coated with 20% squalane. The carrier gas is helium (1.25 L/hour). The column temperature is 100 C. The results obtained by the two methods described above have been compared using a synthetic gas mixture (Air Liquide, Paris, France). The results are reported in Table 17.6.

2. Synthesis of Vinyl Chloride The process effluent stream contains hydrochloric acid, ethylene and vinyl chloride. The analytical difficulties are obvious. It is impossible, for example, to prepare calibration mixtures because ethylene and hydrochloric acid would react rapidly under pressure in a metal cylinder. It is for the solution of these problems that the concept of the deferred standard was first applied and the use of the gas density balance as a calibration detector investigated (37). a. Experimental Conditions

The instrument used is a Car10 Erba (Milan, Italy) Fractomatic. The column used is made of Teflon tubing, 4 mm id., 4.2 m long, divided in two sections (0.80 and 3.40 m long, respectively). It is packed with Teflon 6, coated with 15%SF-96 (General Electric), prepared using the procedure described by Saint-Yriex (46) (see Chapter 6). The column and the packing material are cooled at 0 O C prior to packing, which hardens the support particles, facilitates their handling and packing and avoids destroying the particle structure. The column temperature is 55 O C. The carrier gas is hydrogen, the flow rate 2 L/hour. The detector is a TCD, with serial, semi-diffusion cells, using W X wires (GowMac, Bound Brook, NJ, U.S.A.). The bridge current is 250 mA. The sample volume is approximately 1.5 mL. b. Column Lifetime

The columns easily passed the 1,000 hour test. In the field, the column lifetime proved to exceed 1 year, with continuous (24 hour/day) operation. The column is changed every year. c. Gas Circuit

The gas circuit includes two valves, a sampling valve and a switching valve for back-purging (see Figure 17.16). The only materials with which the sample and its components are in contact during the analysis are Hastelloy C (sampling and

721

*-&

I

11 ' Selector

5

b Detector

Figure 17.16. Schematic of the gas circuit for the analysis of the effluent stream in the vinyl chloride

synthesis. The selector valve selects the analyte, stream effluent or deferred standard.

switching valves, unions, detector block), Teflon (column, packing support, connecting tubes), SF-96 and the detector wires. Figure 17.17 shows the chronology of events during the analysis.

d. Deferred Standard Ethylene was chosen as deferred standard, since it is a component of the sample analyzed, and certainly the least reactive and the safest to store and handle. Pure ethylene is injected with the same valve as the sample (see Figure 17.17). TABLE 17.7 Relative Response Factors of Ethylene, Hydrochloric acid and Vinyl Chloride (37) Components

Relative response factor (w/w)

Ethylene Hydrochloric acid Vinyl chloride

1.oo 1.38 1.555

Relative response factors on a TCD, with semi-diffusion measuring cells in series (Pretzel Gow-Mac cells). Carrier gas: hydrogen. References on p. 739.

122

v1

0

-

Figure 17.17. Chronology of events during the analysis of the effluent stream in the synthesis of vinyl chloride. Identification of the compounds in the chromatogram. 1, Ethylene (sample). 2, Hydrochloric acid. 3, Ethylene (standard). 4, Vinyl chloride.

e. Calibration

The response factors of hydrochloric acid and vinyl chloride relative to ethylene (w/w) were determined using the GDB as a calibration detector (see Chapter 14). Because of the chemical aggressiveness of hydrochloric acid a solid nickel balance was used for the calibration. The response factors are reported in Table 17.7.

f: Sample Line A long transfer line is used for this analysis, because of the presence of tars. They can be more easily backflushed from the transfer line, with a stream of nitrogen, than from the column (see Figure 17.4). The line is 10 m long, made of 1 mm i.d. Teflon tubing. Its temperature is kept at 170°C by steam flowing in a concentric metal tube. The sample and the deferred standard are injected successively by the same valve. Prior to injection the flow is stopped and the end of the sample line connected to atmospheric pressure for 20 seconds. A selecting valve alternates filling the sample loop with the sample and the standard.

123

15 rnin

Figure 17.18. Typical chromatogram of the effluent stream of the vinyl chloride synthesis plant (37).

g. Results

Figure 17.18 shows a typical chromatogram, with the successive elution of a tiny amount of air, ethylene (from the sample), hydrochloric acid, ethylene (deferred standard) and vinyl chloride. Also shown is the small disturbance resulting from the injection of the deferred standard. The base line is automatically set to zero twice during each analysis, after elution of the air peak and before elution of the standard. All peaks tail, probably a consequence of the nature of the analysis. Figure 17.19 shows a bar graph record corresponding to a few hours of operation of the process. I t illustrates another possible use of the alarm function of the deferred standard. After a few hours of satisfactory operation, with a constant response for the standard, a severe thunderstorm seriously perturbed the electrical power supply of the plant and the operation of the process. This is illustrated by a kick in the standard response, followed by oscillations for a couple of hours. The References on p. 139.

724 7h

6h

5h

4h

I

3h

2h

lh

I

time

I

-1

i

Figure 17.19. Bar graph record of the composition of the effluent stream of the vinyl chloride synthesis plant. A drop of concentration of the three main components, with a drop in yield, takes place during the first hour. Everything remains stable for four hours, when a thunderstorm perturbs the plant electrical power supply, causing the kick in the deferred standard peak height and in the yield. The gas chromatograph and the plant recover (37).

TABLE 17.8 Comparison between Chromatographic and Volumetric Analysis of Hydrochloric Acid Essays

Chromatography

(W weight)

Volumetric titration (I% weight)

Relative difference

(W) 1 2 3 4 5

66.34 65.71 61.04 62.55 63.40

68.33 68.07 65.09 65.67 62.51

3.0 3.6 - 2.9 5.0 - 1.4

Hydrochloric acid is absorbed by bubbling a known volume of gas in water, followed by titration.

125

response of the standard remains within the specifications, however, except during the transient, allowing a record of the excursion of the process and its recovery. Quantitative analyses have been performed by chemical methods on the effluent stream. Hydrochloric acid is analyzed by absorption of the content of a known volume of gas in an alkaline solution and titration. Differences between 3 and 5% (relative) for HC1 concentrations around 60% have been observed (47). Data are reported in Table 17.8. 3. Analysis of the Gas evolved During a Chloration Process

One of the analyses developed for this process required the separation of the following gases in less than 5 minutes: oxygen, nitrogen, carbon monoxide, carbon dioxide, ethylene and chloroethane. The difficulty of this problem lies in the need to use several columns to achieve the separation of oxygen and nitrogen, the separation of permanent gases and the analysis of organic vapors.

0

E

0

0 .-c 2

I

I

I

\

m n Q

v)

H ~ u x 2

I

I

I

\

I

I

Figure 17.20. Schematic of the gas circuit used for the analysis of the gas effluent stream in the chloration process.

References on p. 739.

126

l3I

0 2 N2

CO

W

Figure 17.21. Chronology of events in the analysis of the effluent of the chloration process.

The following experimental conditions were selected: Instrument: Car10 Erba (Milan, Italy) Fractomatic CT. Column 1: stainless steel, 2 mm i.d., 1 m long; packed with 100-200 pm particles of 80 m2/g silica (Spherosil, Rhone Poulenc), coated with 10% diethylene glycol succinate. Column 2: stainless steel, 2 mm i.d., 1.40 m long; packed with 50-80 mesh Porapak Q (Waters), treated with 0.01%phosphoric acid (48). Column 3: stainless steel, 2 mm id., 1 m long; packed with Molecular Sieve 5A. Temperature of the columns: 80°C. Carrier gas: hydrogen, flow rate 5.8 L/hour. Detector: TCD with serial, semi-dipfusion cells. Bridge current: 250 mA. The requirement that the entire analysis be performed within 5 minutes led to a rather complex gas circuit, with several switching valves (see Figure 17.20). Two sampling valves are used, for the sample and for the deferred standard (nitrogen). Each one is completed by a second valve to adjust the pressure in the sample loop to atmosphere. Three switching valves are used, permitting the carrier gas to bypass of any of the columns. Figure 17.21 shows the chronology of events taking place

721 5 2

6

DS ( N z )

I 4

3

7

Lsd It

5I min

I

I

I

I

Figure 17.22. Typical chromatogram supplied by the process gas chromatograph analyzing the effluent of the chloration process. 1, Nitrogen (deferred standard). 2, Chloroethane. 3, Oxygen. 4, Nitrogen (sample). 5 , Carbon dioxide. 6, Ethylene. 7 , Carbon monoxide.

during an analysis. Finally, Figure 17.22 shows a typical chromatogram. The resolution between all the bands is excellent; it would probably be easy to halve the analysis time if needed. The response factors of the various components relative to nitrogen have been determined using the GDB as a calibration detector. 4. Analysis of Gaseous Ammonia The components of this industrial stream are: air, carbon dioxide, ammonia and water. Since there is no other component, the quantitative analysis is derived from the peak area ratios and there is no deferred standard. The following experimental conditions were selected. Column: Teflon tubing, 4 mm i.d., 4 m long; packed with 80-100 mesh oxide) (48). Chromapore (poly-2,6-dimethyl-para-phenylene Column temperature: 70 O C. Carrier gas: helium, flow rate: 2.5 L/hour. Detector: TCD, with two serial, semi-diffusion cells (Pretzel, Gow-Mac), bridge current 210 mA. Sample size: 1.5 mL. A long transfer line is used. Figure 17.23 shows a typical analysis. The relative response factors have been measured with the GDB. The results are given in Table 17.9. References on p. 739.

728

H2O

Figure 17.23. Analysis of an ammoniacal gas stream (37).

The accuracy of the quantitative results has been checked by comparison with the results of two other methods, a chemical method and the method of O t h e r and Frolich (50). The results of this comparison are reported in Table 17.10. The excellent agreement observed confirms the validity of the chromatographic method, the soundness of the sampling procedure used, as well as the validity of the calibration performed with a GDB. TABLE 17.9 Response Factors of Some Compounds Relative to Ammonia (37) Components

Response factor

1.o 1.34 1.65 0.97 1.015 ~~

~

~

Factors determined with the gas density balance (seeChapter 14, Section 11.3), assuming the TCD to be linear in this concentration range. Helium carrier gas.

729

TABLE 17.10 Chromatographic Results Compared to the Other-Frohlich Method in the Case of NH,, C02, H20 Analysis (37) Control

ChromatotOPPhY

OthmerFrohlich Method

Deviation between the two methods - Ref. chromatography (%)

50.8 34.0 15.2

50.9 33.6 15.5

+0.2

50.5 35.0 14.5

50.9 33.7 15.4

51.8 33.7 14.5

52.6 31.9 15.5

51.4 33.8 14.8

52.9 31.5 15.6

50.9 32.3 16.8

52.8 31.6 15.6

- 1.2

+ 2.0

+0.8 - 3.7 + 6.2

+ 1.5 - 5.3 + 7.0

+ 3.0 - 6.0 + 5.4 + 3.7 - 2.2 - 7.0

NH3/C02 Ratio Obtained by Chromatography and Chemical Method Control

Chromatography

Chemical analysis

Deviation between the two methods (%)

1 2 3

1.51 1.50 1.44

1.57 1.52 1.51

+4 1.3 4.85

+ +

Figure 17.24. Analysis of the effluent of the reactor preparing phthalic anhydride. 1-3. Unknowns. 4, Benzaldehyde. 5, ortho-Tolualdehyde. 6, Maleic anhydride. 7, Citraconic anhydride. 8, Unknown. 9, Ethylene (deferred standard). 10, Benzoic acid. 11, Phthalic anhydride.

References on p. 739.

730

5 i/ i I'

20 hours

5

10

1

Figure 17.25. Bar graph record of the composition of the effluent of the reactor for the synthesis of phthalic anhydride. 1, orrho-Tolualdehyde.2, Maleic anhydride. 3, Ethylene (deferred standard). 4, Benzoic acid. 5, Phthalic anhydride. The deferred standard has a constant area. The concentration of the main product oscillates slightly. The concentration of other products, especially tolualdehyde, varies much more widely.

5. Synthesis of Phthalic Anhydride The control of the synthesis of phthalic anhydride is an excellent example of a problem where the conventional calibration methods are difficult or even impossible to apply (37,41). The deferred standard solves the calibration problem easily. TABLE 17.11 Quantitative Results Obtained by the Deferred Standard Technique in Phthalic Anhydride Synthesis (37) Date

September 8th. 1969 9th 10th 16th 18th 19th 26th 29th 30th

Results expressed in g/m3 Benzaldehyde

o-Tolualdehyde

Maleic anhydride

Citraconic anhydride

Benzoic acid

Phthalic anhydride

0.020 0.020 0.020 0.020 0.025 0.025 0.020 0.020 0.020

0.055 0.070 0.035 0.110 0.110 0.090 0.170 0.195 0.210

5.815 5.515 5.670 5.630 5.665 5.730 5.110 5.315 5.060

1.250 1.205 1.245 1.140 1.200 1.200 1.080 1.145 1.100

0.400 0.430

56.00 56.20 57.30 55.30 55.10 55.00 55.00 55.00 54.65

0.445 0.445 0.430 0.390 0.370 0.370

731

The column is packed with Chromosorb PAW (80-100 mesh), coated with 4% phosphoric acid and 10% LAC 446. Figure 17.24 shows a typical chromatogram. The various components of the effluent are completely resolved. The stream sampled is at 180°C. The column is at the same temperature. The sample size is 512 pL. A 1.29 pL volume of ethylene is injected as a standard, 12.50 minutes after the sample. Figure 17.25 shows a 20-hour bar graph record of the analytical results. The stability of the deferred standard peak demonstrates the proper functioning of the gas chromatograph. The results show a good stability of the process, but some significant fluctuations, and a rather large excursion of the concentration of ortho-tolualdehyde, a reaction by-product. In this case there is no other analytical method available to test the accuracy of the results. A comparison with the material balance of the plant shows an excellent agreement with the integration of the concentration data supplied by the gas chromatograph (see Table 17.11).

6. Analysis of Recycled Styrene This stream contains a variety of aromatic hydrocarbons (35). The following experimental conditions were selected: Instrument: Carlo Erba (Milan, Italy) Fractomatic. Column: stainless steel, 1 mm i.d., 6 m long (1 m + 5 m); packed with 160-200 pm, 80 m2/g silica particles (Spherosil) coated with 10%diethylene glycol succinate. The short segment is back-purged at the end of the analysis.

0,

aJ C 0,

9 c h Y

w

+0

0

0 x

0

2

hI

15 rnin

I

I

10

5

Figure f7.26. Chromatogram of a recycled styrene stream.

References on p. 739

132

Column temperature: 155 C. Carrier gas: nitrogen, flow rate 0.36 L/hour. Detector: FID, polarized jet. Sample size: 0.5 pL, liquid, with a Siemens sampling valve. Deferred standard: ethylene, injected with a gas sampling valve placed upstream the sample injection valve (see Figure 17.10~). The analysis time of about 15 minutes could be markedly reduced by increasing the flow velocity, or reducing the column length. Figure 17.26 shows a typical chromatogram. Quantitative analyses were performed by using the response factors of the key compounds relative to the standard, as measured with the GDB. The use of narrow bore columns, or modified gas-solid chromatography does not raise any serious difficulty in adapting the instrument. The liquid sampling valve operates very satisfactorily. 7. Airborne Pollution Analysis in a Polymerization Plant

In this case the plant management wanted to follow the concentration in the working area of the following compounds: vinyl acetate, ethyl acrylate, styrene and butyl acrylate (42). The following experimental conditions were selected: Instrument: Car10 Erba (Milan, Italy) Fractomatic. 1

3 min 4'

Figure 17.27. Analysis of atmospheric pollutants in a plant (42). Experimental conditions, see text. 1, Vinyl acetate (93 vpm). 2, Ethyl acrylate (95 vprn). 3, Styrene (58 vpm). 4, Deferred standard, ethylene (51 vpm). 5, Butyl acrylate (74 vpm).

733

Column: stainless steel, 4 mm i.d., 30 cm long; packed with 150-200 pm particles of 200 m2/g silica (Spherosil), coated with 25% of diethylene glycol succinate. Column temperature: 90 O C. Carrier gas: nitrogen, flow rate 7 L/hour. Detector: FID, polarized jet. Sample size: 0.58 mL of air. Deferred standard: ethylene. In this case the deferred standard proved extremely useful. In addition to its classical advantages, already discussed above, it gave confidence to the.workers in the ability of the instrument to properly control the pollution inside the plant. 10

12

-9

o1 - - I 6

1

4

2iFe 1

5 vprn

-styrene

24 &vinyl

acetate 8 vprn

E

10

-9

23

-8

I

-4

20 -3

I

2

4 -~ D.S.

Deferred Standard Ethylene

Figure 17.28. Bar graph record of the atmospheric pollution in the plant. The number and the step identify each location where a sample is grabbed. Pollution levels are low and erratic. The stability of the deferred standard peak validates the results (42).

734

The requirement for the analysis was to check 10 different locations in the plant and to make a measurement at any given place every 30 minutes. The analysis should thus be completed in 3 minutes. The chromatogram on Figure 17.27 shows how this is possible, using a short column packed with a large surface area, modified adsorbent (see Chapter 7). Figure 17.28 shows a typical bar graph record. The analyzed stream is identified by a bar having a height proportional to its rank. The deferred standard peak demonstrates that the gas chromatograph is working well, although in most cases there is no detectable level of pollution. Without the deferred standard the confidence in the results given by the same instrument would not be very high. With conventional methods, calibration of the detector for those types of compound, in the concentration range investigated (0-20 ppm) is quite impossible, or at best unreliable. Calibration mixtures are impossibly difficult to prepare as these compounds would readily adsorb on the surface of the container walls. Again, the use of the deferred standard offers an easy solution, the response factors relative to the deferred standard being most conveniently and rapidly determined with the GDB (see Chapter 14). The good resolution and fast analyses allowed by the modified gas-solid chromatographic columns have permitted the use of a portable gas chromatograph to perform the same analysis. The column is made with the same material, but it is shorter and now operates at ambient temperature. A chromatogram is shown in Figure 17.29.

Figure 17.29. Analysis of the atmospheric pollutants in a polymerization plant, using a portable gas chromatograph (Century).

735

8. Analysis of Chloral

The control analysis of chloral (CC1,-CHO) is usually performed by chemical methods, which require the intervention of a chemist to grab a sample and perform the analysis in the laboratory. These methods are not readily adaptable to automation. The use of gas chromatography with steam as a component of the mobile phase (see Chapter 7) is an elegant solution to a difficult problem, since chloral is usually found in waste water, from which it must be recovered before sending the water to the sewage. The analysis is carried out directly on the waste water, without any previous treatment, by injecting a known volume into the gas chromatograph operating under the following conditions. Column: stainless steel, 4 mm i.d., 0.50 m long; packed with Porapak P. Column temperature: 132' C. Carrier gas: nitrogen, 2 L/min, steam, 1 L/hour. Detector: FID, with polarized jet. Sample volume: 0.5 to 1 pL. Figure 17.30 shows three chromatograms obtained with different matrices: - a mixture of chlorinated hydrocarbons (Figure 17.30A),

5 min

d 7 rnin

Figure 17.30. Quantitative analysis of chloral in various matrices, using steam as a component of the carrier gas (see text). A, In chlorinated hydrocarbons. Chloroform, carbon tetrachloride, 1,2-dichloroelhane, trichloroethylene. 1,1,2-trichloroethane. B, In 1.2 dichloroethane, at trace level. C, In waste water, at trace level.

References on p. 739.

136

in 1,2-dichloroethane (Figure 17.30B), in waste water (Figure 17.30C). In this last case, concentrations well below 1 ppm can be easily detected with the equipment used. -

9. On-Line Control of a Dicldorodifluoromethane Process The control of the synthesis process of dichlorodifluoromethane (Freon F12) requires the continuous analysis of the following trace components: - trichlorofluoromethane (Fll), - dichlorofluoromethane (F21), - chlorodifluoromethane (F22). The concentration of these impurities i s of the order of a few hundred ppm, so a process control gas chromatograph equipped with a flame ionization detector was selected, rather than one using a thermal conductivity detector. For reasons explained above, a packed column is used. The main component (F12) tails and this interferes with accurate quantitation of the impurities. Accordingly, a combination of several successive valve switchings was chosen. Heartcutting of the impurities band and their transfer to a second column permits the elimination of the interference with the main component band. Backflushing out of the second column of the bands of the impurities, which have been excessively broadened, followed by the injection of the backflushed band in a third column, permits the elution of much narrower peaks of the impurities. Finally the backpurging of the first column t

:0 sec

t

:65

sec Delector Backflush Coi 2

0

Vf VZ

0

v1

0

'Dm t

:109 sec

Backpurging

F21

DS

F22

Figure 17.31. Principle of the multi-columnon-line analysis of the impurities in dichlorodifluoromethane.

737

-

A u x CG

Figure 17.32. Schematics of the columns and valves setup for the on-line analysis of impurities in dichlorodifluoromethane. S, sample. DS, deferred standard. CG, carrier gas. Aux CG, auxiliary carrier gas. Atm 1, Atm 2, atmospheric pressure.

permits the elimination of any possible heavy component. Figure 17.31 illustrates the principle of this three step analysis. The schematic of the actual set-up is shown on Figure 17.32. For the analysis, a modified gas-solid chromatography packing (see Chapter 7) is used. The three stainless steel columns (4 mm id., 1, 0.5 and 3 m long, respectively) are packed with 200-250 pm porous silica particles (Spherosil, Rhone-Poulenc), 35 m2/g, coated with 2.5% (w/w) of Carbowax 20M. The column temperature is 65 O C, the carrier gas (nitrogen) flow rate is 3 L/hour. The hydrogen flow rate to the FID is 2 L/hour and the air flow rate is 15 L/hour. The sample size is 397 pL. Trichlorofluoromethane (F11) is used as deferred standard. The volume injected (0.54 pL) is small enough that the impurities contained in this product are not detected. Table 17.12 gives the timing of the events during this analysis and Figure 17.33 shows a typical chromatogram. The weight response factors of F21 and F22 relative to Fl1 are 0.41 and 0.55, respectively, under the experimental conditions described. The repeatability of the retention times is excellent. The average retention time calculated for 20 successive chromatograms has changed by less than 1%after 2,230 cycles. The deferred standard proved useful not only for an on-line check of the reliability of the analytical performance of the gas chromatograph, but also in considerably simplifying the calibration procedure. Calibration of the detector response is much easier and more accurate through the use of the response factors References on p. 739.

738 F 22

F 12

I

I

h

1,

7minutes a

I

Figure 17.33. Typical chromatogram in the on-line analysis of dichlorodifluoromethane.

TABLE 17.12 Event Timing in the Analysis of Freon Time

Function

(set)

0 65

109 110 140 150 173 212 352 384 390 420

Sample injection Heartcut Col. 2 Backflush Col. 2 Separation Col. 3 Backpurge Col. 1 DS line put to atm. DS injection Sample line to atm. Detection of F22 Detection of F11 Detection of DS Detection of F21 Refill sample loop Refill DS loop Sample injection Heartcut Col. 2

Valves open: white (W) or black (B) Atm 2

DS

Atm 1

S

v1

v2

B

B

W

W

B

B

B

B

W

W

B

W

B W W W

B B W W

W W W B

W W

W W

W

W

W

B

W

W W W

B

B

B

B

B

W

B

B

W

W

B

B

relative to the deferred standard than when using conventional methods, such as the injection of samples of standard calibration mixtures. In the case of the Freon mixture, continuous vaporization of a stream of liquid sample would be necessary (see Chapter 14, Section 1.2). 10. Conclusion

These are but a few examples selected among the most significant applications that we have studied during the last twenty years. The combination of the calibration techniques developed around the use of the GDB, of the deferred standard, of the Deans techniques of column switching and of modern digital electronics and

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microcomputers permits the solution of almost any process control analysis problem. Among the most spectacular results are the solution to difficult plant mass balance problems. For various reasons dealing with economics and financial problems, with material auditing and with pollution control, it is important to know in detail what happens to the products which enter the plant. Trying to solve this problem permits the discovery of all kinds of interesting problems, phenomena and stones. Process gas chromatography offers a very powerful tool in investigations of that kind. We can give here two examples, those of a chloration process giving a complex mixture of C1, C2 and C3 chlorinated hydrocarbons and an oxidation process giving mixtures of alcohols, aldehydes, acids, etc. The material balance calculated after the chromatographic analysis of the effluents of the reactor gives an account of the fate of 98%of the different feeds of the chloration process (see Section IV.3). Because pure compounds, especially the C3, C4, etc aldehydes could neither be purchased nor prepared at a sufficient degree of purity to proceed with conventional calibration procedures, the material balance of the process had to be calculated from approximate chromatographic results obtained by conventional methods. The mass balance results were erratic and did not account for more than 86% of the reagents. After implementation of the deferred standard method and using the GDB for determination of the response factors with the impure compounds available (see Chapter 14), the mass balance of the plant reached 95% of the feeds. These results explain why a good chromatography team and high quality equipment is a very profitable investment.

LITERATURE CITED (1) D.J. Fraade, National Petroleum Refiners Association, Technical Paper 62.36 (1962). (2) R.F. Wall, Znstrum Technol., 14, 59 (1967). (3) F.W.Karasek, Sci. Amer., 220, 112 (1969). (4) S.J. Bailey, Control Eng.. 23 (a), 22 (1976). (5) C.G. Fellows, Control Eng., 4 (6). 75 (1957). (6) E.M. Thomason, ZSA J., 10, 56 (1963). (7) J.C. Sternberg, in Gas Chromatography, L. Fowler Ed., Academic Press, New York, NY, 1963,p.

161. (8) D.E. Manning, Instrum. Technol. 15, 67 (1968). (9) D.J. Burges, Proc. Soc. Anal. Chem., 5, 132 (1968). (10) M.R. Cutler, Proc. Soc. Anal. Chem.. 5, 133 (1968). (11) A. Derose, Proc. SOC.Anal. Chem., 5, 134 (1968). (12) L. Fowler, Instrum. Technol., 16, 46 (1969). (13)W.H. Topham, Znstrum. Technol., 17, 51 (1970). (14)A. Klein, Control Eng., 22 (12),39 (1975). (15) M.D. Weiss, Control Eng., 24 (9),66 (1977). (16) C.S.F. Pine, Talanta Review, 14, 269 (1966). (17) I.G. McWilliam, in Aduances in Chromatography, J.C. Giddings and R.A. Keller Eds., M. Dekker, New York, NY, 1968,p. 163.

740 (18) F.D. Martin, Instrum. Technol.. 24, 51 (1977). (19) R. Villalobos, R.O. Brace and T. Johns, in Gus Chromatography, H.J. Noebbels, R.F. Wall and N. Brenner a s . , Academic Press, New York, NY, 1961,p. 39. (20) G.S. Turner and R. Villalobos. in Gus Chromatography, N. Brenner, J.E. Callen and M.D. Weiss Ekis., Academic Press,New York, NY, 1963,p. 363. (21) W.M. Crum, 17th Proc. Natl. Instr. Symp., 8, 263 (1962). (22) R. Villalobos and G.S. Turner, ISA J., 10, 67 (1963). (23) R. Villalobos, Chem. Eng. Progr., 64,55 (1968). (24) R. Villalobos, Chem. Eng. Prog., 64, 55 (1968). (25) G.S. Turner and W.M. Crum, 18th Proc. Nail. Instr. Symp., 9, 77 (1963). (26) R.W. Smith, A.W. Wotring, L.H. Johnson and L.W. Morgan, ISA J., 24, 131 (1977). (27) R. Villalobos and G.S. Turner, Instrum. Technol., 23, 51 (1976). (28) A. Giraud, Rev. Inst. Pet.. 18, 271 (1963). (29)J.L. Foumenteze, Rev. Metall., 1967. 61. (30)J. Smith and R. Villalobos, ISA Trans., 7 (4), 273 (1968). (31) J.R. Fair, B.B. Crocker and H.R. Null, Chem. Eng., 19 (9), 146 (1972). (32) R.A. Foster, Chem. Eng., 22 (3). 65 (1975). (33) L.K. Barnes, 18th ISA Annual Conference and Exhibit, September 1963. (34) K.K. Konrad, Greenbrier Co., private communication, 1970. (35) C.L. Guillemin, Mesures, 41, l(1976). (36) R. Villalobos, Instrum. Technol., 14,59 (1967). (37) C.L. Guillemin, J. Vermont, P. Juston, P. Ferradini, A. Artur and A. Peyron, J . Chromatogr. Sci., 9, 155 (1971). (38) C.L. Guillemin, Mesures, 37, 87 (1972). (39) M.Goedert and G. Guiochon, Anal. Chem., 45,1188 (1972). (40)C.L. Guillemin, Mesures, 37, 99 (1972). (41) C.L. Guillemin, Instrum. Technol., 4,43 (1975). (42) C.L. Guillemin, J. High Resolut. Chromutogr. Chromutogr. Commun., 3, 620 (1980). (43) C.L. Guillemin, Colloque IRA, Arles (France), 1979, p. 112. (44)C.L. Guillemin, J. Chromatogr., 239, 363 (1982). (45) G. Follain, Colloque IRA, Arles (France), 1979, p. 23. (46) A. Saint-Ynex and J. Le Simple, Bull. Soc. Chim. France. 1967, 4365. (47) C.L. Guillemin, F. Auncourt, J. Du Crest and J. Vermont, J. Chromatogr. Sci., 7, 493 (1969). (48) G.C. Carle, J. Chromatogr. Sci., 8, 550 (1970). (49)J. Tranchant, Z. Anal. Chem., 236, 137 (1968). (50) D.F. O t h e r and G.F. Frohlich, Ind Eng. Chem., Process Des. Deu., 3, 270 (1964).

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APPENDIX

CHROMATOGRAPHY LEXICON -AAbsolute Retention Time. This name is sometimes used for the time elapsed between the injection of the sample and the appearance of the maximum concentration of the band of the compound. This is more often and properly called the Retention Time. In some cases, it is defined as the mass center or first moment of the concentration distribution. The two definitions are different for non-symmetrical peaks. See p. 13. Symbol: t,. Absolute Retention Volume. The net retention volume. This is NOT the volume of gas corresponding to the absolute retention time. For this reason the two terms should be avoided. See p. 13. Symbol: V,. Activation of Adsorbent. Many adsorbents used in gas chromatography adsorb readily water and, possibly, some laboratory pollutants during storage. The adsorbent surface is then much less polar and the adsorption energy is considerably decreased. The product gives small retention volumes and exhibits a low degree of selectivity. Furthermore, because the carrier gas is usually dry, the sorbates are slowly desorbed and the column retention properties drift, preventing the achievement of reproducible results. Before using it in gas-solid chromatography, it is necessary to eliminate these sorbates from the adsorbent under dry atmosphere or vacuum. This is especially true with molecular sieves, silica gel and alumina. Adjusted Retention Volume (Time). Retention volume (time) less the dead volume (time). The adjusted retention time is the time spent in the stationary phase by a retained compound. It is more properly called the true retention volume (time). See p. 13. Symbols: V i (t;). Adsorbents. Materials, usually exhibiting a large specific surface area, which adsorb organic vapors more strongly than the carrier gas. The value of the adsorption constant depends on the structure, molecular weight, polarizability and dipole moment of the vapor, so it differs from compound to compound, making separation possible. Adsorbents most useful in GC are: graphitized carbon black, silica gel, zeolites (molecular sieves), alumina, porous polymers and activated carbons. See p. 182.

Adsorption. Physico-chemical process by which there is a difference in concentration at equilibrium in a bulk phase, gas or liquid, and at the interface between this phase and another one. There can be adsorption at a gas-solid, a liquid-solid or a

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gas-liquid interface. In all cases, such an adsorption results in a contribution to the retention of a compound. This is the essential or only contribution in gas-sdid chromatography, but *adsorptionat either the gas-liquid or the liquid-solid interface, or at both, may often constitute an important contribution to retention in gas-liquid chromatography. See pp. 77-82. Adsorption Chromatography. An implementation of chromatography using an adsorbent as stationary phase. Also called Gas-Solid Chromatography. See p. 77. Adrorption Coefficient.Henry’s law coefficient of proportionality between the amount of vapor sorbed on an adsorbent and the partial pressure of the compound in the gas phase. See p. 77. Symbol: K or KH. Adsorption Isotherm. The composition of a gas-solid system at equilibrium is a function of the amount of material involved. There is a relationship between the partial pressure of the vapor in the gas phase and the surface coverage of the adsorbent by the sorbed molecules. This relationship, which is not linear, is called the distribution or adsorption isotherm. In all cases, when the partial pressure of the vapor becomes close to its vapor pressure, the amount sorbed increases indefinitely, by a process known as capillary condensation, where the small pores fill up with liquid. At very low partial pressures, the curvature of the isotherm can be either positive (towards the surface coverage axis) or negative (towards the pressure axis). In the first case the amount adsorbed increases faster than the partial pressure and the chromatographic peak will start to front or lead ( t R increases with increasing sample size) when the column is overloaded. In the second case the amount adsorbed increases more slowly than the partial pressure and the peak starts to tail ( t R decreases with increasing sample size). The most classical isotherm is the Langmuir isotherm, with a negative curvature. See Chapter 5. Aerogels. Many of the adsorbents used in GC are prepared in the liquid phase, from a dispersed gel system. If the solvent contained in the gel can be removed without significant shrinkage of the gel matrix and the dry structure does not collapse, the product is called an aerogel. This is the case with silica gels and with the glass gels obtained by alkaline etching of borosilicate glasses, followed by a heat treatment, which produces regular-sized pores of somewhat controllable dimensions. Gels which shrink or collapse upon removal of the dispersing agent are called “xerogels”. Air Retention Time. Obsolete term for gas hold-up time. See p. 13. Alkali Metal Flame Ionization Detector. See Thermoionic Detector. Alumina. Precipitated alumina (from aluminum salt solutions) can be dried to give a porous adsorbent with a large specific surface area (ca 200 m2/g). The adsorption energy depends much on the amount of residual water (measured by the degree of activation in the Brockman scale; the grade I is the most active and the driest). By

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contrast with silica gel, whose surface is mildly acidic, the surface of alumina is basic. Hence it presents a different selectivity towards polar compounds, especially those carrying oxygen and/or nitrogen atoms. Apiezon. Originally prepared as vacuum greases, these products are supposed to be high molecular weight saturated hydrocarbons, obtained as residues of molecular distillation of heavy petroleum cuts. They are markedly more polar as a stationary phase than squalane, and contain significant amounts of polar products (oxidation products?) which can be removed by simple liquid chromatography on Florid. The most popular is L; M and N have also been used. Their maximum temperature of use is around 250°C. Argon Ionization Detector. This detector was described by Lovelock in 1958. It is more sensitive than the flame ionization detector and has a shorter time constant. It is, however, more sensitive to pollution and has a lower dynamic linear range. The principle of the detector uses the reaction of organic vapors with excited, metastable argon atoms, leading to the ionization of these vapors, with the formation of electrons which are collected. The current obtained is a measure of the mass flow of compounds into the detector. The metastable argon atoms are formed by collision of the argon atoms with accelerated secondary electrons produced by irradiation of the gas contained in the detector cell by the P-rays emitted by a radioactive foil (wSr, 63Ni, 3H) placed on the detector wall. He, Ne, Kr, H,, N,, O,, CO, CO,, CH,, halogens, and fluorocarbons, all of which have an ionization potential larger than the excitation potential of argon, give no response. The detector is quenched by water. See pp. 472-476. Asymmetry. Ratio of the front and the tail half-widths of the peak. Sometimes the ratio of the front and tail widths at a fractional height, such as 0.10. See p. 19. Symbol: As. Auerage Currier Gas Velocity. Column length divided by the gas hold-up time of the column. See p. 41. Symbol: ii. Axial Molecular Diffurion. Mass transfer process by diffusion along the axis of the column. It results from the very existence of a compound band, which creates a concentration gradient parallel to the column axis. Molecular diffusion proceeds after Fick’s law and produces a band spreading effect which increases with increasing time spent in the column. See p. 96. Symbol in the HETP equation: B.

-BBackflush. A technique for the GC analysis of complex mixtures or mixtures containing heavy compounds of little specific interest. After the separation of the light components has been performed and their elution achieved, the flow of carrier

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gas is reversed and the heavy components are eluted from the column inlet. Provided backflush lasts longer than direct flow, the heavy, but still volatile, components do not accumulate in the column. Alternatively, a precolumn can be used and backflushed while the analysis is performed on the main column. A significant time saving is achieved. In some cases a quantitative estimate of the total amount of the heavy components can be obtained from the area of the composite backflushed zone. See pp. 344-346. Backpurging. A technique for the routine quantitative analysis of complex mixtures containing heavy compounds considered as of no analytical interest. Differs from backflushing in that the compounds are vented without being detected. See pp. 341-343 and 352. Band. A zone of mobile phase containing a compound. It is often used synonymously with peak or zone. Usually peak conveys an idea of a symmetrical or quasi-symmetricalband, i.e. rather narrow, well behaved. A band or zone will often be highly unsymmetrical. Band Broadening. A process which takes place under the combined influence of axial diffusion and radial resistance to mass transfer, and which leads to the elution of zones which are markedly wider than the injection band of the sample. See Chapter 4. Band Width. See peak width. Measured at half-height or on the base line. See pp. 16-20. Symbol: w . Base Line. Signal of the detector when no compound is eluted of the column. This represents the detector background signal, offset to place the base line on the zero of the recorder chart. Measurements of peak height or area are done with respect to the base line. Ideally it should be an almost straight line with minor tremors, showing the background noise. The instabilities of the base line are drifts and noise. Base Line Drift. Any low frequency change in the detector signal. It often arises from flow rate changes, sometimes associated with temperature drift of the column oven. Also attributed to column bleeding, in temperature programming analysis. May be due to the elution of large amounts of very strongly retained material injected long before the current analysis was started. See pp. 639-644. Bleeding. Loss of stationary phase. It can occur either by decomposition of the phase or by evaporation in the carrier gas stream. As the speed of these two phenomena increases rapidly with increasing temperature there is a maximum temperature above which the stationary phase should not be operated. This temperature depends on the amount of phase in the column and on the nature of the solid support used. Bleeding results in (i) a progressive decrease of the retention volumes, (ii) an increased background current, which becomes temperature-dependent, and

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an increased base line noise, (iii) a marked drift following an exponential rise in temperature programming and (iv) sometimes a significant decrease in column efficiency. When silicone phases are used, bleeding results in the deposition of silica flakes on the burner of flame ionization detectors, which creates noise and may alter the response. See pp. 694-695. Bonded Stationary Phases. A new type of stationary phases, used mostly in HPLC, but employed also in GC. They derive from silica or glass adsorbents, by reaction of the surface with a substituted chlorosilane. HC1 is eliminated and the rest of the silane molecule is bonded to the surface. A large variety of silanes have been used, leading to the fixation on the silica surface of methyl-, butyl-, octyl-, dodecyl-, octadecyl-, aminopropyl-, phenylalkyl-, cyanopropyl-, alkyldiol-, etc. These phases have properties intermediate between those of coated liquids (in thin films) and regular adsorbents. Brockman Scale. A series of six dyes for which adsorption on alumina (i.e. retention volumes) increases in a given order. Adsorption is a function of the water content of the adsorbent. Various samples of alumina can be compared as potential stationary phases for a separation by the retention data (i.e. R , in TLC) of these dyes, or by the determination of which dyes stay on top of the column, which ones move to the bottom, and which ones are eluted rapidly. Unfortunately, the original Brockman scale uses carbon tetrachloride as an eluent and is dangerous to use. Bulk Property Detector. Any detector which measures the change in a physical property of the mobile phase when a compound is eluted. The thermal conductivity detector, spectrophotometric detectors, etc., are bulk property detectors. A differential method must be used, to determine small changes of the corresponding property. Accordingly, these detectors are sensitive to drifts of any parameter, such as temperature, which may change the value of the measured property. They tend to be less sensitive than solute property detectors. See pp. 397-411. By-puss Injector. A type of injector using a gas chamber which can be isolated from the main stream of carrier gas, to be filled with the sample, and then, by actuating valves, can be placed in the main stream of mobile phase.

-CCapacity Factor or capacity ratio of the column. Ratio of the times spent by the compound in the stationary and the mobile phase. The most convenient parameter to characterize the retention. See pp. 15 and 57-70. Symbol: k'. Capillary Column. See Open Tubular Column. The name is improper, because tubes of any diameter, large or small can be used to carry out GC separations. See Chapter 8.

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Carbowax. Trade name for polyethyleneglycols. The number associated with the name is related to the average molecular weight. These compounds are rather polar and well suited to the analysis of compounds which have several oxygen functions and a rather small saturated chain or skeleton. They are usually terminated by OH groups, which adds to their polarity and decreases their thermal stability. Kovats has described a process of methyl termination. Carrier Gas. The mobile phase in Gas Chromatography. Catharometer (also written Katharometer, notably in German). See Thermal Conductivity Detector. Celite. Diatomaceous earth, used for the preparation of supports for GC. The diatomite is fused with a small amount of a flux (sodium carbonate), at 900°C. Depending on the conditions of the treatment, it is white or pink. The material has a large porosity but a small specific surface area (3-8 mz/g). So it can hold a large amount of liquid phase if needed, but does not retain most solutes by adsorption. Chromathermography. A chromatographic process using a temperature gradient moving slowly along the column and obtained by moving an oven along the column at a constant speed. This is a form of displacement gas chromatography, in which the zones stabilize at the temperature at which their migration rate is equal to the speed of the oven. Although zones tend to be narrow and spreading is limited, the resolution power obtained by this method is not very large. This method seems to be inferior to temperature programming in nearly all cases. Chromatogram. Plot of the detector signal versus time. It is usually supplied by a recorder, sometimes by a computer. Chromatograph. The instrument used to separate substances by chromatography. Chromatography. A separation process discovered by Tswett. Separates the components of a mixture based on the difference between their equilibrium constants between a stationary phase and a mobile phase which percolates across the bed of stationary phase. The stationary phase is either an adsorbent or a liquid spread over an inert support. The mobile phase is a fluid, gas, high density gas or supercritical fluid or liquid. Chromosorb. A popular trade name for (a) supports for gas chromatography (packed columns); (b) porous polymers, used as adsorbents for the analysis of light polar molecules. The supports are designated by letters: A, G, P, T and W, or by a number, and come in different mesh sizes. A is similar to P, but is supposed to have a larger porosity and be able to carry a large coating ratio. G is a hard diatomaceous earth with a low specific surface area and a low porosity, supposed to have a relatively inert surface and carry low coating ratios. P is Celite treated with an

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alkaline flux at high temperature, to reduce the specific surface area and the chemical activity; it is pinkish. T is a screened Teflon powder, for use as a support for the analysis of extremely polar or aggressive gases. It is difficult to pack properly. W is a white diatomaceous earth (“Celite”). Chromosorb A, G, P and W are also available acid washed, or silanized, to increase their chemical inertness. The porous polymers are designated by a number (101 to 108), depending on their composition. Most are crosslinked polystyrenes, some contain polar monomers such as acrylonitrile or acrylic esters. Column. Chromatography is carried out by percolating a mobile phase through a bed of stationary phase. In gas chromatography the bed must be contained in a leakproof tube, so the gas phase cannot escape. In gas chromatography there are three different kinds of columns: the traditional packed column, the capillary or open tubular column, and the wall coated or support coated or porous layer open tubular column. See Open Tubular Column (OTC), Packed Column (PC) and Support Coated Open Tubular Columns (SCOT). See Chapters 6-8. Column Performance. Number of theoretical plates of the column. See p. 18 and Chapter 4. Column Switching. Procedures permitting the use of several columns to perform the analysis of a difficult or complex mixture. Often used for routine trace analysis. Preferred to temperature programming in process control analysis and in many cases in routine laboratory analysis. Today called multidimensional chromatography. See pp. 340-384. Compressibility Correction Factor. Corrective factor derived by James and Martin, to correct retention volumes, flow rate and flow velocity for the effect of the compressibility of gases and of the pressure drop. Because of the viscosity of gases, it is necessary to apply a certain pressure at column inlet, and a given mass of gas there occupies a smaller volume than at column exit. The effect of the passage of this mass on the migration of a band depends on the exact position of the band. See p. 41. Symbol: j. Concentration Sensitive Detector. A type of detector the response of which is proportional to the concentration of analyte in the eluent. See pp. 397-401. Continuous Chromatography. Chromatography is usually a batch separation process. A certain amount of mixture is injected in the column and, after a certain time,

purified fractions are collected. Another batch can then be processed. A number of attempts, not entirely successful so far, have been made to run preparative chromatography in a continuous mode. The column must be moved, either by moving the packing material in the direction opposite to the carrier gas, or by rotating the column. Considerable technological difficulties have been met in both approaches and have not yet been fully solved.

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Corrected Retention Volume (Time). The retention volume (time) corrected for the effect of the compressibility of the carrier gas. See p. 14. Symbol: OR). Correction Factor. (i) See Compressibility Correction Factor. (ii) Also means the coefficient which is used to correct peak areas for the difference between the response factor of the detector for different compounds (see Response Factor). Coulometric Detector. A selective detector principle used in gas chromatography. The column effluent is heated at 800 O C and reacted so that compounds containing nitrogen, sulfur and halogens give ammonia, sulfur dioxide and halohydric acids, respectively. These gases are measured coulometrically in an electrolytic cell were they are absorbed. The eluites can also be oxidized to carbon dioxide which is measured in a coulometer. The detector is then non-selective. This last implementation has been less successful than the first one. Craig Machine. An automatic separation machine using a large number of interconnected tubes, for liquid-liquid extraction. The separation depends on the values of the distribution constants of the different components of the mixture between the two immiscible liquids. There is a superficial analogy between this process and chromatography, which is often used to explain the concept of theoretical plates. See pp. 7-10. Cross-section Detector. The first type of ionization detector described. The column eluent flows through a cell containing a P-ray radioactive source. A potential is applied across the cell and a current is collected which is a function of the ionization cross-section of the gas contained in the cell. When a gas or a vapor is eluted from the column, the ionization current changes. The sensitivity is modest, the detection limit being one or two orders of magnitude larger than for the TCD. The principle was abandoned very early on. Cut and Weigh. A procedure for the determination of the peak area in quantitative analysis. The peaks of each component of the mixture on the chromatogram are cut with scissors and the pieces of paper are weighed, together with a square of paper having a known side length. Errors arise from incorrect drawing of the base line, incorrect cutting of the peaks and lack of homogeneity of the paper. The method is very economical in terms of investment and very costly in manpower. See p. 634. Cutting. A switching valve technique which permits a large reduction of the analysis time by shortening the column and letting the heavy components elute from a short column section while the important components have been separated on a long column. See pp. 347-349.

-DDeactioation. A treatment of the stationary phase support and possibly of the column wall and gas lines, to remove active adsorption sites having a strong

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adsorption energy and possibly a slow desorption kinetics and being responsible for band tailing or even for the partial or total loss of some sample components. Deactivation is mainly carried out by coating with nonvolatile strongly polar compounds (e.g., detergents) or with appropriate polymers, by chemical treatment of the surface (e.g., washing with an acid or even with aqua regia), by silanization or by using a polar vapor mixed with the carrier gas (e.g., steam or ammonia). Dead Volume (Time). The retention volume (time) of an inert, i.e. non-retained, compound (often improperly called ‘air’). Also called the gas hold-up of the column, the retention volume of an inert or a non-retained compound or of ‘air’. See p. 13. Symbol: t , or to. Deferred Standard. Pure compound or, rarely, a simple mixture injected independently from the sample, using a different valve and at a different time, so the peaks of the deferred standard do not interfere with those of the sample. Provides a continuous check of the reliability of the chromatograph and permits easy calibration and increased accuracy. See pp. 703-718. Deriuatization. Formation by a suitable chemical reaction of a selective derivative which is less polar or more volatile and thus is more readily amenable to gas chromatographic analysis. E.g., transformation of fatty acids into their methyl esters or of sugars into their per(trimethylsily1)ethers. Detection Limit. The smallest amount or concentration of a compound which may be detected with a given detector or using a given analytical procedure. It is typically taken as the amount of product giving a signal three times as high as the background noise. This does not guarantee detection of the corresponding compound at this concentration every time. A ratio of five at least is necessary. See pp. 402-405. Detector. A device which monitors the composition of the column eluate, by measuring a property of the carrier gas or of the eluates or analytes. See Chapter 10. Diatomaceous Earth. The most common starting material for the preparation of liquid phase support in gas chromatography. Also known as Celite, Kieselguhr, or under commercial names such as Chromosorb. They are fossiles, remains of microscopic, single-cell microorganisms. They are formed mainly of silica and contain various metal oxides in small amounts. See pp. 181-193. Differential Detector. Detector which measures the change in property of the eluent as a function of time. It gives a signal proportional to the concentration or mass flow of analyte. The total amount of material eluted from the column is related to the integral of the signal during the elution. See p. 397. Diffusion. A process of slow spatial drift of molecules, due to their constant, random motions, known as Brownian motion. Molecules drift away from their original

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position in space. As a statistical result, there will be a net drift from the regions where the concentration is large to those where it is small. Diffusion is governed by Fick's law which states that the diffusive flux or net drift (number of molecules. crossing a surface area in unit time) is proportional to the concentration gradient. The proportionality coefficient is the diffusion coefficient. See p. 95. Symbol: Dg or 4 . Unit: cm2/sec. Displacement. A form of chromatography in which the mobile phase is replaced just after injection of the sample by a fluid more strongly retained than the last component of the sample to be eluted. There has been very little application of this method in gas chromatography, probably under the influence of the erroneous belief that the displacer must be much more strongly sorbed or solved than the most retained compound of the analyzed mixture. It just needs to be somewhat more retained. An a value of 1.2 is certainly large enough. See p. 7. Distribution Coefficient. See Partition Coefficient. Drift. See Base Line Drift. Dynamic Linear Range. Ratio of the largest amount of a component for which the detector response remains linear (change in the response factor smaller than 5%), to the detection limit. See p. 407.

-EEddy Dif@ion. Contribution to band broadening due to the unevenness of the flow velocity distribution around the packing particles in a packed column. Molecules travel along the column following paths of different lengths, at different velocities. This results in a contribution to the variance of their residence time in the column, which is independent of the nature of the compound and its retention, but depends on the particle size and size distribution, and probably on the packing quality, although this last factor has never been properly elucidated. See pp. 97-100. Effective Peak Number. Number of peaks with a resolution of unity that can be placed between two successive n-alkanes. Characterizes the separation power of a column. See p. 26. Symbol: EPN. Effective Plate Number. Number of theoretical plates of a column calculated with the adjusted or true retention time, instead of the absolute retention time. It is mainly used with open tubular columns. See p. 18. Symbol: Neff. Efficiency of a column. Ability of a column to easily separate a complex mixture or a group of closely related compounds. It is measured by the number of theoretical

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plates, the effective plate number, the peak capacity or the separation number. See p. 18 and Chapter 4. Symbol for the plate number: N . Electrolytic Conductivity Detector. (Also Coulson or conductivity detector.) A detector in which the eluite is oxidized in an excess of oxygen at column outlet, the eluate is extracted with water and the conductivity of the solution measured continuously. The detector responds to halogens, nitrogen and sulfur. It has been used for pesticide analysis. Electron Capture Detector. Electrons from a radioactive source are used to ionize the carrier gas and form very low energy electrons in the detector cell. Some compounds with high electron affinity (halogen derivatives, highly conjugated molecules, etc.) can capture these electrons and give negative ions which are much less mobile than electrons and react much faster with positive ions. The charge carriers in the detector cell are collected periodically (10 to 100 kHz). The current obtained decreases with increasing concentration in the eluent of compounds which have some electron affinity. It is a measure of the concentration of these compounds in the sample. See pp. 447-457. Electronic Integrator. Electronic device which provides the area of the peaks recorded during a chromatographic analysis. It replaced the manual methods of integration and the mechanical integrators during the late 'sixties. Modern instruments include a microprocessor and can achieve sophisticated tasks. Unfortunately, some of them have been programmed by computer technicians not fully aware of analytical problems. See pp. 635-638. Electron Mobility Detector. An ionization detector used mainly for the analysis of permanent gases. It is based on the variation of the mobility of thermal electrons with the composition of the gas. Eluate. The fluid at column outlet. Usually the mobile phase or a mixture of mobile phase and the vapor of the analyzed compounds. Eluent. The mobile phase in chromatography. Eluite. The vapor of analyte eluted off the column. Elution. The classical form of chromatography in which the sample is injected as a narrow plug, the different components of the sample move at different speed and are separated into a series of bands, under the influence of the flow of mobile phase. External Standard. Pure compound or calibration mixture injected from time to time, between analytical sequences of samples of the stream controlled. See p. 653.

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-FFlame Ionization Detector. Detector based on the formation of ions during the oxidation of organic compounds in an oxygen-rich hydrogen flame. These ions are collected and the current measured. The combustion of hydrogen gives very few ions, so the hydrogen flame gives a low background current with little noise. The elution of almost all organic compounds (exceptions, H,C=O, CCl,, etc.) gives a current corresponding to around 10 to 20 mC/g of carbon. The detection limit is very low. See pp. 437-447. Flame Photometric Detector. Detector based on the emission of photons during the oxidation of organosulfur and organophosphorus compounds. Two photomultipliers protected by two different filters collect the photons. This permits the selective detection of either P- or S-derivatives. The detector response is linear for phosphorus, quadratic for sulfur. See pp. 463-466. Flash Pyrolysis. A mode of sampling nonvolatile compounds for gas chromatographic analysis. See Pyrolysis Gas Chromatography. Flow Meter. A device permitting the determination of the volume flow rate of the carrier gas or the gas streams used for the detectors. The most common devices used are the soap bubble meter, which measures the rate at which a soap bubble rises in a calibrated glass tube, and the bead flow meter in which the gas stream raises a bead or cone in a slightly conical, calibrated, vertical glass tube, up to a height that is a function of the flow rate. The accuracy of these devices is poor. Flow Rate. The volume of carrier gas passing through the column per unit time. Usually it is measured at standard temperature and pressure, sometimes at column temperature and/or outlet pressure. See Chapter 2. Symbol: F. Flow Rate Programming. A technique used sometimes in gas chromatography for the elution of strongly retained compounds. The inlet pressure, hence the carrier gas flow rate is increased, either stepwise or progressively, after a first, isorheic elution period, during which most of the compounds of interest are eluted. Most bulk property detectors give a drifting signal during flow rate programming. Only mass flow detectors give a useful response. See p. 52. Frontal Analysis. A form of chromatography in which the mobile phase is suddenly replaced by a stream of a dilute solution of sample in the mobile phase. Each component breaks through the column at a time which depends on the strength of its interaction with the stationary phase. See p. 6. Frontal Ratio. Ratio of the gas hold-up time to the compound retention time (uncorrected or corrected). See p. 15. Symbol: R,.

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Fronting. The term used to characterize unsymmetrical peaks with a slow rising front and a very sharp tail, such as results from an anti-Langmuir isotherm, when the amount of analyte solved or sorbed by the stationary phase increases faster than its concentration or partial pressure in the mobile phase. The opposite is tailing (q.v.). See Chapter 5.

Gas-Adsorption Layer Chromatography, Mode of chromatography that uses as stationary phase an adsorbent modified by coating of a small amount of a low vapor pressure liquid, usually one monolayer or a fraction of a monolayer. Also called modified gas-solid chromatography or modified adsorption chromatography. See Chapter 7. Gas Density Balance. A detector measuring the difference between the density of the pure carrier gas and that of the column eluent. This is the only detector for which relative response factors of two compounds can be calculated exactly from first principles. See pp. 411-423. Gas Hold-up Time (Volume). Retention time (volume) of an inert or non-retained compound on a chromatographic column. In GC the gas hold-up volume is practically equal to the volume of the column available to the gas phase. Symbol: t , or to. See p. 13. Gas-Liquid Chromatography. The form of chromatography that uses a gas as mobile phase and a non-volatile liquid as stationary phase. Gas-Solid Chromatography. The form of chromatography that uses a gas as mobile phase and an adsorbent as stationary phase. GC, GLC, GSC. Gas chromatography, gas-liquid chromatography, gas-solid chromatography. GC-MS. An analytical instrument and the techniques which make use of it. It is the combination of a gas chromatograph, separating the components of a mixture, and a mass spectrometer, analyzing the column eluate and generating mass spectra for the compounds resolved. See pp. 543-557. Glass Beads. A non-porous support for the liquid phase in GLC. The coating ratio must be small enough to prevent excessive accumulation of the liquid in pools around the contact points between beads. The beads are preferably etched to hold the liquid phase in surface pores. Golay Column. See Open Tubular Column. Golay Equation. T h eplate height expression for open tubular columns.

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-HHeadspace Analysis. An analytical procedure for the volatile compounds contained in a complex matrix, such as body fluids, foods or beverages. It consists in analyzing an aliquot of the gas phase in equilibrium with the sample contained in a closed vessel. It avoids rapid pollution and destruction of the column by the repetitive injection of nonvolatile materials contained in these samples. It requires less experimental work than solvent extraction and involves a lower risk of pollution. Calibration is a critical problem, because the solubility of the analytes in the matrix is often very different from that in pure water. Heartcutting. A technique for the routine quantitative analysis of complex mixtures. A fraction of the eluate containing the compounds of interest, usually trace components, is trapped and reinjected in another column on which the components can be separated and quantitized. Also used to eliminate the band of a major component. See pp. 346-350 and 355-360. Height Equivalent to a Theoretical Plate. A measure of column efficiency. Value obtained by dividing the column length by the number of theoretical plates. See p. 19 and Chapter 4. Symbol: HETP or H. Helium Detector. An argon (or Lovelock) ionization detector working with helium as carrier gas. Since metastable helium has a higher energy than the ionization potential of all molecules, except He and Ne, it permits the sensitive detection of all gases and vapors. It is exceedingly sensitive to pollution. See pp. 472-477. HETP. See Height Equivalent to a Theoretical Plate. Hold-up Time (Volume). See Gas Hold-up Time (Volume). Hot Wire Detector. See Thermal Conductivity Detector.

-1Inert Compound Retention Time. See Gas Hold-up Time. Injection Port. The device through which the sample is injected into the carrier gas stream with a syringe. It is closed with a septum, held tighly by a metal nut, and heated at the appropriate temperature to permit rapid vaporization of the analytes. Inlet Splitter. See Splitter. Inlet System. See Sampling System.

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Integral Detector. A detector which gives a signal proportional to the accumulation of sample mass eluted through the column. Total condensation of the analytes on a piezoelectric quartz crystal gives an integral detector. Interface. Device placed between a gas chromatograph and another analytical instrument, such as a mass spectrometer or an infrared spectrophotometer. The purpose of the interface is to make the flow rate, pressure and temperature of the gas stream compatible with proper operation of the spectrometer. Internal Standard. Compound added in a known amount to an aliquot of the. mixture to be analyzed. After proper calibration, the quantitative composition of the mixture is derived from the peak area ratio of the compounds of interest and the internal standard. The compound(s) used as internal standard should be chemically similar to those analyzed, eluted rather closely but must be well resolved from all other components. See p. 653. Interstitial Volume. Part of the column volume which is available to the gas phase. Also called dead volume or gas hold-up. It contains the interparticle and intraparticle porous volumes. Ionization Detector. Any detector which transforms the analyte into ions which are collected and counted. Isorheic. Mode of operation of a GC column in which the gas flow rate is kept constant. The term is little used because flow rate programming has not proven to be a useful technique. In truth, the carrier gas flow velocity changes in temperature programming, which is not an isorheic mode of GC. Isothermal Chromatography. The mode of elution of a gas chromatographic column in which the column temperature is kept constant. Opposite: temperature programming (4.v.).

-JJames and Martin Correction Factor. Correction factor relating the outlet carrier gas velocity to the average velocity and the apparent retention volume to the corrected retention volume. Takes into account the influence of the column pressure drop and the ideal gas compressibility. See pp. 41-44.

-KKatharometer. See Thermal Conductivity Detector. Kieselguhr. A brand of diatomaceous earth used to prepare inert support for gas-liquid chromatography. See Diatomaceous Earth and Chromosorb.

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Kouats Index. Retention index. The normal alkanes are used to establish a scale of retention. See pp. 486-490 and 508-515. Symbol: RZ or I . -L-

Lungmuir Isotherm. The most simple isotherm of adsorption, resulting from the finite surface area of the adsorbent. It assumes the formation of a monolayer of sorbate on the surface. The rate of desorption is proportional to the fraction of the surface area occupied by the sorbate molecules. The rate of adsorption is proportional to the partial pressure of the sorbate and to the fraction of the surface area which is free. As a result the amount sorbed is related to the partial pressure by: m = aP/(l+ bP). Leading. See Fronting. Limit of Detection. See Detection Limit. Linear Gas Velocity. Parameter related to the carrier gas flow rate. Usually the flow rate measured at column outlet divided by the surface area of the column cross section available to the gas phase (outlet carrier gas velocity). Also the ratio of column length to the dead retention time (average carrier gas velocity). These two velocities are related by the compressibility correction factor. See p. 12 and Chapter 2. Symbols: uo and u. Linearity. (i) Situation in which the equilibrium isotherm between the mobile and stationary phases is linear (linear chromatography). (ii) Behavior of a detector whose response is proportional to the concentration of compound in the mobile phase (linear detector). See Dynamic Linear Range. Linear Range. Amount of sample (sometimes concentration) above which the detector response is not linear but exhibits the onset of saturation. Often taken as the amount (concentration) at which the response is 58 lower than extrapolated for a linear response. see p. 405. Liquid Loading. See also Phase Ratio. Amount of stationary phase contained on 100 g of packing material (in gas-liquid chromatography, or gas-adsorption layer chromatography). See pp. 195-199. Liquid Phase. The high-boiling or thermostable liquid used to impregnate a porous support and which is used as solvent or stationary phase in gas chromatography. Logarithmic Dilution Method. A calibration procedure using a special device composed of a flask with a fast agitator and a flow rate controller. A known amount of a volatile compound is injected in the flask, while a constant flow rate stream of gas

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is used to constantly dilute the vapor. The concentration of the vapor in the gas effluent decreases exponentially with increasing time. The time constant of the exponential decay is the ratio of the flask volume to the gas stream flow rate. See pp. 591-595. Lovelock Detector. See Argon Ionization Detector. Lower Detection Limit. See Detection Limit.

-M-

Muss Sensitive Detector. A type of detector the response of which is proportional to the mass flow rate of analyte to the detector cell. See p. 399. Muss Transfer Resistance. Term of the plate height equation accounting for the kinetics of exchange between the mobile and the stationary phases. It contains several contributions, ascribed to the radial diffusion in the mobile phase (between the center of gas streamlets and the particule surface), diffusion in the stagnant mobile phase contained inside the particles, the kinetics of adsorption-desorption (GSC) or the diffusion across the droplets of stationary liquid phase (GLC). See pp. 97-102. Matrix. Usually the whole bulk of the sample, when one or a few components are analyzed. McReynolds Constants. The set of differences between the retention indices of a selection of probe solutes on a certain stationary phase and on squalane. These constants characterize the selectivity of the phase for compounds of a certain type. They permit the calculation of the retention indices of other compounds on the corresponding stationary phase. See p. 518. Mesh. The dimension of the particles of support or adsorbent used to pack a column. Refers to the size of the screen mesh used to sort the particles. Methyl Silicone. Silicone polymers of high molecular weight, used as general purpose stationary phases in GLC. They have a low polarity and are very stable. Mobile Phase. The camer gas in gas chromatography. Molecular Dijfwion Term. See Axial Molecular Diffusion. Molecular Sieves. Synthetic silico-aluminate crystals, similar to the natural mineralogical compound zeolites, which incorporate water molecules in narrow, communicating channels. The water molecules may be eliminated by heating under vacuum, without modifying the crystal network. The specific surface area is very large. These adsorbents have an extremely large adsorption capacity for the molecules which are

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small enough to penetate inside the channels, a very small one for the molecule: which are too large or bulky. Product used in GSC to separate argon and oxygen. krypton and nitrogen. Multidimensional Chromatography. Term improperly used for various implementations of Column Switching (q.v.) using columns made with different stationary phases.

-NNet Retention Time. The retention time corrected for pressure drop along the column and for the gas hold-up of the column. Adjusted retention time corrected for pressure drop. Corrected retention time less the dead time. See p. 14. Symbol: t N . Net Refention Volume. The retention volume corrected for pressure drop along the column and for the gas hold-up of the column. See p. 14. Symbol: VN. Noise. High frequency fluctuations of the base line signal of the detector.

-0Open Tubular Column. A chromatographic column made with an empty tube, whose walls are coated by a layer of stationary phase. Usually the tube has a narrow diameter, hence these columns are often called capillary columns. See Chapter 8. Symbol: OTC.

-PPacked Columns. Long tube packed with an Adsorbent or a Solid Support coated with a liquid phase and used as a Chromatographic column. See Chapters 6 and 7. Packing. Material contained by the column. It is responsible for the retention. Partition. Equilibrium between a solvent and a gas phase. Responsible for the retention in gas-liquid chromatography. See Chapter 3. Partition Coefficient. Equilibrium constant in a partition phenomenon. Usually the ratio of the concentration at equilibrium in the gas and stationary phases. See p. 60. Symbol: KR or KR,. Peak. Concentration profile of a compound at column outlet. Trace of the detector signal on a recorder chart during the elution of one compound. Synonymous with band and zone, but often implies a better behavior. Peak Area. Area enclosed between the peak profile and the base line on the recorder trace. More generally integral of the difference between the detector signal and the

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interpolation of the base line. See Chapter 15. Symbol: A. Peak Base. Sometimes used to designate the interpolation of the base line under the peak, between its extremities. Peak Capacity. Number of peaks with a resolution of one which can be placed between two peaks or which can be eluted in a given range of capacity ratio (between k; and k;, usually between 0 and 7.4 or between two successive n-alkanes). Symbol: TZ. Peak Height. The maximum difference between the detector signal and the background during the elution of a peak. Distance between the maximum of the peak and its base, measured parallel to the signal axis. See p. 27. Symbol: h. Peak Leading. Deviation from symmetry characterized by a rise from base line slower than the return to base line. Usually due to column overloading. Peak Symmetry. Characterizes the shape of the profile and the deviation of the elution behavior from a totally linear one. Deviation from symmetry may originate in mixed retention mechanism, with slow kinetics, in column overloading or in poor injection technique. The asymmetry, or ratio of the peak front and tail half width, is often used as a measure. See p. 19. Peak Tailing. Deviation from symmetry characterized by a return to base line slower than the peak rise. Peak Width. The segment of the peak base which is intercepted by its two inflexion tangents. See p. 18. Symbol: w . Peak Width at Half-Height. The distance intersected by the peak profile on a line parallel to base line and bisecting the peak height. Symbol: w ~ , ~ . Phase Ratio. The ratio of the volumes available to the mobile and stationary phases. The gas hold-up corrected for gas compressibility divided by the volume of liquid in the column. Phenyl Silicones. A very popular type of stationary phases for the analysis of compounds with very low vapor pressure. They are stable above 300OC. They include many commercial products, among others the SE‘s, OV’s and DC‘s silicone oils, greases and rubber. The ratio of phenyl to methyl groups varies from 0 to ca 25%.

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Photoionization Detector. An ionization detector using irradiation by a beam of high energy, far UV photons to ionize the eluate vapor. See pp. 466-471. Photometric Detector. See Flame Photometric Detector. Planimeter. A device used to measure the surface areas enclosed by irregularly shaped curves. Used long ago to measure the peak areas of chromatograms. Slow, tedious and not very accurate. See p. 635. Plate Height. Length of the column corresponding to one theoretical plate. Height equivalent to a theoretical plate. See Chapter 4. Symbol: H. Plate Theory. A theory of chromatography which describes the separation as a step by step process involving successive equilibria between mobile and stationary phases in an imaginary series of containers. PLOT or Porous tayer Open Tubular Column. Variety of open tubular columns where the stationary phase is a layer of adsorbent coated on the inner wall or a layer of support impregnated with liquid phase. See pp. 278-279. Polarity. A loose term employed to characterize the electronic properties of molecules. A molecule which has a strong dipole moment is polar. Often molecules which have large quadrupole moments or even large polarizability have been characterized as being polar. A universal polarity scale of stationary phases has long been an elusive quest. See p. 521. Polyesters. A very popular type of liquid phase used for the analysis of a wide variety of mixtures. They include poly(ethyleneglyco1) adipate, succinate and sebacate, poly(neopenty1)glycol adipate and succinate. Polyglycols. A very popular type of liquid phase for the selective analysis of alcohols or other compounds capable of forming hydrogen bonds. They include Carbowaxes (polyethyleneglycols)and Ucons (polypropyleneglycols). Polystyrene Gels. Porous particles prepared by copolymerization of styrene and divinylbenzene, with the possible addition of some polar substituted derivatives. These products have a large specific surface area. Small molecules of gases or volatile compounds may penetrate the gel by diffusing between the chains. Most used are the products known under the names Chromosorb 100 and Porapak. Porupak. Reticulated polystyrene-polydivinylbenzene copolymers used as stationary phase in gas-solid chromatography. Their composition and structure are qualitatively analogous to those of the products of the Chromosorb 100 series. Pressure Drop. Difference between inlet and outlet column pressures. Symbol: 6P or p .

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Pressure Gradient. Difference between inlet and outlet column pressures divided by the column length. Differential of the pressure with respect to the abscissa. See Chapter 2. Pressure Programming. See Flow Rate Programming. Programmed Temperature Gas Chromatography. See Temperature Programming. Pyrolysis Gas Chromatography. A method of analysis of nonvolatile samples by gas chromatography, using flash pyrolysis. The nonvolatile sample (usually a polymer) is heated very rapidly to a high temperature (800 to 1,000O C). During this phase the sample degrades thermally. The result of the GC analysis of the mixture evolved can be used as a fingerprint to identify the original material.

-RRadial Diffusion. See Mass Transfer Resistance. Recorder. Apparatus which transforms the detector signal into a plot of detector signal versus time: the chromatogram. Reduced Plate Height. A dimensionless number expressing the column efficiency, as the ratio of the plate height to the average particle size of the packing. See pp. 111-113. Reduced Velocity. A dimensionless number expressing the carrier gas velocity, as the product of the actual gas velocity by the average particle size, divided by the diffusion coefficient of the solute in the carrier gas. Also known in chemical engineering as the Peclet number. See pp. 111-113. Relative Response Factor. Ratio of the detector response factors for two compounds. See p. 401. Relative Retention. Ratio of the adjusted or net retention volumes or times of two compounds, or of their capacity ratios. See pp. 20 and 65. Symbol: a. Resistance to Mass Transfer. The phenomena which cause equilibrium between two phases to proceed at a finite rate. Their kinetics control the extent to which the concentration in one phase lags behind its equilibrium value, and therefore the degree of band broadening that takes place during elution (see pp. 97-102). There are three main sources of resistance to mass transfer in a chromatographic column, usually referred to as the diffusion through the mobile phase stream, the diffusion through the stagnant mobile phase in the particles and the diffusion through the liquid phase.

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Resolution. Degree of separation between the bands of two compounds. Usually the ratio between the difference in their retention time and their average band width. See pp. 22-25. Symbol: R. Response Factor. Ratio between the amount of a certain compound and the peak area obtained. Depends on the detector and its settings. Usually referred to the amount injected. See p. 401. Response Time. Delay between the time when a concentration change (step) occurs in the detector cell and the moment the signal reaches a certain fraction of the corresponding value. Time constant of the detector response, assuming it is a first order system. See p. 408. Retention Factor. Logarithm of the retention of a compound relative to n-nonane, Rx,9.Can be calculated easily by measuring the relative retention of the compound studied to the most closely eluted n-alkane and the relative retention of two successive n-alkanes, since beyond propane there is a linear relationship between the logarithm of the corrected retention time and the number of carbon atoms. This system is much less popular than the retention indices. Retention Index. See Kovats Retention Index. A system of retention data which uses the alkanes to define a scale. See pp. 20 and 486-490. Retention Time. (i) Absolute, or uncorrected: time elapsed between injection of the sample and elution of the peak maximum. (ii) Adjusted: absolute retention time less the dead time or 'air' retention time. (iii) Corrected: absolute retention time corrected for the gas compressibility. (iv) Net: absolute retention time corrected for both the compressibility of the mobile phase and the gas hold-up of the column; also called totally corrected retention time. (v) Specific: the net retention time at standard temperature and pressure divided by the amount of liquid phase in the column or the total surface area of adsorbent. (vi) True: synonym of adjusted. (vii) Uncorrected: cf absolute. See pp. 11 and 13-15. Retention Volume. The volume of mobile phase or carrier gas which flows through the column during a time equal to the corresponding retention time. There exist accordingly absolute, adjusted, corrected, net, specific, true and uncorrected retention volumes (cf Retention Time). See pp. 13-15. Reversing. A technique of column switching similar to storing (see Storing) where there is no need for a compensation column. See p. 349.

-SSample Loop. Part of a sampling valve which is usually replaceable. Tube loop in which an aliquot of a gas sample is placed prior to its transfer to the sampling port and the carrier gas stream. See pp. 327-339.

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Sampling Port. Often synonymous with injection port. Also the volume at the top of the column where a gas sample is mixed with the carrier gas stream. Sampling System. The system permitting the selection of a volume of sample representative of the mixture to be analyzed and its transfer to the carrier gas stream, just on the top of the column. See pp. 286-300 and 327-339. Sampling Value. Two-position valve used to introduce a sample for analysis into the chromatograph. In one position, the carrier gas flows directly to the column, while a stream of sample sweeps the sampling loop. In the other position, the sample stream is sent directly to waste, while the carrier gas sweeps the loop and carries the sample to the column through the sampling port. Sampling valves are automatic (electric or pneumatic) or manual, rotary or sliding, and inject gas or liquid samples. Most have six ports. More complex ten and twelve port valves are available permitting simultaneous column switching and sampling. See pp. 327-339. SCOT or Support Coated Open Tubular Column. Synonymous with porous layer open tubular column. Selective Detector. A detector which gives a different response factor for different compounds. Since all detectors are'selective to a certain degree, the term tends to be used to qualify a detector which gives a large response for compounds belonging to some chemical classes and a very small response for the other compounds. See Chapter 10. Selectiuity. Name sometimes given to the relative retention or ratio of adjusted retention times or of capacity ratios of two compounds. See p. 400. Sensitiuity. The response factor of a detector, especially in relation to the influence of ambient parameters. Since detectors may have a large response factor in some unit, but this fact is unrelated to the intensity of the signal noise, a detector with a large sensitivity may not be very sensitive, i.e., may not detect small concentrations of analytes. There is some ambiguity in the words sensitivity and sensitive. Detection limit is a well-defined term the use of which should be preferred. See p. 401. Separation Factor. Alternative definition of the resolution. See p. 26. Separation Number. Ratio of the difference of the retention times of two compounds and their average peak widths at half height. Septum. Thin disk of a self-sealing elastomer used in the design of an injection port, on the top of which it is held tightly. Permits the injection of gas or liquid samples with a syringe. The septum keeps a leakproof seal around the syringe needle and closes behind the needle when it is withdrawn. Septa are usually made of silicone rubber, sometimes of high-temperature resistant Viton or similar material. See p. 332.

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Signal to Noise Ratio. In chromatographic data collection, usually the ratio of the signal at peak maximum to the noise range. Silica Gel: Porous gel of hydrated silica. Used as adsorbent in gas-solid chromatography. Silicone. A polymer with an -[Si-01- backbone chain and a large majoiity of CH, groups bonded to the Si atoms. All groups can be methyl, or some can be phenyl, heptafluoropropyl, cyanoethyl, etc. Usually they have a high thermal stability. They decompose by giving products which have a small response on the FID, which is why they are often unnoticed. They give strong peaks at certain characteristic masses in GC-MS. Silylation. A common method of derivatization where a hydroxyl, a primary or secondary amine or some other group with a reactive hydrogen atom is reacted with an appropriate silicon derivative, usually a chlorotrimethylsilane, another substituted chlorosilane, a substituted disilazane, etc., to give a silyl ether. The most popular derivative is the trimethylsilyl ether. These ethers are much more volatile and more stable than the parent compounds, and much easier to analyze by gas chromatography. Slurry. A thick dispersion of a GC support or adsorbent in a solvent or a solution of stationary phase or modifier. See p. 200. Solid Support. Finely divided solid material, whose particles are usually but not necessarily porous, coated by the liquid used as stationary phase.This permits rapid mass transfer between the liquid and the gas phase and prevents convective mixing of the stationary phase. See pp. 181-193. Solute. This word is very often used as a synonym for sample or analyte, even in gas-solid chromatography, where there is no solution. Solute Property Detector. Detector that does not respond to the mobile phase. Its background signal does not depend on the changes of properties of the mobile phase due to fluctuations of temperature or pressure. The signal depends only on the concentration of analytes. Such a detector is selective. Specific Retention Volume. The net retention volume at standard temperature and pressure divided by the amount of liquid phase in the column or the total surface area of adsorbent. See pp. 14 and 61-62. Symbol: Vg. Splitter. A device used to inject an extremely small sample on an open tubular column. Typical samples injected with a syringe are 1 pL in volume. A standard

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OTC accepts sample loads 2 to 3 orders of magnitude smaller. The sample is injected in a conventional injection port and the gas stream split between the OTC and a side stream which is vented through an adjustable needle valve. The trouble with these devices is that it is difficult to achieve fast vaporization, a small vaporization chamber volume and a thorough mixing of the vapors to the carrier gas. Some segregation takes place and the split ratio depends on the molecular weight of the component. Accordingly, the sample injected to the column is not an aliquot of the mixture to be analyzed. Various designs have been suggested to remedy this situation. See pp. 286-300. Squalane. A polyisoprenic saturated hydrocarbon, 2,6,10,15,19,23-hexamethyltetracosane. Boiling point 35OoC, upper limit temperature in GC 120OC. A widely known, often used stationary phase which is considered to be totally non-polar. It has been taken as the reference in most polarity scales. It is well suited for the separation of hydrocarbons and weakly polar compounds, such as halogen substituted hydrocarbons. Standard Addition. A procedure for quantitative analysis which involves the preparation of additional samples by adding known amounts of the component to be quantitized to the original mixture. If the detector is linear, no calibration is necessary. The method is applicable only to mixtures with low vapor pressure and is very tedious and time consuming. See p. 652. Standard Deviation. The standard deviation of a Gaussian curve characterizes its width. The profile of a chromatographic peak is often very close to Gaussian. See p. 16. Symbol: a. Start. The time when the sample is injected on the column. Stationary Phase. Packing material contained in the column. The active solid (adsorbent) or the support coated or impregnated by the liquid. Storing. A technique of column switching which permits keeping the bands of a number of components immobilized in a column while the rest of the mixture is eluted from another column. This permits the use of several columns and a single detector to perform an analysis. See pp. 347, 349 and 352-355. Support. See Solid Support. Support Coated Open Tubular Column (SCOT column). See PLOT or Porous Layer Open Tubular Column. Switching Value. Valve used to change the pathway of gas streams during an analysis. It permits the selective transfer of some compounds from one column to

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another, a change in the order in which the carrier gas flows through a series of columns, the transitory trapping of some compounds, etc. See p. 341. Syringe. The most popular device for the injection of samples on chromatographic columns. They are high precision instruments, with an accuracy and precision depending essentially on the skill of the analyst. They are available for the injection of gases and liquids, in a wide range of capacities. See p. 332.

-TTailing. A form of peak asymmetry in which the band front is sharp and the rear part returns slowly to the base line. Peak tailing can be ascribed to three types of causes. (i) A dead volume accessible only by diffusion in the mobile phase line, e.g. in the injection device or in the detector, or a large detector response time; (ii) a slow kinetics of mass transfer between the mobile and stationary phases; (iii) too large a sample volume, resulting in a non-linear equilibrium isotherm. See Chapter 5.

Temperature Programming. A mode of gas chromatography in which the column temperature is raised progressively during the course of the analysis. Most often the temperature is raised linearly. This permits the elution of low boiling compounds at a low temperature where they can be separated, and the elution of high boiling compounds at a high temperature where their retention is not prohibitively long. See pp. 83-88. Theoretical Plate. Imaginary element of the column characterizing the speed of equilibrium between the two phases. Distance along the column over which equilibrium takes place. Measure of the peak broadening or of the column efficiency. see p. 94. Thermal Conductivity Detector. A very popular detector based on the variation of the thermal conductivity of gases with their composition. Generally a high thermal conductivity gas such as hydrogen or helium is used as mobile phase. When organic vapors are eluted the thermal conductivity decreases. As a result the temperature of two heated resistors increases. This unbalances a Wheatstone bridge containing these resistors. The bridge potential is a measure of the concentration of eluite in the carrier gas. See pp. 423-437. Thermistor. A semiconductor, the resistance of which decreases rapidly with increasing temperature. Used in thermal conductivity detector. Thermoionic Detector. A selective detector for gas chromatography. A hydrogen flame is burned along a pellet of an alkaline metal (Rb or Cs) salt. The response is greatly enhanced for derivatives of phosphorus, nitrogen, sulfur and halogens. See pp. 457-463.

767

Trap. Glass or metal device connected to the detector exit and cooled down to a proper low temperature, at which the components separated by the column can be condensed and collected at a high degree of purity. Triangulation. A procedure for the determination of the area of the peaks recorded on a chromatogram. The area is derived from the product of the peak height by its area at a certain fractional height. See pp. 631-633. True Retention Time (Volume). The time elapsed (the volume of carrier gas flowing through the column) while the solute is in the stationary phase. This is equal to the retention time (volume) corrected for the column gas hold-up (but not for the pressure drop along the column). See p. 13. Symbol: t; (V,').

-UUltrasonic Detector. A detector for gas chromatography based on the variation of the sound velocity in a gas with its composition. The detector measures the beat frequency between two ultrasonic beams, one passing through a reference cell filled with pure camer gas, the other one through a cell swept by the column eluent. In spite of interesting qualities, this detector has not been successful. Uncorrected Retention Time. Time elapsed between injection of the sample and elution of the band maximum. See p. 11. Symbol: t,.

-VVan Deemter Equation. Equation relating the plate height of a gas chromatography column to the experimental conditions. Especially designed to relate the plate height to the mobile phase flow velocity. It gives the plate height as the sum of three terms, accounting for the contributions of molecular axial diffusion, eddy diffusion and resistance to mass transfer. This last contribution is broken down into the sum of several contributions, accounting for diffusion in the mobile gas phase, in the stagnant gas phase (inside the particles) and in the liquid phase. See pp. 105-110. Van der Wads Forces. Responsible for molecular interactions between all kind of molecules. They result from the fundamental imbalance between the positive charges (protons) that are highly localized in the nucleus of the atom and the negative charges (electrons) that are distributed over all the space occupied by a molecule. This asymmetry results in an attraction between neutral species, even when there is no other electric force. Vapor Phase Chromatography. Ancient term used for gas-liquid chromatography.

768

Variance. For a Gaussian profile, this is equal to the square of the standard deviation. For any distribution, it is related to the second moment of this distribution. See p. 17. Void Volume. Dead volume, retention time of an inert compound or gas hold-up of the column. Should be corrected for gas compressibility. see p. 13.

-WWall Coated Open Tubular Column (WCOT Column). See Open Tubular Column. Watson-Biemunn Interface. An interface between a gas chromatograph and a mass spectrometer in which the eluent mass flow rate is reduced and the proper gas pressure for entering the MS source is achieved by selectively leaking the carrier gas through a sintered glass tube, terminated at both ends by a narrow capillary. Stream splitting is achieved at the same time as a 10 to 100 fold enrichment in solute vapor. See p. 552. Wheatstone Bridge. An electric circuit with two arms, supplied by a common power source. It is used in many GC detectors, especially the thermal conductivity detector and the gas density balance. When the bridge is balanced, no signal is recorded in the diagonal between the two arms. A change in one of the four resistances of the bridge results in a current passing through the diagonal. -Z-

Zeolites. See Molecular Sieves. Zone. Synonym of band.

769

SUBJECT INDEX

A Absolute retention time, 14, 741 Absolute retention volume, 14, 741 Accuracy: definition, 567 in quantitative analysis, Chapter 16 Activation of adsorbents, 741 Activity coefficient, 58 influence of solvent molecular weight on, 62 influence on retention data, 58, 60 Adjusted retention time, 14, 741 Adjusted retention volume, 14, 741 Adsorbents, 182, 741 activation of, 741 classification of, 79 pore size distribution, 79 Adsorption, 76-82, 741 Adsorption chromatography, 76, 742 Adsorption coefficient, 76, 742 Adsorption isotherm, 742 Adsorption on support, influence on retention data in GLC, 73-75 Advanced packed columns, Chapter 7 Aerogels, 742 Alkali metal flame ionization detector, see TID Alumina, 742 Ammonia, on-line analysis of, 727-729 Amplifier, influence on apparent column efficiency, 115 Analog integration, 30 Apiezon, 743 Area allocation for unresolved peaks, 646-650 case of a trace component, 650 case of peaks of comparable size, 647-649 Area of peaks, 27, Chapter 15; see also Peak area by computer, 639-646 acquisition frequency, 641-642 A/D conversion, 639-640 data transfer, 640-641 noise filtering, 642-643 peak detection, 643 peak integration, 644 precision, 645-646 by Condal-Bosch method, 634 by cutting and weighing, 634 definition, 758 by electromechanical integrator, 635 by electronic integrator, 636 error correction for, 637

770

by planimetry, 635 by product of height and width at half height, 633 by triangulation, 633 measurements of, Chapter 15 by computer methods, 638-646 by manual methods, 631-635 by semi-automaticmethods, 635-638 Area or height of peak in quantitative analysis, 672-673 Areas of peaks to composition, calculation procedures, 650-658 Argon ionization detector, 411,471-472, 743 Artefacts, 498-500 ghost peaks, 498 lost peaks, 499 moving peaks, 499 Asymmetry of peaks, 20, 632, 743 Average carrier gas velocity, 12, 41, 743 Axial diffusion, contribution to HETP, 96-97, 743

B Backflush or backflushing, 344-346, 743 example, 346 valve system for, 344 Backpurging, 341-343, 353-355,744 Deans system for, 300-303, 353-355 example, 342-343 valve switching for, 342 Band, I44 Band asymmetry, 19 Band broadening, Chapter 4, 744,see also Resistance to mass transfer, Axial diffusion contribution of the detection and amplifier, 115 contribution of the equipment, 113-117 contribution of the injection system, 113-114 effect of sample size, 127-150 random motion model, 94 sources of, 94 various contributions to, 96-102 Band plot method, 172-173 Band tailing, 117,141-144 Band width, 16-20,744 Base line, 744 drift of, 408,639-644.744 stability of, 407-408 Bleeding, 694,695, 744 Bonded stationary phases, 745 Brockman scale for alumina, 745 Bulk property detector, 397-411,745 By-pass injector, 745

C Calibration, Chapter 14 by conventional methods, 589-601

771 for gases, 589-595 for traces of volatile compounds, 596-597 for volatile liquid samples, 595-596 with diffusion cells, 598-600 with permeation tubes, 600-601 comparison between conventional methods and GDB, 607-608 for process control gas chromatography, 696,713 for unknown compounds, 656 with an exponential dilution flask, 591-595 with a gas density balance, 601-609 of a FID, 603 of a TCD, 602-603 Capacity factor, 15, 57-70, 745 Capacity ratio, 57 Capillary column, Chapter 8,745; see also OTC Carbowax, 746 Carrier gas, 746 data on, 417 dilute steam as, 233-244 flow rate, optimization of, 174-176 second virial coefficient (data), 68 selection of, 306 thermal conductivity of, data, 426 velocity profile, 40 viscosity, 37, 39 Catharometer, 746;see also TCD Celite, 746 Characterization of stationary phases, see Stationary phases, characterization Chloral, on-line analysis of, 735 Chloration gases, on-line analysis of, 725-727 Chromathermography, 746 Chromatogram, definition, 746 Chromatograph, Chapter 9, 746 influence on column efficiency, 113-117 schematics, 4 Chromatography, 2,746 Craig model, 7 data, 10 definition, 2, 746 ideal, 147-150 modes, 6 Chromosorb, 746 Classification of detectors: ECD, 454 FID, 443 FPD, 465 GDB, 419 HID, 475 PID, 469 TCD, 431 TID, 462 Coating, see Support coating, OTC, preparation of Coating ratio, 29 Column, Chapters 6-8, 747

772

Columns, long, 44 Column capacity factor, 15, 57-70, 745 influence of gas phase non-ideality on, 66-70 Column data, definitions, 28 Column diameter (OTC): and efficiency, 195 and sample size, 194 0ptimiZati011 Of, 122-123 Column efficiency, see HEW Column efficiency data, definition, 16 Column gas volume, 48 Column inner diameter, 28 Column lifetime, 694-695 Column overloading, 127-150 Column packing, 203-205 Column performance, 18, Chapter 4, 747 Column permeability, 37, 38 Column series, 177-181 apparent column capacity factor of, 50 flow rate through, 49 gas hold-up of, 50 HETP of, 110-111 intermediate elution times of, 373 retention time of, 49 Column switching, 340-384, 747 Column temperature, optimization of, 120-121 Column tubing, nature of, 193; see also OTC, preparation of Column tubing, selection of, 193-195 Combination of stationary phases, 177-181 Complexation, influence on retention data, 70-73 Composition of sample, calculation procedures from peak area, 650-658 Compressibilitycorrection factor, 41-43, 747 Computer integration, 30; see also Area of peaks, by computer Concentration at peak maximum, 28 Concentration discontinuities, 147-148 Concentration sensitive detectors, 397-401, 747 Confidence limits on a result, 566 Connectors and tubings, influence on column efficiency, 114-115 Continuous chromatography, 747 Corrected retention time, 14,748 Corrected retention volume, 14, 748 Correction factor, 748 Coulometric detector, 748 Coupled mass transfers, 99 Craig machine, 7-10,748 Cross section detector, 748 Cut and weigh method of peak area determination, 634,748 Cutting, 347, 349, 352, 354, 748; see also Storing, dynamic method

D Darcy law, 37,42 Deactivation of support, 748

773 Dead volume. 13, 749 Deans method of column switching, 300-303, 351-362: see also Backpurging. Heartcutting. Switching procedures advantages of. 360-362 examples of, 302. 351, 361 Deferred standard, 655-656, 703-718, 749 alarm functions of, 708-712 and calibration of detectors. 713 and maintenance of on-line gas chromatographs, 713 applications of, 714-739 implementation of, 707-708 in process control GC. 703-718 principle of, 705-706 Derivatization, 749 esterification with diazomethane. 540 with methanol-BF,, 540 hydrogenation, 542 trimethylsilylation. 541 Detection limits of detectors. 402-405, 749 definition, 403 ECD. 454 FID, 444 FPD, 466 GDB. 420 HID, 476 PID. 470 TCD, 432 TID, 463 Detector time constant. influence on column efficiency. 115 Detectors. Chapter 10, 749 base line drift of, 397, 408 calibration of, Chapter 14 cell volume of. 397, 409-410 classification of, 397-400 concentration sensitive. 398-399 contributions to band broadening due to, 408-410 detection limit of, 397. 402-405 dynamic linear range of, 397, 405-407 general properties of. 395-41 1 linearity of, 397 maintenance and cost of, 410-411 mass sensitive. 397, 399-400 predictability of the response of, 410 reliability of, 397. repeatability of the response of. 410 response factors of, 401 -402 response time of, 397. 408-409 selectivity of, 397, 400-401 sensitivity of, 397. 401-402 signal noise of, 397. 407 use of non-linear. 406 Determination of solution properties by GC. 70 Diatomaceous earth. 181-193. 749 Dichlorodifluoromethane, on-line analysis of. 736-738

774

Differential detectors, 397, 749 Difficult analyses, gas hold-up time for, 44 Diffusion, 95, 749 Diffusion cells (for calibration), 598-600 Diffusion coefficients: in the stationary phase, 100-101 of gases: influence of temperature on, 95-96 of organic vapors in gases, 95-96 prediction of, 96 Dilution of analyte during the analysis, 404-405 Displacement chromatography, 7,750 Distribution coefficient, 60,750 Drift of base line, 639-644, 750 Dynamic linear range of detectors, 405-407, 750

E ECD, 447-457 classification of, 454 constant current, 450 constant voltage, 450 detection limits of, 454 dynamic linear range of,454 linearity of, 454 maintenance and cost of, 457 principle of,448-451 pulsed voltage, 450 reaction mechanism of, 448-450 response factors, 451-456 influence of the carrier gas flow rate, 451 influence of the nature of the carrier gas, 451 influence of the polarization voltage, 453 influence of the temperature, 452-453 parameters affecting, 451-453 prediction of, 455-457 relative, (data), 455-456 schematics of, 449 selectivity of, 454 sensitivity of, 454 stability of, 454 Eddy diffusion, 97-100, 750 Effective peak number 26, 750 Effective theoretical plates, number of, 18, 750 Efficiencyof a column, 18, Chapter 4, 750; see also HETP Electrolytic conductivity detector, 751 Electron capture detector, 447-457, 751; see details at ECD Electron mobility detector, 751 Electronic integrator, 30, 635-638, 751 systematic errors, 637 Eluate, 751 Eluent, 751 Eluite, 751

775 Elution, 6, 751 rate, 57 Equipment specifications, 116-1 17 Equivalent temperature in programmed temperature analysis, 86 Error propagation coefficients, 674 Errors in quantitative analysis, Chapter 16 Experimental conditions of a GC analysis, optimization of, Chapter 6 Exponential dilution flask, 591-595 examples of use, 593-595 External standard, 653-654, 751

F FID, 437-447 classification of, 443 detection limits of, 444 dynamic linear range of, 445 linearity of, 445 maintenance and cost of, 447 principle of, 437-440 reaction mechanism of, 438-440 response factors, 440-447 influence of the air flow rate, 441 influence of the flame temperature, 440-442 influence of the flow rate of the carrier gas, 442 influence of the hydrogen flow rate, 440 influence of the polarization voltage, 442-443 parameters affecting, 440-443 prediction of, 445-447 schematics of, 437 selectivity of, 444 sensitivity of, 444 Film thickness, influence on retention volume of, 196-199 Flame ionization detector, 437-447, 752; see details at FID Flame photometric detector, 463-466, 752; see details at FPD Flash pyrolysis, 752 Flooding of the column, 134-135 Flow meter, 389-390, 752 Flow of gases, 35, Chapter 2 Flow rate, Chapter 2, 752 controller, 326-327 fluctuations, effect on precision of peak area, 675-678 optimization of, 174-176 programming, 52, 752 Flow structure, 36 Flow velocity, 12, 37 in temperature programming, 51 measurements of, 47 optimization, 174- 176 FPD, 463-466 classification of, 465 detection limits of, 466 dynamic linear range of, 466

776 maintenance and cost of, 466 principle of, 464 response factors, 464-466 influence of the gas flow rates, 464-465 influence of the photomultiplier voltage, 464 parameters affecting, 464-465 prediction of, 466 schematics of, 463 selectivity of, 465 sensitivity of, 465-466 Frontal analysis, 6, 752 Frontal ratio, 15, 752 Fronting, Chapter 5, 753

G Gas-adsorption layer chromatography, 75, 213-233, Chapter 7, 753 Gas chromatograph, Chapter 9 ancillary equipment for, 384-390 description of, 320-321 flow meter for, 389-390 flow rate and pressure controllers for, 323-327 oven for, 384-385 pneumatic system for, 321-327 sampling system for, 327-339 sampling valves for gases in, 327-331 sampling valves for liquids in, 331-338 serial and parallel flows, designs of, 321-323 switching valves for, 340-384 temperature controller for, 384-389 temperature programmer for, 386-389 Gas density balance detector, 411-422, 753; see details at GDB Gas flow,definitions, 12 Gas hold-up time, 11, 13, 41, 42, 753 for difficult analyses, 44 for open tubular columns, 45 in column series, 50 measurement of, 493 optimization of, 45 Gas hold-up volume, 11, 13, 29, 48, 753 Gas-liquid chromatography, 2, 753 Gas molecular diffusion coefficient, 95-96 Gas samples, injection, 327-331 Gas-solid chromatography, 2, 753; see also Modified GSC practical applications, 82-83 GC, 2.753 GC-FTIR, 557-561 data acquisition and handling, 560 interface, 559 principle, 558 GC-MS. 543-557,753 chromatographic problems in the design of, 554-556 data acquisition and handling, 554

777

interface, 549-553 direct, 550 molecular separator, 551 open split interface, 551 plastic membrane interface, 552-553 purpose of, 549-550 Ryhage separator, 551 Watson-Biemann separator, 552 ion analyzer, 545 ion detector, 546 ion source, 545 ionization methods, chemical ionization, 548 electron impact, 547-548 linearity of, 556 molecular separator for, 551 open split interface for, 551 plastic membrane interface for, 552-553 principle of MS,544-547 response factors of, 556 Ryhage separator for, 551 selectivity of, 555 sensitivity of, 556 Watson-Biemann separator for, 552 GDB, 411-422 accuracy of, data, 422 classification of, 419 detection limits of, 420 dynamic linear range of, 420 linearity of, 420 maintenance and cost of, 422 principle of, 412-414 response factors of, 413-419, 421-423 absolute, 413-414 influence of the bridge current on, 418 influence of the detector design on, 418 influence of the nature of the carrier gas on, 414-415 influence of the reference gas flow rate on, 415-417 influence of the temperature on, 417-418 parameters affecting, 414-419 prediction of, 422 relative, 414, 422-423 schematics of, 412 selectivity of, 419 sensitivity of, 420 stability of, 420 GLC, 2, Chapter 3, 753 Glass beads. 753 Golay equation, 105-108, Chapter 8; see also OTC Graphitized carbon black: coated with polymers, 231 properties of, 230-232 used in modified GSC, 230-232 GSC. 2, 76-82, 153

778

H Headspace analysis, 754 Heartcutting, 300-304, 346-350, 355-360,754 Deans system for, 300-304, 355-360 examples of, 302, 346, 351, 359, 361 valve system for, 303, 346-349 Height equivalent to a theoretical plate, 19; see also HETP Height of peaks, see Peak height Height or area of peak in quantitative analysis, 672-673 Helium detector, see HID Helium ionization detector, 472-477; see details at HID Henry constant of adsorption, 77 and retention data, 77-78 influence of temperature on, 80 Henry law, 59 coefficient of, 77, 742 HETP, 19, Chapter 4, 754 and column parameters, 174 and resolution, 117-118 apparent, of a column series, 110-111 influence of experimental parameters: amplifier, 115 carrier gas velocity, 102-109 coating ratio, 109 column inner diameter (OTC), 105-108 column length, 110 connecting tubes, 114-1 15 detector properties, 115 equipment, 113-117 injection system, 113-114 nature of the carrier gas, 108 particle size (packed columns), 108-1 10 pressure gradient, 102-105 sample size, 141-146 of open tubular columns, 105-108 of packed columns, 108-110 properties of, 105-110 HID, 472-477 classification of, 475 detection limits of, 476 dynamic linear range of, 476 maintenance and cost of, 476 principle of,472-474 response factors of, 476 influence of the purity of He on, 474 parameters affecting, 474 schematics of, 473 selectivity of, 476 sensitivity of, 476 Hold-up time, 13, 754 Hold-up volume, 13, 754 Hot wire detector, see TCD

779

Hydrocarbons, on-line analysis of, 718-719 Hydrogen, on-line analysis of, 718-719 Hyphenated techniques, Chapter 12

I Ideal chromatography, 147-150 Identification of unknowns, 533-543; see also Derivatization using on-line hydrogenation, 542-543 using post-column reactions, 538-539 using selective detectors, 533-538 Index, see Retention index Inert compound retention time, see Gas hold-up time Injection of samples, 327-338 Injection port, 754 Injection system, see Sampling system influence of, on column efficiency, 113-114 Inlet splitter, 286-300, 764 Inlet system, 286-300, 327-339 Inlet to outlet pressure ratio, 37 Instrument, description of, 320-321 Instrument, see Gas chromatograph Instrumental errors, 673-674 Integral detectors, 755 Interface, 755; see also GC-MS, interface Internal normalization: of corrected peak areas, 652 of peak areas, 651 Internal standard, 653. 755 Interstitial volume, 755 Ionization detector, 755 Isorheic chromatography, 755 Isotherm effect, 129-131 Isothermal chromatography, 755

J James and Martin correction factor, 12, 14. 41-44, 755

Katharometer, see TCD Kieselguhr, 755 Kovats index, 486-490, 508-515, 756; see also Retention index

L Langmuir isotherm, 756 Limit of detection, 402-405. 756 Linear gas velocity, 12, Chapter 2, 756 Linear range of the detector response, 405, 756

780 Linear regression: coefficients of the best straight line, 569 confidence limits, 569 principle, 568 Linearity, 756 Linearity of detector response: ECD, 454 FID, 445 FPD, 466 GDB, 420 HID, 476 PID, 471 TCD, 432 TID, 463 Liquid loading, 195-199, 756 Liquid phase, 756 Liquid samples, injection of, 331-338 Local gas velocity, 37 Logarithmic dilution method, 591-595, 756 Long columns, 44 Lovelock detector, see HID Lower detection limit, 402-405, 757

M Mass balance equations, 135-138 Mass flow sensitive detectors, 399-400, 757 Mass transfer kinetics in GSC, 79 Mass transfer resistance, 97-102, 757; see also Resistance to mass transfer Matrix (sample), 757 McReynolds constants, 518, 757; see also Stationary phase, characterization Mean of a series of measurements, 565 Median of a series of measurements, 565 Mesh size, 29, 757 Methyl silicones, 757 Mixed phases, 177-181 Mixed retention mechanisms, 70-75 adsorption, 73-75 complexation, 70-73 Mobile phase, 757 Modified GSC, 213-233 accuracy of analyses obtained by, 226 advantages of, for industrial analysis, 224-226 application to fast analysis, 219-224 coating adsorbent for, 228-230 coating silica gel for, 228-230 column efficiency in, 218-222 drying adsorbent for, 227-228 flow velocity in, 219-223 graphitized carbon black for, 230-232 influence of support specific surface area in, 218-219 long term column stability in, 225 porous polymers for, 233

78 1

preliminary trials, 220-222 preparation of adsorbent for. 227-230 preparation of silica gel for. 227-230 relative retention on graphitized carbon blacks, 231 sample size in, 226 selection of silica gel for, 217-218 selection of specific surface area for, 222 thermal treatment of packing material for, 230 use of steam as carrier gas in, 226, 237-244 Molecular sieves, 757 Molecular weight determination, from GDB response, 533-535 Monomer pollution, on-line analysis of, 732-734 Multidimensional chromatography, 758

Net retention time, 14, 758 Net retention volume, 14. 758 Noise of detector, 407, 758 Non-ideality of carrier gas: influence of, on gas velocity, 48 influence of, on retention data, 66-70 Number of effective theoretical plates, 18 Number of theoretical plates, 10. 18. Chapter 3

On-line control analysis, Chapter 17 On-line gas chromatograph, Chapter 17 advantages of deferred standard in. 713-714 calibration of, 696 column life time in. 694-695 control unit of, 692 data display of the, 693 deferred standard, 703-717 alarm function of, 708-712 and preventive maintenance, 713 applications of, 714-739 calibration function of, 713 implementation of, 707-708 principle of, 705-706 description of, 690-693 design of switching valves for, 695 maintenance and cost of, 702 maintenance of, 705 oven of, 691 pneumatic system of, 692 reliability of. 704 response time of. 705 sampling, 696-701 location of the analyzer, 702 long transfer lines, 699-700

782 sample treatment, 701 sampling line, 696-700 start-up of the analyzer, 702 On-line gas chromatography: applications of, 718-739 credibility of, 704 methodology for, 694 present status and problems of, 704-705 Open tubular columns, Chapter 8, 758; see details at OTC advantages of, over packed columns, 46 gas hold-up time of, 45 permeability of, 46 Optimization of experimental conditions, 118-122, Chapter 6; see also Selection of first step, 155-164 second step, 164-181 Optimization strategy, 154-155 OTC (open tubular columns), Chapter 8, 247-310 classification of, 251-253 evaluation of, 279-286 analytical test for, 280-281 measure of the permeability for, 281-282 properties of the HETP and, 282-284 separation number for, 285 value of the phase ratio, 284 various parameters for, 285-286 guidelines for the use of, 304-310 injection techniques for, 286-300 on-column injection, 295-298 programmed temperature vaporizers, 298-300 . Ros injector, 293-294 sample size, 286-288, 306-307 spht-splitless systems, 291-293 splitting systems, 288-291 instrument for: column switching, 300-303 injection techniques, 286-300 instrument problems, 286-303 origins of, 248-251 preparation of, 253-279 coating of the wall, 268-272 deposit of BaCO,, 262 deposit of NaCI, 262 dynamic coatin!, 268-271 etching of glass tubing, 261 glass tube drawing, 257-259 immobilization of the liquid phase, 272-279 leaching with HCI, 265 nature of the tubing used, 256-260 of porous layer columns, 278-279 problems to be solved, 253-256 reaction with polyglycols, 265 selection of a deactivation procedure, 266-267 selection of tubmg for, 256-257 silanization procedures, 265-266

783 silica tubings, 260, 267 static coating, 271-272 support coated columns, 279 surface treatment of glass tubing, 260-267 thick films, 276-277 various etching treatments, 264 whiskers growing, 262-264 selection of carrier gas for, 306 wettability of the wall by the phase, 255-256 wide bore columns, 277-278 Outlet flow velocity, 12, 37 Overloading of columns, 127-150

P Packed capillary columns, 252 Packed columns, Chapters 6 and 7, 758 Packing material, 181-192; see also Column packing inorganic, characteristics of, Table 6.4. 182 organic, characteristics of, Table 6.5, 184 Parallel flow gas chromatograph, 322-323 Particle size, 28. 38 distribution, 38 optimization of, 122-123 Partition, Chapter 3, 758 Partition coefficient, 60, 758 assumption of solution thermodynamics in the prediction of, 66 influence of adsorption on support, 73-75 influence of gas phase non-ideality, 66-70 Peak, 758 Peak area, 12, 26, Chapter 15, 758 and sample size, 570-574 determination of, 30, Chapter 15 from computer acquired data: influence of data point density and precision on, 670 integration window and precision of, 670 precision of, 669-672 signal to noise ratio and precision of, 670 smoothing and precision of, 670 from electronic integrator, precision of, 668-669 from recorder chart, precision of, 665-668 or peak height in quantitative analysis, 672-673 precision of, 665-672 effect of parameters fluctuations for FID, 681-684 effect of parameters fluctuations for TCD, 679-681 bridge voltage, 679-681 flow rate, 679-681 temperature, 679-681 effect of pressure and flow rate fluctuations, 675-678 effect of temperature fluctuations, 678 Peak asymmetry, 20 Peak base, 159 Peak capacity, 26, 759

784

'

Peak height, 12, 27, 759 from computer acquired data, precision of, 664 from recorder chart, precision of, 663 measurement, precision of, 663-665 or area in quantitative analysis, 672-673 Peak integration, 30 Peak leading, 759 Peak profile, influence of sample size on, 141-146 Peak standard deviation, definition, 16 in time, length and volume units, 16 Peak storing, see Storing Peak symmetry, 20, 759 Peak tailing, 759 Peak variance, definition, 16 properties, 17 Peak width, 11, 18, 759 at half-height, 759 relative, 18 Permeability of the column. 37, 38 of open tubular columns, 46 Permeation tubes (for calibration), 600-601 Phase ratio, 29, 58, 759 Phenyl silicones, 759 Photoionization detector, 466-471; see details at PID Phthalic anhydride, on-line analysis of, 730-731 PID, 466-471 classification of, 469 detection limits of,470 dynamic linear range of, 471 ionization potentials of various compounds, 468 maintenance and cost of, 471 parameters affecting the response of, 468-469 prediction of the response factors of, 470-471 principle of, 467 schematics of, 467 selectivity of, 469 sensitivity of, 470 Planimetry, 635, 760 precision of, 667 Plate height, Chapter 4, 760; see also HETP Plate theory, 760 Pneumatic system, 321-327 Polarity of stationary phases, 521, 760 Pollutants in water, analysis of, with steam in carrier gas, 242-244 Pollution, on-line analysis of, 732-734 Polychlorinated hydrocarbons, optimization of analytical conditions of, 165-181 Polyesters, 760 Polyglycols, 760 Polymeric phases, 101 Polystyrene gels, 760 Poorly resolved peaks, quantitative analysis of, 27 area allocation, 646-650 Porapak, 760 Porous layer OTC,252, 278, 279, 760

785 Porous polymers, in modified gas-solid chromatography, 232-233 properties of, 232-233 Precision, 567 Precision in quantitative analysis, Chapter 16 Pressure controller, 323-325 Pressure correction factor, 42, 43 Pressure drop, 35-38, 760 Pressure fluctuations, effect on precision of peak area, 675-678 Pressure gradient, Chapter 2, 37, 761 Pressure profile, 40 Pressure stability, specifications for precise measurements, 677 Principle of detectors: ECD, 448 FID, 437 FPD, 464 GDB, 412 HID, 472 PID. 467 TCD, 423 TID, 458 Process control analyzers, Chapter 17 Process control gas chromatograph, see On-line gas chromatograph Programmed temperature analysis, 83-88 optimization of, 87-88 prediction of retention temperatures in, 84-87 retention time in, 83 selection of program rate for, 87-88 selection of starting temperature for, 87 Propagation of errors. coefficients, 674 Propagation of large concentration bands, 148-150 Pulsed injection, 336-338 Pyrolysis gas chromatography, 761

Q Qualitative analysis, Chapter 11; see also Derivatization from retention data, 500-515 using post-column reactions, 538-539 using selective detectors, 535-538 Quantitative analysis, Chapters 13-16 calculation procedures, 650-658 definition of peak area, 27 definition of peak height, 27 determination of peak area. Chapter 15 determination of response factors, Chapter 14 principles of, Chapter 13 sources of error, Chapter 16 Quantitative data, definition, 27

R Radial mass transfer, 98-100 Random walk model, 17. 94

786 Raoult law, 58 Reduced carrier gas velocity, 111-113 Reduced plate height, 111-113, 761 Reduced velocity, 111-113,761 Relative response factor, 401, Chapter 14,761 Relative retention, 21, 65,761 simple measurement of, 31 Repeatability, 566 Reproducibility,567 Resistance to mass transfer, 98-102, 761 and adsorption/desorption kinetics, 102 contribution to the column HETP, 97-102 in the flowing mobile phase, 97-100 in the liquid phase, 100-102 in the stagnant mobile phase, 100 Resolution, 22-25, 762 and column efficiency, 117-118 of unequal peaks, 23-25 Response factor, 401, 570-574, 762 determination, Chapter 14 accuracy and precision, 609-626 by conventional method, 589-601 gas samples, 589-595 liquid samples, 596-601 volatile liquid samples, 595-596 for TCD or FID, with GDB, 601-609 with a gas density balance, 601-609 with diffusion cells, 598-600 with exponential dilution flask, 591-595 with permeation tubes, 600-601 for a concentration sensitive detector, 572-573 for a mass flow sensitive detector, 573-574 of a detector, definition, 401-402 relative, 588 reproducibility,609-626 stability, 609-626 and properties of the chromatographic system, 612 Response factors of detectors, prediction of ECD, 455-457 FID, 445-446 and detector characteristics, 621-626 FPD, 466 GDB, 422 HID, 476 PID, 471 TCD, 432-436 and detector characteristics, 613-621 TID, 463 Response time, 408,762 Retention, relative, 21; see also Relative retention Retention data, Chapter 3 accuracy of, 497 effect of artefacts, 498-500 effect of errors on gas hold-up time, 495 effect of overloading,491

787 definition, 13 influence of gas phase non-ideality on, 66-70 in qualitative analysis, Chapter 11 plots, see Retention data plots reproducibility : effect of mixed mechanisms, 492 effect of noise, 496-497 influence of fluctuations of ambient parameters, 493-495 influence of sample size, 483-485, 491 instrumental sources of error, 493-497 of absolute data, 483-485 of relative data, 485-486 sources of errors, 490-497 stability (long term), 491-492 thermodynamics, 170 Retention data plots, 501-512 Hammett equation, 507 log k' versus carbon atom number, 501-503 log k' versus log k ' on another phase, 504-505 log Vg versus boiling point, 503-504 log Vg versus vapor pressure, 503-504 triangular diagrams 505-507 Retention factor, 486, 762 Retention index, 20-22, 486-490, 762 additive contributions to, 508-511 of functional group, 510-511 of the chain methylene groups, 508-510 constitutive relationships of, 511-512 increments, see Retention index increments in programmed temperature analysis, 86-87 non-Kovats indices, 490 properties of, 486-490 temperature dependence of, 487-488 Retention index increments, 489, 512-515 calculation of, with Rohrscheider constants, 513 prediction of, 513-515 Retention temperature in programmed temperature analysis, 84-86 Retention time, 11, 13-14, 41-42; see also Retention volume absolute, 13, 741 adjusted, 13, 741 corrected, 14, 748 influence of sample size, 141-142 net, 14, 758 of air, 11 of an inert compound, 11, 41, 42 true, 13, 14, 767 Retention volume, Chapter 3 absolute, 13, 741 adjusted, 13, 741 assumption of solution thermodynamics in the prediction of, 66 corrected, 14, 748 definition, 13-15 in gas-liquid chromatography, 60-65 and the activity coefficient, 57-62

788 influence of adsorption on support, 73-75 influence of gas phase non-ideality, 66-70 influence of solute vapor pressure, 64 influence of solvent surface tension, 74 influence of temperature, 63 on polymeric phases, 62 in gas-solid chromatography, 77-78 and the Henry constant, 78 influence of average pressure, 82 influence of carrier gas adsorption, 82 influence of carrier gas non-ideality, 81 influence of temperature, 80 in modified gas-solid chromatography, 215-216, 219-224 influence of steam concentration in carrier gas, 240-241 influence of support surface, 75 net, 14, 758 of an inert compound, 13, 48 specific, 14, 60, 764 totally corrected, 14 true, 14, 767 Reversing, 349-350, 356-357, 762 example, 350, 357 valve system for, 349, 356, 357 Rohrschneider constants, 513-515; see also Stationary phase, characterization

Sample loop. 327-339, 762 volume, precise determination of, 583-586 Sample size: and peak area, 570-574 influence on band width and HETP, 141-146 influence on peak profile, 141-146 influence on retention time, 138-146 measurement of, 575-586 error made, 673 high boiling compounds, 578 with gas sample, 575-576, 578-580 with liquid sample, 580-583 with volatile liquid sample, 577 Sampling lines for process control gas chromatographs, 697-700 Sampling port, 763 Sampling system, 286-300, 327-339, 763 for gas samples. 327-331 for liquid samples, 331-338 pulsed injection, 336-338 syringes, 332-333 valves, see Sampling valves vaporization chambers, 332-333 Sampling valves, 327-339, 763 membrane valves, for gas samples, 328-329 piston valves: for gas samples, 331 for liquid samples, 333-336

789 repeatability of, 339, 578-583 rotary and sliding valves, for liquid samples, 336 rotary valves, for gas samples, 329-330 sliding valves, for gas samples, 330-331 Selection of experimental conditions, Chapter 6 band plot method, 172-173 carrier gas flow rate, (1st step) 162, (2nd step) 175-177 column length, (1st step) 160-161, (2nd step) 164-169 column temperature, (1st step) 161-162, (2nd step) 169-175 column tubing, 193-195 for OTC, 304-310; see also OTC particle size and size distribution of the support, 189-192 phase ratio, 196-199 stationary phase, 156-158 support, 156-158, 181-192 support treatment, 183-190 window diagram method, 173-175 Selective detection, Chapter 10, 763 for qualitative analysis, 535-538 use of ECD, 536 use of smell, 536-537 Selectivity of detectors, 400-401, 763 Sensitivity of detectors, 401, 763 Separation and column parameters, 167 Separation data, definition, 20 Separation factor, 26, 763 Separation number, 26, 763 Septum, 332, 763 Serial flow, 321-322 Signal to noise ratio, 402, 764 Silanized support, retention on, 75-76 Silica gels, 764 physicochemical properties of, 215-217 properties of, 214-230 surface density of silanols, 215-217 used in modified gas-solid chromatography, 214-230 Silicone, 764 Silylation, 764 Slurry, 201, 764 Solid support, 181-193, 764 Solute, 764 Solute property detector, 764 Sorption effect, 128-129 Sources of band broadening, 94-95, 96-102; see also Mass transfer resistance Sources of errors in quantitative analysis, 662-673 Specific retention volume, 14, 61-62, 764 Spike of sample. in qualitative analysis, 484 Splitter, 286-300, 764 Squalane, 765 Standard, deferred, 703-718, 749 Standard, external, 653, 751 Standard, internal, 652, 653, 755 Standard addition, 652, 765 Standard deviation, 16, 765

790 Standard deviation of a series of measurements, 565 Start, 765 Stationary phase, 765 characteristics of, Table 6.8, 206 characterization of, 516-521 with factor analysis, 520-521 with McReynolds constants, 518-519 with Rohrschneider constants, 517-518 classification, 516-526 by polarity scale, 521-522 by selectivity diagrams, 522-523 combination of, 177-181 general properties of, 3 limit temperature of, 694-695 polarity of, 158-160 practical selection of, 526 selection of, 156-158,523-526 by numerical taxonomy, 524-525 by polls, 525-526 by the nearest neighbor method, 523-524 Steam as carrier gas, 233-244 control of the composition of, 235-236 production of, 234-236 properties as carrier gas, 237-244 selection of steam/inert gas ratio, 236-237 Storing, 341-349, 352-355,765 dynamic method, 347-349 example, 352, 354 static method, 349, 354 valve system for. 347-349, 352 Student function, 566 Styrene, on-line analysis of, 731 Support: coating of conventional supports, 201-202 procedure for, 201-203 coating of Teflon powder, 203 particle size and size distribution, 189-192 silanization of, 185-188 treatment of by acid wash, 189 by basic wash, 189 by fluidization, 192 for the elimination of metal oxides, 189 Support coated open tubular column, 765 Switching procedures, 340-384 advantage of Deans method for, 360-362 calculation of lengths of column segments, 362-384 calculation of switching times, 362-384 combination of, 340, 350-351 with Deans method, 351-362 with valves, 340-351 Switching valves, 340-351, 765 Syringe sampling: for gases, 575-576

791

for solutions of high boiling compounds, 578 for volatile liquids, 577 repeatability of,575-578 Syringes, 332-333, 766

T Tailing, 117, Chapter 5, 766 TCD, 423-426,766 classification of, 431 cleaning procedure for, 436 dynamic linear range of, 432 linearity of, 432 maintenance and cost of,436 principle of, 423-426 response of: absolute, 425-426 influence of the bridge current on,428-429 influence of the carrier gas flow rate on, 427 influence of the geometry on, 429-431 influence of the nature of the carrier gas on, 426-427 influence of the nature of the sensors on, 427-428 parameters affecting, 426-431 prediction of, 432-436 schematics of, 424 selectivity of, 431 sensitivity of, 432 stability of, 432 Temperature fluctuations and precision on peak areas, 678 Temperature programming, 83-88, 766; see also Programmed temperature analysis instrument for, 386-389 Theoretical plate, 94, 766 effective, 18 height equivalent to, 19 local height equivalent to, 19 number of, 10, 18 Thermal conductivity detector, 423-436; see details at TCD Thermal conductivity of carrier gases, Table 10.4, 426 Thermistor, 766 Thermoionic detector, 457-463; see details at TID Thin liquid phase films, 75-76 TID, 457-463, 766 classification of,462 detection limits of, 463 dynamic linear range of, 463 maintenance and cost of,462 principle of, 458-460 reaction mechanism of, 458-460 response o f influence of the air flow rate, 461 influence of the carrier gas flow rate, 461 influence of the hydrogen flow rate, 461 influence of the nature of the alkaline salt, 461

792 parameters affecting, 460-461 prediction of, 463 schematics of, 458 selectivity of, 462 sensitivity of, 463 Time. gas hold-up, 13,753 Time, retention, see Retention time Totally corrected retention volume, 14 Trap, 767 Triangulation, 631-633,767 precision of, 667 True retention time, 14,767 True retention volume, 14,767

TZ,26

U Ultrasonic detector, 767 Uncorrected retention time, 11, 767

V Valve sampling: for gases, 578-580 for liquids, 581-583 repeatability, 578-583 Valves, column switching with, 340-351 Valves, sampling, see Sampling valves Valves, switching, see Switching valves Van Deemter equation, 105-110,767 Van der Waals forces, 767 Vapor phase chromatography, 767 Vaporization chamber, 332-333 Variance, 17,768 Variance of a series of measurements, 565 Velocity profile, 40 Vinyl chloride, on-line analysis of, 720-724 Virial coefficient, influence on retention data, 67 Viscosity of carrier gas, 37 data, 39 influence of pressure on, 39 influence of temperature on, 39 Void volume, 13, 768 Volume, gas hold-up, 13, 753;see also Gas hold-up volume Volume, retention, see Retention volume

Wall coated open tubular column, 251-252; see also OTC Watson-Biemann interface, 552, 768 Wheatstone bridge, 768 Window diagram method, 173-175, 180-181

793

Z Zeolites, 768 Zone, see Band

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MicrocolumnHigh-Performance Liquid Chromatography by P. Kucera

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Polymer Characterization by Liquid Chromatography by G. GliSckner

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Optimization of Chromatographic Selectivity. A Guide to Method Development by P.J. Schoenmakers

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Selective Gas Chromatographic Detectors by M. Dressler

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Chromatography of Lipids in Biomedical Research and Clinical Diagnosis edited by A. Kuksis

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Selective Sample Handling and Detection in High-Performance Liquid Chromatography. Part A edited by R.W. Frei and K. Zech

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Aqueous She-Exclusion Chromatography edited by P.L. Dubin

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High-Performance Liquid Chromatography of Biopolymers and Biooligomers. Part A: Principles, Materials and Techniques by 0. Mikei

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Quantitative Gas Chromatography for Laboratory Analyses and OnLine Process Control by G. Guiochon and C.L. Guillemin