Polymer Spectroscopy

Polymer Spectroscopy Edited by

ALLAN H. FAWCETT The Queens University of Belfast, Belfast, Northern Ireland, UK

JOHN WILEY & SONS Chichester • New York • Brisbane • Toronto • Singapore

Copyright © 1996 by John Wiley & Sons Ltd, Baffins Lane, Chichester, West Sussex PO19 IUD, England National International

01243779777 (+44) 1243 779777

All rights reserved. No part of this book may be reproduced by any means, or transmitted, or translated into a machine language without the written permission of the publisher. Other Wiley Editorial Offices John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, USA Jacaranda Wiley Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Canada) Ltd, 22 Worcester Road, Rexdale, Ontario M9W ILl, Canada John Wiley & Sons (SEA) Pte Ltd, 37 Jalan Pemimpin #05-04, Block B, Union Industrial Building, Singapore 2057

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBNO 471960292 Typeset in 10/12pt Times by Thomson Press (India) Ltd, New Delhi Printed and bound by Antony Rowe Ltd, Eastbourne This book is printed on acid-free paper responsibly manufactured from sustainable forestation, for which at least two trees are planted for each one used for paper production.

LIST OF CONTRIBUTORS

Gordon G. Cameron Department of Chemistry, University of Aberdeen, Meeston Walk, Old Aberdeen AB92UE, Scotland, UK Michelle Carey Department of Chemistry, Imperial College of Science, Technology and Medicine, South Kensington, London SWl'2AY, UK Trudy G. Carswell Chemistry Department, University of Queensland, Brisbane, QLD 4072, Australia Francesco Ciardelli Dipartimento di Chimica e Chimica Industriale, Universita of Pisa, Via Risorgimento 35, 56126 Pisa, Italy Iain G. Davidson Department of Chemistry, University of Aberdeen, Meeston Walk, Old Aberdeen AB9 2UE, Scotland, UK Christine Duch Chemistry Department, University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, Wales, UK Allan H. Fawcett School of Chemistry, The Queen's University of Belfast, Belfast BT95AG, Northern Ireland, UK Adriano Fissi, CNR Institute of Biophysics, University of Pisa, Via Risorgimento 35,56126 Pisa, Italy Jerome Fournier Chemistry Department, University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, Wales, UK R. Wayne Garrett Chemistry Department, University of Queensland, Brisbane, QLD 4072, Australia J. G. Hamilton School of Chemistry, The Queens University of Belfast, Belfast BT95AG, Northern Ireland, UK

Robin K. Harris Department of Chemistry, University of Durham, Science Laboratories, South Road, Durham DHl 3LE, UK James R. Hayden Chemistry Department, University of Wales, Swansea, Singleton Park, Swansea SA28PP,Wales,UK Patrick J. Hendra Department of Chemistry, University of Southampton, Highfield, Southampton SO95NH, UK Ian R. Herbert Department of Chemistry, University of Durham, Science Laboratories, South Road, Durham DHl 3LE, UK David J. T. Hill Chemistry Department, University of Queensland, Brisbane, QLD 4072, Australia Oliver W. Howarth Centre for Nuclear Magnetic Resonance, Department of Chemistry, University of Warwick, Coventry CV4IAL, UK Roger N. Ibbett Department of Chemistry, University of Durham, Science Laboratories, South Road, Durham DHl 3LE, UK Jack L. Koenig Department of Macromolecular Science, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106-7202, USA

W.F.Maddams, Department of Chemistry, University of Southampton, Highfield, Southampton SO95NH,UK James H. O'Donnell Chemistry Department, University of Queensland, Brisbane, QLD 4072, Australia (Deceased) David Phillips Department of Chemistry, Imperial College of Science, Technology and Medicine, South Kensington, London SW72AY, UK Osvaldo Pieroni Dipartimento di Chimica e Chimica Industriale, and CNR, Institute of Biophysics, Universita di Pisa, Via Risorgimemto 35, 56126 Pisa, Italy Peter J. Pomery Chemistry Department, University of Queensland, Brisbane, QLD 4072, Australia

Adrian R. Rennie Polymers and Colloids Group, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 OHE, UK R. W. Richards Department of Chemistry, University of Durham, Durham DHl 3LE, UK J. J. Rooney School of Chemistry, The Queen's University of Belfast, Belfast BT9 5AG, Northern Ireland, UK

H.W.Spiess Max-Planck-Institute Germany

fur Polymerforschung, Postfach 3148, D-55021 Mainz,

Alan E. Tonelli Fiber and Polymer Science Program, College of Textiles, North Carolina State University, PO Box 8301, Raleigh, NC 27695-8301, USA Graham Williams Chemistry Department, University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, Wales, UK Mark A. Whiskens Department of Chemistry, University of Durham, Science Laboratories, South Road, Durham DHl 3LE, UK Catherine L. Winzor Chemistry of Department University of Queensland, Brisbane, QLD 4072, Australia Robert J. Young Manchester Materials Science Centre, University of Manchester, Grosvenor Street, Manchester Ml 7HS, UK

Contents

List of Contributors .............................................................

xiii

Introduction to Polymer Spectroscopy ..........................

1

1. NMR Characterisation of Macromolecules in Solution .......................................................................

7

1.1

Introduction ...................................................................

7

1.2

Branched Molecules: Polyethylene and a Polyester System ..........................................................

9

1.3

The Microstructure of Linear Chains ............................

15

1.4

The Participation of a Charge-Transfer Complex in a Free Radical Polymerization Reaction ......................

22

1.5

The Polymerization of Dienes ......................................

25

1.6

Ring-Opening-Metathesis Polymerizations ..................

30

1.6.1

Stereoselectivity in ROMP .........................

32

1.6.2

Distribution of trans Double Bonds in High cis Poly(Norbornene) .........................

36

1.6.3

Regioselectivity in ROMP ..........................

41

1.6.4

Direct Observation of Tacticity ...................

45

References ...................................................................

52

2. Conformation: the Connection between the NMR Spectra and the Microstructures of Polymers .........

55

1.7

2.1 2.2

Introduction ................................................................... 13

Substituent Effects on C Chemical Shifts .................. This page has been reformatted by Knovel to provide easier navigation.

55 56

v

vi

Contents 2.3 2.4

2.5

γ-Gauche Effect Method of Predicting NMR Chemical Shifts .............................................................

60

Applications of γ-Gauche Effect Analysis of Polymer Microstructures ...............................................

64

2.4.1

Polypropylene (PP) ....................................

64

2.4.2

Propylene-Vinyl Chloride Copolymers (P-VC) ........................................................

67

2.4.3

Poly(Propylene Oxide) (PPO) ....................

68

2.4.4

Poly(Vinylidene Fluoride) (PVF2) ................

81

NMR Spectroscopy as a Means to Probe Polymer Conformations ..............................................................

84

2.5.1

Styrene-Methyl Methacrylate Copolymers (S-MM) ...................................

84

Ethylene-Vinyl Acetate (E-VAc) Copolymers ................................................

88

NMR Observation of Rigid Polymer Conformations ..............................................................

92

References ...................................................................

93

3. ‘Model-Free’ RIS Statistical Weight Parameters from 13C NMR Data .....................................................

97

2.5.2 2.6 2.7

3.1

Introduction ...................................................................

3.2

Methods ........................................................................ 100

3.3

Some Calculation Details ............................................. 101

3.4

Individual Polymers ...................................................... 102

3.5

The Calculated RIS Parameters .................................. 109

3.6

β-Gauche Effects .......................................................... 111

3.7

Coupling Constants ...................................................... 111

3.8

Characteristic Ratios .................................................... 113

3.9

Conclusions .................................................................. 114 This page has been reformatted by Knovel to provide easier navigation.

97

Contents

vii

3.10

Acknowledgement ........................................................ 115

3.11

References ................................................................... 115

4. NMR Studies of Solid Polymers ................................ 117 4.1

Introduction ................................................................... 117

4.2

The Techniques ............................................................ 118

4.3

High-Resolution Carbon-13 NMR of Polymers ............ 121

4.4

Proton Spin Relaxation ................................................. 125

4.5

Discrimination in Carbon-13 Spectra ........................... 128

4.6

Spectra of Abundant Spins ........................................... 131

4.7

Conclusion .................................................................... 132

4.8

Acknowledgements ...................................................... 132

4.9

References ................................................................... 133

5. Multidimensional Solid-State NMR of Polymers ...... 135 5.1

Introduction ................................................................... 135

5.2

Multidimensional Solid-State NMR Spectra ................. 137

5.3

Examples ...................................................................... 138 5.3.1

Increase of Spectral Resolution ................. 138

5.3.2

Separated Local Field NMR ....................... 140

5.3.3

Wideline Separation Experiments .............. 141

5.3.4

2D and 3D Exchange NMR ........................ 142

5.3.5

Chain Alignment from 2D and 3D NMR ...... 144

5.3.6

Domain Sizes from Spin Diffusion Experiments ............................................... 146

5.3.7

Spatially Resolved Solid State NMR .......... 146

5.4

Conclusion .................................................................... 148

5.5

Acknowledgements ...................................................... 149

5.6

References ................................................................... 149 This page has been reformatted by Knovel to provide easier navigation.

viii

Contents

6. NMR Imaging of Polymers ......................................... 151 6.1

6.2

Introduction ................................................................... 151 6.1.1

Basis of NMR Imaging ............................... 151

6.1.2

Relaxation Parameters in NMR Imaging .... 153

6.1.3

Resolution in NMR Imaging ....................... 155

6.1.4

Utility of NMRI ............................................ 155

6.1.5

Image Processing ...................................... 156

Advanced Imaging Techniques .................................... 156 6.2.1

6.3

Chemical Shift Imaging .............................. 156

Applications of NMRI to Polymers ................................ 159 6.3.1

Detection of Voids in Composites .............. 159

6.3.2

Detection of Nonuniform Dispersion of Filler ........................................................... 161

6.3.3

NMRI of Physical Aging ............................. 161

6.3.4

NMRI Studies of Diffusion in Polymers ...... 162

6.3.5

Desorption of Liquids from Polymers ......... 165

6.3.6

Multicomponent Diffusion as Studied by NMRI ......................................................... 167

6.3.7

Absorption-Desorption Cycling of Liquids in Polymers .................................... 169

6.4

Acknowledgements ...................................................... 171

6.5

References ................................................................... 171

7. Fourier Transform Infrared and Raman Spectroscopies in the Study of Polymer Orientation .................................................................. 173 7.1

Introduction ................................................................... 173 7.1.1

The Basis of Orientation Measurements by Infrared Spectroscopy ........................... 174

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Contents 7.1.2 7.2

7.3

ix

The Basis of Orientation Measurements by Raman Spectroscopy ............................ 176

........................................................................................ 177 7.2.1

Experimental Techniques on Static Samples ..................................................... 177

7.2.2

Infrared Spectroscopic Studies on Oriented Polymers ..................................... 180

7.2.3

Raman Spectroscopic Studies on Oriented Polymers ..................................... 182

Time Resolved Measurements .................................... 185 7.3.1

The Response of a Viscoelastic System to Sinusoidal Stress ................................... 185

7.3.2

Experimental .............................................. 187

7.3.3

Some Examples of Dynamic Linear Dichroic Infrared Studies ............................ 192

7.4

Elastomers Under Stress ............................................. 198

7.5

Conclusion .................................................................... 200

7.6

References ................................................................... 201

8. Deformation Studies of Polymers using Raman Spectroscopy ............................................................. 203 8.1

8.2

8.3

Introduction ................................................................... 203 8.1.1

Polydiacetylene Single Crystals ................. 204

8.1.2

Extension of the Technique to Other Materials .................................................... 206

High-Performance Polymer Fibres ............................... 206 8.2.1

Aromatic Polyamide Fibres ........................ 206

8.2.2

Polyethylene Fibres ................................... 210

Isotropic Polymers ........................................................ 214 8.3.1

Urethane-Diacetylene Copolymers ............ 214

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x

Contents 8.3.2 8.4

Deformation Studies .................................. 217

Composites ................................................................... 221 8.4.1

Single-Fibre Composites ............................ 221

8.4.2

Interfacial Micromechanics ......................... 224

8.5

Conclusions .................................................................. 227

8.6

Acknowledgements ...................................................... 228

8.7

References ................................................................... 228

9. Spin-Label Studies of Heterogeneous Polymer Systems ...................................................................... 231 9.1

Introduction ................................................................... 231 9.1.1

9.2

Synthesis of Spin Labels ............................ 232

Theoretical Background ............................................... 235 9.2.1

9.2.2

Correlation Times ...................................... 235 9.2.1.1

Fast Motion ................................... 239

9.2.1.2

Slow Motion ................................... 240

The Glass Transition and T50G ................... 240

9.3

Heterogeneous Systems .............................................. 242

9.4

Polymer Blends ............................................................. 245

9.5

References ................................................................... 251

10. The Use of ESR Spectroscopy for Studying Polymerization and Polymer Degradation Reactions .................................................................... 253 10.1

Introduction ................................................................... 253

10.2

Experimental ................................................................. 254

10.3

Results and Discussion ................................................ 255 10.3.1 Free Radical Polymerization ...................... 255 10.3.1.1 Identification of the Radicals in the ESR Spectrum ........................ 255

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Contents

xi

10.3.1.2 Measurement of Radical Concentration ................................ 256 10.3.1.3 Monomer Concentration during Polymerization ............................... 256 10.3.1.4 Radical Concentration during Polymerization ............................... 257 10.3.1.5 Correction for Changing Sensitivity of the Spectrometer ..... 259 10.3.1.6 Kinetic Analysis ............................. 260 10.3.1.7 Crosslinking Methacrylate Monomers ..................................... 261 10.3.2 Polymer Degradation by High-Energy Radiation ................................................... 263 10.3.2.1 Poly(Methyl Methacrylate) ............. 263 10.3.2.2 Polystyrene ................................... 267 10.3.2.3 Random Copolymers of Methyl Methacrylate and Styrene ............. 268 10.3.2.4 ESR and the Mechanism of Radiolysis ...................................... 269 10.4

Conclusions .................................................................. 273

10.5

Acknowledgements ...................................................... 273

10.6

References ................................................................... 273

11. Dynamics of Bulk Polymers and Polymerizing Systems as Studied Using Dielectric Relaxation Spectroscopy ............................................................. 275 11.1

Introduction ................................................................... 275

11.2

Amorphous Polymers: Phenomenological and Molecular Aspects ........................................................ 276

11.3

Crystalline Polymers ..................................................... 280

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xii

Contents 11.4

Liquid Crystalline (LC) Polymers .................................. 282

11.5

Real-Time Studies of Chemical and Physical Changes ....................................................................... 288

11.6

Conclusions and Future Prospects .............................. 293

11.7

Acknowledgements ...................................................... 294

11.8

References ................................................................... 294

12. Light Scattering from Polymer Systems .................. 297 12.1

Introduction ................................................................... 297

12.2

Small Angle Light Scattering (SALS) ........................... 298 12.2.1 Semi-Crystalline Polymers ......................... 298 12.2.2 Phase-Separating Polymer Mixtures .......... 305

12.3

Quasi-Elastic Light Scattering (QELS) ......................... 309 12.3.1 Dilute Polymer Solutions ............................ 309 12.3.2 Gels ........................................................... 311 12.3.3 Semi-Dilute Solutions and Trapped Chains ....................................................... 313 12.3.4 Surface Quasi-Elastic Light Scattering (SQELS) .................................................... 316

12.4

Conclusions .................................................................. 321

12.5

References ................................................................... 321

13. Neutron Scattering from Polymers ........................... 325 13.1

Introduction ................................................................... 325

13.2

The Principles of Neutron Scattering ........................... 325

13.3

Neutron Experiments .................................................... 329 13.3.1 Studies of Polymer Dimensions: Small Angle Scattering ........................................ 330 13.3.2 Polymers at Surfaces-Reflection ................ 333

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Contents

xiii

13.3.3 Polymer Dynamics-Quasi-Elastic Scattering .................................................. 334 13.4

Some Examples of Recent Progress ........................... 336 13.4.1 Studies of Copolymers ............................... 336 13.4.2 Adsorption at Surfaces ............................... 339 13.4.3 Kinetics and Polymer Motion ...................... 341

13.5

Final Remarks ............................................................... 342

13.6

References ................................................................... 342

14. Optical Activity and the Structure of Macromolecules ......................................................... 347 14.1

Introduction ................................................................... 347 14.1.1 Origin of Optical Activity in Macromolecules ......................................... 347 14.1.2 Objective .................................................... 350

14.2

Chiroptical Properties of Photochromic Polypeptides ................................................................. 351 14.2.1 Polypeptides Photoresponsive to UV Light ........................................................... 351 14.2.1.1 Azobenzene-Containing Polypeptides .................................. 351 14.2.1.2 Light-Induced Conformational Changes ........................................ 352 14.2.1.3 Photosimulated AggregationDisaggregation Effects .................. 355 14.2.2 Photomodulation of Polypeptide Conformation by Sunlight ........................... 357 14.2.2.1 Spiropyran-Containing Polypeptides .................................. 357

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xiv

Contents 14.2.2.2 Photomodulation of Conformation ................................. 360 14.2.2.3 Photoinduced Variations of Viscosity ........................................ 366 14.3

References ................................................................... 367

15. Polymer Luminescence and Photophysics ............. 369 15.1

Introduction ................................................................... 369

15.2

Probes of Order in Polymers ........................................ 370

15.3

Probes of Sub-Group Motions ...................................... 372

15.4

Photochemistry in Polymers ......................................... 372

15.5

Excimer-Forming Polymers .......................................... 374

15.6

Dynamics of Luminescence ......................................... 376

15.7

Fluorescence Decay in Vinyl Aromatic Polymers ........ 377 15.7.1 Diffusional Models ..................................... 379 15.7.1.1 Random Walk Migration, Evenly Spaced Chromophores ................. 380 15.7.1.2 Random Water, Random Distribution Chromophores ........... 380 15.7.1.3 Multiple Trap Energies .................. 381 15.7.1.4 Reversible Excimer Formation ...... 381 15.7.1.5 Diffusion of Energy and Chromophore ................................ 381 15.7.1.6 Fluorescence Anisotrophy Measurements .............................. 385

15.8

Conclusion .................................................................... 387

15.9

Acknowledgements ...................................................... 388

15.10 References ................................................................... 388

Index .................................................................................. 391 This page has been reformatted by Knovel to provide easier navigation.

INTRODUCTION TO POLYMER SPECTROSCOPY A. H. FAWCETT

The Queen's University of Belfast

Historically there was a difficulty in dealing with macromolecules that was simply the realisation of their large size; the organic chemist's early painstaking methodology for isolating, studying and recognising the readily obtained small natural product molecule did not lend itself to the examination of many natural macromolecules such as cellulose and rubber. Such chemists, used to identifying their substances by the melting point complemented by similar studies on the derivatives and then the slow construction of the molecule by use of a developing repertoire of piecemeal reactions, were slow to accept how readily high polymers might be man-made by a simple but powerful repetitive process. Ancient practices and evolving technology might utilise materials such as wood, leather, silk and cotton, but the true macromolecular nature of these materials was not appreciated until about 60 years ago, and methods for exploring the large molecule and the development of appropriate concepts for a proper scientific enquiry took time to evolve. Spectroscopy has played a role in this process, light scattering in particular being used to show how high molecular weights might be, and NMR spectroscopy latterly being used to identify polymer structures. Now spectroscopy is at the heart of modern developments within polymer science, being used not only to characterise the microstructure of the chains, but also to monitor their dynamics, so important in determining the physical properties of interest to the materials scientist and engineer, and to explore the interesting properties that are being introduced in the search for special effects to be used in devices. Two developments have given us insight into polymers at the molecular level, the first being the spectroscopic techniques for recognising molecular components and the manner in which they are linked together, which is the topic of the first part of this book. Of course, the analytical problem of recognising a particular polymer is less severe to the man who chose the monomer and the polymerisation process (and any plasticiser or stabiliser) than it is to a would-be emulator, but the proper description of the microstructure of a macromolecule is as essential to the developmental chemist (Chapter 1) as it is to his competitor. For this purpose, NMR spectroscopy has now overtaken IR spectroscopy as the Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

analytical tool in general use. A second advance, much associated with Flory, was the development of statistical mechanical methods. These have provided insight into the equilibrium configurations of the isolated polymer chain and the manner in which modest thermal energies develop elaborate configurations within the backbones and any side chains, so that the calculations of the mean values of such quantities as dipole moment and end-to-end distance are complex, yet focus upon such readily visualised ideas as the potential surface for the conformations of each pair of adjacent bonds. NMR spectroscopic quantities such as chemical shift and coupling constant may be considered in just these terms, as Tonelli has described for us (Chapter 2). One has only to reflect on a subject area such as liquid crystals, where so often the description is formulated by the physicist in terms of unit cell properties, to realise how much closer workers with polymers routinely think in terms of molecular structure, and are able to link a certain molecular feature to an interesting property. Configurational elaborations are the prime characteristic of molecules rendered extremely long by the repetitive enchainment of a small number of simple residues: Ciardelli et al. describe the manner in whch stimuli such as light may induce changes in the structure of pendent groups and so in polymer-solvent interactions that are amplified by the connectivity of the system to cause profound changes in the equilibrium statistics of the single chain, and hence in its solution properties. Indeed, a group of chains may so be led to associate reversibly (Chapter 14). The manner in which light interacts with chromophores in bulk polymers, located either within the standard residues or merely within minor components such as end groups, is the subject of Phillips and Carey's contribution (Chapter 15). There are two interrelated factors to be disentangled—the manner in which light is absorbed, whether it is retained or migrates, and how the energy is eventually used, together with the dynamics of the moieties involved in this process. Excimer formation, luminescence, fluorescence and other photophysics processes are all subject to such factors as spacing constraints and the timescales of segmental motions, which in the bulk are not merely the property of a single molecule. Although the physical chemistry of the chain isolated in solution is well understood, the question of its performance within the bulk has thus become the subject of much study. Rapid movement between adjacent conformations ceases below the glass transition of an amorphous polymer, and in the crystalline state packing effects become significant and restrict configurations to a very few. The question of the location of the backbone is readily tackled: spectroscopic techniques for studying the configurations of the polymer in amorphous and crystalline phases within the bulk are well established; neutron scattering is a prime, if expensive, tool for the determination of molecular dimensions and for the study of dynamics (in a quasielastic scattering mode) and is now being developed as a method for studying surface structures (Chapter 13). The contrast is obtained by use of perdeuterated molecules. Light scattering is a more familiar

tool for investigating polymers; the method was introduced originally by such luminaries as Debye, and has developed, with the availability of lasers, in the quasielastic mode, not just for chains isolated in solution but also for gels, when various modes of motion may be inferred from treatments of the fluctuations of the intensity of the light scattered. The technique is now applied to studying phase separating mixtures and events within polymers upon surfaces (Chapter 12). Richards also covers the small angle light scattering method as used to investigate semi-crystalline polymers. IR and Raman spectroscopy characterise the high frequency vibrations of the skeleton and pendent atoms of the macromolecule, and so immediately tell us what groups are present; they have a useful analytical capacity to distinguish, for example, a poly(methyl methacrylate) (PMMA) from a PVC or a polyolefin. Vibration modes extend over several simple oscillators (such as bonds and bond angles); in the crystalline state they reflect the arrangement adopted within the unit cell, from which IR bands and Raman shifts follow conventional symmetryrelated selection rules. They may be used to measure crystallinity, as such. In the amorphous state conformational elaborations are not averaged out on the timescale of the vibration. Observed bands are thus composite and relatively broad, and although they may indicate whether in a rubber a double bond is cis or trans, and may measure the presence of methyl groups in low density polyethylene, band frequencies are not as sensitive as solution NMR spectroscopy to microstructure details extending over several residues. The fine structure observed in the shifts of linear polymers is itself a topic of careful consideration, as Tonelli and Howarth et al. have described (Chapters 2 and 3). The conformational origin within vinyl polymers of the patterns displayed in 13 C shifts is now well established, and provides the best source of information on tacticity and residue sequence, so that one might attempt to discriminate between mechanisms for propagation, such as those of the Bernoullian and Markov type, those involving charge-transfer complexes, and mechanisms involving catalysts derived from metal complexes (Chapter 1). Once one has evidence on the reaction mechanism, one may proceed to the design of new and better catalysts. Like vibration spectroscopy, NMR in the solid state, made feasible by the cross polarisation-magic angle spinning dipole decoupling method, is similarly rather insensitive to microstructural issues within the crystalline and amorphous states, but interesting results may be obtained when carefully chosen systems are compared: Harris presents the cases of the 4/1 helix of syndiotactic polypropylene and the 3/1 helix of isotactic polypropylene, the former clearly displaying sensitivity to the helix structure through the gamma-gauche effect so that internal and external methylenes are distinguished, and the latter displaying some sensitivity to the helix sense of the neighbouring chains (Chapter 4). The solid state NMR method is capable also of sensing inhomogeneities such as arise from microcrystals within a homopolymer such as polyethylene, and within blends of two different and only partly compatible polymers (Chapters 4 and 5), an area

that is similarly tractable by modern two-dimensional methods that are being developed within IR spectroscopy (Chapter 7). Both chemical shift and IR vibration frequency of one chain are sensitive to the nature of the neighbouring chains, particularly if an interaction such as a hydrogen bond is possible. The timescale of magnetic polarisation decay is capable of being linked to the size of the inhomogeneities. Mobility as measured by proton or carbon NMR relaxation times is a property of matter, including polymeric materials and any permeated liquid, that may be sensed by a scanning technique and displayed in an image form, usually in two dimensions. Koenig surveys for us the various applications he has made, the images providing an interesting comparison with the more conventional light and electron microscope viewing methods (Chapter 6). Vibration spectroscopy is sensitive, as Hendra and Maddams describe (Chapter 7), to such factors as anisotropy within such samples as uniaxially drawn rods and biaxially drawn films, allowing their properties to be optimised from an understanding of the molecular process. Such well established use of IR spectroscopy is now being succeeded by dynamic dichroic methods, to reveal how the backbones and side chains separately respond to imposed cyclic stresses. This provides a fascinating account of the manner in which different modes of motion come into play. A development of Raman spectroscopy described by Young is the response of certain vibrations in the spectrum to a progressive strain imposed upon the material, a technique that may exploit recent instrumental developments such as charge coupled device cameras and the confocal Raman microscope (Chapter 8). For a composite material, the technique allows us to answer a question such as the manner of the distribution of strain along a polyaramid fibre within a matrix that initially bears the imposed stress; the particular interest is the length of fibre required to take up the strain. The timescale of the response of a polymer to a stimulus ranges from the high frequencies of IR radiation through to the low frequencies or long time scales of diffusion of the whole molecule by the reptation mechanism, a process that is amenable to study by dielectric relaxation spectroscopy, as in studies on cispolyisoprene by Adachi. The dielectric response is present only from polar units, and is governed by the location of the dipoles, whether within side chains or backbones, in the geometry of the dipole itself and the geometry and flexibility of the neighbouring segments. For the chain in solution, simple and satisfactory accounts are available in these terms, and only in special cases do the dipoles themselves mutually organise to control the response. For the bulk material, whether in crystalline, amorphous or liquid crystalline form, cooperations between chains may be significant. For example, the alpha relaxation of crystalline polyethylene is a progression of a kink in one chain within a crystalline region, as computer simulations have modelled: it is the linear all-trans neighbours that define the tube within which the single chain performs (Chapter 11). Distributions of correlation times may be extremely wide in an amorphous material, but how

much this derives from variations in local conformations and orientations of the dipole within the chain in question, and how much from intra-chain influences (which may themselves have a response) is, as they say, a very good question! The same issues arise when studying the dynamic mechanical behaviour of polymers, a method closer to the concerns of the polymer engineers. Perhaps the developing power of NMR spectroscopy to measure correlation functions and the magnitude of the orientational jump and to identify the pathways of the motion will help provide an answer to these questions (Chapter 5). As Spiess describes, the NMR method might measure the angle of displacement, as well as its frequency, for poly(oxymethylene), displaying helical jump dynamics. Two-dimensional and three-dimensional experiments are now being performed to measure motions and to determine order within oriented solids (Chapter 5). The use of a paramagnetic probe coupled with electron spin resonance (ESR) monitoring provides information, within the timescale range of 10"3 s to 10"7 s, of a complementary nature, for by sensing the mode of rotation of the radical within the polymeric matrix, it measures the behaviour of the "holes", the packets of free volume, that facilitate the movements of the chains and play a vital role in the glass transition, Tg, phenomena. Locating the radical on the chain or at its end allows one to sense the extra degree of freedom at a polymer chain end (Chapter 9). The ESR technique in this book is applied to a second issue, monitoring the radicals actually responsible for a polymerisation of pure monomer plus a certain amount of crosslinker, the interest lying in the changes that take place to create a new regime when the gel effect operates, during which termination reactions are much retarded by the immobilisation of the radicals, as they are also in the final period, when the development of a glass is the cause of onset of a third regime (Chapter 10). O'Donnell's work monitors the radicals by ESR and the unreacted groups by near-IR spectroscopy, to reveal new insight into the kinetics during these periods. This study of the chemistry of free radical polymerisation is succeeded by a discussion of an equally important topic, as far as industrial use is concerned, the detailed chemistry of degradation by ionising radiation of polystyrene and poly(methyl methacrylate): following such training, O'Donnell's previous students helped develop microlithography. This book records the principal lectures given at a Conference in Grasmere organised by the Macro Group. The proceedings of two of the previous conferences with this subject area and sponsorship have also been published [1, 2] and provide a useful indication of the developments that have occurred over recent years in the practice and value of polymer spectroscopy.

REFERENCES [1] KJ. Ivin (Ed.), Structural Studies of Macromolecules by Spectroscopic Methods, John Wiley & Sons, London, 1976. [2] A.H. Fawcett, Br. Polym. /., 1987,219,97 and following papers.

1 NMR CHARACTERISATION OF MACROMOLECULES IN SOLUTION A. H. FAWCETT, J. G. HAMILTON AND J. J. ROONEY School of Chemistry, The Queens University of Belfast, Belfast BT9 5AG, Northern Ireland, UK

1.1 INTRODUCTION The NMR method of studying the microstructure of macromolecules is the most effective available, provided that the materials can be obtained in solution. The method is now routinely employed to characterise and to identify the structures present in polymers, both those in common use and those created by the chemist when working with new monomers or new catalyst systems [1-6]. Derivatives of polymers and reactions on polymers are similarly accessible to study. The NMR parameter that is sensitive to these structural issues is the chemical shift, commonly measured in ppm from an internal reference. It senses readily information on the framework of the polymer—its connectivity—by providing information on the number and type of atoms linked to each particular nucleus, and also senses such factors as the relative chirality of pairs of such centres and cis/trans isomerism within double bonds. The nucleus most often employed for both man-made and natural macromolecules is 13C, despite its being rather dilute (only 1% of the carbons). This is because in the spectrum the dispersion of shifts is particularly large; much detail or fine structure is generally encountered that is directly related to the polymer structure itself, and signal intensity is rarely a problem with modern high field instruments. Many other NMR-active nuclei such as 19 F and 31 P may be used too when they are present in the macromolecule. Proton NMR spectra are complicated by the presence of coupling effects between the spins of the protons if, as is usual, the protons are present on directly bonded carbon atoms. In certain cases these coupling effects are of extreme value: as Bovey showed for poly(methyl methacrylate) [2,7], the tacticity of the polymers may be identified directly, and the value of vicinal coupling constants provides information on the conformational properties of the bond [5,8]. However, frequently, as for example with polyolefins, they conceal the shift effects associated with the microstructure Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

by creating a multiplicity of splittings, a complicating factor which may be relieved only by the use of a substantial proportion of selective deuteration, as has been demonstrated for polypropylene [9,10]. We may note two rather special cases of proton NMR spectra: for highly syndiotactic polystyrene the methylene protons, being equivalent, have a simple three line 1:2:1 pattern that derives from the coupling effect of the two flanking methine protons [ H ] . The highly isotactic polymer has a slightly more complex but still recognisable spectrum [12]. Features in the spectrum of the atactic polymer are quite unrecognisable, as proton coupling effects intermingle with chirality effects, coupled with substantial chemical shift anisotropy from the phenyl ring [13]: each main chain carbon bears at least one proton, a situation that is unfortunately more usual. We are familiar with only one case, involving the furfurol oligomer bis(5-furfuryl-2-furylmethane), in which the methylene protons are more sensitive to position than is the carbon of the same group; this is probably because the central methylene protons sample the anisotropic shielding cone of the furan rings in a manner different from that for the protons of the flanking methylene groups, but the carbons, being in the plane of the rings, experience a constant effect [14]. During the last 25 years the development of the NMR method, firstly in terms of the power of the magnet employed and secondly by turning to computer-based operating systems, has often been stimulated, if not driven, by the need to understand polymer microstructure. In 1971 the chemical companies Dow, ICI and Du Pont themselves commissioned new magnets that increased the magnetic field beyond 5 T in order to pursue their studies of polymers so vital to their business. This magnetic field, equivalent to more than 200 MHz in terms of the proton resonance frequency, was achieved by employing superconducting windings at cryogenic temperatures [15]. The stronger the magnetic field, the greater the sensitivity and the dispersion of shifts (and the closer the proton spectra come to being first order). Initially man-made polymers were the subjects of study, but more recently biological polymers have been the targets. The last ten years has seen field strengths in common use rise to 11.74 T (equivalent to 500MHz for protons and 125.7 MHz for carbons) by the adoption of superconducting magnets, and similar technical improvements associated with versatile signal transmitter and receiver coil design have also come into common practice. Indeed, 17.5 T instruments have recently been announced. Just as important as these developments in magnet design has been the introduction of pulsed Fourier transform methods, for these permit the performance of new types of experiment by the computerised systems that control the production, acquisition and processing of the experimental data. New pulse sequences increasingly made available by instrument manufacturers within their software suites permit the routine performance of these new experiments: an early example is the distortionless enhancement polarisation transfer, or DEPT, experiment to identify the number of protons attached to a carbon by controlling the final

proton pulse flip angle [16]. A later example is provided by 2-D and 3-D experiments, the introduction of which has made the connectivity of the carbon and protons much clearer [17,18], has much reduced the problem of distinguishing coupling effects from shift effects by providing extra dimensions for displaying the NMR signal, and has even provided an extra structure-discriminating route [19-22]. One development that exploits the storage of data on the computer base for subsequent processing can be optimised for a particular purpose, such as resolution enhancement using the Lorentz-Gaussian transformation technique, in which the free induction decay data is multiplied by the product of a Lorentzian and a Gaussian weighting function prior to the Fourier transformation [23]. Similarly, the computer base has been used for some time to control measurements within the time domain and to provide values for such parameters as T1, the spin-lattice relaxation time, which is sensitive to the motions of the chains, such as those of polysulphones, whose dynamic response is dispersed on opposite sides of the Larmor frequency when made from 1-olefins and 2-olefins [24]. The nuclear Overhauser enhancement (NOE effect) is also sensitive to the motions of the polymer chains, and good practice, when careful quantitative measurements of 13 C signals are required, is to use instrument settings that eliminate the NOE [25], so preventing it from enhancing the signals of certain carbons relative to those of others.

1.2 BRANCHED MOLECULES: POLYETHYLENE AND A POLYESTER SYSTEM We choose to start our discussion of the 13 C chemical shift effects in macromolecules with a mention of the substitution parameter schemes such as those of Grant and Paul [26], which were introduced into polymer spectroscopy by Bovey at an earlier conference in the series [I]. The rule that a carbon's chemical shift increases by a fairly constant increment when a covalently attached hydrogen atom is replaced by a methyl group, the alpha effect, has proved of value when spectral assignments are made. Similar parameters associated with substitution at progressively more remote sites, the beta, gamma and even delta effects, have been established and found to diminish in magnitude (alpha = 11 to 2.5 ppm, beta = 9 to 7ppm, gamma= —2.5ppm, delta = O to 0.5ppm). Although quite precise values are often given [2,3], the values of these parameters are sensitive to the exact structure of the site of supposed structural change, and the best practice utilises model compounds close to the target structures, as in Randal's studies on the side chains of polyethylene [27-29]. A development of this substitution approach, which is appropriate to molecules containing heteroatoms, is to study the effect on chemical shifts of replacing a —CH 2 — group with another atom or group. This has been used to predict shifts in molecules and polymers containing

Figure 1.1 100 MHz 13C NMR spectrum of a high density polyethylene sample in solution at 125 0C. The spectrum shows peaks from end groups (E) and methyl, ethyl and butyl side chains. The sample had been irradiated at 423 K with 300 KGy of gamma rays [32] and shows minor features near 29,32 and 41 ppm from the H structures thus formed —O—, —NH— and —SO 2 — groups, the electronegativity of these groups causing in general a down-field effect. Thus, the shifts of polymers containing heteroatoms may also be predicted from first principles, for assignment purposes, if the shift of the corresponding hydrocarbon is known [30]. For the high density polyethylene spectrum of Figure 1.1, the main feature is the intense signal at 30 ppm from the long runs of methylene units. The shifts of the end groups (marked E 1 , E 2 , E 3 as we move inwards from the methyl signal) are the next feature, but a number of resonances from side chains are present. The methyl group of a butyl side chain coincides with E 1 , but the second methylene group, E 2 , is distinguished at % 23.4 ppm. The methyl groups of a small proportion of ethyl side chains (Etx) and methyl side chains (Me1) are also seen at 20 and 11 ppm respectively. The main chain carbons at the root of and next to the branches are also seen, the assignments for those next to the butyl unit being shown in the first part of Scheme 1. Methyl and ethyl side chains are probably derived from traces of propene and but-1-ene within the ethylene feedstock. The features from these are clear, but are in very small proportions compared with the end group signals for this linear polyethylene.

-CH2-CH2-CH-CH2-CH2CH 2 -CH 2 -CH 2 -CH 3 Bu3 Bu2 Buj Butyl side chains to polyethylene —CH2-CH2-CH-CH2-CH2-CH2-CH2-CH-CH2-CH2H crosslinks

— CH2-CH2-CH-CH2-CH2CH2-CH2-CH2Y links / long branches (1)

Scheme 1 Elementary structure in polyethylenes.

Application to the field of low density polyethylenes was prompted by the need to understand the high proportion of carbons in the form of methyl groups (perhaps as much as 8%), an early result from the IR spectra. The studies led to the recognition of an elaborate branched structure, for the production of which the mechanism of Roedel, backbiting by the propagating radical, was introduced. The normal process produces butyl side chains as a result of a cyclic transition state of five carbons-I-one hydrogen for the intramolecular hydrogen atom abstraction. Ethyl side chains (Et) may have formed by two consecutive backbitings. Randal has characterised low density polyethylene and related copolymers by carbon-13 NMR spectroscopy: complex dendritic structures are revealed by the analysis [30]. Long side chains form also by intermolecular abstractions of hydrogen atoms—chain transfer to polymer. A study of linear low density polymers, the side chains of which, as they derive from a 1-olefin component of known structure and occurrence, are well-defined, allowed the derivation of substitution parameters appropriate to the polyethylene problem itself, gave much security to this approach [27,28], and so led to the full assignment of the methylene carbon shifts dispersed on each side of the main signal at 30.0 ppm from the long runs of methylene groups. More assignments subtle were also found, such as a distinction between the methyl groups at the end of butyl side chains (14.21 ppm) and those at the ends of longer chains (14.01 ppm) [29]. Besides the use of substitution parameters, assignments were also made using special spectrometer settings: APT (attached proton test) and DEPT techniques allow the direct recognition of quaternary carbons, of methylenes and of methyls and methines together [30]. A coherent view of the complex dendritic structure of free radically-produced low density polyethylene is now available. The usual microstructural features of high density polyethylene, alkyl side chains, have also been observed in ultra high molecular weight polyethylene, but in much smaller proportions [31].

A related study has been the elucidation of the crosslink structures induced within polyethylene by high energy radiation. The secondary carbon radicals thus produced by C—H bond scission may diffuse by hydrogen atom abstraction. They have been shown to combine in pairs to form H type junctions, and to create Y type junctions by reactions with the vinyl end groups of the chains and with primary carbon radicals produced by main chain scission. In each case the shifts characteristic of the new structure were identified [32]. The shifts of the H junctions are distinct, being 41.1, 31.9 and 28.7 ppm respectively at the (CH) junction and the first and second linked carbons, as is shown in Scheme 1, but the shifts of the Y junctions coincide with those at the roots of long branches, and their formation is recognised only when a careful comparison has been made of the areas of these shifts before and after irradiation. In a similar area, that of the characterisation of branched and network polyesters from difunctional acids and tri- or tetra-functional alcohols, in systems that were first used about 150 years ago when there was no understanding of their polymeric nature, our studies have found a similar sensitivity in the NMR spectrum [33] within the 55-75 ppm region, where the carbons of the alcohol and ester functions are found; see Scheme 2. The shifts of the carbons of glycerol [33] or erythritol [34] during the progressive conversion of alcohol functions to ester groups by a reaction with succinic anhydride change after each step by a few ppm in a manner that is readily recognised, for the sequence in time and symmetry of substitution of the molecules that form reflects the greater reactivity of the primary alcohol sites. Thus, replacing the —O—H group of an alcohol with an O—H

i

I CH2-CH-CH2-O-H O-SA-OH O—H III CH 2 -CH-CH 2 O—SA-OH O—SA-OH

II CH 2 -CH-CH 2 -O-H O-H O-SA-OH O—H IV CH 2 -CH-CH 2 -O-SA-OH O—SA-OH

O—SA-OH V CH 2 -CH-CH 2 -O-SA-OH

l O — S A - OH Scheme 2 Primary oligomers of glycerol and succinic acid

—O—succinate has at the first, second and third carbons alpha, beta and gamma effects of respectively +2.6, —3.1 and — 0.4 ppm [33]. (These alpha, beta and gamma parameters correspond to the beta, gamma and delta parameters of Grant and Paul [26] because of the intervening oxygen atom.) If the second site of the succinic acid residue subsequently forms an ester, the shifts of the previously linked glycerol residue appear in slightly different places. Thus, a glycerol residue linked 1, 3 within a chain has different shifts from one linked 1, 3 at the end of a chain and from the oligomeric 1,3-discuccinate (III). We have introduced the term III" for such a chain-extending unit and III' for a unit at the end of a branch, the number of primes indicating how many of the second, and more remote, acid groups have reacted. The shifts of the glyceryl residues of the oligomers of Scheme 2 thus provide good guides to the shifts of glyceryl residues at branch points (V), in chain extenders (III and IV) and at chain ends (I and II) in the highly branched or fractal polymers that may be made, thus allowing the assignments of Figure 1.2. The trisuccinate oligomer V can be readily obtained in pure form [33], unlike the other oligomers. It may be polymerised in a single process by heating in a vacuum, where succinic acid is first lost as the anhydride to the vapour phase, and the vacated alcohol site (in a III or IV type residue, for which evidence is present in Figure 1.3) then forms an ester with an acid group of another oligomer. The consequence of this development of linkages is seen in the shifts of each carbon of the glycerol residue, where extra fine structure develops as the molecule evolves towards a dendritic or fractal structure. The initial molecule is a heptamer (XV of Scheme 3 [33]), but others emerge. The shifts are sensitive not only to whether the link at the remote site has formed an ester, but also (in the case of the central carbon) to whether that site was a primary or a secondary alcohol. The shifts of the network node are sensitive to the structure of the immediately

Figure 1.2 13C NMR spectrum at 126 MHz of the mixture of oligomers formed by the reaction of glycerol with succinic anhydride [33]. Only the region of the glycerol residue shifts is shown. The oligomers are identified in Scheme 2; G refers to glycerol

Figure 1.3 13C NMR spectrum at 126MHz of the mixture of oligomers formed by heating oligomer V in a vacuum at 1800C. Parts (a) and (c) for 40 min, part (b) for 20 min, part (d) for 60 min. The labels refer to Scheme 3. The region of the glycerol residue shifts is shown in (a), and for the higher resolution plots (b-d) only the signal from the central methine carbon. The resolution of the latter parts was obtained with zero line broadening. Reproduced with permission from [33] adjacent nodes when the link is succinic acid, but not if glutaric acid is used, for the extra methylene group renders the linkage too remote. In Figure 1.3 the shifts at three early stages may be seen, as the molecules evolve towards a polymeric form of III: peaks z and y 3 we assign to the shifts of the primary and secondary glycerol carbons when the primary carbon is linked to another glycerol residue; peaks yx and y 2 come from a secondary carbon of a glycerol which is linked through a succinic acid residue to respectively a primary and a secondary site of a glycerol residue, as shown in Scheme 3. These distinctions in the fine structure are relatively minor, are best observed with a high field system [33], and assist in the development of the chemistry of the formation of fractal polyesters. Novel liquid crystalline forms, for example, have been produced using such means, the

XV [V'- S A - VT 3 y3 z yi 1 H—O—SA-O—CH 2 -CH-CH 2 -O—SA-O—CH-(—CH 2 -O-SA-OH) 2

XVI

O—SA-OH 3 y3 z H-O-SA-O-CH2-CH-CH2-O-SA

[V-SA-V"- SA-Vl

I HO—SA-O

I O Y2 CH-CH 2 -O-SA-OH zCH2 O

H-O-SA-O-CH 2 -CH-CH 2 -O-SA HO—SA-O

xvn

[V 1 -SA-V] 3 k c* 2 1 H—O—SA-O—CH 2 -CH-CH 2 -O—SA-O—CH-(—CH 2 -O-SA-OH) 2 O—H Scheme 3 Some higher oligomers of glycerol and succinic acid; the numbers are those of ref. [33] mesogenic units being present as pendent groups demonstrably in full complement upon what was a poly(erythntolfractal glutarate [ O — H ] 2 backbone [34].

13 THE MICROSTRUCTURE OF LINEAR CHAINS The first microstructural issue of linear homopolymer chains that we examine is tacticity, which we illustrate with spectra from two systems from our own work: the poly(alkyl cyanoacrylates) [ - C H 2 - C ( C N ) C O O R - ] , which constitute a vinylidene system the spectra of which are shown in Figure 1.4, and the polyalkene sulphides and sulphones: [—CH 2 —CHR—S—] and [—CH 2 — CHR—SO 2 —], spectra of which are shown in Figure 1.5. We show meso or m dyad structures of two of these polymers in Scheme 4. Note how the two chiral centres of the first polymer appear to be equivalent, but for the second polymer the equivalence is less immediately evident, for the residues contain three bonds

Figure 1.4 NMR spectra of poly(ethyl cyanoacrylate) samples. Part (a) has the main chain methylene proton signals at 400 MHz of samples prepared in acetone with sparteine as initiator (A2) and in THF with cinchonidine as initiator (A5). Part (b) shows the 13C spectrum of the side chain methylene carbons of the samples A2 and A5, with triad and pentad assignments [38] (a) C N H CN I I I —C—C—C— C O H CO I (b) I OEf ; OEt

H CH2-CH3 I I -SO2-CH2-C-SO2-CH2-C-SO2CH2-CH3 H

Scheme 4 Meso structures of poly(ethyl cyanoacrylate) and poly(but-l-ene sulphone). The projections have the backbones in a planar ziz-zag, and show the chain from above and in successive residues a particular atom is in turn in the "up" and the "down" position. Triad, tetrad, pentad and longer sequences may be obtained by the successive inclusion of extra residues and may be recognised by NMR. The stereochemical structure of these longer sequences are described in terms of the m or r relationships of the successive pairs of chiral centres [2,3]. In the case

ppm

ppm

Figure 1.5 13C NMR spectra of the backbone methylene carbons of (a) a tactic poly(but-l-ene sulphide), (b) of the tactic poly(but-l-ene sulphone) made from it by oxidation, and (c) of an atactic polysulphone. The dispersion of shifts of the sulphone polymer is greater because of the gamma-gfaucfie effect of the oxygens. The small peak at 6 = 49.2 ppm is from H — H sequence.

of the first polymer the residues, as they have just two backbone carbons, are sensitive to influences equally from each direction along the chain, and mr and rm heterotactic sequences are identical as far as the signals from carbons at or pendent to the central chiral centre are concerned. At high resolution the influence of the next two chiral centres may be expressed, so we may be able to distinguish the rmrr and mmrr pentads. For the polysulphides and polysulphones the residues have three components, so that the influence upon chemical shifts of one residue that derives from the chiral centres of the two neighbouring residues is diflferent, and depends upon the direction: thus, an mr sequence will not for symmetry reasons have the same shifts as an rm sequence. (The mechanism that generates shift multiplicity depends upon fine differences in bond rotation populations for different chiral sequences that are coupled to the gamma-^auc/ie interactions, as Tonelli describes elsewhere [8]). As in the related olefin oxide and styrene oxide polymers [34,35], the residues of the polysulphide predominantly orientate in only one direction, so that head to head junctions are also encountered, and provide minor features in the spectrum, as we indicate in Figure 1.5. This type of enchainment has been termed positional isomerism, orienticity [3] or regioselectivity, the last term being used below for ring-opening metathesis polymerisation (ROMP) systems. Another consequence of the presence of three distinct groups in each residue of the linear backbone is the possibility of optical activity, a property that independently permits recognition of isotacticity [37]. We first discuss the spectra of poly(ethyl cyanoacrylate), proton spectra being shown in Figure 1.4(a) and the corresponding 13 C spectra in Figure 1.4(b) [38]. We use the classical route, first used by Bovey and Tiers for poly(methylmethacrylate) [2,7], PMMA, for determining the type of tacticity that predominates. They recognised the four-line pattern of an AB quartet in the 60 MHz spectrum of a predominantly isotactic polymer in the signal from the main chain methylene protons within a meso dyad—this was distinctly different from the single line from the methylene protons of a racemic dyad that was found in a polymer produced by a different mechanism (the absence of an effect from the coupling constant deriving from the equivalence of the two protons). For our assignment two polymers were available, poly(ethyl cyanoacrylate)s that had been made in different solvents and with different chiral initiators for the anionic polymerization process (it transpired that the solvent was the important factor). In contrast to the case with PMMA, an AB quartet was not immediately apparent in the proton NMR spectrum, and a pair of clear lines (a and b in Figure 1.4(a)) considered for part of such a system was found to be unsuitable: the splitting between the lines was not —14 Hz (the value of a geminal coupling) nor were there signals nearby at that splitting. Moreover, their relative intensities changed in a simple manner with the value of the tacticity parameter deduced from the 13 C NMR spectrum. They were thus assigned to rrr and rrm fine structure, and these assignments were confirmed by checking their relative

intensities with values predicted with the aid of a single (Bernoullian) tacticity parameter obtained from the side chain methylene carbon spectrum. Discrepancies between the Bernoullian and the experimental intensities were of the order of 2% within both proton and carbon spectra. The direct recognition of an AB quartet in spectra such as those of Figure 1.4(a) was prevented by partial overlap of m dyad signals dispersed by tetrad effects and a coincidence with the remaining r-centred tetrad, as a two-dimensional experiment has subsequently made clear [39]. The main components of the AB structure lie near 2.6 and 2.8 ppm. In the carbon spectrum pentad effects were resolved within the rr-centred triad of the side chain methylene carbons (Figure 1.4(b)). The two peaks of the mr-centred triad may be assigned as indicated in the figure to mrmm and (mrmr + rrmm) sequences, of expected relative intensities of 0.100 and 0.096 respectively of A2; the remaining sequence rrmr, of Bernoullian intensity 0.02, is apparently not resolved in the signal. This set of pentads may be more readily recognised on the basis of more clearly different line intensities in the spectrum of A5. They and the other peaks were assigned, once the chains were recognised as being predominantly isotactic, on the manner in which their intensities varied with the value of P1-, a practice which is widely adopted when samples of different tacticities are available. In the case of polyacrylonitrile [—CH 2 —CH(CN)—], which gives an atactic polymer when the free radical reaction is performed in solution, enhancement of the tacticity to Pf values as high as 0.70-0.87 has been provided by performing a polymerisation when the monomers were constrained, or lined up, within a urea canal complex. This allows the development within the 13 C NMR spectrum of intense peaks from certain heptads [12], the emphasis providing clear indication of the origin of the signals from sequences of high isotactic content. The fine structure of the 13 C NMR signals from the methyl groups of polypropylene displays pentad and partial heptad fine structure, for the assignment of which a number of methods were adopted, depending mainly upon the availability of polymers of known tacticity, as their crystal structures had previously been determined, but also using 13C-labelled model compounds of known stereo sequence content [40]. Highly isotactic polystyrene has been produced using a titanium trichloride-derived catalyst [41]. Once such a material is available the spectra may give an insight into the manner in which the process behaves: a catalyst for isotactic polypropylene sometimes allows errors in stereochemistry, but these are immediately corrected, as the presence of mrrm but not mrmm pentads testifies [2]. Such interesting evidence on the manner in which a catalyst functions helps us to understand the mechanism; we conclude this review with an account of such effects discovered in our studies of ring-opening metathesis polymerisation, or ROMP, which likewise use metal-centred catalysts. The Bernoullian nature of the free radical or ionic propagation in a polymer may be ascertained from the relative intensities of the rr, mr -I- rm, and mm components of the triad fine structure, as in our studies of the side chain

methylene group in poly(ethyl cyanoacrylate)s. Provided that each new chiral centre forms in a manner that depends only upon the type of the previous chiral centre, so that only one statistical parameter is involved for dyad occurrences, the weights of the triads are respectively [2,3] (1 - F1)2,2P1(I - P1) and (P,)2. Using in turn (from left to right) the first two areas, the second two, and then the first and third of each part of Figure 1.4(b), we solve for P1 to obtain 0.63,0.72 and 0.68 for sample A2, values which are hardly significantly different from each other; and for sample A5 we have correspondingly 0.52, 0.60 and 0.56, which are close. A test for Markov behaviour is provided by the relationships involving two parameters [2, 3]: JV/m) = « = (nn)/(2(m)) = (mr)/(2(mm) + (mr)) and P(m/r) = w = (rm)/(2(r)) = (mr)/(2(rr) + (mr)), where P(r/m) is the probability that an r dyad will follow an m dyad. Markov behaviour has u + w < 1.00. For the cyanoacrylate spectra of Figure 1.4(b) the values of u and w are respectively 0.28 and 0.66 for polymer A2 and 0.46 and 0.54 for polymer A5, indicating that both polymerisations are close to Bernoullian. Sample A2, which deviates more from the ideal was made using as initiator sparteine. As this compound is a dinitrogen base, it may enhance the formation of a complex between the oppositely charged initiator and the propagating ends of the chain in a zwitterion. A clear case of Markov behaviour is given below. The statistical index P = 4IS/H2 = (4(mm)(rr)/(mr)2] has been used to characterise the isotactic acrylonitrile polymers prepared within the canal complexes [12]. Two distinct mechanisms were identified from the dependence of this index upon the isotactic content, a much stronger dependence being found for the polymers produced at low temperatures after irradiation than for those produced during irradiation at a moderately low temperature, for which canal coherence might have been upset by the evolution of heat and the irradiation itself. The second aspect of linear polymers from our own field may be considered as a whole, for polysulphones may be obtained by oxidation of polysulphides as well as by the free radical copolymerisation of SO 2 with an olefin. Indeed, this chemical change is beneficial to the spectroscopy, for fine structure develops as a result of oxidation, as may be seen in Figure 1.5, where the shifts, each at 500 MHz, of the methylene carbons of an isotactic polysulphide and the polysulphone prepared from it are displayed in parts (a) and (b) respectively. As discussed elsewhere [2, 5, 8], fine structure may be the consequence of gamma-grawc/ie interactions weighted according to the occupancy of the intervening bond conformational states. In this case the fine structure undoubtedly develops a larger dispersion and becomes more sensitive to the stereochemistry because we have introduced oxygens gamma with respect to each main chain carbon; such oxygens may cause a shift effect as large as — 9.4 ppm, the particular value

depending upon the conformation adopted by the intervening C—S bond [30,42]. Poly(l-olefin sulphone)s have been found to be atactic when made from the monomers by the free radical reaction; when first observed the backbone carbons showed incipient or clear triad fine structure [41,42]. The first carbon of the side chain displays dyad stereochemical sensitivity at low resolution, the upfield half of the signal being assigned to an m dyad when a comparison was made with an isotactic poly(propylene sulphone) made by oxidising an isotactic polysulphide [41]. The poly(but-l-ene sulphone)s prepared by free radical means showed similar spectra of the main chain methine when examined at high field (Figure 1.5(c)), showing clearly mm, mr + rm, and rr triads, as labelled by comparison with the other spectrum, that of the optically active polymer prepared from a polysulphide. The test on the Markov nature finds M = 0.51 (±0.01) and w = 0.480 (±0.005), giving u + w = 0.99 (±0.01), so the free radical polymerisation process was clearly Bernoullian. For the polymer prepared by oxidation of the polysulphide the parameters are w = 0.25 (±0.01) and w = 0.51 (±0.01), giving M + W = 0.76 (±0.02) and indicating the Markov nature of the polymerisation process the polysulphide precursor had experienced. (From the spectrum of the polysulphide itself we were able to obtain only one parameter, P1 = 0.66, a number very close to w/(u + w) = 0.67, as expected.) It may well be that the polysulphide formation was not Bernoullian, for the catalyst used was an optically active zinc-centred species that favoured the R enantiomer of the sulphide, and the monomer itself contained an excess of the S enantiomer [44]. A second feature in the spectrum reflecting the polysulphide formation mechanism is the presence of three minor features near 49.2 ppm in Figure 1.5(b) that we associate with head to head structures. During propagation, the sulphide anion at the end of the chain may occasionally attack the methine carbon site as well as the methylene carbon site in the monomer, and this remains when the polysulphone is prepared. We note that the heterotactic triads signal of Figure 1.5(c) has more than three components, consistent with the mr and the rm heterotactic sequences being distinguishable; as the relative intensities of the four not quite resolved lines for the atactic polymer of Figure 1.5(c) are roughly in the proportion of 1:2:3:2, and the four heterotactic-centred sequences mmrm, mmrr, rrmm and rrmr would be expected to have similar proportions (as Pr = P1n) = 0.5), one of these pentads must be sensitive to an extra chiral centre. Our most recent work in this area has shown that tactic main chains may be obtained in a free radical reaction if the 1-olefin bears a chiral centre of a particular type (K 6r S) at the site next to the olefin group: the carbon NMR spectrum then displays from each atom within or close to the backbone widely spaced pairs of peaks, the relative intensity within each pair being 6:4 or 7:3. This reflects within a residue a preferred relationship of the two chiral centres [45], the one initially present within the olefin and the second created by the addition reaction.

1.4 THE PARTICIPATION OF A CHARGE-TRANSFER COMPLEX IN A FREE RADICAL POLYMERIZATION REACTION A long-standing issue in the formation of alternating copolymers, such as are found when electron-rich and electron-deficient monomers polymerise by free radical means, has been the question of the role of the charge-transfer complex in the polymerisation mechanism. For poly(olefin sulphone) feeds, many experimental techniques have demonstrated that the complex is present, but is the complex incidental or is it the reacting species? One possibility is that each type of radical may react only with the other type of monomer; a second is that the charge-transfer adduct itself is the only reacting species [46]. In Scheme 5 below these two possibilities are shown respectively as the vertical (c + d) and the horizontal (a) propagation reaction paths. The rate-determining step for polymerisation is apparently the reaction of an electron-deficient radical, presumably a sulphonyl radical, with an electron-rich monomer, presumably either an olefin (d) or the olefin part of a charge-transfer complex (a), for substitution to the olefin group enhances the rate. AU the reactions are written as reversible in Scheme 5: there is a wealth of experimental evidence in support of this, for example, the olefins are known to isomerise at temperatures above and below the ceiling temperature for polymer formation, and the ESR spectrum of the radicals present indicates that this may be both C-based and S-based. P-SO2-C-C* SO2

JcSo 2

P-SO/ + C=C - = - P-SO2-C-C-SO* e dC=C

P-SO2-C-C" Scheme 5 The free radical formation of poly(but-2-ene sulphone) through chargetransfer complex reaction (horizontal route) or successive monomer addition (descending route) If the precise alternation in the chain residues is the only criterion, there is no way of distinguishing between the two mechanisms. However, the stereochemistry of the but-2-ene sulphone residues and their relationship to the cis or trans nature of the olefin does provide a guide [43,46]. Broadly speaking, two methyl shifts are encountered: at high temperatures, whichever olefin is used, there is a single shift at « 9 ppm, but at low temperatures, if the trans but not the cis olefin

Figure 1.6 13C NMR spectra at 101 MHz of the methyl groups of s/B three samples of poly(but-2-ene sulphone) recorded in DMSO-J6 at 70 0C. The samples SCH/7, U27 and U23 were prepared at - 95 0C, - 63 0C and - 84 0C respectively, the last from the cis olefin and the first two from the trans olefin. Lowering the temperature has increased the intensity of the signal at 13 ppm from the meso residues obtained from the trans olefin, but the signal from the polymer made from the cis olefin at an intermediate temperature shows a much greater proportion of the racemic residues, with their methyl shift at 9 ppm [46]

is used, there is a new peak at 13ppm; see Figure 1.6 for three examples. The assignment of the order of the methyl carbon shifts to meso or to racemic but-2-ene residues is not straightforward; since a gamma-gauche effect from the oxygen atom of the sulphone group (9.4 ppm) may well be larger than the gamma-gauche effect from a methyl group (6.4 ppm), the shift distinction may be associated with the conformations of the C—S bonds, rather than with that of the C—C bond as we first assumed [42]. We now make the assignment of the meso and racemic structures on the basis of the similarity of the order of the shifts in the polymers to models of known structure. The molecule alpha-2,3-bis(isopropylsulphonyl) butane has the structure shown in Figure 1.7(a), according to X-ray measurements, making it the centrosymmetric meso form [46]. The central unit corresponds exactly to a residue of a poly(but-2-ene sulphone) chain that is flanked by structures corresponding to a little over half the alkane component of the next residue. The carbon shift of the central methyls is at 13.7 ppm, compared with 10.0 ppm for the corresponding shift in the racemic molecule, shift differences that are found in the polymers, too. (The IR spectra show similar correspondences [46]). The fact that at low temperatures the trans olefin converts to polymer with partial retention of the configuration of the two prochiral centres

T/C

Figure 1.7 (a) The model bis(isopropylsulphonyl) butane in the crystal [46], showing its centrosymmetry and meso characteristic of the central portion; (b) plots of meso residue content against temperature of preparation for the series of poly(but-2-ene sulphone)s prepared from cis and trans olefin, curves (i) and (ii) respectively. That there are two distinct curves indicates that the charge-transfer complex is a significant reacting species. The solid symbols record the results from the spectra of Figure 1.6

on the olefin-CT complex and that the cis olefin converts similarly suggests that the reaction does proceed along path a of Scheme 5 at these low temperatures, when large proportions of the charge-transfer complex are present. At the higher temperatures the polymer and the monomer structures are not related, both yielding mainly racemic residues, consistent with alkyl radicals being present long enough during the polymerisation for radical inversions to eliminate the memory of the initial structure. Chain microstructure therefore indicates that the complex is a reacting species at low temperatures. We cannot tell whether the complex exclusively reacts, and the sulphonyl radical partly dissociates (path b), or whether paths a and c are alternatives, a being becoming favoured as the temperature is lowered, to some extent reflecting the greater stability of the charge-transfer complex. The rise in meso content when cis olefin is the precursor probably indicates that path c is used even at low temperatures, and that then the radical intermediate favours less a mode of reaction that yields the racemic type of product.

1.5 THE POLYMERISATION OF DIENES The manner in which dienes become entrained within polymer chains depends upon a number of factors, such as the type of mechanism (free radical, ionic or coordination), the nature of the diene itself, and whether other monomers are involved. If one double bond reacts, a chiral centre is formed and the polymers may be tactic, if 1,4-addition (or 4,1-addition) takes place the main chain incorporates a double bond whose cis or trans nature may be important in determining properties such as the glass transition temperature, and the reaction of a second double bond can cause crosslinks. The case of polychloroprene has been described by Ebdon [47], where proton shifts are sufficient to detect head to tail (2.35 ppm), head to head (2.5 ppm) and tail to tail (2.2 ppm) enchainments of this unsymmetrical monomer [47]. For poly(butadiene)s, sequence triads involving three different types of residue—cis and trans 1,4-residues within the main chain and 1,2-residues involving pendent vinyl groups—may be distinguished even with a 270 MHz spectrometer in the region of the spectrum between 127 and 133 ppm, where are found the resonances of the 1,4-residues (see Table 1.1 and Figure 1.8). The assignments were obtained using a number of polymers of distinctly different but recognisable microstructure. When the spectrum is obtained under conditions that avoid NOE enhancement of signal intensity, and long delays between pulses reduce systematic errors in signal proportions, from this region and that of the pendent vinyl groups (at 114 and 143 ppm) compositions accurate to better than 1% may be claimed [25]. In this study of polybutadiene rubbers, when three different methods were compared, it was found that the microstructures as determined by the Raman and 13 C NMR methods

Table 1.1 Triad sequences within the main chain olefinic region of the carbon-13 NMR spectrum of poly(butadiene)s [25]. Reproduced from [25] with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidiington OX5 IGB, UK Carbon Atom Peak No. Triad assignment Shift (ppm) -C=C*I vtv 13L8 2 ctv, ttv 131.4 3 we 130.7 4 ctv, ttv 130.6 5 ccv, tcv 130.2 6 ctc,ctt 130.2 7 vcc, vet 130.1 8 ttc, ttt 130.1 —*C=C— 9 ctv, ttv 129.9 10 ccc, tec 129.7 11 cct, tct 129.5 12 ctv, ttv 129.3 13 vtc 128.5 14 vtt 128.4 15 vtc 128.2 16 vcc 128.1 17 vet 127.9 18 vcv 127.8 *Note: v = vinyl, c =* cis, t = trans.

were in good agreement but that the IR method was much less consistent [25], as peaks were not very distinct and extinction coefficients were too variable. We illustrate the reactions of dienes by our studies on furans as monomers in free radical copolymerisations with acrylonitrile (AN), work undertaken to develop the polymer chemistry of materials that may be obtained from renewable resources. We have found that a variety of structures may be entrained within a polyacrylonitrile chain; to some extent their proportions depend upon the presence and the nature of substituents at the position alpha to the furan ring [48-50]. Only furan, the least aromatic of the heterocycles, seems to behave in this way. The five-membered furan ring remains intact. The differentiation of structures of types I and II was performed on the basis of the shifts of model compounds obtained by reacting furan and methylfuran with the 2-cyanopropyl radicals from decomposing 2,2'-azobis(isobutyronitrile), AIBN. The carbon shifts of the polymer residues were consistent with attack at the alpha or C 2 position of furan and at the C 5 position of methylfuran by the acrylonitrile radical. The furan radical that forms then propagates in the manner of a diene either through the more remote alpha position or through the adjacent beta position. A minor proportion of I residues from methylfuran in which the polymer AN radical had attached to the C 2 were also detected from the appearance of minor shifts at 130 ppm (see Figure 1.9) from the beta carbons,

Figure 1.8 13 C NMR spectrum of an anionically prepared polybutadiene at 25 0 C in CDCl 3 at 60 MHz. The labels correspond to the peak numbers and triad sequences of Table 1.1. In this study [25] extreme care was taken in obtaining quantitative information: avoidance of the nuclear overhauser enhancement was achieved by decoupling only during the signal acquisition; pulse angle 90°, 40000 scans, 33 s pulse delay. Reproduced from [25] with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington OX5 IGB, UK shifts that reflect the different arrangement in this residue of the methyl and nearest nitrile groups. The appearance at this place of the olefinic shifts is readily rationalised in terms of a beta effect of 3.7 ppm and a gamma effect from the nitrile group of —5.5 ppm. Other peaks were found in both proton and 13C spectra in the region below the shifts from the acrylonitrile residues, and other possible structures were sought,

i

H

in

iv

v

vi

Scheme 6 The structures of five residues derived from furan in acrylonitrile (AN) copoiymers, and the methylfuran radical

Figure 1.9 13C NMR spectra of the low field region of (a) a dimethylfuran copolymer, (b) a methylfuran copolymer, and (c) a furan copolymer. Assignments of the nitrile carbon of the AN residues, of the olefinic carbons of the furan residues and of the bridgehead and other carbons next to an oxygen are indicated but a certain proof of a third type of structure was more elusive. The characteristic feature was a proton shift at « 3.9 ppm [49], a position appropriate to a proton on an ether carbon, and olefinic protons were thought to be lacking. We present a relevant set of reactions in Scheme 7. It was eventually recognised [49] that the addition of an excess of the furan monomer, which promoted II-AN-furan sequences, had the effect of reducing the proportion of the unknown furan residue, presumably by preventing the participation of the II structures in a second reaction (d) to give a structure of type III. Once ~ II-AN-AN' radicals were reduced in proportion by this means, the signals from the II structures became clearly enhanced in the spectrum, as route (a) was then taken. This

Scheme 7 Possible reactions of a II structure in a second manner during the acrylonitrile copolymerisation [49] revealed the origin of the previously obscure third structure. A proof of the entrainment of AN-furan Diels-Alder products was made by observation of the shifts of the residues formed by a direct copolymerisation involving an endo adduct of furan and a mixture of endo and exo adducts: the carbon and the proton spectra together indicated that both adducts can become entrained within an acrylonitrile chain [48] to yield a structure of type IV, with carbon shifts at 80ppm from the bridgehead sites and corresponding proton shifts at about 4.7 ppm. A careful inspection of the region near 130 ppm in the spectrum of each polymer (Figure 1.9) reveals that each carbon of the I residues has two shifts, a feature that we attributed to the influence of the chirality of the nearest —CHCN— chiral centre. No feature that we could associate with the cis or trans junctions to the ring were identified, although for the I residues, if not the II residues, the structural variation seemed possible. Inspection of the spectra at a higher field strength found a further set of peaks whose intensities increased as the furan content rose from « 5 to 25% of the residues. This was attributed to a small sequence effect. In an effort to clarify the sequence fine structure, both of the various furan residues and of the acrylonitrile residue signals un-field, we added Lewis acids in the hope of causing alternation of the residues by enhancing the electron deficiency of the acrylonitrile radical through a coordination to the nitrile group. When the polymerisation was performed in the presence of a mild Lewis acid such

as ZnCl2, it was found instead that, although the yields were enhanced by an order of magnitude, the furan proportion was increased only a little, but the pattern of the predominant II structures became modified considerably [50]. For the 2-methylfuran systems, the shift of the 5-proton was diminished relative to the shifts of the other furan protons. The search for their new position in the spectrum, to provide structural evidence for the effect of the Lewis acid upon the reaction mode, was performed with deuterium NMR spectroscopy, the methylfuran monomer having been deuterated at the single alpha position. In reactions leaving a furan ring from radicals of structure V at the end of chains, the deuteriums were found to have transferred from the furan radical to the Lewis acid-activated monomer (creating D—CH 2 —CHCN ~ , shift at 1.5 ppm) and to acrylonitrile radicals (creating ~CH 2 —CHDCN, 2.2 ppm). This latter group was also identified at 14.3 ppm in the 13 C NMR spectrum, where it was particularly prominent if an independent source of hydrogen atoms, in the form of a chain-transfer agent, had been added [48]. Despite the transfer reaction and the disproportionation promoted by the Lewis acids, processes which would be expected to lower molecular weights, yields of the free radical reaction were greatly enhanced and gels were produced, presumably through a crosslinking second reaction of II residues, and the proton NMR signals consequently became broader [50]. Isotopic enhancement may be also illustrated by Bevington et al.'s exploration of the use of the*3C-enriched free radical initiators l,l'-azobis(phenylethane) and AIBN in preparing butadiene polymers [51] and the use of dimethyl 2,2'azobis(isobutyrate) to initiate the polymerisations of styrene, acrylonitrile, methyl methacrylate and methyl acrylate [52]. The signals from the ends are thus rendered more intense, and become observable in a standard 13 C NMR spectrum, where they display information on the manner in which the initiator radicals have attacked the first monomer to become incorporated at the start of the polymer chain: one can thus compare initial and mean tacticities. In a further use of isotope enrichment, Moad and Willing found that selective 13 C enrichment of one monomer together with carbon-13-proton correlation NMR spectroscopy allowed the separation of tacticity and sequence effects; they used this approach for studying copolymers of butyl methacrylate with methyl methacrylate [53].

1.6 RING-OPENING-METATHESIS POLYMERISATIONS Polymers formed by the ring-opening metathesis polymerisation (ROMP) reaction [54] exhibit a wide variety of microstructures which may be evaluated by specctroscopic techniques. The first ROMP polymers were analysed by IR spectroscopy [55], but that can only determine the absolute stereochemistry of

the double bonds in the polmer, and provides no information on the sequences in which such microstructural variations might occur. This limitation is largely overcome by 13 C NMR spectroscopy, where sensitivity to change in substitution and stereochemistry up to six carbon atoms remote from the particular carbon under observation is regularly seen [54], In the remaining part of this article we deal almost exclusively with polymers formed from the bicyclic olefins norbornene, norbornadiene and their derivatives, but will also discuss some work with oxygen-containing analogues, thus providing a comprehensive range of different microstructural types. These monomers have a substantial ring strain, so they are good candidates for ROMP.

P * polymer chain

Scheme 8 The ROMP reaction of Scheme 8 is catalysed by metallacarbenes [54] that have been formed from a wide variety of transition metal salts, often but not exclusively in the presence of an organometallic co-catalyst in systems similar to the industrially important Ziegler-Natta catalysts. In addition, there are now many examples of metathesis of both cyclic and acyclic olefins using well-defined metal carbene complexes [56]. In the former systems, which are considered here, the metallacarbene catalyst is formed from the various catalyst components and is very active, the concentration of active sites being extremely low but each site having a very high turnover number [57]. As a result, observation of the working catalyst by any spectroscopic or other means is not possible. We view the polymers, with their different microstructural features, as a "tape recording" of events at the catalyst site which may be "read" through the medium of 1 3 C NMR spectroscopy. For highly strained monomers these events are the primary ones up to high conversion. One may, by careful choice of monomer, study the potential of different catalysts to behave in a stereoselective or regioselective manner. Thus, with a symmetrical monomer such as norbornene [58], norbornadiene [59] or their 5,6 [60] or 7-substituted derivatives [61,62] we have obtained polymers with a variety of cis main chain double bond contents and distributions. In a number of the 7-substituted examples, fine structure on certain 13 C NMR resonances is observed which is attributable to tacticity effects. Conversely, one may use the unsymmetrical monomers such as 1-substituted derivatives [63] and delineate the propensity of the different catalysts to regioselectivity, which manifests itself as head-tail bias in the polymer.

In the case of these substituted derivatives, the polymers formed with most catalyst systems exhibit fine structure in the spectra due to each of the possible microstructural variations, leading to very complex spectra. We have made very extensive use of chain transfer to acyclic olefin to obtain lower molecular weights, and consequent line narrowing in the spectra of the polymers, to optimise resolution. Also, certain of the catalysts at our disposal may behave in a very stereospecific and regiospecific manner, allowing one to pinpoint certain lines in more complex spectra. These techniques, combined with the excellent resolving power and sensitivity of modern high field NMR instruments, have allowed complete and unambiguous assignment of most spectra.

1.6.1 STEREOSELECTIVITYINROMP There are two basic types of stereoselectivity observed in the ROMP of cyclic olefins, both of which may be observed in the 13 C NMR spectra of the polymers. The double bonds which form part of the main chain may be either cis or trans, and in the case of the prochiral monomers norbornene, norbornadiene, their symmetrically substituted derivatives and their chiral unsymmetrically substituted derivatives the residues may be enchained in such a way as to yield tactic or, more commonly, atactic polymers [54]. A representation of atactic poly(norbornene) is shown in Scheme 9, where cis and trans double bonds are associated with r or m dyad units respectively.

Scheme 9 Thus polymers with a given cis double bond content may be prepared with an appropriate catalyst, as is shown in Table 1.2. Resonances from the various olefinic and cyclopentane ring carbon atoms are observed and fine structure due to the effect of two or three neighbouring double bonds is resolved, Figure 1.10. One of the earliest observations to be made from these spectra was that the relative line intensities of the various cc, ct, tt and tc (etc.) resonances indicated that the distribution of cis and trans double bonds was non-random, and that there was an increasing tendency towards a blocky cis distribution as the cis double bond content of the polymer increased [58]. An explanation was suggested, based upon chain propagation involving different metallacarbenes which had been distinguished in terms of the stereochemistry of the last-formed double

Table 1.2

Fraction of cis double bonds in ring-opened polymers of norbornene, norbornadiene and derivatives obtained with different catalysts Catalyst

Monomer

RuCl3

MoCl 5 /Bu 4 Sn

OsCl3

WCl6/Me4Sn

ReCl5

Ref.

0.05

-

0.50

0.55

1.00

[54]

0.00

-

0.15

0.55

0.95

[61]

0.10

-

-

0.55

0.95

[60]

0.37

0.90

0.51

0.82

[59]

0.20

0.97

0.42

1.00

-

0.36

0.73

1.00

[66]

0.10

-

0.39

-

1.00

[66]

0.00

0.31

0.10

0.75

1.00

[63]

0.05

0.11

0.30

0.70

1.00

[65]

- [62]

bonds. In essence this theory emphasised the importance of steric effects at the catalyst site. Blocks of cis double bonds are obtained by propagation through a species P c (see Scheme 10) where the last-formed double bond is cis and where the next monomer unit reacts with the metallacarbene while the previously

Figure 1.10 * 3C NMR spectrum of poly(norbornene) with %60% cis, randomly distributed, main chain bonds

Scheme 10 formed cis double bond is still in the coordination sphere of the metal. The steric constraint thus imposed aligns the incoming monomer unit in a cis orientation, leading to the formation of another cis double bond. The kinetically distinct Pt species is believed to be too bulky sterically to be a chain carrier at all, and it relaxes to a species P in which the last-formed double bond has left the coordination sphere of the metal; the monomer has then the opportunity to react in either a cis or a trans orientation, with the trans orientation preferred on steric grounds. This phenomenon is also observed in the case of the stereospecific metathesis of acyclic olefins [68], where, in the pre-equilibrium stage of the reaction, cis products are often formed from cis substrates and trans from trans. Inspection of Table 1.2 shows that the cis content of polymers formed from bidentate chelating olefins is significantly higher than that observed with the mono-olefin analogue. The highly stereospecific and rather unreactive RuCl3 catalyst exhibits extreme behaviour, as it is highly trans-directing with norbornene, and incidentally with many other mono-olefin derivatives, but highly cis directing when using endodicyclopentadiene as monomer [66]. It is significant that the catalytically active residual solution from RuCl3/endo-dicyclopentadiene polymerisation also produces high cis polymers with norbornene derivatives, and that exo-dicyclopentadiene gives the "normal" high trans polymer. The link between steric crowding of the catalyst site and cis stereospecificity is therefore well established, both by ourselves [66] and by others [69].

1.6.2 DISTRIBUTION OF trans DOUBLE BONDS IN HIGH cis POLY(NORBORNENE) The NMR spectra of both the cyclopentane ring and the olefinic carbon atoms in poly(norbornene) are sensitive to the stereochemistry of the neighbouring double bonds and, as seen above, this leads to cc/ct; tt/tc doublets for the cyclopentane ring carbon atoms. There is, however, the possibility of quartet fine structure for both cis and trans olefinic carbon resonances, owing to the inequivalence of the carbon atoms in a given double bond [64], as in Scheme 11. CH=CH

m t/c

uc * crt

Cft

c/c

Scheme 11 In the spectrum of a poly(norbornene) of intermediate cis content, Figure 1.10, this fine structure is well resolved for the cis resonance, but overlapp of the etc and the ttt components occurs in the trans resonance. In high cis polymer two different types of non-random trans double bond distribution have been observed. Figure 1.11 shows the spectra of two polymers, one prepared using ReCl5, Figure 1.1 l(a), and the other using OsCl3, Figure 1.1 l(b) in the presence of benzoquinone, another chelating ligand which imposes a high a s directive effect [7O]. In these high cis polymers one would expect, statistically, that trans double bonds would almost always be flanked by cis double bonds, leading to high tc/tt ratios for the cyclopentane ring carbon atoms and a strong etc signal for the olefinic trans resonance. In fact, inspection of Figure l.ll(a) shows that the reverse is the case for the ReCl5-catalysed polymer; here the various ct and tt lines are of approximately equal intensity, and the centre component of the trans olefinic resonance which arises from isolated trans, etc, or blocks of trans, ttt, has become only a shoulder on the ttc line. This means that trans double bonds tend to occur in pairs in these predominantly cis chains. Mechanistically, this can be seen as a chain error repair process, where the aberrant formation of the first trans double bond is corrected by the formation of a second before resumption of cis double bond formation. An analogous phenomenon has been observed in the largely isotactic polymerisation of certain alpha-olefins [2], where 13 C NMR spectroscopy has shown that the small proportions of syndiotactic (r) junctions that occur are found in pairs, as evidenced by the relatively intense rmmr and mmrr pentad signals. Here the catalyst site, which normally selects the same prochiral face of the monomer in each cycle, occasionally reacts at the other face, leading to an aberrant r junction. Choice of the original prochiral face in the next

catalytic cycle results in the continuous formation of isotactic polymer: this mechanism is marked by the presence of pairs of syndiotactic (r) junctions. Alternatively the catalyst, having chosen a different prochiral face, continues to do so. The result is the formation of a polymer containing isotactic blocks joined by single syndiotactic (r) junctions, i.e. the initial error is propagated, and is visible in the 13 C NMR spectrum as the occurrence of mrmm and mmrm pentads. Here again an analogous situation exists in some ROMP's of norbornene and derivatives, and is seen in the polymerisation of norbornene using the benzoquinonemodified OsCl3 catalyst, Figure 1.1 l(b). In this case, and in contrast to the ReCl5 polymer of Figure 1.1 l(a), the various tt lines are three to four times as intense as the tc lines, with a concomitant increase in the intensity of what must be the ttt component over the ttc and ctt lines in the olefinic trans resonance. This indicates that the small percentage of trans double bonds occur in tn blocks (n > 2). The same phenomenon is observed in polymers formed from 1-methylnorbornene [63], Figure 1.12. At the cis junction in these high cis polymers, monomer addition occurs in a head-tail manner (see below) but the small proportion of trans junctions shows no bias. However, it may be clearly seen that in the polymer formed using the WCl 6 /Me 4 Sn catalyst, Figure 1.12(a), trans double bonds tend to occur in pairs, as evidenced by the low intensity ttt/ctc signals, whereas in the polymers formed from the OsCl3 catalyst, Figure 1.12(b), there is a tendency to form blocks. If there is propagation through metallacarbenes of octahedral symmetry with a vacant alternating ligand position such as described above, these species may be chiral, with the formation of tactic polymer. Furthermore, cis double bond formation will be associated with syndiotactic junctions and trans double bonds with isotactic junctions, as in Scheme 12. If, however, the catalyst site is achiral, or

Scheme 12 chiral but undergoing racemisation faster that propagation, then atactic polymer will result, and r or m dyads may be associated with either cis or trans double bond [67]. Initially (see below) with poly(norbornene) no fine structure was observed, which could be attributed to this tacticity effect, but it was realised that polymerisation using one enantiomeric form of a chiral norbornene derivative (Scheme 13) would translate the tacticity effect into a bias toward head-head (HH) and tail-tail (TT) addition for syndiotactic polymers, and head-tail (HT) addition for isotactic polymers [65].

fa)

ppm

(b)

ppm Figure 1.11 13C NMR spectra of high cis poly(norbornene): (a) 90% cis prepared using ReCl5 catalyst, and (b) 93% cis prepared using a modified OsCl3 catalyst

ROMP

Scheme 13

(a)

(b) 13

Figure 1.12 Olefinic region of the C NMR spectrum of poly(l-methylnorboraene) formed with (a) the WCi 6 /Me 4 Sn catalyst and (b) the OsCl 3 catalyst: (a) Reproduced by permission of Huthig & Wepf Verlag from [63]

This analysis was made possible because the chemical shifts of the various olefinic carbon double bonds in these unsymmetrically substituted norbornene derivatives are very sensitive to whether they are in an HH, TT or HT/TH unit, as can be seen for the case of poly(l-methylnorbornene) [63] in Figure 1.12. It was therefore possible to examine a range of metathesis catalysts for their ability to produce tactic polymers. In fact, a range of tacticities was observed, with extremes in behaviour being represented by the ReCl5 catalyst, which produced an all-ds syndiotactic polymer [65] and the W(mesityl) (CO)3 catalyst, which produced a high trans isotactic polymer [71].

1.6.3 REGIOSELECTIVITY IN R O M P The above method of tacticity determination depends upon there being no regioselectivity, i.e. no bias towards HT or HH/TT addition in the polymerisation of the racemate, and in fact this is the case with 5-substituted norbornene derivatives. Placement of a methyl substituent on the double bond results in complete regioselectivity [72], but much more interesting is the case where an alkyl group is in the bridgehead position, as in poly(l-alkylnorbornene) [63, 73]. These monomers exhibit a strong catalyst- and substitutent-dependent selectivity, which again may be observed in the 13 C NMR spectra of the polymer, Figure 1.13. For example, high trans polymer may be prepared using either RuCl3 or OsCl3 as catalyst, but whereas the RuCl3 catalyst is non-regioselective the OsCl3 catalyst exhibits a strong bias towards the HT addition of monomer (Figure 1.12(a)). This effect may be explained in terms of different polarities of the respective [ M t ] - = C + C ^ pi-bonds as they engage the monomer double bond, Scheme 8, in a [2 + 2] cycloaddition reaction which is the initial step of the ROMP reaction [74,75]. As expected, steric effects are also important, and the more bulky ethyl substituent induces a HT bias in the polymer formed using the RuCl3 catalyst [73] and enhances the HT bias in the OsCl3 case [70][73], Figure 1.13(b). In this context a particularly interesting and unique example of the alternating copolymerisation of enantiomers was demonstrated in the polymerisation of 1methylnorbornene with the ReCl5 catalyst [63,75]. The analysis relied on the fact that the hydrogenated forms of these polymers (but see more recent work, p. 52), unlike their unsaturated precursors, exhibited fine structure due to the presence of ring dyad units of different tacticities. This catalyst gave a poly(l-methylnorbornene) which on 13 C NMR analysis, Figure 1.14, was shown to be all-cis and all HT, in contrast to the OsCl3 catalyst, which produced an all-trans and all HT polymer, Figure 1.13. Both polymers were hydrogenated, and it was found that whereas in the OsCl 3 case one line exhibited doublet fine structure, which must be due to the m/r effects, the ReCl5 polymer gave only the down-field line, indicating that the polymer was tactic. The

Figure 1.13 Olefinic region from the 13C NMR spectrum of all-trans polymer formed from various 1-alkylnorbornenes with different catalyst systems, (a) Reproduced by permission of the Society of Chemical Industry, London, from Br. Polym. J., 1984,16,2; (b) Reproduced by permission of the Society of Chemical Industry, London, from [73]

ppm 13

Figure 1.14 Olefinic region of the C NMR spectrum of poly(l-methylnorbornene) formed using a ReCl5 catalyst; the polymer is all HT all-cis and syndiotactic (compare Figure 1.12 (a) andd (b)). Reproduced by permission of the Society of Chemical Industry, London, from Br. Polym. J., 1984,16, 2

fact that it was syndiotactic was shown by using the OsCl3 catalyst to polymerise optically resolved monomer, which must result in an isotactic all-trans polymer. The 13 C NMR spectrum of the hydrogenated product gave only the up-field line of the original m/r pair, thereby proving the syndiotactic nature of the poly(lmethylnorbornene) prepared using the ReCl5 catalyst. Such a polymer can only form at a catalyst site which alternates in chirality in each catalytic cycle, and thus is required to choose alternate enantiomeric forms of the monomer in successive catalytic cycles. An alternating copolymer of enantiomers was thereby formed. It was therefore highly significant that, in this context, we were unable to form ring-opened polymer from optically resolved monomers with the ReCl5 catalyst. Here again we may draw parallels with Ziegler-Natta polymerisations, Scheme 14. In the syndiotactic polymerisation of propylene [76] the catalyst is

Scheme 14

selecting a different prochiral face of a monomer (which exists in only one molecular form). In the case of the 1-methylnorbornene monomer, Scheme 15, reaction is restricted to one face (exo) of the molecule [61], but two chiral forms are available. In each case the polymer is H-T biased, and the catalyst site alternates in chirality in each catalytic cycle.

Scheme 15

Scheme 16

13

C NMR studies of the ROMP of certain 7-substituted norbornadiene derivatives provided a remarkable example of a substituent-dependent regioselectivity, Scheme 16. 7-methylnorbornadiene [62] and 7-f-butoxynorbornadiene [77] were polymerised using a range of catalysts; whereas the 7-Me derivative behaved in the expected manner with almost exclusive attack at the anti face of the molecule (13C NMR spectra of the polymers are discussed below), catalyst attack occurred with almost equal facility at both syn and anti faces in the 7-r-butoxy derivative. In this reaction it is envisaged that the lone pair of electrons on the 7-oxy substituent interacts with the electrons of the syn double bond, and the normal [2 + 2] cycloaddition, which occurs on anti attack, becomes a facile pseudo [3 + 2] cycloaddition, overcoming the apparent steric crowding at the syn face [62]. 1.6.4 DIRECT OBSERVATION O F TACTICITY 13

C NMR spectra of polymers formed when there is unsymmetric substitution in the norbornene monomer, as shown above, have been very useful in demonstrating the regioselectivity of various catalyst systems. In addition, these substituents are responsible for a decrease in the conformational mobility of the polymer chain, and consequently fine structure which may be due to tacticity is resolved in certain cases. The situation is complicated, however, by the possibility that such splittings may be due to longer range HT effects when HT, HH and TT sequences are present in the polymer chain. Positioning the substituent at C 7 retains the chain stiffening effect without splittings due to a regio effect; the observed fine structure may then be attributed to tacticity effects, especially in high cis or high trans polymers where remote c and t effects do not interfere. These 7-substituted derivatives are also important because much of the above mechanistic interpretation depends upon the assumption that attack on the norbornene molecule occurs at the exo face. The result of ring-opening polymerisation of mixtures of syn- and anft'-7-methylnorbornene [61] shows that this assumption is valid. Thus, only poly(«nr/-7-methylnorbornene) was obtained from the polymerisation of syn/anti mixtures, although a small proportion of syn isomer was incorporated in some cases. With particularly active catalysts the syn isomer could be homopolymerised. More recently, and in relation to the regioselectivity studies discussed above, 7-methylnorbornadiene was prepared and polymerised [62]. The importance of these polymers (for NMR analysis) lies in the excellent resolution of the 13 C NMR spectra which may be achieved and the fact that ring tacticity may be observed directly in addition to cis/trans ratios and distribution. For example, the spectrum of the high trans polymer of anft'-7-methylnorbornene, Figure 1.15(b), which is atactic, showing sensitivity to m/r dyads, may be compared with its tactic high cis analogue, Figure 1.15(a). The syndiotactic nature of this latter polymer is inferred from the known behaviour of the ReCl5 catalyst discussed earlier. Other catalyst systems produce a variety of microstruc-

(a)

ppm

(b)

ppm

Figure 1.15 * 3C NMR spectra of poly(anft'-7-methylnorbornene): (a) syndiotactic all-cis polymer prepared using the ReCl5 catalyst; (b) atactic all-trans polymer prepared using the RuCl5 catalyst. Reproduced by kind permission of Elsevier Science Publishers from [61]

(a)

ppm

(b)

ppm 13

Figure 1.16 C NMR spectra of poly(anfi-7-methylnorbornene): (a) an intermediate cis-tactic polymer prepared using the W(mesit) (CO) 3 /EtAlCI 2 catalyst system, and (b) an atactic polymer of similar cis content prepared using the WCl 6 /Bu 4 Sn catalyst system. Reproduced by kind permission of Elsevier Science Publishers from [61]

ture types, and it is interesting that one can subtly change the behaviour of, for example, a W-based catalyst by changing the oxidation state and ligation. The W(mesityl) (CO)3 complex and the WVI hexachloride catalyst both produce polymers of intermediate and similar cis double bond content, Figure 1.16(a) and (b) respectively, but in the former case cis double bonds are associated solely with r dyads and trans with m, whereas in the latter case cis or trans double bonds may be associated with m or r dyads [61]. In keeping with the general principle that polymerisation of monomers that have a pair of double bonds capable of chelation at the catalyst site leads to the formation of high cis polymer [66], polymers formed from 7-methylnorbornadiene were generally high cis. Resolution of the various microstructural features is also observed in the* 3 C spectra of these polymers, but paradoxically it is in the C 7 , tt line, Figure 1.17 (which shows no fine structure in the 7methylnorbornene case), which is clearly resolved here; exactly the opposite situation holds for the C7, cc line. One can therefore estimate cis content, blockiness and tacticity of the various double bond dyads from this resonance alone, which may be checked for consistency by reference to the fine structure of other resonances in the spectrum.

Figure 1.17 The C 7 resonance in the 13C NMR spectrum of poly(7-methylnorbornadiene) prepared using the WCl6/Me4Sn catalyst system. Reproduced by permission of Huthig & Wepf Verlag from [62]

(a)

ppm

Figure 1.18 125 MHz 13C NMR spectrum of (a) poly(l-methylnorbornene), all cis, all HT, atactic, prepared using a tungsten carbene complex, (b) the same polymer prepared using the ReCl5 catalyst

An important consequence of the foregoing discussion is that it is impossible to predict which resonance will be split by any of the possible microstructural features, and one must therefore be careful not to assume that a polymer is, for example, tactic simply because no fine structure is resolved. Also, spectra of polymers taken on modern high field instruments (125 MHz for 13C) may show up fine structure not resolved on lower field instruments. A most apposite example of this was observed recently in the * 3 C NMR spectroscopy of polymers formed from 1-methylnorbornene using a tungsten alkylidene complex [78]. A spectrum was taken initially at 62.5 MHz and fine structure was not observed. The polymer was high cis, all HT, assumed to be syndiotactic and thought initially to be another example of the alternating copolymerisation of enantiomers described in detail above. However, on obtaining the spectrum at high field (125 MHz, Figure 1.18(a), each line exhibited considerable fine structure, showing that the polymer was in fact only partially syndiotactic [79]. In contrast, it was gratifying to observe that the alternating copolymer of enantiomers formed from this monomer using the ReCl2 catalyst, Figure 1.14, when re-examined at 125 MHz), Figure 1.18(b), had a spectrum almost devoid of fine structure, thereby demonstrating its tactic nature and allowing the assignment of some of the lines in the more complex spectrum of the atactic polymer.

1.7 REFERENCES [1] F.A. Bovey, high resolution carbon-13 studies of polymer structures, in K J . Ivin (Ed.), Structural Studies of Macromolecules by Spectroscopic Methods, John Wiley & Sons, London, 1976. [2] F.A. Bovey, Chain Structure and Conformation of Macromolecules, Academic Press, London, 1982. [3] J.L. Koenig, Chemical Microstructure of Polymer Chains, John Wiley & Sons, Chichester, 1980. [4] J.L. Koenig, Spectroscopy of Polymers, ACS Professional Reference Book, American Chemical Society, Washington, 1992. [5] A.E. Tonelli, NMR Spectroscopy and Polymer Microstructure, VCH Publishers, Berlin, 1989. [6] A.H. Fawcett, Synthetic macromolecules, p. 333 in G. Webb (Ed.), Special Periodical Report on Nuclear Magnetic Resonance, The Royal Society of Chemistry, Cambridge, 1993. [7] F.A. Bovey and J. Tiers, J. Polym. Sci., 1960, 44,173. [8] A.E. Tonelli, Chapter 2, p. 55, in this book. [9] F. Heatley and A. Zambelli, Macromolecules, 1969,2,618. [10] A. Zambelli and A. Segre, J. Polym. ScL, B, 1968, 6,473. [11] N. Ishihara, T. Seimiya, M. Kuramoto and M. Uoi, Macromolecules, 1986,19,2464. [12] M. Minagawa, H. Yamada, K. Yamaguchi and F. Yoshi, Macromolecules, 1992,25, 503. [13] A.M. Aerdts, J.W. de Haan and A.L. German, Macromolecules, 1993, 26, 1965. [14] A.H. Fawcett and W. Ddamda, MakromoL Chem., 1982,183, 2799.

[15] J.K. Becconsall, P.A. Curnuck and M.C Mclvor, Appl. Spectrosc, 1971,4, 307. [16] D.T. Pegg, D.M. Doddrell and M.R. Bendall, J. Chem. Phys., 1982,77, 2745. [17] R.E. Emst, G. Bodenhausen and A. Waokaun, Principles of Nuclear Magnetic Resonance, Clarendon Press, Oxford, 1987. [18] H. Friebolin, Basic One- and Two-Dimensional NMR Spectroscopy, VCH, New York

and Weinheim, 1991. [19] F.C. Schilling, F. A. Bovey, M. D. Bruch and S. A. Kozlowski, Macromolecules, 1985, 18,1418. [20] P.A. Mirau and F.A. Bovey, Macromolecules, 1986,19, 210. [21] JJ. Kotyk, P.A. Berger and E.E. Remsen, Macromolecules, 1990, 23, 5167. [22] G.R. Quinting and R. Cai, Macromolecules, 1994,27,6301. [23] A.G. Ferrige and J.C. Lindon, J. Magn. Reson,, 1978, 31, 337. [24] A.H. Fawcett, S. Fee and L.C. Waring, Polymer, 1983,4,1571. [25] J.A. Frankland, H.G.M. Edwards, A.F. Johnston, LR. Lewis and S. Poshyachinda, Specirochim. Ada, Part A, 1991,47A, 1511.

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D.M. Grant and E.G. Paul, J. Am. Chem. Soc,, 1964,86, 2984. J.C. Randal, J. Polym. ScL, Polym. Phys. Ed., 1973,11, 275. J.C. Randal (Ed.), NMR and Macromolecules, ACS Symp. Ser., No. 247,1984, 256. J.C. Randal, CJ. Ruff and M. Keltermans, Reel Trav. Chim. Pays-Bos, 1991,110,543. A.H. Fawcett, KJ. Ivin and C. Stewart, Org. Magn. Reson., 1978, 11, 360, and references cited therein. A. Kaji, Y. Akitomo and M. Murano, J. Polym. Set, Part A: Polym. Chem., 1991,29, 1987. Q. Zhu, F. Horii and R. Kitamaru, J. Polym. ScL, Part A: Polym. Chem., 1990, 28, 2741. A.H. Fawcett, M. Hania, K.-W. Lo and A. Patty, J. Polym. ScL, Part A: Polym. Chem., 1994,32, 815. A.H. Fawcett and M. Hania, unpublished results. F. Heatley, Y.Z. Luo, J.F. Ding, R.H. Mobbs and C. Booth, Macromolecules, 1989, 21, 2713. F. Heatley, G.E. Yu, M.D. Draper and C. Booth, Eur. Polym. J., 1991, 27,471. F. Ciardelli, O. Pierone and A. Fissi, Chapter 14, p. 347 of this book. A.H. Fawcett, J. Guthrie, M.S. Otterbum and D.Y.S. Szeto, J. Polym. ScL, Polym. Lett., 1988,26,459. A.H. Fawcett, D.Y.S. Szeto and D. Pepper, in preparation. A. Zambelli, P. Locatelli, G. Bajo and F.A. Bovey, Macromolecules, 1975,8,687. R. Mani and CM. Burns, Macromolecules, 1991, 24, 5476. A.H. Fawcett, F. Heatley, KJ. Ivin, CD. Stewart and P. Watt, Macromolecules, 1977,10, 765. R.H. Cole, P.W. Winsor, A.H. Fawcett and S. Fee, Macromolecules, 1987, 20,157. N. Spasky and P. Sigwalt, Bull. Soc. Chim. Fr., 1967,4617. A.H. Fawcett and R.K. Malcolm, Polym. Int., 1994,35,41. S.A. Chambers, A.H. Fawcett, J.F. Malone and S. Fee, Macromolecules, 1990, 23, 2757. J.R. Ebdon, The characterization of diene polymers by high resolution proton magnetic resonance, in K. J. Ivin (Ed.), Structural Studies of Macromolecules by

Spectroscopic Methods, John Wiley & Sons, London, 1976, p. 241. [48] C-W. Chau, A.H. Fawcett, J.N. Mulemwa and C-E. Tan, Polymer, 1992, 193, 257. [49] A.H. Fawcett, J.N. Mulemwa and C-E. Tan, Polym. Commun., 1984,25, 300.

[50] C-W. Chau, A.H. Fawcett, J.N. Mulemwa, L.-W. Poom, A. Surgenor and C-E. Tan, Makromol. Chem., 1992,193, 257.

[51] J.C Bevington, D.A. Cywar, T.N. Huckerby, R.A. Lyons, E. Senogles and D. A. Tirrell, Eur. Polym. J., 1991,27, 603. [52] J.C. Bevington, R.A. Lyons and E. Senogles, Eur. Polym. J., 1992, 28,283. [53] G. Moad and R.I. Willing, Polym. J., 1991,23,1401. [54] KJ. Ivin, Olefin Metathesis, Academic Press, London, 1983. [55] W.L. Truett, D.R. Johnson, LM. Robinson and B. A. Montague, J. Am. Chem. Soc, 1960,82, 2337. [56] J.H. Oskam and R.R. Schrock, J. Am. Chem. Soc,1993,115,11831. [57] KJ. Ivin, B.S.R. Reddy and JJ. Rooney, J. Chem. Soc, Chem. Commun., 1981,1062. [58] KJ. Ivin, D.T. Laverty and JJ. Rooney, Makromol. Chem., 1977,178,1545. [59] B. Bell, J.G. Hamilton, O.N.D. Mackay and JJ. Rooney, J. MoI. CataL, 1992,77,61. [60] R.M.E. Greene, KJ. Ivin, G.M. McCann and JJ. Rooney, Makromol. Chem., 1987, 185,1993. [61] J.G. Hamilton, KJ. Ivin and JJ. Rooney, J. MoI. CataL, 1985,28, 255. [62] J.G. Hamilton, JJ. Rooney and D.G. Snowden, Makromol. Chem., 1993,194, 2907. [63] J.G. Hamilton, KJ. Ivin, G.M. McCann and JJ. Rooney, Makromol. Chem., 1985, 186,1477. [64] R.M.E. Greene, J.G. Hamilton, KJ. Ivin and JJ. Rooney, Makromol. Chem., 1986, 187, 619. [65] H.T. Ho, KJ. Ivin and JJ. Rooney, J. MoI. CataL, 1982,15, 245. [66] J.G. Hamilton, KJ. Ivin and JJ. Rooney, J. MoI. CataL, 1986,36,115. [67] KJ. Ivin, D.T. Laverty, J.H. O'Donnell and JJ. Rooney, Makromol. Chem., 1979, 180,1989. [68] J.G. Hamilton, KJ. Ivin, G.M. McCann and JJ. Rooney, J. Chem. Soc, Chem. Commun., 1984, 1379. [69] D.L. Barnes, N.W. Eilerts, J.A. Heppert, W.H. Huang and M.D. Morton, Polyhedron, 1994,13,1267. [70] J.G. Hamilton and JJ. Rooney, ubpublished results. [71] G.I. Devine, H.T. Ho, KJ. Ivin, M.A. Mohammed and JJ. Rooney, J. Chem. Soc, Chem. Commun., 1982, 1229.

[72] TJ. Katz, SJ. Lee and M.A. Shippey, J. MoI. CataL, 1980,8,219. [73] J.G. Hamilton, KJ. Ivin and JJ. Rooney, Br. Polym. J., 1988, 20,91. [74] H.T. Ho, B.S.R. Reddy and JJ. Rooney, J. Chem. Soc. Faraday Trans. 1, 1982, 78, 3307. [75] J. G. Hamilton, K. J. Ivin, J. J. Rooney and L. C. Waring, J. Chem. Soc, Chem. Commun., 1983, 159. [76] J. Boor, Ziegler Natta Catalysts and Polymerization, Academic Press, New York, 1979. [77] J.G. Hamilton and JJ. Rooney, J. Chem. Soc, Chem. Commun., 1992, 370. [78] J.-L. Couturier, C. Paillet, M. Leconte, J.-M. Basset and K. Weiss, Angew. Chem. Int. Ed. EngL, 1992,31, 628. [79] J.-M. Basset, J.G. Hamilton, M. Leconte and JJ. Rooney, ubpublished results.

2

CONFORMATIONITHE

CONNECTION BETWEEN THE NMR SPECTRA AND THE MICROSTRUCTURES OF POLYMERS A. E. TONELLI Fiber + Polymer Science Program, College of Textiles, North Carolina State University, PO Box 8301, Raleigh, NC 27695-8301, USA

2.1 INTRODUCTION The resonance or Larmor frequency of a spin-1/2 nucleus is highly sensitive to the local molecular environment in which it resides. When placed in a strong, static magnetic field H 0 of several tesla, the cloud of electrons about the nucleus produces orbital currents resulting in the creation of small local magnetic fields, which are proportional to H 0 , but are opposite in direction. These local induced magnetic fields effectively screen or shield the nucleus from H 0 and result in the nucleus experiencing a net local magnetic field Hloc = H 0 (1 — a), where a is the screening constant, a is highly sensitive to chemical structure, i.e., the numbers and types of atoms and groups of atoms attached to or near the observed nucleus. It is the dependence of a upon molecular structure that lies at the heart of NMR's utility as a probe of molecular structure. Any structural feature that alters the electronic environment around a nucleus will affect its screening constant o and lead to an alteration in its resonance frequency or chemical shift 8. Consequently, to predict the chemical shift of, say, a 13 C nucleus in a particular molecular environment, the electronic wave function of the molecular system in the presence of the strong applied field H 0 must be known. For this reason it has been extremely difficult to make a priori predictions of the resonance frequencies or chemical shifts of spin-1/2 nuclei [1-4]. If, for example, we wish to calculate the relative chemical shifts of the 13 C nuclei in methane and methyl fluoride, we must be able to determine accurately the electronic wave functions of both molecules in the presence of Ho; Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

To date it has not been possible to make accurate predictions of the chemical shifts observed for spin-1/2 nuclei, even when applying the most sophisticated ab initio quantum mechanical methods. Instead, the empirically observed effects of substituents and local conformation have been used to correlate chemical shifts (usually 13C) with the microstructures of molecules, including polymers [5].

2.2 SUBSTITUENT EFFECTS ON 13C CHEMICAL SHIFTS Substituent effect rules useful in predicting the 13C chemical shifts observed in the 13 C NMR spectra of paraffinic hydrocarbons have been derived [6-9]. 13 C chemical shifts are ordered in terms of the effects produced by substituents attached to the observed carbon at the a, /?, and y positions. Some of the data used to establish these rules are reproduced in Tables 2.1-2.3, where it is apparent that each carbon substituent added a and/or j? to the observed carbon C° deshields it by ^ 9 ppm. On the other hand, each carbon y-substituent results in shielding of % 2 ppm of the observed carbon. Using these substituent rules makes it possible to assign the 13 C NMR spectra of paraffinic hydrocarbons, including their highly branched members. Table 2.1 a-substituent effect on ^13C [10]


a-effect, ppm

(a)

0

CH 3 -^H

(b)

0

CH 3 -I- 01 CH 3

5.9

8.0

/CH3 CH I *[

16.1

10.2

25.2

9.1

279

27

0

(C)

"21

/CH 3

°CH-f-aCH3 (d)

Xa

CH3

/CH3

° c 4; cH3 (e)

XT01CHs >CH 3

Table 2.2

0-substituent effect on S* 3 C [ 10] <513C from TMS, ppm

(a)

5.9

(b)

15.6

^-effect, ppm

9.7

8.7

(C)

24.3

7.2

(d) 31.5

Table 2.3 y-substituent effect on <5*3C [10] <513C from TMS, ppm

y-effect, ppm

(a)

15.6

(b)

13.2

-2.4

(C)

11.5

-1.7

(d)

8.7

-2.8

(e)

25.0

(0

22.6

(g)

20.7

(h)

18.8

-2.4

-1.9

-1.9

H-T

H-H:T-T

Figure 2.1

Possible regiosequences of monomer units in P P Table 2.4 Value OfS13C observed in the speatra of H - T [13] and H - H : T - T [14] PPs <5 13 Cvs.TMS, fl ppm Carbon CH CH 2 CH 3

H-Tb

H-Hc

T-T c

28^5 46.0 20.5

37X) 15.0

31.3

"All S13C values are averaged over the different stereosequences [14]. ''Schilling and Tonelli [ H ] . c M611eretal. [12].

We may understand why the 13C nuclei in head-to-tail (H-T) polypropylene (PP) (see Figure 2.1) resonate in the order CH2, CH, CH 3 from low to high ISeId (see Table 2.4) in terms of their a-, /?-, and y-substituent effects. Methine carbons have two additional a- (4- 18ppm) and two additional y-substituents (—4ppm) compared with methyl carbons and should resonate 18 — 4=14 ppm downfield. Methylene carbons have two additional p- ( + 18ppm), one fewer a- (-9ppm), and two fewer y-substituents (+ 4 ppm) compared with the methine carbons, and should resonate 18-9 + 4 = 13 ppm further downfield. Suppose that PP possesses head-to-head (H-H) and tail-to-tail (T-T) units in addition to the predominant H-T enchainment of monomer units. As seen in Figure 2.1, the H-H methine carbons have an additional /?- ( + 9 ppm) and two fewer y-substituents (+ 4 ppm) than H-T methine carbons, and should resonate 9-1-4=13 ppm downfield from their H-T counterparts. T-T methylene carbons have one fewer y8-( — 9 ppm) and two more y-substituents (—4 ppm) than the H-T methylene carbons, and should move — 9—4 = —13 ppm upfield from the H-T methylene resonances. H-H methyls should resonance - 2 ppm upfield from the H-T methyls, because they have a single additional y-substituent. Note in

ISOTACTIC

ATACTIC

SYNDIOTACTIC

ppm vs. TMS

Figure 2.2 25MHz PP [13]

13

CNMR spectra of (a) isotactic, (b) atactic, and (c) syndiotactic

Table 2.4 that all these expectations are borne out in the 13 C NMR spectra of H-T PP [11] and H-HiT-T PP [12], and are consistent with the a-, j?-, and y-substituent effects on 13 C chemical shifts derived from paraffins. However, it is clear from the 13 C NMR spectra of three PP samples presented in Figure 2.2 [13] that the multiple resonances appearing in the spectrum of atactic-PP(b), which are well known to be produced by different stereosequences [11], cannot be explained by the usual a-, /?-, and y-substituent effects. Each methyl carbon in PP has one a-, two /?-, and two y-substituents, each methine carbon has two a-, two /?-, and four y-substituents, and each methylene carbon has two a-, four /?- and two y-substituents independent of stereosequence. Some factor other than numbers and types of a-, /J-, and y-substituents, and which depends on PP stereosequence, must be responsible for the multiplicity of

resonances observed in the atactic PP spectrum. As we shall shortly see, that other factor is the stereosequence-dependent local conformation of the PP chain [11,13,14].

23 y-GA UCHE EFFECT METHOD OF PREDICTING NMR CHEMICAL SHIFTS We have mentioned that y-substituents in paraffinic hydrocarbons shield carbon nuclei relative to unsubstituted carbons. In Figure 2.3 it is apparent that the observed carbon C° and its y-substituent CY can alter their mutual arrangement (distance and orientation) via rotation about the central of the three bonds which separate them. Note that the distance between C° and Cy (do_y) is reduced from 4 to 3 A on changing their arrangement from trans to gauche. Grant and Cheney [15] first suggested a conformational origin for the y-substituent effect on S* 3 C. Polarization of the C°-H and C7-H bonds as a result of their compression by proton-proton (o-y) repulsion was suggested as the source of y-gauche shielding. More recently, Li and Chesnut [16] have suggested that the shielding y-effects correlate with attractive van der Waals forces and not repulsive steric interactions, though they still suggest that the gauche arrangement of the observed carbon and its y-substituent is required for shielding. Seidman and Machiel [17] concluded, based on semiempirical and ab inito quantum mechanical calculations, that the y-substituent effect is conformational

Figure 2.3 Newman projctions of an n-alkane chain in the (a) trans (<£ = 0°) and gauche ( = 120°) conformations

in origin, but is not exclusively attributable to the proximity of the interacting C° and (7 groups. Most recently, Barfield and Yamamura [4] concluded that nuclear shielding of the methyl carbons in n-butane is dominated by changes in the paramagnetic contributions for the C 1 —C 2 and C 1 —H bonds, rather than the steric compression of C 1 —H bonds produced by the crowding of terminal methyl groups in the gauche conformation. Though its fundamental origins remain uncertain, the y-substituent effect on (513C values has a conformational sensitivity and, as we will shortly demonstrate, is potentially useful in characterizing both the conformations and the microstructures of polymers. For a carbon nucleus to be shielded by a y-substituent we have suggested that they must be in a gauche arrangement (see Figure 2.3). This suggestion is supported by comparing the <513C values observed for the methyl carbons in n-alkanes. The methyl carbons in n-butane and higher n-alkanes have a single y-substituent, whereas the methyl carbons in n-propane have no y-substituents, but the same number and kinds of a- and jS-substituents as the higher n-alkanes. In their crystals the n-alkanes adopt the extended, all-trans conformation, where both methyl carbons are trans to their y-substituents. If the y-substituents are trans to the methyl carbons in the higher solid n-alkanes, then we would expect (513CH3 (solid C n H 2n+2 , n ^ 4) = (513CH3 (liquid n-propane). VanderHart [18] has observed the methyl carbons in the solid n-alkanes with n — 19,20,23, or 32 to resonate between 15 and 16ppm (relative to TMS), while the methyl carbon in liquid n-propane resonates at 15.6ppm. [19] On the other hand, in the liquid state, the methyl carbons in the higher n-alkanes (n ^ 4) resonate upfield at 13.2-14.1 ppm. [19] Of course in the liquid state the C—C bonds in n-alkanes possess a significant gauche content, and this results in the shielding of <513CH3 for n-butane and the higher n-alkanes compared to that observed for the methyl carbons in n-propane or the higher solid n-alkanes in the all-trans conformation. If we know how much gauche character Pg is possessed by the central bond between C° and X y [ C ° — C ^ - C - X 7 ] , then we can estimate the shielding produced by Xy, yc x, when in a gauche arrangement with C°. This procedure is illustrated in Figure 2.4, where the gauche shielding effects of the y-substituents C, OH, and Cl are derived. As an example, when the shielding produced at the methyl carbon in n-butane by the other methyl group (its y-substituent), i.e., A(5 13 CH 3 = <513CH3 (n-butane)-(5 13 CH 3 (n-propane)= 1 3 . 2 - 1 5 . 6 = - 2 . 4 ppm, is divided by the gauche character of the intervening bond, P9 = 0.46: yc,c = A(513CH3/P^= -2.4/0.46= - 5 . 2 ppm. When this procedure is applied to n-butane, 1-propanol, and 1-chloropropane, the following y-gauche shielding effects are derived: yc c = — 5.2 ppm, 7C,OH = —7.2 ppm, and yCtC1= —6.8 ppm. We now see that the shielding at a carbon nucleus produced by a y-substituent in a gauche arrangement can be comparable in magnitude ( - 5 to - 7 ppm) to the deshielding ( + 9 ppm) caused

CH3-CH2-CH2-CHj % gauche = 46 Xc-c "^i

»-5.2ppm

CH 3 -CH 2 -CH 2 -OH 7 % gauche = 74

t - o = ~-M= -?-2ppm CH3-CH2-CH2-C*7 % gauche s 60.0 y

c - a = ^

^ - 6 . 8 ppm

Figure 2.4 Derivation of the y-gauche shielding produced by the y-substituents C, OH, and Cl (see text) by the more proximal a and /? substituents. More important, however, is the conformational dependence of the y-substituent effect on 13 CNMR chemical shifts. Any variation in the microstructure of a molecule which affects its local conformation can be expected to be reflected in its S13C values via the y-gauche effect. Let us complete our discussion of the conformational connection between the microstructures and NMR spectra of polymers, which is provided by the conformationally sensitive y-gauche effect, by considering the nonequivalent S13C values for the isopropyl methyl carbons in several branched alkanes [8,20, 21] as presented in Table 2.5. Even though the isopropyl methyl carbons in each alkane have the same a-, /?-, and y-substituents, we note in column 2 that the observed nonequivalence progressively decreases as the number of carbons separating the terminal isopropyl group from the asymmetric center is increased. This behavior can be understood [22] if we focus on the source of the nonequivalent <513C values observed for the isopropyl methyl carbons in 2,4dimethylhexane (2,4-DMH). In Figure 2.5 we have illustrated the possible staggered conformations about the C 2 - C 3 backbone bond in 2,4-DMH, since these determine whether or not the isopropyl methyl carbons Csc, C bb are y-gauche to the asymmetric carbon C 4 . From the probabilities of finding bond C2-C3 in the trans (t), gauche + (g 4-), and

13

Table 2.5 Nonequivalent

C NMR chemical shifts for the isopropyl methyl carbons in branched alkanes A<5, ppm Alkane Obsd.0 Calcd.

C C I I C—C—C—C—C—C C C I I C

C

I

I

C—C—C—C—C—C—C—C C C I

1.0 (1,9,1.1,0.9)*

1.6,1.1,0.9

0.1

0.04

I

c—c—c—c—c—c—c—c—c

o.o

o.o

" Observed between ambient temperature and 480C. (Kroschwitz et al. [20], Lindeman and Adams [8]; Carman et al. [21]. •Observed at - 1 2 0 , 25, and 90 0C (Tonelli et al. [22].

Figure. 2.5 (a) 2,4-DMH in the all-trans conformation; (b) Newman projections illustrating rotational states about the C2-C3 backbone bond of 2,4-DMH [22] gauche — (g - ) rotational states (Pn Pg+,Pg_), we obtain Pt + P9+, P9 + + P9 _ as the probabilities for gauche arrangements between Csc and Cbb, respectively, and their y-substituent C 4 . Bond rotation probabilities are obtained from the conformational model developed by Mark [23] for ethylene-propylene copolymers:

Pt = 0.38, Pg+ = 0.0 and Pg_ = 0.61. Thus, C 4 is y-gauche to Csc with probability 0.39 and to C bb with probability 0.62. We expect the nonequivalence between Csc and Cbb to be AS13C = (0.39 -0.62) x y c c = - 0.23( - 5.2 ppm) =1.1 ppm, where we have adopted the value yCtC = — 5.2 ppm derived from n-butane. The observed nonequivalence (1.0-1.1 ppm) is in close agreement with the value expected from the y-gauche conformational calculation. The temperature dependence of the observed magnetic nonequivalence is also successfully reproduced by the y-gauche effect calculations, leaving little doubt that its origin is the conformationally sensitive y-gauche effect. From the Newman projections in Figure 2.5 it might be expected that the t and g — conformations would be equally populated. However, it is well known [24] that rotational state probabilities for the backbone bonds in linear chain molecules depend on the conformations, or rotational states, of neighboring bonds. The asymmetric center at C 4 generates intramolecular interactions which depend simultaneously on (f> and neighboring bond rotations (see Figure 2.5(a)), which render Px^ Pg_. The values of Pt and P9_ approach each other as the asymmetric center is further removed from the terminal isopropyl group, leading to a reduction in the expected nonequivalence of the isopropyl methyl carbons. This expectation is borne out in Table 2.5, where it is both observed and predicted that the magnetic nonequialence of isopropyl methyl carbons vanishes once they are separated by more than four carbons from the asymmetric center. It is apparent from this example that the microstructural sensitivity of 13 C NMR chemical shifts can have a conformational origin. <513C depends on the local magnetic field, which is influenced by the local conformation in the vicinity of the resonating carbon nucleus. The local conformation is determined by the neighboring microstructure. Hence, the microstructural sensitivity of 1 3 C NMR has its basis in the dependence of the local conformation on microstructure microstructure -> conformation -* H loc -+(513C The shielding of 13 C nuclei by y-substituents in a gauche arrangement (ygauche effect) enables us to both complete and simplify the conformational connection between the microstructures and NMR spectra of polymers. y-gauche effect

microstructure

c l 3

-,

•
2.4. APPLICATIONSOF y - GA UCHE EFFECT ANALYSIS OF POLYMER MICROSTRUCTURES 2.4.1 POLYPROPYLENE(PP) We are now in a position to understand the stereosequence sensitivity of the 613C values observed [11] for atactic PP (see Figure 2.2(b)). When the methyl carbon

ppm vs. TMS 13

Figure 2.6 (a) C NMR spectrum at 90.52 MHz of the methyl carbon region in atactic PP in 20% w/v n-heptane solution at 67 0C. (b) Simulated spectrum obtained from calculated chemical shifts, as represented by the line spectrum below, assuming Lorentzian peaks <0.1 ppm in width at half height [13] region of this spectrum is expanded [13] we see in Figure 2.6(a) that over 20 resonances are observed. Because there are 10 and 36 distinct pentad and heptad stereosequences [25], the 1 3 CNMR spectrum of atactic PP shows sensitivity to heptad stereosequences in the methyl region. An atactic PP heptad is illustrated in Figure 2.7 along with Newman projections detailing the y-gauche interactions involving the methyl group. It is clear that in the t and g~ backbone conformations the methyl group is gauche to its y-substituents, the backbone methine carbons (a). To predict the 13C chemical shifts expected for the methyl carbons in atactic PP we simply have to calculate the trans/gauche probabilities for these backbone bonds in each of the 36 heptad stereosequences. When this is carried

Figure 2.7 (a) Conformations of a four carbon fragment of a PP chain; (b) heptad of PP; observed methyl is marked by asterisk out with the Suter-Flory [26] RIS (rotational isomeric state) model for PP, and the resultant probabilities of finding CH 3 in a gauche arrangement with its y-substituents Ca are multiplied by the shielding produced by this arrangement (y CH3Ca = — 5ppm), we obtain [13] the predicted methyl 13 C chemical shifts presented in the form of a stick spectrum at the bottom of Figure 2.6(b). Because the y-gauche effect method of calculating 13 C chemical shifts only leads to the prediction of stereosequence-dependent relative chemical shifts, we are free in the comparison with observed spectra to translate the calculated shifts to obtain the best agreement with the observed (513Cs. This has been done in Figure 2.6, where the agreement between the observed and calculated methly <513C values has been used to make the stereosequence assignments indicated there. The y-gauche effect method of assigning resonances in the methyl region of the 13 C NMR spectrum of atactic PP to heptad stereosequences has been achieved without recourse to the study of PP model compounds or stereoregular PP's (see Figure 2.2(a) and (c)) and without assuming a particular statistical model to describe the frequencies or populations of stereosequences produced during polymerization. By achieving agreement between the observed 13 C chemical shifts and those predicted by the y-gauche effect method, we have not only determined the microstructure (stereosequence) of this polymer, but in addition we have

stringently tested its conformational characteristics as embodied in the RIS model. Clearly then, it is possible to use 13 C NMR spectroscopy to test or derive the conformational characteristics of vinyl polymers by comparison of observed 13 C NMR spectra with the 5 13 Cs calculated via the y-gauche effect method. This approach has been pursued with success to test the local conformational characteristics of several vinyl polymers [13, 27, 28] and provides the basis for the discussion presented in the subsequent chapter of this volume. Having established the assignment of resonances observed in the methyl region of the 13 C NMR spectrum of atactic PP to the appropriate heptad stereosequences, one might ask what use can be made of this detailed configurational information. Through an analysis of the intensities of the observed resonances we may learn if any simple statistical model, such as Bernoullian or Markovian statistics, can describe the polymerization of atactic PP. In Figure 2.6 we compare the observed and simulated 13 C NMR spectra of the methyl region of atactic PP. The simulated spectrum was obtained [13] by assuming Lorentzian peaks of < 0.1 ppm width at half height for each of the 36 heptad chemical shifts calculated by the y-gauche effect method. The relative intensities or heights of these heptad peaks were then adjusted to obtain the best simulation of the observed spectrum. The comparison presented in Figure 2.6 makes it apparent that we have been able successfully to simulate the methyl region of the 13 C NMR spectrum of atactic PP based on our ability to calculate and assign all of the heptad stereosequence resonances. Thus, from this successful simulation we know how much of each heptad stereosequence is present in our atactic PP sample. When we compare these heptad stereosequence populations with those predicted by simple statistical models, we are able to conclude that our atactic PP sample cannot be described by any simple statistical polymerization model, such as Bernoullian or first-order Markovian. It has been subsequently shown by Inoue et al. [29] that a two site model of Ziegler-Natta polymerization of propylene [30] adequately describes the distribution of stereosequences observed in atactic PP. At one of the catalyst sites the monomer addition obeys Bernoullian statistics, and at the other site a predominance of monomer units is added in only one of the two possible configurations (R, S or d, /). As we can see, the y-gauche effect prediction of 13 C NMR chemical shifts in vinyl polymers permits assignment of their 13 C NMR spectra, provides an opportunity to test or derive an RIS model description of their conformational characteristics, and may also permit a test of their polymerization statistics. 2.4.2 PROPYLENE-VINYL CHLORIDE COPOLYMERS (P-VC) Although propylene (P) does not homopolymerize under free-radical initiation [31], it can be incorporated to a minor degree in a copolymerization with vinyl

chloride (VC) leading to P-VC copolymers with up to 15mol% P units. The combination of low P content and the inability of P to homopolymerize under these conditions results in P-VC copolymers where all P units are isolated by long uninterrupted runs of VC units. Consequently, we may study the stereochemistry of the comonomer sequences containing the isolated P units, i.e., .. V C - V C - V C - V C - V C - V C - P — V C - V C - V C - V C - V C - V C . . . , and compare them with the stereosequences found in the two homopolymers PP and PVC. The methyl carbon regions of the 1 3 CNMR spectra of two PP samples are compared with the methyl carbon region observed in the P—VC copolymer [32] in Figure 2.8. The PP sample A in (a) is a typical commercial atactic material [11], and the PP sample B in (b) is a heptane-soluble fraction of a research-grade material [33]. The stick spectrum in (b) was calculated as just described; the y-gauche effect13C chemical shifts calculated for the methyl carbons in the P-VC copolymer (c) were obtained by employing Mark's [34] RIS conformational model of P-VC copolymers. Comparison of the methyl resonances in P-VC and PP reveals a decreased sensitivity to stereosequence for the P-VC copolymer. The methyl carbon resonances in P-VC are sensitive to pentad stereosequences, whereas in PP heptad sensitivity is observed. In Table 2.6 the 13 C chemical shifts calculated for the methyl carbons in several heptad stereosequences of P-VC and PP are compared. As observed, the methyl carbon chemical shifts calculated for P-VC are sensitive to pentads, but PP methyl carbons show significant heptad sensitivity. This difference in stereosequence sensitivity between the methyl carbons in P-VC and PP is directly attributable to differences in their conformational behavior as embodied in their RIS models. Local bond conformations reflect pentad sensitivity in P-VC and heptad dependence in PP. In addition, note that the overall spreads in methyl carbon chemical shifts observed in P-VC and PP are 2.7 and 2.0 ppm, respectively, with the P-VC methyl carbons resonating about 1 ppm upfield from those in PP. These observations are also reproduced by the calculated chemical shifts, which employ the same y-effect (yCH3,cH = — 5 ppm) and further indicate differences in the conformational behavior between P-VC copolymer [34] and PP homopolymer [26].

2.4.3

P O L Y ( P R O P Y L E N E OXIDE) (PPO)

r°i (CH3CHCH2) Propylene oxide exists in both R and S optical forms owing to its asymmetric methine carbon. If during polymerization only one of the C—O bonds in the cyclic monomer is cleaved, then it is possible to generate four different

ppm vs. (CH^) 4 Si

Figure 2.8 (a) Methyl carbon region of the 50 MHz 13C NMR spectrum of PP sample A; (b) methyl carbon region of the 50 MHz 13C NMR spectrum of PP sample B with stick spectrum of 13C chemical shifts calculated for the methyl carbons in atactic PP; (c) P-methyl carbon region of the 50MHz 13 CNMR spectrum of P-VC copolymer with stick spectrum of 13C chemical shifts calculated for the methyl carbons in P-VC

Table 2.6 13C NMR chemical shifts calculated for the methyl carbons in several heptad stereosequences of P-VC and PP* A<5,* ppm Heptad r(rmrm)r m(rmrm)r r(rmrm)m m(rmrm)m r(mrrm)r m(mrrm)r m(mrrm)m

P-VC 0 -0.01 -0.01 -0.03 0 -0.04 -0.07

PP 0 -0.07 -0.05 -0.10 0 -0.07 -0.12

Tonelli and Schilling [32]. *A<5 is the difference in chemical shift among the various heptads containing the same central pentad stereo sequence. VCH?CH = - 5 ppm was used for both PP and P-VC.

ISOTACTIC, RRR OR SSS

SYNDIOTACTIC, RSR OR SRS

HETEROTACTIC-1 RRSORSSR

HETEROTACTIC-2 SRR OR RSS

stereochemical triads in the regioregular head-to-tail (H-T) PPO polymer. These H-T triads are presented below in planar zigzag projection. If, however, during the ring-opening polymerization [35, 36] both C—O bonds in propylene oxide are subject to cleavage, then, in addition to the H-T PPO triads above, three additional structural triads or regiosequences are possible for PPO. These are illustrated here for the all-/* regioisomers, where H-T, H-H, T-T, and T-H refer to the directions of neighboring monomers, and where H is the methine end and T is the methylene end of the monomer unit. Each CH3 H

H

HCH3H

/VxVV\ H

H H ^CH3 H3C

H

(T-H: T-T) CH3 H

CH 3 HH

AWV\ H

JCH3

HH H (T-T: H-H)

HH

H

CH 3 HH

HH

HCH 3 .H CH3

H

H

(H-H: T-H) of these regioirregular triads, with H-H and T-T additions, can be further subdivided on stereochemical grounds, as was done above for the regioregular H-T triads. Thus, when both regiosequence and stereosequence are considered, 16 unique structural triads can potentially exist in PPO. It is worth mentioning that, independent of regiosequence (H-T, H-H, T-T), an m-diad consists of RR or SS neighboring units, whereas an r-diad consists of RS or SR neighboring units. However, the methyl groups in a H-T m-diad are on opposite sides of the planar zigzag projection, while in H-H and T-T diads they are on the same side. The methyl groups in r-diads are on the same side of the backbone when the diad is H-T, but on opposite sides in both the H-H and T-T r-diads. This is a direct consequence of the number of bonds separating asymmetric centers in H-T (three bonds) and in H-H or T-T (two or four bonds) regiosequences. Because the PPO repeat untit contains three protons (two methylene and one methine) whose resonances overlap extensively, it has not been possible to use

1

H NMR spectroscopy [37-42], even at 500 MHz, to determine the microstructure of PPO. Deuteration at the methine carbon simplifies the 1 H NMR spectra of PPO [38-41], and two-dimensional 1 H NMR spectroscopy [42] also leads to greater separation of the overlapping proton resonances. However, even the application of these special synthetic and spectroscopic techniques has not been completely successful in establishing the microstructures present in PPO. Carbon-13 NMR generally offers the potential for greater spectroscopic resolution than 1 HNMR and might be expected to be better suited for the analysis of PPO microstructure [43-47]. This expectation is realized for regioregular (all H-T) PPO, where CH and CH 2 carbon resonances are separated by 2 ppm, and permits the unambiguous assignment [45] of PPO stereosequences. However, as we will demonstrate here, the methine and methylene carbon resonances in regioirregular (H-T, H-H, T-T) PPO do overlap [48]. The methine and methylene carbons in PPO have the same numbers and types of a and p substituents (CH -• two a-C, one a-O one /?-C, and one /?-O; CH 2 -+ one a-C, one a-O, two /J-C, and one /J-O) independent of whether or not they are part of H-T, H-H, or T-T units (see the triad representations above). Because the deshielding of a carbon nucleus produced by a- and /?-carbon substituents is very similar ( « + 9 ppm), the relativex 3 C chemical shifts of both CH and CH 2 carbons in PPO should depend solely on their y-gauche interactions. In regioregular PPO the H-T methine carbons have two y-substituents (two CH) and the methylene carbons three y-substituents (two CH 2 , one CH3). We therefore expect, as is observed [45], that the methylene carbons will resonate upfield ( « — 2 ppm) from the methine carbons. In regioirregular PPO the H-H methine carbons have three y-substituents (two CH 2 and one CH 3 , or one CH, one CH2, and one CH3), as do the H-T methylene carbons, and the T-T methylene carbons have two ysubstituents (two CH, or one CH and one CH2), like the H-T methine carbons. We therefore expect the H-H methine and H-T methylene carbon resonances and the T-T methylene and H-T methine resonances to overlap, based on their having the same numbers and types of a-, /?-, and y-substituents. In earlier studies of PPO using 13 C NMR [45], confusion developed in assigning resonances to carbons of the H-H:T-T defects that result from the catalyst occasionally cleaving the CH—O linkage instead of the CH 2 —O bond when opening the propylene oxide ring. The possible mixing of overlapping methine and methylene carbon resonances was not considered. Additionally, spectral analysis of lowermolecular-weight samples must take into account the contributions of carbon nuclei in the chain-end structures. Our approach [48] in analyzing the 13 CNMR spectra of PPO was first to define the type of carbon represented by each resonance, i.e., methine, methylene, or methyl. Application of the DEPT and INEPT pulse editing techniques [49] permitted achievement of this objective. Second, by analysis of PPO samples differing in molecular weight we were able to assign those resonances belonging to end-group carbons. The third and final step in the analysis was to assign the

H-H and T-T defect resonances using the y-gauche effect method to calculate (513C values. The carbon nuclei in PPO are shielded by carbon and oxygen y-substituents. From 13 CNMR studies of alkanes and their oxygenated derivatives [19], y c c = —4 to — 5ppm and yc,o = —6 to — 8ppm seem likely for the shieldings produced by C and O y-substituents when in a gauche arrangement with carbon nuclei in PPO. The numbers of such y-gauche arrangements were determined from the bond conformation probabilities calculated for PPO with the RIS model developed by Abe etal. [5O]. This conformational description developed for regioregular (H-T) PPO was modified [48] so as to permit the calculation of bond conformation probabilities in the H-H and T-T portions of PPO as well. Effects of both regiosequence and stereosequence were explicitly considered when calculating relative 13C NMR chemical shifts in PPO via the y-gauche effect method. The results of these calculations for the carbon nuclei in the H-H and T-T defect structures of PPO are presented in Table 2.7. Note the significant differences between the <513C values predicted for the regular H-T and defect H-H and T-T carbons. 13 CNMR spectra of PPO 4000 (M = 4000) and isotactic PPO (M = 14 500) are presented in Figure 2.9. All three carbon types display chemical shift sensitivity to the stereochemistry of the polymer chain. The assignment of resonances to the regioregular portions of PPO (see Table 2.8) is made by comparison of the two spectra, and agrees with earlier work [44,45]. In contrast to 13 C NMR observations for most vinyl polymers, the observed sensitivity of the PPO carbon chemical shifts to stereochemistry is very small. The total spread of S13C is only 0.12, 0.20, and 0.25 ppm for the methyl, methine, and methylene carbons, respectively. This can be contrasted to atactic PP [11], where the range of chemical shifts due to stereosequences is 2.0, 0.5, and 2.0 ppm for the same carbon types. The reduced sensitivity in PPO reflects the presence of three bonds between chiral centers in contrast to the two bonds in vinyl polymers. The limited chemical shift sensitivity is predicted by the RIS model for PPO [50]. On the basis of y-gauche shielding interactions, a spread of H-T chemical shifts of % 0.5 ppm is predicted for each of the three carbon types. The DEPT technique [49, 51] permits spectral editing in such a manner that spectra containing only a specific carbon type can be produced. In Figure 2.10 we show results of DEPT measurements on atactic PPO 4000 for the methine and methylene carbons only. At the vertical gain used in acquiring these spectra the H-T resonances are off scale, and we are observing the resonances of the defect H-H and T-T structures as well as the chain-end carbons. In (a), all CH and CH2 resonances are observed, whereas in (b) and (c) only the CH and the CH2 resonances, respectively, are observed. The most striking feature of these DEPT editing spectra is the observation that there are clearly methine carbon resonances in the upfield region previously thought to contain exclusively methylene resonances, and there also are methylene resonances in the downfield portion of

Table 2.7 Calculated 1 CH3

I

-CH

2

1

13

2 a

CH3 b

I

-CH-O-CH

1

C NMR chemical shifts for poly(propylene oxide) [48] at 23 0 C

2

I

2

3 CH3 3 Diad

Carbon

a

CH 3 I 2 2 2 2 3 3 4 4 5 CH 2 I 2 2 2 2 3 3 4 4 5 CH 1 2 2 2 2 3 3 4 4 5

m r m r m

b

3

2

4

4

2

-CH-O--

5

5

a

C

d

r r m m r m

m m r r m r -

m m r m r

l

-O-CH-CH-O-CH

m r m m m r r m

5 CH 3

d

I

-CH-O-CH-CH

2

4 CH 3

c

r r m

m m r r m r r m m

Chem. shift, PPmb 0.00 0.45 0.49 0.75 0.79 0.53 0.82 0.02 0.04 0.00 0.00 -0.15 -0.19 + 0.20 + 0.25 + 4.40 + 4.73 + 4.75 + 4.78 0.00 0.00 -4.49 -4.45 -4.49 -4.45 -4.48 -4.48 -0.25 -0.27 0.00 + + + + + + + +

"The dash (-) indicates either m or r diad placement. T h e + and - indicate downfield and upfield shifts, respectively, relative to the position of the 1 or 5 (H-T) carbons.

the spectra previously thought to contain only methine resonances. [These observations are confirmed by INEPT spectra (not shown) [48] in which methylene resonances can be observed with negative intensity but methine signals appear as positive peaks.] Certain H-H: T-T and/or end-group resonances at % 73.5 and 75.6 ppm can only be observed in the edited spectra, as they are completely obscured by the H - T peaks in a normal FT spectrum.The

ppm vs. TMS 13

Figure 2.9 50.31 MHz CNMR spectra of (a) atactic PPO 4000, and (b) isotactic PPO, observed [48] at 23 0C in C6D6. see Table 2.8 comparison of resonances in the three spectra of Figure 2.10 permits us to identify each resonance as to carbon type, methine or methylene. To assign resonances produced by various end-groups we compare the spectra observed for PPO 4000 (DP = 69) and PPO1000 (DP = 17) as presented in Figure 2.11. Results of a DEPT measurement on PPO 1000 agree with those for PPO 4000 in establishing the carbon type represented by each resonance. AU of the visible resonances in Figure 2.11 (a), other than the labeled H-T peaks, can be attributed to the end-groups, because the number of such groups is about 3 times that of the H-H: T-T defects in the low-molecular-weight PPO 1000. All of the

Table 2,8 * 3C NMR chemical shifts and relaxation data [48] for headto-tail carbons in poly(propylene oxide) at 230C Chem. shift,a T1, Carbon Resonance ppm s type Stereosequence "1 75J5 078 CH mm 2 75.64 0.80 CH mr + rm 3 75.50 0.81 CH rr 4 73.78 0.51 CH2 m 5 73.54 0.50 CH2 r 6 73.47 0.50 CH2 r 7 17.79 1.03 CH 3 rm,mr,rr 8 17.71 1.03 CH 3 mm,rm, mr, rr 9 75.73 CH mm 10 73.77 CH2 m 11 17.72 CH 3 mm -Figure 2.9.

CH 2 and CH end-group resonances occur in the H - T methine region between 75.0 and 76.5 ppm. DEPT spectra of PPO 1000 (not shown) [48] indicate that no end-group CH resonances are hidden by the H-T methylene resonance at 73.5 ppm. Comparison of DEPT spectra permits the specific assignment of end-group methine (1) and methylene (2) resonances. Note in Figure 2.1 l(a) the end-group methylene resonances at «75.6 ppm, which add to the complexity of the H - T CH region. Comparison of the spectra in Figure 2.11 permits the identification of end-group resonances in PPO 4000 and, by elimination, those resonances that are crosshatched must result from carbons in the H-HrT-T structures. These H-H: T-T peaks are identified as to carbon type from the DEPT spectra in Figure 2.10. A summary of the methine and methylene carbon resonances and their assignment to H-H:T-T defects or end groups appears in Table 2.9. The methyl regions of both atactic PPO samples are displayed in Figure 2.12. Resonances attributable to methyl carbons in or adjacent to an end-group can be assigned by comparison of (a) and (b), where it can be seen that all H-H: T-T defect resonances occur downfield from the H-T peaks. A summary of the methyl carbon data is given in Table 2.10. In order to make the assignments of the carbon nuclei in the H-H: T-T structures, a comparison was made between the experimental chemical shift data (Figures 2.10 and 2.11 and Tables 2.9 and 2.10) and the relative chemical shifts for each carbon type resulting from the y-gauche effect calculations (Table 2.7). The calculated data indicate a lack of sensitivity for all carbons to the nature of the stereochemistry across the T-T portion of the chain (diad c in Table 2.7). In addition, for the H - H methyl and methylene carbons 2 and 3, diad b strongly affects their chemical shifts, but diad a has a much smaller influence. The H - H

ppm vs. TMS

Figure 2.10 Methine and methylene (a), methine only (b), and methylene only (c) 50.31 MHz*3C NMR DEPT spectra of atactic PPO 4000 observed [48] at 23 0C in C6D6

methine carbons, however, are expected to show only a very minor stereochemical dependence. Using the calculated shift data of Table 2.7, it is possible to make the specific assignments given in Tables 2.9 and 2.10. The H-H methine carbons 2 and 3 are predicted to be significantly upfield of the H-T CH resonances (at « 72.8-73.8 ppm) and are observed most clearly in the DEPT editing spectrum (Figure 2.10 (b)). Methine carbon 4 cannot be resolved from the H-T CH resonances. For the CH 2 carbons (Figure 2.10 (a)) the group of resonances slightly downfield of the H-T methylene resonances is assigned to carbon 2, while the methylene resonances (3, 4, 6, 7) shifted downfield into the H-T CH region are assigned to carbons 3 and 4. Despite differences in the magnitudes of calculated and observed shifts for the H-H: T-T vs, H-T methine and methylene carbons

ppm vs. TMS

Figure 2.11 50.31 MHz 13CNMR spectra of (a) atactic PPO 1000, and (b) atactic PPO 4000 observed [48] at 23 0C in C6D6 (1 indicates methine and 2 indicates methylene.) The crosshatched resonances result from the H-HiT-T structure (see below), the predicted direction of relative y-gauche shielding for each carbon permits a consistent set of assignments as given in Table 2.9. These results illustrate the difficulties faced by early workers in assigning the 13 C NMR spectrum of PPO. At first glance one is tempted simply to divide the 73-76 ppm region into two parts, methine and methylene. However, a careful interpretation of the chemical shift effects produced by the H-HiT-T structures shows that a large number of the methine and methylene resonances should overlap, and that the identity of carbon types can be ascertained only by DEPT or INEPT editing experiments [51]. In addition, the comparison of PPO samples differing in molecular weight is necessary to identify the chain-end carbon resonances. The differences in the magnitudes of the S13C values observed and calculated for methine and methylene carbons in the H-HiT-T and H-T PPO structures may stem from the slightly different /J-substituents [19] present in each of these structural environments. The methine and methylene carbons in both H-T and H-HiT-T structures are P to oxygen ( C H - C H 2 - O and C H 2 - C H - O ) , and the methylene carbons are /? to methyl carbons (CH 2 —CH—CH 3 ). However,

Table 2.9 13C NMR chemical shift assignments and relaxation data [48] for the methine and methylene carbons of atactic PPO 4000 at 230C Chem. shift," T\, Resonance ppm Assignment* s I 76J6 —CHE 0.93 2 76.29 —CHE 0.80 3 76.26 -CH23,4 0.80 4 76.21 -CH23,4 0.77 5 76.10 -CH2E 1.19 6 75.98 -CH23,4 0.56 7 75.88 -CH23,4 0.59 8 75.24 —CHE 0.82 9 75.13 -CHE 0.81 10 75.08 -CH-,-CH2E 0.81 II 75.02 -CH2E 0.90 12 74.96 -CHE 1.08 13 74.91 -CHE 1.18 14 74.46 -CH22 1.04 15 74.26 -CH22 0.50 16 74.02 -CH22 0.51 17 73.82 —CH2,3 18 72.97 -CH2,3 0.61 19 72.93 -CH2,3 0.64 20 72.87 —CH2,3 0.68 21 72.06 -CH2E 2.16 22 72.03 -CH2E 2.16 23 73.30 -CH2,3 24 75.65 -CH2E 25 75.57 -CH2E •Figure 2.10. *E indicates chain end structure; 2,3,4 indicate H-H: T-T defect structure (see Table 2.7).

the H-T methine and H-HrT-T methylene carbons are /J to methylene carbons ( C H - O - C H 2 and C H 2 - O - C H 2 ) , whereas H-T methylene and H-HrT-T methine carbons are p to methine carbons (CH 2 —O—CH and CH—O—CH) (See Table 2.7). On the other hand, H-HrT-T and H-T methyl carbons have precisely the same a- and 0-substituents. The fact that the calculated and observed <513C values agree so closely for the methyl carbons (see below) lends support to the suggestion that slightly different /?-substituents for H-T and H-HrT-T methine and methylene carbons may be the source of the disparity between the magnitudes of their measured and calculated <513Cs. The methyl carbon resonances of the H-HrT-T structures are assigned in Table 2.10. Both the calculated magnitudes and the directions of the methyl resonances relative to H-T resonances agree with the observed results (Figure 2.12(a)). The three defect resonances (peaks 4, 5, 6) are assigned to carbons

ppm vs. TMS

Figure 2.12 Methyl region of the 50.31 MHz 13CNMR spectra of (a) atactic PPO 4000, and (b) atactic PPO 1000 observed [48] at 23 0C in C6D6. See Table 2.10 2 and 3 (Table 2.7). Because of the predicted overlap resulting from stereosequences, we cannot make further specific assignments in this region of the PPO spectrum. Note that in Tables 2.8-2.10 values of the spin-lattice relaxation time T1 are presented for each resonance. These were determined by the inversion recovery method and were utilized to insure that quantitative spectra were obtained. From the methyl carbon data (Figure 2.12(a)) we are able to estimate that PPO 4000 contains 2.2% inverted, or defect, H-HrT-T units and has a number-average molcecular weight Mn = 5400, or DP = 93, based on the end-group resonance intensities. This may be compared with Mv = 4000, or DP = 69, provided by the manufacturer and based on KOH hydroxyl number. With the aid of multiple-pulse editing techniques (DEPT, INEPT) and the y-gauche effect calculations of relative 13 CNMR chemical shifts, we [48] have

Table 2.10 * 3C NMR chemical shift assignments and relaxation data [48] for the methyl carbons of atacticPPO4000at23°C Resonance "1 2 3 4 5 6 7 8 9 10 11

Chem. shift,0 ppm Assignment* 19.27 E 19.24 E 18.99 E 18.74 2,3 18.51 2,3 18.38 2,3 17.29 E 19.31 E 19.26 E 19.02 E 17.31 E

T19 s 1.65 1.65 1.80 0.99 0.96 0.92 1.09

•Figure 2.12. *E indicates chain end structure; 2, 3, indicate H - H . T - T defect structure (see Table 2.9).

assigned the 1 3 CNMR spectrum of PPO, including the determination of carbon resonances resulting from chain-end structures. Analysis of the expected differences between the y-gauche interactions of the methine and methylene carbons in H-T and H-H:T-T PPO structures indicated that H - H i T - T methine resonances should overlap with the H-T methylene signals and the H - H i T - T methylene and H-T methine peaks should also overlap. It was this analysis that prompted our reinvestigation and assignment of the 1 3 C NMR spectrum of PPO. From these assignments it was possible to determine quantitatively the number of H-HiT-T defects incorporated in PPO through occasional ring opening of propylene oxide monomer at the CH—O bond. In addition, identification of chain-end structures permitted an estimate of the number-average molecular weight, and (though not discussed here) determination of specific terminal structures also provided insight concerning the polymerization mechanism of PPO.

2.4.4 POLY(VINYLIDENE F L U O R I D E ) (PVF 2 ) With the application of a triple-resonance scheme [52], which simultaneously broad-band decouples both proton and fluorine nuclei while observing carbon nuclei, it was possible to obtain 1 3 CNMR spectra of fluoropolymers that were free of both 1 3 C - 1 H and 1 3 C - 1 9 F J-couplings. As an example, the triple resonance 13 C NMR spectrum of poly(vinylidene fluoride) (PVF 2 ) was successfully interpreted with y-gauche effects of ycc = — 2 ppm and yCF = — 2 to

—4ppm, and an estimate of 3.2% was made for the content of H-HrT-T defect structures shown below -CF 2 -^ CH2-*-CF2-^ CH2-*- CH2-CF2 J- CH2 -*-CH2 -^CF2 -*- CH2 -^CF2 -^CH 2 Having successfully analyzed [53] the 13 C NMR spectrum OfPVF2 containing a small number of inverted units [3.2% of H-H: T-T monomer additions as observed by integration of detect (H-HrT-T) and normal (H-T) resonances], we now attempt to assign and analyze the 1 9 FNMR spectrum of the same PVF 2 sample. The 1 9 FNMR spectrum of PVF 2 measured at 84.6 MHz is presented in Figure 2.13(a). Three small resonances appear 3.2, 22.0, and 24.0 ppm upfield

<X> p p m Figure 2.13 Observed and calculated [54] 19 F NMR spectra of PVF 2 : (a) measured at 84.6MHz; (b) measured at 188.2 MHz; (c) calculated. Vertical expansion in (a) is x 8, in (b) x 40.

from the main H-T fluorine resonance at 91.9 ppm (relative to CFCl3) and are attributed to the fluorine nuclei belonging to H-H: T-T inverted units [55,56]. We may write expressions for the relative 1 9 FNMR chemical shifts SF of the H-T and H-H: T-T fluorines in terms of their y-gauche effects (y FF and yFC) and the bond rotation probabilities (P) which determine the frequencies of y-gauche interactions: 5JT = (I+P t )y F ,c SF = (1 + 0.5 Pt,d + 0.5 Pt>e)yF,c + (1.5 - 0.5 Pt,c)yF,F, S¥ = (1 + 0.5 Pue + 0.5 Puf)yFtC + (1.5 - 0.5 P J y F i F , <5£ = (l+O.5P t , h + O.5P u )y F , c .

(1) (2) (3) (4)

Comparison of Equations' (1) and (4) reveals that <5F~T an 8F are most similar. Thus, SF — SF~T = 3.2 ppm, which leads directly to <5Fc = +30 ppm (shielding). By elimination, \SF — S¥\ = 2 ppm, which yields <5FF = +15 ppm. Substitution of <5FF = 15 ppm and <5FC = 3Oppm into Equations (1-4) leads to calculated SF values shown as sticks in (c) of Figure 2.13, and which compare well with the observed spectrum in (a) recorded at low field strength. At 188MHz four additional defect resonances (1, 5, 6, and 7) appear in the 19 FNMR spectrum OfPVF2 [see (b) in Figure 2.13]. Ferguson and Brame [57] also observed these additional defect peaks and tentatively assigned them to defect structures drawn in Figure 2.13(b) based on a-, /?-, and y-substituent effects derived from the CF 2 resonances observed in various saturated, partially fluorinated linear alkanes. In addition to SF~T, 8F, SF, and 8F, 19 F chemical shifts were also calculated for the defect fluorines 1,5,6, and 7. 19 F y-effects (yF,CH2; 7F,CF2^ anc * yFF) were least-squares fitted to produce the best agreement between observed and calculated <5F values [see (b) and (c) of Figure 2.13]. Best agreement was achieved for yFfCH2 = yF,CF2 = )V,c = 25-30 ppm and yF F = 1 5 ppm, confirming the assignments proposed by Ferguson and Brame [57] and the y-effects derived from the more prominent defect resonances 2, 3, and 4 observed at lower field strength. Measurement of the intensities of the defect resonances and comparison with the total intensity of all observable resonances yields an estimate of 3.4% defect H-H:T-T addition in this sample of PVF 2 . This compares well with the 3.2% defect estimate described earlier using the 13 CNMR analysis. The 1 9 FNMR spectra of poly(vinyl fluoride), poly(fluoromethylene), and poly(trifluoroethylene) were also successfully interpreted [54] with very similar y-gauche effects (y F F =15ppm and y F C = 25-30 ppm), leading to a detailed accounting of their stereo- and regiosequences. In addition to eliminating the need for triple resonance observation [52] of 13 C NMR spectra, 1 9 F NMR spectra of fluoropolymers [54] are much more sensitive to their microstructures, because the conformationally sensitive y-gauche shield-

ings of their 19 F nuclei are nearly an order of magnitude greater than the shieldings observed for their 13 C nuclei. Clearly 1 9 FNMR provides a vastly superior means for characterizing the microstructures of fluoropolymers compared with 13 CNMR observations.

2.5 NMR SPECTROSCOPY AS A MEANS TO PROBE POLYMER CONFORMATIONS 2.5.1 STYRENE-METHYLMETHACRYLATE COPOLYMERS (S-MM) The advent of two-dimensional NMR techniques [58-61] has resulted in a rebirth of 1 HNMR as a means of studying molecular structure. Extensive Jcoupling of protons, which unduly complicates one-dimensional 1 HNMR spectra, is used to advantage in 2D 1 HNMR to map the connectivity of molecules. Those protons that are scalar J-coupled, and therefore interact between the 90°r.f. pulses, evidence cross peaks in a 2D 1H COSY (correlated spectroscopy) spectrum. If an additional 90°r.f. pulse is inserted between the two 90°r.f. pulses of the 2D 1 H COSY experiment, then the correlating influence or interaction between proton spins which results in cross peaks is their direct, through space, dipolar coupling or NOE (nuclear Overhauser effect). This 2D technique is referred to as NOESY and permits a mapping of all proton spins in the sample which are closer than « 4 A. Let us illustrate how the 2D 1 HNMR technique NOESY, i.e., NOE correlated spectroscopy, can be applied to regularly alternating styrene-methyl methacrylate (S-MM) copolymer to learn about its conformational characteristics. The methylene region of the 500MHz 2D NOESY spectrum of the regularly alternating S-MM copolymer is presented in Figure 2.14. The stippled cross peaks correspond to the intermethylene interactions occurring in the S-centered co-hetero S-MM triad seen below: CO-HETERO

These intermethylene N O t cross peaks appear to fall into three categories based

ppm fromTMS ppm from TMS F

2

Figure 2.14 Expansion of the phase-sensitive proton NOESY spectrum at 500 MHz and 800C, showing only the methylene region [62]. Geminal interactions are indicated by crosshatched cross peaks, and intermethylene interactions by stippled cross peaks. The designations S, M, and W refer to the strengths (cross peak volumes) of the intermethylene proton interactions on their intensities: one strong (S), H^-H1; two medium (M), H e -H^ and Ht-Ht'; and one weak (W), H e -H( etc. corresponding to short, medium, and longer interproton distances, respectively (see Heffner et al. [62] for details of the proton peak assignments). By combining portions of the conformational descriptions derived for styrene, methyl acrylate, and methyl methacrylate homopolymers [63-66], Koinuma et al. [67] developed an RIS model for the 1:1 alternating S-MM copolymer. When this RIS model is utilized to calculate the conformation probabilities for the bond pair flanking the styrene methine carbon in the co-hetero S-MM triad illustrated above, it is possible to calculate [62] the average intermethylene

proton distances corresponding to the four cross peaks in Figure 2.14. This procedure is illustrated in Figure 2.15 and Table 2.11. The only three conformations allowed for the co-hetero S-MM triad are drawn in Figure 2.15 along with the probability calculated for each. The intermethylene proton distances rHH calculated for the same S-MM triad are listed for each conformation in Table 2.11. When these rHH values are raised to the — 6 power and averaged over the three possible conformers shown in Figure 2.15 according to the calculated probabili-

FRACTlON

Figure 2.15 Ball-and-stick models of the styrene-centered MM-S-MM co-hetero triad, showing the tt, tg +, and g-t conformations, with 20° deviations from exact staggering [62]

Table 2.11 Intermethylene H-H distances (rHH) calculated [62] for the co-hetero styrene-centered triad (see Figure 2.15) r

HH> A

i>i t,t(-20°,20°) t,g+(-20°,100°) g-,t(-100°,20°) <0 lf *2> <l92>

He-Ht> 189 3.74 3.74 0.0010(0.0027)"

He-He, Ho 2.63 3.68 0.0016' (0.0016)*

Ht-Ht, Ho 3.68 2.63 0.0016(0.0020)*

H e -H t 220 2.59 2.59 0.0063fl (0.0030)*

a

r~£ averaged over all three (^1, ^ 2 ) conformations. *Same as above, except 0 , , ^ 2 = 0, ± 120° in the ^g* states (Heffner et al. [62]).

ties also listed there, the entries in the next-to-last row of Table 2.11 are obtained. These values should be proportional to the strengths of the intermethylene proton-proton cross peaks seen in Figure 2.14, and this is indeed the case. The agreement between the predicted and the observed pattern of NOESY cross peaks for the co-hetero triad of 1:1 alternating S-MM copolymer confirms the validity of the Koinuma et al. [67] conformational model. It is particularly noteworthy that this agreement requires the assumption of «20° displacements from the perfectly staggered rotational states as predicted for the backbone bonds in polystyrene by Yoon et al. [63] (see the Newman projections below). As an example, in the t, t conformation (see Figure 2.15), 0, # 2 = — 20°, 20° because this produces relief from steric interactions of the phenyl ring and the methyl methacrylate C^ as seen in the following Newman projections:

If perfectly staggered states t(0°), g ± (+120°) are assigned in the calculation of intermethylene proton-proton distances, then the results in the bottom row of Table 2.11 are obtained, i.e., all interactions (<**„„» are approximately the same. It is apparent from Figure 2.14 that this is not the case. More recently Mirau et al. [68] have derived intermethylene proton-proton distances rHH directly from the NOESY spectra of 1:1 alternating S-MM. A comparison was made with the distances rHH of Table 2.11 after conformationally averaging according to the Koinuma et al. [67] RIS model. Reasonable agreement was obtained, as indicated by the following observed and (calculated) conformer populations: t, t = 0.58 + 0.05 (0.53), t,g + = 0.24 ± 0.05 (0.20), and g - , t = 0.18 ± 0.05 (0.27). In addition, it was found that an 11° displacement from

perfectly staggered rotational states produced rHH values in closest agreement with those obtained from NOESY cross peak intensities, adding further support to the Koinuma et al. [67] RIS model, which assumed 20° displacements. This ID NOESY 1 HNMR study of 1:1 alternating S-MM copolymer marked the first attempt to derive the conformational characteristics of a flexible polymer in solution through a direct measurement of conformationally averaged interproton distances.

2.5.2 ETHYLENE-VINYL ACETATE (E-VAc) COPOLYMERS Recently, a conformational description (RIS model) has been developed for ethylene-vinyl acetate (E-VAc) copolymers [69] by merging the RIS model descriptions of the constituent homopolymers [70, 71]. Unfortunately no measurements of microstructurally and conformationally sensitive properties have been reported for these copolymers. Traditional global measures of polymer conformation, such as mean-square end-to-end distances and dipole moments, are not yet available for E-VAc copolymers. However, the 1 3 CNMR spectra of a complete series of atactic E-VAc copolymers have been assigned [72-74]. Through comparison of ^ 13 C values calculated [28] via the y-gauche effect method to those previously observed and assigned in E-VAc 13 C NMR spectra, we may evaluate the ability of the RIS model derived for E-VAc copolymers to describe the microstructural sensitivity of the local copolymer conformation, thereby providing an alternate means for testing its validity. Wu and Ovenall [72,73] assigned the low field (22.6 MHz for 13C)13C NMR spectra of E-VAc copolymers by comparison with the 1 3 CNMR spectra recorded for the E-VAc model compounds presented below.

Later Sung and Noggle [74], employing higher field observations (62.9 MHz for 13C) and using paramagnetic shift reagents, corrected some of the earlier assignments made by Wu et al. [72,73]. Even so, they were not able conclusively to discriminate between the assignment of resonances belonging to the methine carbons in the mrmr, rrrr, and mrrm stereosequence pentads of atactic PVAc. We calculated [28] the S13Cs expected for the methylene and methine carbons in the complete series of E-VAc copolymers using ycc = — 3 ppm and 7c,o — — 5 ppm and the RIS model recently developed for these copolymers [69]. Figure 2.16 presents a schematic comparison of methine carbon 5 13 C values observed and calculated for E-VAc copolymers. A similar comparison of E-VAc methylene carbon <513C values is displayed in Figure 2.17. Whereas the chemical shifts calculated for the methine carbons in E-VAc copolymers only reflect differences in the numbers and kinds (ycc and yco) of magnetic shieldings produced by their microstructurally sensitive gauche arrangements with C and O y-substituents (see Figure 2.16), the methylene carbon chemical shifts (see Figure 2.17) reflect in addition different numbers of P-OAc substituents. Wu et al. [72, 73] found /J-OAc = + 5 ppm from their model compound studies, and this value was employed in the calculation of E-VAc methylene carbon chemical shifts. Note the close agreement between <513Cs observed and calculated for the backbone carbon nuclei in E-VAc copolymers. This provides strong support for the efficacy of the RIS model [69] recently developed for these copolymers. In addition, <513Cs calculated for the backbone carbon nuclei in atactic PVAc using

Observed

Calculated

Figure 2.16

Comparison of observed [74] and calculated [28] 13C chemical shifts for the methine carbons in E-VAc copolymers

Observed

Calculated

Figure 2.17

Comparison of observed [74] and calculated [28] 13C chemical shifts for the methylene carbons in E-VAc copolymers

the homopolymer RIS model [71] and the same y-gauche effects employed for E-VAc copolymers generally agree with those appearing in the observed spectrum [74]. This agreement permitted a conclusive assignment of those methine carbon resonances belonging to the mrmr, rrrr, and mrrm pentad stereosequences which Sung and Noggle [74] had been unable to assign unambiguously. In Chapter 3 Howarth et al. describe an extension of the approach employed above to actually derive the conformational descriptions (RIS models) of polymers by comparison of 13 C chemical shifts calculated via the y-gauche effect method with their observed 1 3 CNMR spectra, followed by iterative adjustment of the RIS models until they yield calculated <513Cs in agreement with observed values.

2.6 NMR OBSERVATION OF RIGID POLYMER CONFORMATIONS Although we have dealt exclusively with the analysis of polymer microstructures and conformations by comparison of chemical shifts (<513C, <519F) calculated via the y-gauche effect method and 1 H- 1 H distances, averaged over all conformations available to them, with their observed solution spectra, high resolution, solid state NMR observations can also probe rigidly fixed polymer conformations. It has been demonstrated [75,76] that the 13 C chemical shifts observed in CPMAS/DD 1 3 CNMR spectra of solid polymers are also sensitive to the local rigid conformations of their constituent chains. This has been demonstrated in several instances for crystalline polymers able to crystallize in two or more polymorphs which are distinguishable for the different conformations adopted by their polymer chains. As an example, syndiotactic polystyrene (s-PS) [76] can be crystallized in two conformationally distinct polymorphs, form I, with all-trans, planar zig-zag chains, and form II, where the chains adopt the helical... ttggttgg... conformation, very similar to that observed [77] in syndiotactic polypropylene (s-PP) crystals. CPMAS/DD 1 3 CNMR spectra of both s-PS polymorphs are shown in Figure 2.18. Note in the form II spectrum (b) that two methylene carbon resonances appear at 49.1 and 38.1 ppm (vs. TMS). As half the methylene carbons in form II s-PS are trans to both of their y-substituents(CH's), while the other half are gauche to both of theirs, it is not surprising that two methylene carbon resonances separated by » 2 x ycc (11 ppm) are observed. Identical behavior is observed [78] for s-PP, which also crystallizes in the ...ttggttgg... helical conformation. All the methylene carbons in the all-trans form I crystalline chains are trans to their y-substituents, consistent with the single CH2 resonance observed for this polymorph at 48.4 ppm, which is virtually coincident with that half of the methylene carbons in form II crystals (49.1 ppm) that are also not shielded by their y-substituents.

ppm 13

Figure 2.18 CPM AS/DD C NMR spectra [76] of form I (a) and form II (b) s-PS. The form II sample of (b) was obtained by absorption of dichloromethane into an amorphous, melt-quenched film of s-PS This and many other examples [75, 76, 78] clearly demonstrate the utility of high resolution NMR as a probe of polymer chain conformations as they occur in rigid, solid samples.

2.7 REFERENCES [1] R. Ditchfield, Nucl. Magn. Reson., 1976,5, 1. [2] P.V. Schastnev and A.A. Cheremisin, J. Struct. Chem., 1982, 23,440.

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3 'MODEL-FREE' RIS STATISTICAL WEIGHT PARAMETERS FROM 13 C NMR DATA O. W. HOWARTH, R. N. IBBETT, L R. HERBERT and M. A. WHISKENS Centre for Nuclear Magnetic Resonance, Department of Chemistry, University of Warwick, Coventry CV4 IAL, UK

3.1 INTRODUCTION This chapter describes some new attempts to exploit the rich source of conformational data that is potentially available from the dependence of 13C NMR shifts upon the local tactic sequence in a substituted carbon-based polymer. The main link between shift and conformation is the gamma-gauc/ie effect. This is widely used in the interpretation of 13C chemical shifts in many types of compound. It was initially identified from the classic work by Dalling and Grant [1], and by others [2], on the 13C shifts of hydrocarbons, and especially of methylcyclohexanes, in which specific local conformations could be frozen out by either chemical or physical means. If a molecule contains any partial carbon chain C1-C2-C3-C4, and if Cl and C4 are mutually y-gauche, thus making the C1,2-C3,4 dihedral angle approximately ± 60°, then both C1 and C4 experience an additional shielding, i.e. lowering of <5C, of %5ppm (see Figure 3.1). Similar shifts are observed when CA is replaced by a wide range of groups [3]. The shift effects of different groups do not vary in any obvious way with polarity. Indeed, the shifts that arise from, e.g., hydroxyl substituents may be somewhat smaller than average. However, they do seem to bear some relationship to the bulk of the substituent, and indeed they are often interpreted in terms of steric compression. Various more serious attempts have been made to explain the y-gauche effect by MO computations. The most recent are those of Barfield and Yamamura [4], using an ab initio method with a double-C basis set. Although this level of computation is a little less than that required to give the best available absolute shieldings, it reproduces very adequately a wide range of steric shifts in hydrocarbons (i.e. those dependent solely upon variations in stereochemistry) and also Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

Y - gauche interaction (two of the four present) syn - axial interaction

"P - gaucheT shifts possible at these atoms, because of the A C y - gauche interaction

Figure 3.1 Illustration of stereochemical relationships. In this rotational state, A and B are both y-gauche to the next-nearest non-methylene carbon, and the two A groups are syn-axial to each other, as are the two B groups supports the intuitive assumption that y-gauche contributions to the shift of a given carbon from more than one source are additive. It also draws attention to several other potential steric contributions to carbon shifts, including those that arise from quite modest deviations from dihedral angles of ± 60°. These will be discussed in a later section. Shifts that arise from the y-gauche relationship may be readily computed for polymers, provided that the appropriate RIS (rotational isomeric state) probability parameters [5] are known from calculations of the potential energy surface of the macromolecule. The basic procedure is to start with an estimate, e.g. from molecular modelling calculations, of the free energies and bond angles of the various energy minima found upon rotation of the two (usually) C—C bonds in both the meso (m) and the racemic (r) dyad units of the polymer chain. Neighbouring dyads are then permitted to alter these free energies through the steric restrictions, such as the 1,5 pentane effect, that must apply to the dyad joins. Although these effects extend in theory to an infinite succession of next-neighbours, the calculated sequence dependence of shifts is usually small beyond the heptad/hexad level, at most. Thus one obtains an estimate of the true probabilities for occupation of any dyad in any steric sequence. It is then simple to explore the effects of conformation upon the observed chemical shifts, using, e.g., the y-gauche shift model. Such calculations are described in detail by Tonelli in Chapter 2. They work spectacularly well for polypropylene, with a model having five rotameric states per chain bond. However, Tonelli has pointed out additional factors that must be included when other polymers are considered. One is that the methylene shifts in,

e.g., monohalo vinyl polymers, unlike the methine shifts, show some dependence upon solvent [6]. Another is that no conceivable RIS parameters can explain the rather large steric shifts that distinguish isotactic from syndiotactic poly(methyl methacrylate), either in the solution state or, even more so, in the solid state [T]. These can be up to lOppm in magnitude. A further conceptual challenge arises intuitively. It is reasonable that the shifts at a given sidechain carbon should depend not only upon the proximity of y-gauche atoms, but also upon the identity of the atom or group which will necessarily be syn-axial to it, i.e. its even closer neighbour, in any vinyl polymer. This relationship is illustrated in Figure 3.1. There is also a practical consideration. RIS parameters are not at all easy to calculate in many cases, particularly for disubstituted vinyl polymers. In vinyl polymers with main chain methine groups, a few of the dyad rotamers will often have lower energies than the others, because they place both of the methine protons approximately syn-axial to some other group or chain portion, and thus minimise steric repulsions. However, this is not possible in disubstituted polymers, and indeed even the gauche and trans RIS states themselves are likely to offer poor approximations to the real bond torsional angles. There is also some concern that the contributions of minor conformers may be underestimated if the model assumes unrealistically rigid elements. Furthermore, some polymers have shift patterns for every carbon that depend noticeably upon solvent. Such variations lie beyond the reach of conventional RIS calculations, although they must obviously bear witness to interesting conformational changes caused by the influence of the solvent on the potential energy surface of the macromolecule. The present work is an attempt to address the above challenges by turning the methodology around. Might it prove possible to obtain reasonable RIS statistical weight parameters, of use to other modellers, by treating the carbon shifts as given data and the RIS parameters as variables? Complete sets of such sequencedependent shifts have been fairly reliably assigned at the tetrad/pentad level for many mono- and disubstituted vinyl polymers, and in some cases the spin-spin coupling constants are also available as further constraints on any model. The obvious attraction of this approach is that the RIS variables may be overdetermined. Suppose that one allows only three rotameric states per chain bond, and treats any possible sidechain rotamers as having a constant average contribution. Even if the probability of each dyad rotamer is allowed to vary independently, after due regard for symmetry, there are only 10 undetermined probability ratios in a vinyl polymer. (Note that the ratio of the m- to the r-dyad probabilities is not significant in the present context). To these 10 must be added a single variable, such as the g*g*/g~g~ elements of Flory's Un, matrix [8], which controls the extent by which 1,5 syn-axial chain segments are forbidden. This extent may not be 100% after allowance for minor distortions of the intervening torsional angles, especially when the substituent groups are small, and even more so if they are capable of favourable interactions such as hydrogen bonding. To determine these

11 variables we typically have some 16-30 different steric shifts, or even more if the assignment can be made at the hexad/heptad level. Thus the quality as well as the existence of any shift fit might be used to assess the reliability of the calculation.

3.2 METHODS The first problem that arises with this approach is that the y-gauche contributions from many groups are not known accurately. Some may be estimated from the shifts of molecules is known conformations, e.g. substituted cyclohexanes, but others remain to be established. An underlying principle of the present study is that all such parameters be fixed for a given group, even if it appears in several different polymers. Another principle is that all the carbon resonance patterns of a given polymer must be fitted simultaneously. Indeed, as a further simplification, we specify that the shift effects depend only on the substituent, and not on the type of carbon (e.g. C, CH, CH 2 , CH 3 , CO, CN) under observation. Fortunately, the numerical value of most shift parameters does not in practice greatly affect the resulting RIS weightings, within a reasonable range. It is the shift patterns which dominate the calculation. The second problem is to meet the challenge of polymers such as poly(methyl methacrylate), which fit poorly to any scheme based simply on y-gauche contributions to the methyl shift. Our proposal is that, for such groups, the y-gauche contributions should be subdivided into three separate syn-axial contributions from the appropriate groups S to the carbon under observation. Thus, an a-methyl group in poly(methyl methacrylate) may be y-gauche to the next-nearest unprotonated carbon, but then it must also be sjw-axial either to another a-methyl or to a carboxymethyl group or to the chain methylene in the next dyad. These three will not necessarily cause the same shielding at the original methyl, although their average shielding effect should not very greatly from a typical value of, say, 5 ppm. One should note in this context that a hydrogen atom may be an active substituent, because the shifting unit is in fact both the syn-axial H and also the gauche C, even though we refer to the shielding parameter for brevity as being simply 'syn-axiaF. Indeed, one may not even assume that H necessarily imposes a smaller 'syn-axiaF shielding than any other group. We show below that this model is capable of allowing surprisingly large methyl shifts. The next problem arises from Tonelli's observation that some methylene shifts depend noticeably upon solvent. If these changes are not matched by corresponding changes in other shift patterns, then they cannot be explained by RIS weightings alone. Tonelli and Schilling have suggested [6] that they may arise from differential solvation of m- and r-dyads, which should affect methylene shifts much more that others. We accept this suggestion by creating one more adjustable parameter, a variable, solvent-induced shift difference between m- and

r-methylenes. In most cases this turns out to be small, but even so it turns out in general to give noticeably improved fits. Finally, one must decide on the size of the RIS dyad matrices. In this respect, the present work is not altogether 'model-free'. The main problem is that each gauche state, and perhaps also the trans state, probably exists with two variants [5], so as to ease the concomitant syw-axial repulsions. In cases where detailed calculations have been made [9], these variants typically shift the chain dihedral angle from ± 60° to ± 50° and to ± 70°, with unequal weightings and with a very low or non-existent intervening energy barrier. It would probably be ideal to use a generalised 6 x 6 state model in order to allow for this. However, this would generate an unacceptable number of variables. Instead, we have chosen a simple 3 x 3 state model. This implies the assumption that the probabilities of each nearby pair of rotational states may reasonably be represented by their sum, and thus that the shift contributions from each state are comparable. Barfield and Yamamura [4] have indeed shown that the y-gauche effect varies monotonically with dihedral angle in an approximately sinusoidal manner, so that the shift contributions from the ±50° and from the ±70° angles should be not too different. Although the resulting, simplified RIS parameters will be more artificial, they should retain their usefulness for most calculations simply because of their derivation from experimental data.

3.3 SOMECALCULATIONDETAILS A spreadsheet calculation (using Microsoft Excel version 3.0) was written to convert the 3 x 3 m- and dyad probability matrices into predicted steric shifts, by the usual methods of matrix multiplication, to find overall conformational probabilities. Although the final calculations were only carried out at the tetrad/pentad level, the calculations assumed further, flanking m-dyads in each case in order to give more realistic weightings. The linking U i r matrix was assumed to have one freely variable component, g*g+/g~g~, with the other elements being fixed at unity. This has the effect of permitting all dyad joins equally, except for those which result in syw-axial chain segments. The latter are suppressed in proportion to the variable component. In fact, none of the fitted values of g*g+/g~g~ exceeds the necessary bounds of zero to approximately unity. As described above, a further shift variable was then introduced, to give the same shift increment to each r-methylene resonance. These increments were never large, and typically were less than ±0.4ppm. The resulting shift patterns were compared with the experimental data, which are described in detail below, and the squared shift differences were summed. In some cases one resonance of a polymer shows little spread of shifts, and so cannot be reliably assigned, and here the calculated shifts were constrained within limits set by the overall

linewidth of the data, without regard to their detailed assignment. Such data are represented in the appropriate figures by single, broad Lorentzian peaks. The sums of squared differences were then minimized with respect to the above variables. Minimisation was carried out by the Newton-Raphson method using Microsoft Solver version 3.0. It was almost invariably well-behaved, and for each polymer it converged to give essentially the same results from a wide range of starting parameters. Various calculational refinements were also tested in the hope of improved fits, but, interestingly, they had little extra success. These included attempts to reduce the g~g+/g*g~ elements in U n , to values below unity. This gave good results only with polystyrene. The calculations also permit an estimate of the reliability of individual parameters. In some cases, the data closely defined all the parameters. In others, a few parameters, noted below, rose to unreasonably high values in the final fits, such as y-gauche shifts > lOppm. However, these could be reduced in all cases to reasonable values without a loss of fitting accuracy greater than the experimental errors of shift measurement. The RIS elements were not permitted to become negative. Apart from this, the calculations were deliberately kept as simple as possible, because of the aim of practical usefulness to modellers.

3.4 INDIVIDUALPOLYMERS The method was first tested on polypropylene, because the shifts for this polymer are reliably known as is its accessibility to shift calculations. Furthermore, both the methyl and the chain methylene groups have been shown to give (and receive) y-gauche shifts of close to —5.0 ppm [9]. This usefully reduced the number of variables in the calculation, though in fact little change was observed even if they were allowed to float. The resulting fits, using our simplified 3 x 3 RIS approximation, were not quite as good as those obtained by Schilling and Tonelli [9], especially in that they slightly underestimated the shift contributions from the more distant chain groups. However, the fit was still very good, as is shown in Table 3.1. The syn-axial shift from H was initially permitted to float, but in a variety of calculations it always came close to —4.0 ppm, and so it was fixed thereafter at this value. The next polymer to be tested was poly(acrylonitrile), which is readily available with minor known variations of tacticity within the approximately atactic range. Full shift data for this have not been published and are therefore presented in Table 3.2, using both dimethyl sulphoxide-d6 (DMSO) and waterd 2 /Na + [SCN] " solvents. Our assignment, based on integration rather than peak height and using several minor variations in tacticity, reverses a previous assignment [10] for the CN mrrm and rrrr resonances. The differential effects of distant groups are small and so the assignments are straightforward, except for the unresolvable methylene resonances. Each set of RIS calculations led to a CN

Table 3.1

Relative

13

C shifts in polypropylene

CH^ mmmm mmmr rmmr mmrm rmrm mmrr rmrr mrrm mrrr rrrr

CH^ 0

obs.

calc.

1.99 1.73 1.46 1.10 0.81 1.27 0.96 0 0.27 0.49

1.94 1.72 1.50 1.10 0.84 1.25 1.00 0 0.23 0.43

mmm mmr rmr mrm mrr rr

CH

obs.

calc.

0.79 1.35 2.07 0 0.88 1.81

0.81 1.37 2.03 0 0.93 1.81

mmmm mmmr rmmr mmrm rmrm mrnrr rmrr mrrrn mrrr rrrr

obs.

calc.

0.50 0.45 0.40 0.17 0.14 0.28 0.23 0 0.04 0.08

0.51 0.51 0.51 0.22 0.23 0.25 0.26 0 0.03 0.05

'y-gauche/d sjw-axial parameters: CH 2 , CH 3 - 5.0ppm, (C)H -4.0ppm. RMS error 0.039 ppm.

Table 3.2

Observed

13

C shifts/ppm for poly(acrylonitrile)

CN mmmm mmmr nnmr mmrm rmrm mmrr rmrr mrrm mrrr rrrr

cii

DMSO

water/NaSCN

119.73 119.66 119.59 119.36° 119.29 119.45 119.36 119.00° 119.09° 119.18

122.8 122.7 122.5 122.4 122.3 122.5 122.4 122.0 122.1 122.2

DMSO mm mr rr

26.50 27.04 27.47

water/NaSCN 29.40 29.77 29.85

CH 2 «32.6 «34.3 both almost unresolved

"Some further fine structure is visible.

and syn-axial S shift parameter of —2.84 ppm. The fits are fairly good, although they underrepresent the fine structure in the CN region. The favoured conformations are in reasonable agreement with those deduced by Ganster and Lochmann [11] for 2,4-dicyanopentane in vacuo. Similar calculations were then performed for poly(vinyl alcohol). They are shown as sticks, below the aqueous spectrum, in Figure 3.2. Here the sample is complicated by incomplete removal of acetate groups. However, the removal was >90%, and so the dominant peaks in the spectrum are those of fully hydrolysed regions. The effects of distant groups were once again small. The assignments in DMSO are published [12]: those in water were assigned largely by analogy, although the methylene data were sufficiently different to require some confirmation via homo- and heteronuclear shift correlation experiments. The calculated

CH

CH2

Figure 3.2 100.6MHz 13C(1H) NMR spectrum of poly(vinyl alcohol); CH and CH2 regions. Calculated shifts (with atactic weightings) are shown as sticks below, in the same order of assignment

RIS parameters (Table 3.3) show that H-bonding, even in water, is sufficient to overcome some of the steric repulsions, including those associated with the 1,5 pentane effect, between 5yw-axial chain segments. One possible flaw in the poly(vinyl alcohol) calculations is that the shifts might also be directly and differentially affected by H-bonding. However, an independent study of saccharides in water and in DMSO indicates that this is probably not so. Another interesting feature is that, when the rotamers that were calculated to be dominant were reset to be totally dominant, then the CH shift pattern was

Table 3.3 T polypropylene m-dyad r-dyad poly(acrylonitrile) in DMSO m-dyad r-dyad poly(acrylonitrile) in water m-dyad/NaSCN r-dyad poly(vinyl alcohol) in water m-dyad r-dyad poly(vinyl alcohol) in DMSO m-dyad r-dyad polystyrene m-dyad r-dyad poly(methylacrylonitrile) m-dyad r-dyad poly(methyl methacrylate) m-dyad r-dyad poly(vinyl chloride) m-dyad r-dyad a

Calculated RIS statistical weight parameters"

*v

tg'lg't

tg+fg+t

0

0 0

1 0

0 0.08

0 0

0 0.94

0.08

0 0

1 0

0 0.41

1.79 0.51

0 1.04

0 1

0 0

1 0

0 0.12

0.65 0.51

0 0.96

0.40

-0.01

1 0.22

0 1

0 0

0.40 1.55

0 0

7.51 0.93

0.78

+ 0.32

0 1

0 0

0.69 2.71

0 0

0.23 0

0.75

-0.06

0.18 0

0 0

1 0

0.01 0

0 0

0 2.91

0*

-0.77

0.01

1 0

0.28 0.36

0.39 1.26

0 0

0 0

0.07

-0.22

0.31 0

0 0

-0.19

0.35

0 0

0.00

0.02 0.41 0

1 0

0.37 0.16

0 0

0 0.87

0.00

+ 1.12

9 9

<5(CH2)/ppm

391K 0.22

+ 0.07

373 K 0.41

+ 0.20

300K

295 K

295 K

363 K

363 K

300K 1.01 393 K 0.04 1

g* and g defined as in Flory [5]. g~g+/g+g~ links across the chiral carbons were also completely forbidden in this case.

b

g g+/g+g

tt

essentially magnified by a factor of « 3 . It then fitted quite well with the solid-state data of Terao et al. [13], who obtain a CH shift spread of « 1 0 ppm. Tonelli (Chapter 2) has interpreted solid-state polypropylene shifts in a similar way, based on structures deduced by Bunn et al. [14]. Poly(acrylonrtrile) in DMSO

Poly(acrylonitrile) in water/NaSCN

Poly(vinyl alcohol) in water

Poly(vlnyl alcohol) In DMSO

Figure 3 3 {Continued)

Polypropylene

Polystyrene

Poly(methyiacrylonrtrlle)

Poly(methyl methacrylate)

Figure 3.3 (a),(b) Upper traces: 13 C( 1 H) NMR spectra for eight different polymer solutions, calculated at the tetrad/pentad level. Lower traces: observed shifts, simplified to the same level, and further, to broad Lorentzian peaks of representative width, if overlaps prevent assignment. The numbers are shifts in ppm

The shift parameter for OH did not converge well, however, perhaps because of the unusual number of accessible conformations and the presence of only two types of carbon atom. Values ranging from O to — 5ppm gave acceptable predictions of the observed shifts. To resolve this problem, we instead used an independent and strongly convergent value of — 3.5 ppm, obtained from an extensive study of hexopyranose sugars of known conformation in both water and DMSO [15]. This value is lower than that for H, which may help to explain the otherwise curious observations by Stothers and coworkers [16, 17] on s>w-axial shifts in sterols and related compounds. The other monosubstituted vinyl polymer to be studied in detail was polystyrene. Its spectrum is made complex in the methylene region by large shift influences at the hexad/heptad level. These probably arise from the anisotropic bulk of the phenyl rings. Our calculations are certainly naive in ignoring this anisotropy. The methylene region may speculatively be divided into four broad subsections, approximate assignments of which were checked by the classical area method. Our assignments confirm those of Sato etal. [18]. The unprotonated phenyl carbon shifts are more easily assigned by the same method. The shift calculations were only successful if all gg links across the chiral carbons were fully disallowed. They then gave a broadly reasonable but less than perfect fit. Although this restrictive possibility was also investigated for other polymers, it only gave useful results in this case. The phenyl shift constant converged well, to —4.58 ppm. The next polymer, poly(methylacrylonitrile), presented a more severe test in that there were no remaining variable shift parameters, and also one further resonance region to be fitted. An initial assignment was made following Inoue et al. [19], but with a spectrum taken at higher frequency, and with the methylene sub-areas rechecked. The fit is encouraging although not perfect. Finally, it proved possible to obtain an acceptable fit for poly(methyl methacrylate) using a carbomethoxy shift parameter of —9.50 ppm. This shift was not very well defined by the data, although it must certainly be large. (When it was permitted to float freely in the minimisation, it drifted upward to ^ — 14 ppm, but with only a very minor resulting improvement in the least-squares fit.) If the conformations that we calculate to have highest probability are instead set to be dominant, then the syndiotactic chain becomes all-trans, as observed in the solid state by Speracek et al. [20], and a 4-8.14 ppm shift increment is predicted on going from the syndiotactic to the isotactic polymer. The experimental figure is between + 6.0 and + 8.45 ppm. The fits are all presented in diagrammatic form in Figure 3.3(a) and (b). Calculated relative shifts are plotted upright, with a standard Lorentzian lineshape and with intensities that assume a strictly atactic sample. The vertically inverted plots are idealisations of the experimental spectra. Broad Lorentzian bands are used to depict the extent of any overlapped and hence unassigned resonances. The order of assignment of the resolved peaks, calculated and

observed, is the same in every case expect for the fine structure in the COOMe and CH 3 (mr) resonances of poly(methyl methacrylate). The same fits could not be approximated for any of the polymers by any alternative and significantly different set of minimised RIS parameters. Fits (not shown) have also been successfully generated for poly(vinyl chloride). In this case the experimental steric shifts for both carbon types varied by % 2 ppm. The worst methylene fitting error was 0.11 ppm. The Cl shift parameter minimised to —4.01 ppm, and the mmethylene shift factor was unusually large, at 1.12 ppm.

3-5 THE CALCULATED RIS PARAMETERS The complete set of calculated RIS parameters is presented in Table 3.3, and some of the conformations that are calculated to be dominant are depicted in Figure 3.4. Those for polypropylene confirm the simple predictions that the dominant conformations are the four where no carbon is syn-axial to any other carbon, and that the methylene groups have a very similar bulk to the methyls. However, those for poly(acrylonitrile) deviate markedly from this. Although it remains true that the CN groups, like the methyls in polypropylene, resist being mutually syw-axial, this may be seen from simple modelling to result from unfavourable dipolar alignment rather than from steric interactions. Also, the possibility exists that some other mutual orientations of CN groups may be sufficiently favoured, for the same reason, to override concomitant but less favourable steric interactions, e.g. between CN and the chain methylenes. Such dipolar interactions are very hard to model independently because of the difficulty of defining the local dielectric medium. It is interesting to note that, in the unusually polar solvent D 2 O/Na + [SCN]", the RIS term tt(m) is decreased yet further with respect to that in DMSO solvent. This term involves syw-axial CN groups. Evidently their polar repulsion is increased by the very polar solvent, perhaps because the cations polarise the CN groups further while being sterically unable to interpose themselves. The opposite behaviour is evident in poly(vinyl alcohol). The m-dyad shows a marked preference for the tt and g~g~ conformations (see Figure 3.4) over the more normal tg* and g+t. The tt and g~g" conformations both involve closeness of the OH groups, created presumably by H-bonding, and sufficient to overcome steric repulsions in the latter case. The same pattern holds for the r-dyad. The tg ~ and g~ t conformations are now the ones with syn-axial hydroxyls, and these are again favoured along with the unexpected g~g~ conformer, possibly in a rather distorted form so as to permit another H-bond. The only big effect of changing the solvent from DMSO to water is a large increase in the g+g+(m) term. Perhaps water is able to enhance the intramolecular H-bonding that is sterically possible from this conformation.

poly(acrylonitrile) r-diad, tt rotamer

poly(acrylonitrile) m-diad, tg* rotamer

poly(vinyl alcohol) m-diad. tt rotamer

poly(vinyl alcohol) r-diad, tg rotamer

poly(acrylonitrile)

poly(methyl methacrylate)

m-diad. gg* rotamer

m-diad. tt rotamer

Figure 3.4 Some typical dominant dyad conformations

The calculations for polystyrene are discussed above, and should be regarded with caution. They do, however, yield sensible RIS parameters, which are like those for polypropylene, except for larger repulsions between phenyl and H than between methyl and H. In contrast, poly(vinyl chloride) is intermediate between polystyrene and polypropylene, although in this case a tendency is also evident for neighbouring C-Cl bonds to lie approximately antiparallel, perhaps for dipolar reasons.

The parameters for poly(methylacrylonitrile) are less easy to anticipate, because most conformations will involve either steric or dipolar repulsions. The most likely conformations will be g+f(m), tg+(m), tt(r) and g+g+(r), because these alone allow the CN groups to lie syw-axial to other groups, and not to themselves. The CN group has less steric bulk than, say, methyl. The calculations bear out this prediction, although they do to some extent also permit one conformer, g ~g ~(m), in which neighbouring CN groups are syn-axial. Not surprisingly, for the reasons discussed above, the fit for poly(methyl methacrylate) has the biggest error sum of the present series. Nevertheless, the fit is acceptable given the approximations, which in this case include ignoring the carboxymethyl orientations. Once again, there is a preference for the four conformers as above, because the carboxymethyl group also has a low steric bulk in some orientations. However, the fit also shows a marginal preference for the tt state in the m dyad, consistently with the solid-state data noted above [20]. This will no doubt be made possible by a favourable mutual orientation of the carbonyl dipoles.

3.6

'P-GAUCHE9EFFECTS

The experimental evidence for y-gauche shifts [3] may also point to concomitant shifts of the two carbons that connect the y-gauche groups, as marked in Figure 3.1. These 'fi-gauche' shifts seem to be of the same sign as the y-gauche ones, but of approximately half the magnitude. Unfortunately, because they are smaller, they are less easy to quantify. We have experimented with the inclusion of ft-gauche shifts in our model, with values half those for the corresponding y-gauche shifts. They do not affect the qualitative conclusions above for any polymer, and the fits are generally a little less satisfactory in each case. Thus, although such shifts probably do occur, it is not necessary to include them at the present level of approximation.

3.7 COUPLING CONSTANTS In principle, it is also possible to use interpf oton coupling data in monovinyl polymers to assess the conformational equilibria. For such calculations one needs not only the weightings for the conformations but also their torsional angles, and a reasonable estimate of the appropriate Karplus relationship [21] between the HCCH dihedral angle and the corresponding coupling. In practice, it is not easy to separate the peak splittings due to couplings from those arising from tacticity. In some cases, and for some components, the separation can be achieved by a 2D ./-resolved spectrum [22]. In favourable case this procedure may also provide an assignment, because the methylene protons in an r-dyad will be at least approxi-

CH

CH2

ppm 1

Figure 3.5 Partial 2D ./-resolved H NMR spectrum of poly(acrylonitrile) in DMSOd6. The multiplets are effectively rotated into the vertical dimension. The large peak at 3.06 ppm arises from water, and the uneven ridge marked x is partly an artefact

Table 3.4 Coupling constants 3 polypropylene J(obs)/Hz 7.0 and 6.5 (m) 3 J(calc)/Hz 7.34 and 7.25 (m) 3 poly(acrylonitrile) in DMSO J(obs)/Hz 8.4 and 6.0 (m) V(calc)/Hz 8.16 and 5.85 (m)

7.0 (r) 7.13 (r) 7.5 (r) 7.32 (r)

mately isochronic. Figure 3.5 shows an example of such data for poly(acrylonitrile) in DMSO. The couplings are compared with calculated values in Table 3.4, along with those for polypropylene, which have been deduced from the spectra of oligomers. However, the calculated values are not very sensitive to conformation, and their absolute values depend on what allowance one makes for libration within each RI state when setting the t and g couplings for individual vicinal proton pairs. The present study uses 12.0 Hz (t) and 2.0 Hz (#, polypropylene) or 4.0Hz (g, poly(acrylonitrile)).

3.8 CHARACTERISTICRATIOS One may in principle check RIS calculations [5] by the measurement of characteristic ratios 0 /n/ 2 , particularly as a function of tacticity. However, such correlations present several problems. The published experimental data are limited in extent and show significant scatter. Also, the calculations require a good estimate of the chain torsion angles in each conformer. Nevertheless, some comparisons are possible, because in vacuo modelling calculations are likely to give reasonably accurate torsion angles even when their predictions of energy are suspect. We have used our RIS data together with published torsion angles to calculate the characteristic ratios for polypropylene at various temperatures in the solution state. Table 3.5 shows that they agree well with the experimental data [23]. Earlier calculations tended to fit poorly at the extremes of tacticity, perhaps because they underestimated the contribution of minor conformations. The calculations were performed using the Biosym RIS package, with a 200-unit chain and randomised tacticity.

Table 3.5 syndiotactic atactic isotactic

Characteristic ratios for polypropylene

Calculated ratio

Observed ratio

Earlier estimates

7.6(320K) 5.4(435K) 6.3(305K) 5.3 (420 K) 5.4(400K)

6.7(318K) 5.4(426K) 6.5(307K) 5.0(456 K) 5.9(398K)

11.0(413K) 5.5(415K) 4.2 (413 K)

syndiotactic

atactic

isotactic

Figure 3.6 Observed (squares) and calculated (lines) characteristic ratios for poly(methyl methacrylate) at 333 K, plotted as a function of tacticity. The lines are based on RI states with chain dihedral angles of (upper line) 10,20,100,115, - 1 0 0 and -115°, (central, broken line) 10,20,100,125, - 1 0 0 and -125°, (lower, hatched line) 15,20,100,110, - 1 0 0 and-110°

Calculations were also performed for poly(methyl methacrylate). These were more complex, because modelling shows each RI state to be markedly doubled because of syw-axial interactions. Also, the calculated torsion angles were less reliable than above. We approached this problem by dividing each RI state into torsionally close pairs in the calculation, and assuming equal probabilities for each member of a pair. In particular, this permitted some twist in a chain dominated by tt states. Calculations are presented in Figure 3.6 for three reasonable choices of torsional angle sets. The comparison with experiment [24] is encouraging. However, characteristic ratios alone are not a sensitive test of RIS weightings, for many combinations of weightings will give similar results.

3,9 CONCLUSIONS Although there is no guarantee that our simple model will be capable of predicting the shifts observed for any given polymer, the present fits are encouraging. They were undertaken, in part, to assess the validity of the y-gauche shift model. It is likely that ab initio calculations will soon be able to refine this model. Indeed, the work of Barfield and Yamamura [4] suggests that unusual shifts may arise in rather specific conformations over a narrow range of torsion angles. These may help to explain the rather unexpected shifts sometimes observed in the solid state, but they are less likely to be a problem in the more widely averaged local environments of the fluid state. One may therefore

reasonably propose that the present model generates relative RIS parameters for the fluid state that are of genuine predictive value.

3.10 ACKNOWLEDGEMENT We thank Dr. CJ. Samuel for many helpful discussions.

3.11 REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]

D. Dalling and D.M. Grant, J. Am. Chem. Soc, 1967,89, 6612. D.M. Grant and B.V. Cheyney, J. Am. Chem. Soc, 1967,89,5315. H.-J. Schneider and V. Hoppen, J. Org. Chem., 1978,43, 3866. M. Barfield and S.H. Yamamura, J. Am. Chem. Soc, 1990,112,4747. PJ. Flory, Macromolecules, 1974, 7, 381. A.E. Tonelli and F.C. Schilling, Ace Chem. Res., 1981,14, 235. A.E. Tonelli, Macromolecules, 1991, 24, 3065. PJ. Flory, P.R. Sundararajan and L.C. DeBoIt, J. Am. Chem. Soc, 1974,96, 5015. F.C. Schilling and A.E. Tonelli, Macromolecules, 1980,13, 270. J. Schaefer, Macromolecules, 1971,4,105. J. Ganster and J.R. Lochmann, Polymer, 1990,31,1159. T.K. Wu and M.L. Sheer, Macromolecules, 1977,10, 529. T. Terao, S. Maeda and A. Saika, Macromolecules, 1983,16,1535. A. Bunn, E.A. Cudby, R.K. Harris, KJ. Packer and BJ. Say, J. Chem. Soc,Chem. Commun., 1981,15. P. Hobley and O.W. Howarth, to be published. W.A. Ayer, L.M. Browne, S. Fung and J.B. Stothers, Can. J. Chem., 1976,54, 3272. S.H. Grover, J.P. Guthrie, J.B. Stothers and CT. Tan, J. Magn. Reson., 1973,10,227. H. Sato, Y. Tanaka and K. Hatada, Makromol. Chem. Rapid. Commun., 1982,3,19. Y. Inoue, K. Koyama, R. Chujo and A. Nishioka, Makromol. Chem., 1974,175,277. J. Spevacek, B. Schneider and J. Straka, Macromolecules, 1990, 23, 3042. J. Kowalewski, Prog. NMR Spectrosc, 1977,11,1. W.P. Aue, E. Bartholdi and R.R. Ernst, J. Chem. Phys., 1976,65,4226. W.W. Suter and PJ. Flory, Macromolecules, 1975,8, 765. P.R. Sundararajan, Macromolecules, 1986,19, 415.

4

NMRSTUDIESOFSOLID POLYMERS R. K. HARRIS Department of Chemistry and IRC in Polymer Science and Technology, University of Durham, South Road, Durham DHl 3LE, UK

4.1 INTRODUCTION It is the intention in this chapter to present an overview of some major aspects of NMR studies of solid polymers and to give some examples of applications. It will also provide the background to the more sophisticated multi-dimensional solidstate NMR techniques discussed in Chapter 5. NMR studies of solids can be generally grouped into three types: (a) broadline spectra; (b) relaxation times; and (c) high-resolution spectra. Of course, spin-spin (transverse) relaxation directly affects the observed signal (free induction decay) from pulsed NMR operation, which is Fourier transformed to yield the spectrum, so that the three areas are not totally distinct. This article will address all three aspects but will only relate to 1H, 19 F and 13C NMR. In particular, there will be no discussion of 2H spectra of polymers, important though that topic is. In suitable circumstances other spin- \ nuclei such as 15N, 29 Si and 3 1 P can be relevant, and they will behave much like 13C. Following the discovery of the NMR phenomenon in 1945 by two groups of physicists [1,2] NMR was applied to a wide range of systems, both solids and solutions. However, it rapidly became obvious that solution-state NMR was exceptionally useful to chemists because the high resolution achieved (with linewidths for 1 H less than 1 Hz) allowed small but important effects (i.e. chemical shifts and splittings due to coupling constants) to be observed. Solid-state NMR became for a while the esoteric preserve of a few hardy physicists and physical chemists. This situation became even more apparent after the introduction of the Fourier transform principle made high-quality 13C spectra obtainable. The reason for the relative neglect of solid-state NMR in the period 1955-1975 is apparent from Figure 4.1. Although it is clear that there is some useful information [3] (as the stereoregularity affects the spectrum), the resonances are % 50 kHz in width, with no fine structure. AU information on chemical shifts and coupling constants appears to be lost. The reason for such a disappointing Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

Figure 4.1 200MHz proton NMR spectrum of solid isotactic polypropene: A, high stereoregularity sample; B, low stereoregularity sample situation is that all NMR interaction of importance (especially shielding, dipolar coupling and indirect coupling) depend on the orientation of the local nuclear environment in the applied magnetic field B 0 . In mobile isotropic liquids or solutions the effects are averaged. The average dipolar coupling is zero, so it is eliminated from solution-state spectra; each active nucleus has an intrinsic shielding constant and each nuclear pair a single coupling constant. In solids, there is usually relatively little motion. Moreover, most samples (except single crystals) have a complete range of molecular orientations in the magnetic field. Both these factors lead to substantial line-broadening.

4.2 THE TECHNIQUES Fortunately, a series of techniques can be used to overcome the problems. The most ubiquitous is magic-angle spinning (M AS) [4], which consists of rotating the sample rapidly about an axis making an angle of 54.7° to B 0 (Figure 4.2). In principle this removes all the relevant anisotropies in most circumstances, yielding spectra comparable with those of solutions. Unfortunately, it is not normally possible to spin fast enough (up to 50OkHz would be required for extreme cases such as protons in rigid CH 2 groups). Additional techniques are therefore required. For the observation of dilute spins (such as 13C) in the presence of abundant spins (such as 1H), high-power heteronuclear decoupling (HPHD) is necessary. Combined with MAS, this yields 13 C spectra with linewidths as low as a few Hz in favourable cases (but at least an order of magnitude larger for polymers). However, HPHD is not applicable to the direct

Figure 4,2 The arrangement for magic-angle spinning (diagrammatic)

Figure 4.3 The WAHUHA pulse sequence [5] used for homonuclear decoupling in solids. AU pulse angles are 90°. The r.f. phases are indicated above them. The middle four pulses illustrated form the repeat unit of the sequence, s marks a sampling point observation of abundant spins. Special pulse sequences, using phase-alternated 90° pulses interspersed with single-point measurements, are used instead. Figure 4.3 shows the repeat unit of the simplest such sequence [5], known as WAHUHA. When a suitable sequence is combined with MAS at modest speeds («5kHz), anisotropic effects are removed. This combination of techniques is known as CRAMPS (combined rotation and multiple pulse spectroscopy) [6]. Multiple-pulse techniques of the WAHUHA type are also of value for proton homonuclear dipolar decoupling in experiments where other nuclei, such as 13 C, are observed under either static or MAS conditions. An additional problem, especially for dilute spin- \ nuclei, is that relaxation times in solids can be very long. Consequently normal pulse Fourier transform NMR, which requires delays between pulses of about five times T1, becomes very inefficient. However, a clever double-resonance pulse regime [7] known as cross-polarisation (CP) overcomes this difficulty; see Figure 4.4. During the contact time, magnetisation flows from protons to carbons provided that the radiofrequency powers are matched, enhancing the signal by a factor of « 4 and allowing repetition times to depend on T1 (1H) rather than T1 (13C), the former being generally substantially shorter than the latter. The first example of the CP/HPHD/MAS combination of techniques [8] sparked an explosion of research activity, and polymer chemistry has been one of the principal beneficiaries. Figure 4.5 shows the influence of the HPHD and MAS techniques in securing

Figure 4.4 The cross-polarisation pulse sequence. The contact time (CT) is of the order of ms. DC designates decouple

Figure 4.5 Cross-polarised 75 MHz 13 C spectra of solid poly(methyl methacrylate): A, static, coupled; B, static, proton-decoupled; C, with MAS, coupled; D, with MAS, protondecoupled

Figure 4.6 22.6 MHz 13C CP/HPHD/MAS spectrum of bisphenol-A diglycidyl ether, I. The spinning sidebands of the aromatic peaks are shaded line-narrowing and hence high resolution. The final linewidths are affected by a number of factors, but for polymers a major effect is the range of environments frequently encountered for a given carbon atom when amorphous components are present. Magic-angle spinning, to be fully effective, must be greater than the static bandwidth of the spectrum—in practice for 13 C under HPHD this means the shielding anisotropy. Otherwise additional peaks, known as spinning sidebands, appear in the spectra as satellites around the isotropic resonances, as shown in Figure 4.6 for the monomer I. For many purposes, these are a nuisance, but in fact they contain extra information (on the tensor nature of shielding) and they can be used to extract such data. In other circumstances, spinning sidebands can be used to obtain dipolar coupling constants and thence internuclear distances [9].

4.3 HIGH-RESOLUTION CARBON-13 NMR OF POLYMERS The CP/HPHD/M AS suite of techniques is ideal for the observation of 13 C spectra, which can then be used in the way traditional for solution-state NMR, i.e. to determine chemical structure. However, for solids the local environment of a chemical group is usually rigid, and this introduces further considerations that affect isotropic chemical shifts. These matters relate to crystallography (where appropriate) or, more generally, to molecular packing. The emphasis may be

Figure 4.7 A, 22.6MHz 13C CP/HPHD/M AS spectrum of syndiotactic polypropene [10]; B, projection of the helical chain in the crystal structure of syndiotactic polypropene [12]

Figure 4.8 A, 22.6 MHz *3C CP/HPHD/MAS spectrum of isotactic polypropene [H]; B, projection of the crystal structure for the a form of isotactic polypropene [13]. The central pair of chains have oppositely handed helices

either intramolecular or intermolecular. A well-attested example is polypropene. Figures 4.7 and 4.8 show 13 C spectra [10,11] and structural arrangements [12, 13] for the syndiotactic and isotactic forms respectively. The doubling of the CH 2 signal for the former can be readily seen to be a consequence of the curious helical nature of the chains, which leaves all the CH carbons in equivalent positions but results in two different types of CH 2 carbons—an intramolecular effect. The spectrum for isotactic polypropene, on the other hand, shows small, apparently 2:1 splittings of both CH 2 and CH 3 carbon signals. These can be attributed to the pairing of the polymer chains in the crystalline domains—an mtermolecular effect. Such spectra can be used to examine the effects at the molecular level of polymer processing. Thus, Figure 4.9 shows part of the spectra [14] of annealed and quenched forms of a block copolymer of nylon-6 and a polyether-containing polyesteramide (H) with n « 9 . The linking unit R is phenylene, and O — O represents a polyether component with both ethene oxide and propene oxide

II units. Only aliphatic nylon signals are shown in Figure 4.9, with the carbonnumbering scheme given in III. It is clear that the annealed material gives a much simpler spectrum than the quenched one. AU the resonances in the former can be attributed to the a-crystalline form, whereas additional peaks from both ycrystalline and amorphous forms appear in the latter.

III 13

Similarly C NMR can be used to study polymer degradation. Figure 4.10(A) shows part of the spectrum [15] of a complex cross-linked system containing blocks of a random copolymer of styrene, methyl methacrylate and maleic anhydride, together with cross-linking blocks formed from a polyester-tipped with a /?-hydroxyamine (IV). Figure 4.1OB is of the polymer degraded under moist conditions. Comparison of the spectra shows that there is substantial loss of all

IV

Figure 4.9 Resolution-enhanced 50.3 MHz 13C CP/HPHD/MAS spectra of a nylon6/20% (polyether/polyesteramide) (II) copolymer (CH2 nylon signals only) [14]; A, annealed sample; B, quenched sample

Figure 4.10 50.3 MHz 13 C CP/HPHD/MAS spectra of a cross-linked copolymer (see the text) [15]. A, as synthesized; B, after degradation. The asterisks indicate methylene signals of the polyester moiety

polyester CH2 signals, indicating complete excision of polyester chains (with or without internal break-up) and therefore showing that hydrolysis occurs at the hydroxyamine ends.

4.4 PROTON SPIN RELAXATION For heterogeneous materials, 13 C CPMAS spectra cannot be properly understood without a knowledge of proton relaxation times, which are also of intrinsic importance because of their relation to mobility at the molecular level and to domain structure. Three types of relaxation that need to be considered are: • Spin-lattice (longitudinal) relaxation This refers to magnetisation parallel to B 0 , is characterised by a time T1, involves spin energy, requires motion at the resonance frequency (i.e. hundreds of MHz) and is relatively easily averaged by spin diffusion. • Spin-lattice relaxation in the rotationframe This refers to magnetisation along the radiofrequency magnetic field JJ1, is characterised by a time T1 p, requires motion at a frequency related to the strength of B1 (i.e. tens of kHz) and is somewhat more difficult to average by spin diffusion than T1. • Spin-spin (transverse) relaxation This refers to magnetisation perpendicular to B 0 (in the absence of B1), involves spin phase-coherence (entropy), requires only very low-frequency motion, is not averaged by spin diffusion, and is directly related to the NMR signal (free induction decay). Whereas T1 and T1p are normally exponential or multi-exponential, transverse relaxation for solids takes a more complicated mathematical form (see below), the relevant time constant usually being given the symbol T2. For relatively rigid solid polymers, T1, T l p and T2 are normally of the order of s, ms and /is respectively. Since relaxation times are related to mobility, temperature and phase strongly influence the observed values. The phenomenon of spin diffusion mentioned above is a crucial ingredient of relaxation phenomena in heterogeneous systems such as polymers. It describes transfer of spin polarisation through space without atomic movement, and is caused by the pairwise "flip-flop" term of the dipolar interaction (see Figure 4.11), which itself depends on the inverse cube power of internuclear distances. It is efficient only in homonuclear situations, when little or no energy is required, and thus is particularly important for abundant spins such as 1H. It will cause averaging of some relaxation characteristics between domains in solid polymers when the sizes are small. For lamellar morphology the factor L2DTT is involved, where L = lamellar semi-thickness, D = spin diffusion coefficient and Tx is the relevant relaxation time. Averaging of relaxation occurs when L 2 « DTx. This occurs for domain sizes much less than a few tens of A for T1 p , or much less than a few hundreds of A for T1. Information on spin diffusion can be obtained in principle by the Goldman-Shen pulse

Figure 4.11 Spin diffusion by the flip-flop process (diagrammatic). Letters a-d represent successive situations, with e and f indicating later cases

A

B prep

evol

det

Figure 4.12 The Goldman-Shen pulse sequence [16] for the study of spin diffusion: A, short mixing time; B, long mixing time. All pulse angles are 90°. The r.f. phases are indicated above the pulses. The signal after the initial 90° pulse shows both rapidly relaxing and slowly relaxing components. The terms prep, evol and det refer to the preparation, evolution and detection periods respectively

sequence [16] (Figure 4.12) which prepares the magnetisation of a system of two domains, A and B say, such that the one with a short T2 (A, say) is zeroed. Then the remaining magnetisation is put back into the z direction, where it can equilibrate with B by spin diffusion during an evolution (mixing) time, after which the system is monitored. Unfortunately, quantitative interpretation of the results is complicated by spin-lattice relaxation during the mixing time.

InS

t/ms Figure 4.13 Experimental (300 MHz) and computer-simulated plots [17] for T1p of PVC. The y axis is the natural logarithm of the normalised signal height following spin-locking for a time t. The deviation from the upper straight line is plotted at the bottom left to give the short-time component

Frequently polymer heterogeneity can be monitored by measurement of Tlp. Figure 4.13 shows experimental and computer-fitted plots [17] of spin-lattice relaxation in the rotating frame for a sample of PVC. The decay curve can be satisfactorily fitted by two exponentials, giving 72% with T1p = 8.8 ms and 28% with T l p = 1.5 ms. Whereas this properly indicates heterogeneity, showing that there are more-ordered and less-ordered domains which are greater than a few tens of A, the effect of spin diffusion is to give the data a mixed character, meaning that neither the proportions nor the times are necessarily the intrinsic values of the different domains. In principle, free induction decays (and/or the spectra produced therefrom) should give better information on domain structure. In several ways it makes more sense to analyse the free induction decays directly, rather than the transformed spectra. However, there is no universally accepted algorithm for such analysis, which is not surprising given the complexity of the situation for polymeric systems. We have adopted a mix of three mathematical functions: • Exponential (Lorentzian): S(t) = exp( — t/T2). This is well justified for highly mobile regions. • Weibullian [18]: S(t) = exp[—(r/r 2 H with 1 < n ^ 2. Although this function has no particular justification in theory, it has the merit of varying with the exponent from pure Lorentzian (n = 1) to pure Gaussian (n = 2). • Abragamian: S(f) = exp[ —(£/T2)2] (sin 2nbt)/2nbt. Such a function was proposed by Abragam [19] as an approximation of the CaF 2 1 9 F decay. It

signal

signal

A

B

t/ms

t/ms

Figure 4.14 60 MHz free induction decays for: A, nylon-6; and B, copolymer of nylon-6 and 20% polyether/polyesteramide II (see the text) [14]. The ordinate is signal intensity on an arbitrary scale Table 4.1

Free induction decay analysis of samples of nylon-6 and its copolymer containing 20% of the unit II Nylon-6 Population/%

Copolymer Time/us

Population/%

Exponential 5 64 22 Abragamian 95 18° 78 a The value of b is 21000 and 20000 for the nylon-6 and copolymer respectively.

Time/us 367 18fl

represents a rectangular distribution of Gaussians, and its value lies partly in the fact that it can yield a small oscillation such as is to be expected when there are relatively isolated spin pairs such as CH 2 groups. Figure 4.14 shows free induction decays [14] for nylon-6 and the copolymer containing 20% of the unit II. A small initial oscillation is apparent in each case, and the long-time component in Figure 4.14B is obvious. Table 4.1 shows the results of the analysis. The small amount of the exponential for pure nylon-6 probably relates to additives in the commercial sample. The time constants of the two domains are an order of magnitude different, showing the considerable degree of motional heterogeneity. The proportion of the copolymer which decays slowly clearly reflects the content of II. Of course, for more complete information, other NMR experiments, both 1 H and 13 C, must be performed and the results collated. For copolymer systems deuterated in one component, the phase boundaries can be probed by attempting to cross-polarise from the protons in the second component.

4.5 DISCRIMINATION IN CARBON-13 SPECTRA Proton relaxation data allow the NMR spectroscopist both to interpret 13 C CPMAS spectra and to devise discriminating experiments [20]. One such

lo

9ioS

A

l

B

°9ioS

CT/ms

CT/ms Figure 4.15. Cross-polarisation dynamics for 50.3 MHz 13C spectra of a copolymer of nylon-6 and 40% polyether/polyesteramide (see the text) [14]; variation of peak height S with contact time CT: A, nylon-6-carbons (diamonds indicate the C4/C5 peak, squares are for C2, and circles are for Cl, see III); B, polyether carbons (the symbols are for the peaks at the following chemical shifts: triangles 18.2 ppm, circles 75.8 ppm, squares 73.9 ppm, diamonds 71.2 ppm). S is expressed relative to the peak height of the most intense signal, extrapolated to zero CT. A theoretical curve is shown for Cl in A experiment is variation of the contact time. During the contact time of the CP process, transfer of polarisation will reach a maximum because of the competing effects of creating equilibrium between the 1 H and 13 C spin baths and the loss of proton magnetisation to the "lattice" by spin-lattice relaxation in the rotating frame. When there are domains differing substantially in T 1 ^ 1 H), the optimum contact time for each domain will also differ. Indeed, it is possible to measure (at considerable cost of spectrometer time) values of T 1 ^ 1 H) selectively for different 13 C peaks by variation of the contact time, as shown [14] in Figure 4.15. In the case illustrated, long contact times will clearly favour the polyether carbons. In

A

B

Figure 4.16 Discrimination by contact time for PVC plasticised by 180pph of di-2ethylhexyl phthalate [17]. 300 MHz*3C CP/HPHD/M AS spectra: A, contact time 200 /is; B, contact time 5 ms. The broad peaks arise from PVC and the sharp ones from the plasticiser

such circumstances quantitative measurement of relative signal intensities can be obtained only by extrapolation of the decay curves under long contact to their intercepts at zero contact time. Figure 4.16 shows discriminating spectra for a different polymer situation: PVC plasticised by di-2-ethylhexyl phthalate [17]. The PVC itself is mostly rigid, cross-polarises efficiently but has a short associated T1^(1H). Hence a short contact time reveals PVC peaks strongly. The plasticiser, on the other hand, is mostly very mobile, cross-polarises badly but is influenced by a long T1^1H). It therefore gives intense peaks only at long contact times. A second discriminating pair of experiments consists of comparing a CP/HPHD/MAS spectrum with one obtained without cross-polarisation (sometimes referred to as single-pulse excitation, SPE). Whereas the former depends on proton relaxation, the latter is affected only by carbon relaxation. SPE spectra are likely to be strongly influenced by carbon peaks with short T1(13C), usually in relatively mobile parts of the sample, or, if recycle delays between pulses are long, by all the carbons. Figure 4.17 gives an example [14] for the nylon-6 copolymer containing 20% of II. Whereas the CP spectrum shows mostly signals from crystalline nylon domains, the SPE spectrum is dominated by peaks from the polyether moieties and from amorphous esteramide or nylon regions. SPE spectra can yield quantitative relative intensities of signals if recycle delays are long enough. However, nuclear Overhauser effects can cause complications if the duty cycle of the decoupler is significant.

A

B

Figure 4.17 200 MHz * 3 C MAS spectra of a copolymer of nylon-6 and 20% polyether/ polyester-amide II (see the text) [14]: A, SPE/HPHD mode with recycle delay 5 s; B, CP/HPHD mode with contact time 1 ms and recycle delay 2 s. The broad peaks in A arise from amorphous esteramide or nylon groups. The sharp peaks in A are from PEO or PPO groups

4.6 SPECTRA OF ABUNDANT SPINS As indicated earlier, for direct observation of 1H or 19 F spectra of solids with high resolution, it is necessary to use the CRAMP pair of techniques [6]. As yet these have been underused in polymer NMR, partly because they are more demanding of the instrument electronics than CPMAS operation and partly because residual linewidths, which are frequently several hundred Hz, give only moderate resolution for 1 H, which has a relatively small chemical shift range. However, CRAMPS is excellent for detecting strong hydrogen bonding, which gives proton signals in the S = 10-20 region where there are seldom any other peaks. Moreover, the potential for CRAMPS with 1 9 F for polymers is high, as the shift range is large. Figure 4.18 gives a simple example [21], showing how information on chain^ends can be readily derived. The figure also illustrates the appearance of spinning sidebands. Comparison of Figures 4.18A and B indicates the way in which increasing rotational speed causes sidebands to move out from the centrebands and to weaken. This allows the centrebands to be obtained unambiguously.

A

B

C

Figure 4.18 188.3MHz 1 9 F CRAMP spectra of PTFE samples [21]: A and B, shortchain polymer (^C 2 0 F 4 2 ); C, long-chain polymer. The spinning speeds were A 2.6 kHz; B 5.1 kHz, and C 2.5 kHz. The arrows in B indicate signals from chain ends. The asterisks denote spinning sidebands

47 CONCLUSION The scope for application of NMR to solid polymers is very wide. Information on chemical microstructure, micromorphology and molecular-level dynamics is available. It is important to undertake studies comprehensively using both 13 C and 1 H nuclei, with measurements of both spectra and relaxation times. Various experiments are available for the selective examination of heterogeneous systems. More sophisticated methods are also feasible, as is discussed in Chapter 5

4.8 ACKNOWLEDGEMENTS I am grateful to colleagues whose results are mentioned in this article and whose names are given in the references. I particularly thank S. Friebel, S-W. Tsui and

A.F. Johnson for the collaboration in hitherto-unpublished work, resulting in Figures 4.9,4.14,4.15 and 4.17.1 also thank the UK S.E.R.C. for financial support under grants GR/E 91110 and GR/H 30175 and for allocations of time on the Solid-state NMR Service sited at Durham.

4.9 REFERENCES [1] E.M. Purcell, H.C. Torrey and R.V. Pound, Phys. Rev., 1946,69, 37. [2] F. Bloch, W.W. Hansen and M.E. Packard, Phys. Rev., 1946,69,127. [3] P.W.R. Smith, Ph.D. Thesis, University of East Anglia, 1986. See also IJ. Colquhoun and KJ. Packer, Br. Polym. J., 1987,19,151. [4] For a review, see E.R. Andrew, Int. Rev. Phys. Chem., 1981,1,195. [5] J.S. Waugh, L.M. Huber and U. Haeberlen, Phys. Rev. Lett., 1968,20,180. [6] L.M. Ryan, R.E. Taylor, AJ. Paff and B.C. Gerstein, J. Chem. Phys., 1980, 72, 508. [7] A. Pines, M.G. Gibby and J.S. Waugh, J. Chem. Phys., 1973,59, 569. [8] J. Schaefer and E.O. Stejskal, J. Am. Chem. Soc, 1976,98,1031. [9] J. Schaefer, E.O. Stejskal, R.A. McKay and W.T. Dixon, Macromolecules, 1984,17, 1479. [10] A. Bunn, M.E.A. Cudby, R.K. Harris, KJ. Packer and BJ. Say, J. Chem. Soc, Chem. Commun., 1981, 15. [11] A. Bunn, M.E.A. Cudby, R.K. Harris, KJ. Packer and BJ. Say, Polymer, 1982, 23, 694. [12] P. Corradini, G. Natta, P. Ganis and P.A. Temussi, / . Polym. Sci. C, 1967,16,2477. [13] G. Natta and P. Corradini, Nuovo Cim., 1960,15 (Suppl), 40. [14] S. Friebel, R.K. Harris, S.-W. Tsui and A.F. Johnson, ubpublished work. [15] A. Findlay, Ph.D. Thesis, University of Durham, 1991. [16] M. Goldman and L. Shen, Phys. Rev., 1966,144, 321. [17] M.I.B. Tavares, R.K. Harris and E.E.C. Monteiro, unpublished work. [18] S. Kaufman and DJ. Bunger, J. Magn. Reson., 1970,3, 218. [19] A. Abragam, Principles of Nuclear Magnetism, Oxford University Press, Oxford, 1961, p. 120. [20] R.S. Aujla, R.K. Harris, KJ. Packer, M. Parameswaran and BJ. Say, Polym. Bull., 1982,8, 253. [21] R.K. Harris and P. Jackson, Chem. Rev., 1991,91,1427.

5

MULTIDIMENSIONAL SOLID-STATE NMR OF POLYMERS H. W. SPIESS Max-Planck-Institut fur Polymerforschung, Postfach 3148, D-55021 Mainz, Germany

5.1 INTRODUCTION One of the key goals of materials science is the establishment of structureproperty relationships in order to improve known properties and to permit the design of new materials. This holds in particular for synthetic polymers, whose properties depend on both the molecular structure and the organization of the macromolecules in the solid state: their phase structure, morphology, molecular order and their molecular dynamics [1, 2]. Both macroscopic and microscopic parameters are influenced by the processing that follows the chemical synthesis. This calls for powerful analytical tools that can probe these aspects in the material as it is used predominantly in the solid state. The structural aspects are studied mostly by scattering techniques or by microscopy. Information about dynamic aspects is deduced mainly from scattering or relaxation experiments [3]. Among these nuclear magnetic resonance (NMR) [4,5] is well established for the structural characterization of liquids or compounds in solution, but much less so for solids [6, 7]. Indeed, NMR offers numerous ways to study dynamic aspects over a large range of characteristic rates. The main advantage of NMR is its unprecedented selectivity. It is thus desirable to develop this technique for studying the structure and dynamics of solid polymers [8]. However, owing to the presence of angular-dependent anisotropic interactions, the spectral resolution of solid-state NMR spectra is orders of magnitude lower than that of high resolution NMR in liquids. Important improvements were achieved in the 1970's by combining high-speed mechanical rotation of the sample with ingenious manipulations of the nuclear spins, such as multiple-pulse irradiation, highpower decoupling and cross polarization [9]. Moreover, two-dimensional (and higher) NMR techniques have been introduced that offer fundamental advantages [10]. First, as in liquids, the introduction of a new frequency dimension provides a means of increasing the spectral resolution. Even more important, Polymer Spectroscopy. Edited by Allan H. Fawcett © 19% John Wiley & Sons Ltd

multidimensional spectroscopy also provides routes to new information that is unavailable from one-dimensional spectra even in the limit of high resolution. Experiments can be designed which correlate different spin interactions providing different structural information, or relate various states taken up by the molecular unit during different time periods by exchange, and in this way to probe dynamic processes in real time. Progress in multidimensional solid-state NMR has been hampered by experimental and conceptual difficulties, but these are now overcome [11-14]. This chapter briefly outlines some of the main concepts and illustrates the information available from multidimensional solid-state NMR spectra concerning polymer structure and dynamics through experimental examples selected from the author's laboratory. Polymer dynamics is of central interest in our studies. Of the great variety of molecular motions possible in polymers (e.g., translations, rotation, vibrations), rotations have the most pronounced effects of NMR lineshapes and relaxation parameters.Thus, multidimensional NMR provides essentially unique information about rotational motions. Their timescales may be followed in real time over many orders of magnitude, covering in particular that regime of slow motions which govern the mechanical properties of polymers. Moreover, the higher-order correlation functions provided by multidimensional NMR yield previously inaccessible model-independent information about the geometry of rotational motions, the orientational memory of molecular units involved in complex dynamics, and the nature of nonexponential relaxation in disordered systems. When the information has been collected for a variety of polymers, it should eventually lead to a better understanding of their mechanical and rheological behavior, which is of interest not only for conventional but also for new advanced polymeric materials. Two other aspects are particularly important for establishing structureproperty relationships for polymer materials, namely chain alignment in partially ordered systems and domain sizes in heterogeneous polymer materials. The orientation of macromolecular units is used to improve the properties of polymers for such diverse applications as high-tensile-strength fibres and nonlinear optical materials for information technology. Advanced polymer materials almost inevitably consist of more than one component, which often leads to phase separation. Careful design of the molar ratios as well as the size, composition and morphology of the different phases offers a means to control the mechanical, electrical and optical properties. Small domains that extend over only a few nanometers, and also interfacial regions between the different phases, are particularly difficult to characterize. Major advances have been achieved in these areas by introducing the concepts of multidimensional spectroscopy. The new solidstate NMR techniques nicely supplement well-established scattering and microscopic methods, as we demonstrate by various experimental examples and by explicit comparison.

5.2 MULTIDIMENSIONALSOLID-STATE NMR SPECTRA Solid-state NMR exploits anisotropic, angular-dependent interactions of nuclear spins with their surroundings [4, 5], in particular magnetic dipole-dipole coupling of nuclei among themselves. This leads to broad NMR lines covering « 5 0 kHz for 1 H - 1 H homonuclear coupling and « 2 5 kHz for 1 H- 1 3 C heteronuclear coupling. The anisotropy of the chemical shift results in powder patterns ocvering « 1 5 kHz at a field strength of 7 T. In addition to these magnetic interactions, nuclei with spin / > 1/2 can also have electric quadrupole moments, and are subject to quadrupole coupling to the electric field gradient at the nuclear site. For 2 H ( / = 1) in C- 2 H bonds this leads to spectral splittings of «250 kHz. Since C-H bonds are common in polymers, 2 H labeling is particularly useful. If one of the above mentioned couplings dominates, either because of its strength, or because the others have been suppressed by decoupling, the angular dependence of the NMR frequency in high magnetic fields is alike for all couplings, and is given by: a) = coL + ±A(3cos2O-

I - rjsin20cos2(t))

(1)

Here coL is the Larmor frequency, A describes the strength of the anisotropic coupling: i.e. the anisotropic chemical shift or x3 C - l H dipole-dipole coupling for 13 C and the quadrupole coupling for 2 H, and rj is the asymmetry parameter describing the deviation of the anisotropic coupling from axial symmetry (O ^ Y] ^ 1). The angles 0, are the polar angles of the magnetic field B 0 in the the principal axes system of the coupling tensor. This in turn is often simply related to the molecular geometry; i.e. the unique axis being along a bond direction, e.g. dipole-dipole coupling: 1 3 C- 1 H bond, quadrupole coupling: C- 2 H bond, or perpendicular to an sp 2 plane as for 13 C chemical shift tensors in aromatic rings etc. Depending on the total spin involved, signals described by Equation (1) and their mirror images with respect to coL may be superimposed, and in powder samples the spectra for all orientations are added to yield the powder lineshape (e.g., the Pake pattern for 2 H with spin / = 1). Details of the experiments designed to record multidimensional NMR spectra are not given here, as ample literature exists on the subject [10-13] and an extended monograph is available [14]. However, basis knowledge of solid-state NMR, as in Chapter 4, and of the concept of two-dimensional (2D) Fourier spectroscopy, is needed to read this chapter. A 2D NMR spectrum is generated by recording a two-dimensional data set following pulsed irradiation as a function of two time variables, as shown schematically in Figure 5.1, and subsequent double Fourier transformation. The development of the nuclear spin system in the evolution period with incremented time tx at the beginning of the pulse sequence provides the basis for the first frequency dimension Co1. The NMR signal is detected in the detection period with time 12 at the end of the pulse sequence,

preparation

evolution

mixing

detection

Figure 5.1 Time scheme of two-dimensional NMR [11] providing the basis for the second frequency dimension co2. In the exchange experiments described here, a variable mixing period of duration tm, during which dynamic processes can take place, is inserted between evolution and detection. The concept of 2D spectroscopy is readily extended to three and higher dimensions by inserting additional evolution and mixing times.

5.3 EXAMPLES 5.3.1 INCREASE OF SPECTRAL RESOLUTION Let us first consider experiments which increase the spectral resolution of solid state NMR spectra in order to characterize polymer structure in terms of chemical moieties on the basis of isotropic chemical shifts. This represents the most important feature of standard NMR techniques, and makes up one or two dimensions of many multidimensional experiments in which the chemical structure is correlated with other molecular properties such as mobility or order. In the solid state, the tensorial nature of the chemical shift makes the NMR frequency also depend on the orientation of the molecular unit under study with respect to the applied magnetic field of the NMR spectrometer, cf. Equation (1). Since the orientational dependence of the NMR frequency is comparable with or even larger than the variation of the isotropic chemical shifts of different structural units, the powder patterns resulting from the anisotropic chemical shifts overlap severely in all but the simplest polymer structures. Thus, in many cases a quantitative analysis is virtually impossible. The effect of the anisotropy can be removed by rapidly spinning the sample about an axis inclined at the "magic angle" of 54.7° (magic angle spinning, MAS). However, this is accompanied by a loss of the information about the molecular orientation, which is the basis of structural and dynamic information typical of the solid state. Thus, experiments are desired that retain this information without sacrificing spectral resolution. For moderate spinning speeds in the range of a few kHz, the anisotropic chemical shift is not "spun out", but leads to sideband patterns, from which the anisotropies can be retrieved [15, 16]. However, in complex polymer structures

Figure 5.2 Separation of isotropic and anisotropic chemical shifts: (a) 13C MAS spectrum of an ether sulfone oligomer showing severe overlap of sidebands; (b) 2D 13C sideband MAS spectrum of the same compound showing resolved sidebands [18]

the sideband patterns overlap heavily and hamper a quantitative analysis. By ingenious spin manipulations through multiple-pulse sequences, these sideband patterns can be removed from the spectrum in one dimension and retained in the other [17, 18]. As shown in Figure 5.2, the crowded sideband patterns of amorphous polymers can be nicely resolved in a second frequency dimension and can then be exploited to provide structural and dynamic information.

5.3.2 SEPARATED LOCAL FIELD N M R The dipole-dipole coupling, for instance between 1H and 13 C, or 1 H and 15 N, provides valuable structural information. As the C-H bond lengths are known, the measurements of dipolar splittings can be interpreted in terms of angles between individual bonds and the applied magnetic fields. For proteins, measurements of N - H bond lengths are of considerable interest, as they vary due to hydrogen bonding and therefore contain important structural information. In order to be useful, however, the dipolar patterns have to be separated according to the chemically distinct sites in a molecule or monomer unit as identified by their 13 C or 1 5 N chemical shits. As the dipolar couplings correspond to local fields, such experiments are often named "separated local field" (SLF) experiments [19]. Different schemes have been developed based on sample spinning [20, 21]. If the polymer contains only carbons with a common chemical shift, static techniques can be used [10]. As an example, Figure 5.3(a) displays the 13 C

Figure 53 Separated local field spectroscopy correlating heteronuclear dipoledipole coupling with chemical shifts: (a) ID * 3 Q 1 H spectrum of highly oriented poly(oxymethylene) (POM) with its order axis inclined at 30° with respect to the magnetic field [22]; (b) orientation of chemical shift tensor deduced from this spectrum (principal axes marked by
chemical ShIfV13C-1H dipolar powder pattern for oriented poly(oxymethylene) (POM) [22]. From a quantitative analysis of such patterns, bond lengths and bond angles can be determined, as well as the orientations of the principal axes of the chemical-shift tensor in relation to structural units such as CH 2 groups, Figure 5.3(b). Such information is needed for a quantitative analysis of other experiments exploiting anisotropic chemical shifts.

5.3.3 WIDELINE SEPARATION EXPERIMENTS Multidimensional NMR provides especially interesting information about polymer dynamics. A long-standing method for qualitative characterization of molecular mobility is 1 H wideline NMR spectroscopy. There, large-amplitude motions are detected through the reduction of the dipolar line width. However, ID proton lineshapes leave many questions open, as they typically represent superpositions of broad and narrow lines, and their relation to different structural units is often not obvious. In a straightforward combination of 1 H wideline NMR, cross polarization (CP) and 13 C MAS spectroscopy in a 2D experiment [23], it is possible to separate the dipolar patterns for the different structural units (Wideline SEparation, WISE). This is demonstrated in Figure 5.4, where a WISE

Figure 5.4 2D WISE NMR specrating 1 H wideline spectra for different structural units according to their 13C chemical shifts: (a) conventional 1 H wideline spectrum of a blend of poly(styrene) (PS) and poly(vinylmethylether) (PVME); (b) 2D 1H 13C WISE NMR spectrum indicating different mobilities of the two components [23]

NMR spectrum of a 50:50 wt% blend of poly(styrene) (PS) and poly(vinylmethylether) (PVME) is presented. The 1 H wideline spectrum, Figure 5.4(a), consists of a rather featureless superposition of Components with different dipolar linewidths, which are nicely separated in the second frequency dimension (Figure 5.4(b)) and related to structural units according to their 13 C chemical shifts. Substantial motional heterogeneities, PVME being more mobile (narrower 1 H lines) than PS, are detected despite the fact that the spectrum is recorded about 60 K above the caloric glass transition of this blend, which appears homogeneous by most classical techniques. Such information about the mobility of the different structural units is highly valuable for many practical applications.

5.3.4 2 D and 3D EXCHANGE N M R For a thorough understanding of the chain motions in polymers, qualitative information provided by 1H wideline spectra is not sufficient. In order to relate chain motions to the structure of the polymer itself or to the packing of the macromolecular chains, one requires knowledge about the geometry of the motion, for example, the angles about which a molecular unit rotates during individual motional steps. This information, which is hard to get otherwise, is indeed provided by 2D exchange NMR as applied to rotational motions [12-14]. In simple cases this technique yields elliptical ridge patterns from which the angle about which the molecules have rotated can be directly read off with a ruler [24]. As a specific example, Figure 5.5(a) displays such a 2 H 2D exchange spectrum for poly(vinylidene fluoride) (PVF2), a polymer of considerable technological interest because of its electrical properties. The geometric information from 2D NMR, together with knowledge of the dipole moment change generated by the motion, allowed us to identify the conformational change tgtg«—> gtgt of a chain defect as being responsible for the mechanical and dielectric relaxation in the crystalline regions of this polymer [25]. In a series of papers [26], 2D exchange NMR was applied to study the chain motion of amorphous polymers above their glass transition. For complex motions, even the information accessible by 2D techniques is not sufficient for an adequate description of the motional mechanisms involved in chain dynamics. This is due to the fact that in 2D NMR the orientation of molecules is measured only twice, in the evolution and in the detection periods. Therefore, no information is provided about the trajectory a molecular unit follows when rotating from one orientation to another. In order to distinguish different mechanisms one has to determine the molecular orientation at least three times. This is achieved in 3D exchange NMR. In a 3D exchange spectrum, as displayed in Figure 5.5(b) for natural abundance 13 C in semicrystalline poly(oxymethylene) (POM), different pathways pursued by the molecule lead to different exchange signals, which can therefore be clearly distinguished. From

Figure 5.5 Multidimensional exchange NMR spectra elucidating slow molecular motions: (a) 2D 2H NMR spectrum of crystalline poly(vinylidene fluoride) reflecting chain motions through defect diffusion [25]; (b) 3D 13C exchange spectrum of oriented poly(oxymethylene) reflecting helical jumps in the crystalline regions [14]

analysis of such 3D spectra for different semicrystalline polymers, which pack in helical conformations, helical jump motions have been identified in which the chain units rotate to neighboring positions and translate by one repeat unit [14]. This process can eventually lead to chain diffusion between crystalline and amorphous regions with pronounced effects on the long-term mechanical properties [27].

5.3.5 CHAIN A L I G N M E N T FROM 2D A N D 3D NMR Structural characterization of polymers often requires the determination of the alignment of macromolecular chains. Orientation in polymers is often induced by the production process and has strong effects on product properties. Through the angular-dependent NMR interactions, orientation is amenable to measurement in NMR experiments. In contrast to most classical techniques, the order of both crystalline and amorphous components can be studied. For 2 H- or 13C-enriched samples, one-dimensional experiments are sufficient to obtain orientation distributions in terms of a single angle [28]. In order to reconstruct two-dimensional orientation distributions, or to resolve overlapping patterns in natural-abundance 13 C spectra, multidimensional spectra are required. Two examples are presented in Figure 5.6. Both involve 3D spectra of 13 C in natural abundance. In the case of a biaxially drawn film of poly(ethylene terephthalate) (PET), the orientational distribution was mapped out by flipping the sample between different orientations with respect to the magnetic field (Direction Exchange with Correlation for Orientation Distribution Evaluation and Reconstruction, DECODER) [29]. The NMR signals of the different structural units of PET are completely resolved in the 3D cube and their orientation distributions are thus separately determined [30]. The chain axes are confined to the film plane (full-width-at-half-maximum,fwhm, of 15°), whereas the in-plane distribution is much broader (fwhm approx. 90°). The planes containing the phenylene rings and the carboxyl group are oriented preferentially parallel to the plane of the film (fwhm of 55°). In the case of a liquid-crystalline side-group polymer (Figure 5.6(b)), the extension to a third dimension is performed in order to achieve the necessary spectral resolution [31]. Rotor-synchronized MAS is applied to map out the degree of molecular order along Ox. The sidebands are separated by their order along o2 (see Figure 5.2), and the chemical structure is probed via the isotropic chemical shift along o3. Each dot in the 3D spectrum represents a single sideband of a carbon position in the repeat unit with resolved 13 C chemical shift in the MAS spectrum. This allows the molecular order of relatively complex polymers to be analyzed quantitatively even for liquid-crystalline polymers, where different moieties of the repeat unit exhibit substantially different degrees of alignment [32]. The specific example studied here is a frozen smectic polyacrylate with a phenylbenzoate mesogenic side group and a spacer of six methylene

Figure 5.6 3D NMR spectra for determining molecular order: (a) 3D 13C DECODER NMR spectrum of biaxially drawn polyethylene terephthalate) [30]; (b) 3D 13C MAS spectrum of a liquid-crystalline side-group polymer [31]

units. The 3D MAS NMR spectrum not only reveals a pronounced order gradient from the aligned mesogen to the disordered polymer chain, it also shows that the acrylic carbonyl group exhibits a much higher order than the hydrocarbon units of the main chain. Because of its selectivity, high resolution solid-state NMR is able to reveal that the carbon-carbon bond which links the acrylic carbonyl to the main chain plays a crucial role in the decoupling of the ordered side groups from the polymer chain [31]. 5.3.6 D O M A I N SIZES FROM SPIN D I F F U S I O N EXPERIMENTS In heterogeneous polymers, domain sizes, or structures on the scale of up to a few hundred nanometers, can be investigated. In NMR the proximity of molecular units is probed by spin diffusion [4,14], which is most effective among protons. Thus, NMR is particularly suited for characterizing small domains, nanoheterogeneities or concentration fluctuations on length scales of a few nm, where other methods often fail owing to liminations in resolution or contrast. An advanced approach exploiting 1 H spin diffusion with highly sensitive 13 C detection has been introduced recently [33, 34]. As a particularly clear-cut case, this technique has been applied to a series of symmetric diblock copolymers of PS and poly(methyl methacrylate), PMMA [34]. In Figure 5.7(a) the increase of the carbon signals of the phenyl ring in the PS block after selection of the PMMA block is plotted against the spin diffusion time for various block lengths. The equal lengths of both blocks in the symmetric copolymers ensures a lamellar structure which makes the quantitative analysis of the data easy. PMMA and PS are known to be immiscible. The spin diffusion data yield domain sizes which are consistent with the scaling law M n 0 66 , where Mn denotes the molar mass of the blocks, as predicted theoretically [35]. For comparison, a statistical copolymer, in which no phase separation is possible, and a blend of both homopolymers were included in the data set. The close agreement between experimental intensities and the time dependence calculated from the diffusion equation is apparent in Figure 5.7(b) and demonstrates that domain sizes between 0.5 and 100 nm can be determined quantitatively. This technique has already been applied to a number of homogeneous and heterogeneous polymer systems, in particular to block copolymers containing both mobile and rigid components affording detection of heterogeneities on a scale as small as 2 nm in systems that exhibit a single Tg in differential scanning calorimetry [36]. 5.3.7 SPATIALLY RESOLVED SOLID STATE NMR Eventually one would like to obtain the information about molecular structure and dynamics accessible by solid-state NMR not just for the sample as a whole

(PMMA)

(PMMA)

ppm

signal intensity PS

toilms]

t m 1/2 [ms"*]

Figure 5.7 Spin diffusion as a tool for determining domain sizes in heterogeneous polymers [34]: (a) 13C MAS spectra of the symmetrical diblock copolymer PS-b-PMMA as a function of the diffusion time tm after selection of proton magnetization of the methoxy group in PMMA; (b) signal intensity of the phenyl carbons in PS as function of tm for different molecular weights. The numbers indicate domain sizes obtained from the fit

Figure 5.8 (a) Spatially resolved 2D 13 C spectrum of an injection-molded drawn tensile bar of syndiotactic poly(propylene); (b) geometry of sample [37]

but with spatial resolution. For instance, one would like to distinguish the molecular parameters in regions close to the surface from those in the bulk. In fact, by applying pulsed magnetic field gradients, the concepts of multidimensional NMR can also be used to generate a spatial dimension in 2D spectra through Fourier imaging [10]; see also Chapter 6. As a first example, a spatially resolved 13 C NMR spectrum of a drawn poly(propylene) sample is displayed in Figure 5.8 [37]. It reflects differences of density and chain alignment between skin and core due to the processing of the material, and demonstrates that spectroscopic solid-state NMR imaging is indeed possible. This exciting field is still in its infancy and considerable progress is expected in the near future, as indicated in a recent book on the subject [38] which is based on lectures at an international conference.

5.4 CONCLUSION As these examples indicate, a wealth of information about polymer structure and dynamics is available through advanced multidimensional solid-state NMR techniques. Profound correlations between macroscopic and molecular behavior

are emerging from such studies. Examples are helical jumps or defect diffusion in crystallites, specific local motions in amorphous polymers and conformational transitions coupled to relaxations of larger chain units in highly viscous polymer melts. Such information has already been used successfully in the design of polymers with improved properties. Thus, it can be anticipated that the importance of multidimensional solid-state NMR as an advanced tool of polymer spectroscopy will increase substantially in the future.

5.5 ACKNOWLEDGEMENTS It is a pleasure to thank my coworkers engaged in the work described here: Drs. B. Bliimich, B. Chmelka, J. Clauss, S. Feaux de Lacroix, E. Gunther, D. Schaefer, JJ. Titmann, M. Wilhelm and, in particular, Dr. K. Schmidt-Rohr.

5.6 REFERENCES [1] PJ. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, 1953. [2] J.I. Kroschwitz (Ed.), Concise Encyclopedia of Polymer Science and Technology, John Wiley & Sons, New York, 1990. [3] N.G. McCrum, B.E. Read and G. Williams, Anelastic and Dielectric Effects in Polymeric Solids, Dover Publishing, New York, 1967. [4] A. Abragam, The Principles of Nuclear Magnetism, Oxford University Press, Oxford, 1961. [5] CP. Slichter, Principles of Magnetic Resonance, Springer-Verlag, Berlin, 1980. [6] F.A. Bovey, Nuclear Magnetic Resonance Spectroscopy, Academic Press, San Diego, 1988. [7] CA. Fyfe, Solid State NMR for Chemists, C F . C Press, Guelph, 1983. [8] R. A. Komoroski (Ed.), High Resolution NMR Spectroscopy of Synthetic Polymers in Bulk, VCH, Deerfield Beach, FL, 1986. [9] M. Mehring, Principles of High Resolution NMR in Solids, Springer-Verlag, Berlin, 1983. [10] R.R. Ernst, G. Bodenhausen and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon Press, Oxford, 1987. [11] B. Bliimich and H.W. Spiess, Angew. Chem. Int. Ed. EngL, 1988, 27,1655. [12] K. Schmidt-Rohr, A. Hagemeyer and H.W. Spiess, Adv. Magn. Reson., 1989,13, 85. [13] H.W. Spiess, Chem. Rev., 1991,91, 1321. [14] K. Schmidt-Rohr and H.W. Spiess, Multidimensional Solid-State NMR and Polymers, Academic Press, London, 1994. [15] M.M. Maricq and J.S. Waugh, J. Chem. Phys., 1979, 70, 3300. [16] J. Herzfeld and A.H. Berger, J. Chem. Phys., 1980,73, 6021. [17] A.C. Kolbert and R.G. Griffin, Chem. Phys. Lett., 1990,166, 87. [18] S. Feaux de Lacroix, JJ. Titman, A. Hagemeyer and H.W. Spiess, J. Magn. Reson., 1992,97,435. [19] J.S. Waugh, Proc. Natl. Acad. Sci. USA, 1976, 73, 1394. [20] T. Nakai, J. Ashida and T. Terao, J. Chem. Phys., 1988,88, 6049.

[21] J.E. Roberts, G.S. Harbison, M.G. Munowitz, J. Herzfeld and R G . Griffin, J. Am. Chem. Soc, 1987,109, 4163. [22] K. Schmidt-Rohr, M. Wilhelm, A. Johansson and W. Spiess, Magn. Reson. Chem., 1993,31, 352. [23] K. Schmidt-Rohr, J. Clauss and H.W. Spiess, Macromolecules, 1992,25, 3273. [24] C. Schmidt, S. Wefing, B. Blumich and H.W. Spiess, Chem. Phys. Lett., 1986,130,84. [25] J. Hirschinger, D. Schaefer, H.W. Spiess and AJ. Lovinger, Macromolecules, 1991, 24, 2428. [26] S. Wefing and H.W. Spiess, J. Chem. Phys., 1988,89,1219; S. Wefing, S. Kaufmann and H.W. Spiess, Ibid., 1988,89,1234; S. Kaufmann, S. Wefing, D. Schaefer and H. W. Spiess, Ibid., 1990, 93, 197; D. Schaefer and H.W. Spiess, Ibid., 1992,97, 7944. [27] K. Schmidt-Rohr and H.W. Spiess, Macromolecules, 1991,24, 5288. [28] H.W. Spiess, in LM. Ward (Ed.), Developments in Oriented Polymers, 1, Applied Science, London, 1982, p. 44. [29] K. Schmidt-Rohr, M. Hehn, D. Schaefer and H.W. Spiess, J. Chem. Phys., 1992,97, 2247. [30] B.F. Chmelka, K. Schmidt-Rohr and H.W. Spiess, Macromolecules, 1993,26, 2282. [31] J J . Titman, S. Feaux de Lacroix and H.W. Spiess, J. Chem. Phys., 1993, 98, 3816. [32] C B . McArdle (Ed.), Side Chain Liquid Crystal Polymers, Blackie, Glasgow, 1989. [33] K. Schmidt-Rohr, J. Clauss, B. Blumich and H. W. Spiess, Magn. Reson. Chem., 1990, 28, S3. [34] J. Clauss, K. Schmidt-Rohr and H.W. Spiess, Acta Polym., 1993,44, 1. [35] E. Helfand and Z.R. Wassermann, in I. Goodman (Ed.), Developments in Block Copolymers, 1, Applied Science, London, 1982, Chapter 4. [36] W.Z. Cai, K. Schmidt-Rohr, N. Egger, B. Gerharz and H.W. Spiess, Polymer, 1993, 34, 267. [37] E. Gunther, B. Blumich and H.W. Spiess, Macromolecules, 1992, 25, 3315. [38] B. Blumich and W. Kuhn (Eds.), Magnetic Resonance Microscopy, VCH-Verlagsgesellschaft, Weinheim, 1992.

6 NMRIMAGINGOFPOLYMERS J. L. KOENIG The J. Donnell Institute Professor, Departments of Macromolecular Science and Chemistry, Case Western Reserve University, University Circle, Cleveland, OH 44102-7202, USA

6.1 INTRODUCTION Nuclear magnetic resonance imaging (NMRI) is a technique for measuring spatially resolved features of inhomogeneous samples. The technique has found particular utility in the medical field, where it is used for diagnosis based on the fact that the mobility of water in diseased tissue is different from that in normal tissue. However, in recent years, NMRI has found its way into the field of materials, particularly polymers. NMRI has the capability of measuring inhomogeneities in finished articles by a noninvasive and nondestructive method. Defect or nonuniform areas of the polymeric materials will be clearly shown in the NMR image. NMRI may be considered as a type of chemical microscope and, as such, the concept transcends any other methodology for generating images.

6.1.1 BASIS O F N M R I M A G I N G Nuclear magnetic resonance (NMR) [1] is based on the fact that many atomic nuclei oscillate like tiny gyroscopes when in a magnetic field. In NMR, a sample is placed in a magnetic field which forces the nuclei into alignment. The sample is then bombarded with a radio wave. As the nuclei absorb the radio wave, they topple out of alignment with the magnetic field. As they lose the absorbed energy from the radio wave, they line up again. By measuring the specific radio frequencies that are emitted by the nuclei and the rate at which the realignment occurs, spectroscopists can obtain detailed information about the molecular structure and motion of the sample they are studying. Conventional NMR spectroscopy is used to determine chemical structure, as is described in Chapter 4, but cannot locate the position of the stimulated nuclei. NMRI is a method where the stimulating signal is spatially encoded so that an image can be reconstructed showing the distribution of nuclei in the sample. Polymer Spectroscopy. Edited by Allan H. Fawcett © 19% John Wiley & Sons Ltd

Other than spatially encoding the signal, imaging works on the same principles as standard NMR. The NMRI technique relies on the interaction of nuclei in only a small and controllable region of the sample by placing the sample in a spatially inhomogeneous magnetic field whose nuclear resonance frequency is matched to the r.f. signal in only that region. NMR imaging is involved in obtaining the spatial distribution of all parameters that NMR can detect. The NMR signals inherently depend on nuclear relaxation time constants T1 and T2, which in turn reflect the structural environment of the emitting nucleus. NMR is capable of providing information about molecular structure and motion; consequently, NMR imaging can provide a variety of structural factors measured in situ. There are several ways of spatially encoding the NMR signal [ I ] . One is to apply a linear magnetic field to the original static field (Figure 6.1). The purpose of the nonuniform field is to label, or encode, different regions of the sample linearly with different NMR frequencies. As the magnetic field is varied in a known manner at specific positions within the sample, the frequency of the NMR signal indicates the spatial position of the resonating nuclei (Figure 6.1). In one dimension (D), the position of the sample is related to a frequency by the relationship Ao2

= O)2-

(O0 = y G2Z9

Field Strength

where the magnetic field gradient G = dBJdz. A tailored r.f. pulse with a narrow frequency range is used to excite only those nuclei at corresponding positions in the z dimension. The amplitude of the NMR signal received from the z axis line is a measure of the number of resonant nuclei on that line, and so the NMR spectrum represents a graph of spin density versus distance (neglecting relaxation effects). The field gradient is described by a tensor with nine components but, for large B, we need only be concerned with the three components Ga = BBJBOL, where a = x, y, z.

Sample

Figure 6.1

Position

Diagram of NMR imaging experiment

In three dimensions, one operates in a three-dimensional gradient field. The frequency spectrum (still obtained by Fourier transforming the free induction decay, or FID) gives the number of resonating spins along a specific direction of the field gradient. In fact, each plane perpendicular to the direction of the field gradient has a different resonance frequency, and the signal intensity at that frequency will be proportional to the number of nuclei contained in that plane. In other words, the frequency spectrum is just a projection of the spin density (neglecting relaxation effects for the moment) along the field direction.

6.1.2 RELAXATION PARAMETERS I N N M R I M A G I N G The spin densities and the molecular environments of the nuclei are reflected in the time variation of the amplitude of the measured r.f. signal, and hence are reflected in the intensity of each voxel in the image. (A voxel is the smallest volume that the imaging process recognizes and presents.) When the values of T1 and T2 are different in the voxels of a heterogeneous sample, these differences can be exploited to develop contrast in the NMR images. The pulse sequence that is usually used to measure the T2 relaxation phenomena in images is called multiple spin-echo. At a given repetition time TR, the NMR signal is measured at several different echo times TE. These echoes provide a measure of the T2 relaxation. By repeating the process at different TR values, the T1 relaxation can also be measured. Because differences in relaxation times and spin densities determine image contrast, data on relaxation times are important in the selection of the optimal r.f. pulse sequence for imaging a selected sample. Relaxation times can be measured at any point on an image. The ability accurately to quantify relaxation rates is important in understanding and optimizing image contrast. Spin density, T1 and T2 images can be computed from measurements using pulse sequences with predetermined variations [2]. These fundamental images represent the inherent data in the system, and can be recombined to reconstitute computed images for a given pulse sequence. Contrast in NMRI depends on both material-specific and operator-selected parameters. The material-specific parameters include the spin density and the relaxation times T1 and T2. The operator-selected parameters include the pulse sequence (inversion recovery, spin-echo, etc.) and the pulse delay and repetition times (timing parameters). For a given imaging system and pulse sequence, it is the delay and repetition times in conjunction with the intrinsic material parameters which dictate the appearance of the final image. If the correct pulse sequence is employed and the relaxation times of the two materials are known, it is possible to calculate the delay and/or repetition times that will produce the maximum difference in signal intensity between those materials.

Figure 6.2 The timing diagram for a spin-echo imaging pulse sequence using a selective 90° pulse The spin-echo (SE) technique is the most common pulse sequence applied in MRI today [I]. Images are constructed by acquiring a multitude of projections (typically 256 per image) each with an identical setting of a readout gradient during which the sequence is samples. Each projection is differentiated from the others by a phase difference, which is produced by advancing the phase encoding gradient. As shown in Figure 6.2, the spin-echo method consists of a series of r.f. pulses which are repeated many times in order to achieve a sufficient signal-to-noise ratio. Each projection is produced by a 90° pulse, followed by a 180° pulse for induction of the spin-echo. The 90° r.f. pulse tips the magnetization into the xy plane, where it begins dephasing. The 180° r.f. pulse is applied after a time t, and forces the magnetization to refocus at a time It (also known as the echo time TE) after the 90° r.f. pulse, at which time the data is collected. The frequency encoding gradient Gx causes the spins to precess at different frequencies depending on their position in the static magnetic field. The phase encoding gradient Gy is orthogonal to Gx. Varying the intensity of Gy causes the spins to dephase at different rates, providing the second dimension of a two-dimensional image. The slice selection gradient G2, and the Gaussian-shaped 90° r.f. pulse determine the position and thickness of the region of interest. The data is Fourier transformed in two dimensions to produce the image of the selected slice. The time delay between the observation pulse and the observation is called the "echo time" (TE). The time between two consecutive pulse sequences is labelled as the "repetition time" (TR), and usually ranges from 250 to 2500 ms. Spin-echo techniques have a unique position in NMR applications. The main problem with NMR imaging is the long data collection time, due mainly to the spin-lattice relaxation time T1. Each measurement necessitates a time period of the order of T1 (which is %0.5 s for aqueous systems) for the system to return to

equilibrium magnetization. By using spin-echo repetition, a large number of spin-echoes can be repeated within a T1 or T2 decay period. 6.1.3 R E S O L U T I O N I N N M R I M A G I N G Spatial resolution is limited by the smallest amount of sample that can be detected by NMR. Spatially resolving a given volume in an NMR image is equivalent to doing NMR spectroscopy on that volume. To resolve two spatially distinct volume elements requires the application of a magnetic field gradient of sufficient strength, such that the elements one wishes to resolve are shifted in resonance frequency from each other by an amount greater than the natural linewidth. For a given magnetic field gradient strength, the spatial resolution in NMR imaging is determined by the linewidth [I]:

Ax = (O112ZyGx where col/2 is the linewidth and G, is the gradient strength. For mobile liquids the linewidths are very narrow, and high spatial resolution can be achieved. The highest resolution reached so far is 1Ox 1Ox 100 \im. This corresponds to an observable volume element (voxel) of 10~ 5 mm 3 . Routine measurements on liquids in solids typically have 40 x 40 x 100 ^m resolution. The attainable resolution is limited by spectroscopic and hardware factors. Spectroscopic factors are the linewidth and the spread of the chemical shift of an NMR signal, diffusion processes and susceptibility gradients, both within the object and at its boundaries. Hardware factors may be the magnetic field inhomogeneity or instability, nonlinearity of the magnetic gradient field and the achievable signal-to-noise ratio. The difficulties of solid state imaging arise because the solid state linewidth is «1000 times its solution counterpart. Increasing the gradient by three or four orders of magnitude to maintain spatial resolution in solids imaging is a formidable task, and much effort has gone into finding alternatives to such a brute force approach [3]. 6.1.4 U T I L I T Y O F N M R I NMRI is a means of detecting and imaging previously invisible material imperfections in fabricated articles. Its potential applications in the field of polymeric materials are many and diverse [4]. They include the detection and imaging of subsurface defects, including interfacial flaws and microcracks, and the detection and characterization of areas modified through the introduction of foreign substances such as additives, degradation products, and contaminants. The potential applications are exciting, including dynamic studies of composites and other materials. The NMR imaging technique is a noninvasive monitor-

ing tool, so multiple measurements can be made on the same sample under different conditions. No special sample preparation is required and this makes possible in situ studies of fabricated articles including the superposition of images obtained before and after application of stresses and exposure to environmental factors, including stress, fatigue, temperature and penetrants.

6.1.5 IMAGE PROCESSING The underlying purpose of NMR imaging is to detect the presence or absence of inhomogeneities in situ. By using computer enhancement techniques, it is possible to compare a perfectly fabricated article with a modified piece, and in this manner to concentrate on just what makes each test piece different from the ideal. Defects such as voids and inclusions are represented by very small image discontinuities. Using a technique called edge enhancement, it is possible for the computer to make a numerical microshift of the image that has been stored in digital memory and then display the result. This process can convert images to data for automatic defect recognition. By putting the computer in the loop, we can employ averaging, smoothing and other forms of enhancement to let the computer make the quality decision after it has eliminated superfluous information. The computer can perform gray-scale scanning to detect any areas in the article that are imaging either too lightly or to intensely. Either effect is a sign that bonding is not proper on the fibers.

6.2 ADVANCED IMAGING TECHNIQUES 6.2.1 CHEMICAL SHIFT IMAGING NMRI usually assumes that the spins (usually that of the protons of water) precess at the same frequency but, owing to chemical shift differences arising from different chemical types of protons in substances, some of the spins experience slightly different local fields, and hence precess at different frequencies. The local field change is written as 0H0, where H0 is the static field and a is the chemical shift in parts per million (ppm). In imaging, the presence of two different types of resonating nuclei can lead to overlapping images and artifacts as shown in Figure 6.3. Figure 6.3 [5] shows the results of an image of xylene. Separate images are due to the aromatic and methyl protons and they are separated by % 4.8 ppm from each other. Each individual image is centered at its resonant frequency in the absence of a magnetic field gradient, and therefore the resulting image is smeared. As the read or frequency encoding gradient spreads out resonance frequencies according to positions along the gradient direction, the observed image actually consists of two or more partially overlapping sets of data (one

Figure 63 A cross-sectional chemical shift image of xylene in a vial. Separate images are due to the aromatic and the methyl protons of xylene and are separated by 4.8 ppm from each other corresponding to each type is nucleus). If the resonances are due to different species, two or more different images will be obtained. If all resonances arise from the same molecule, they will have identical spatial distributions and images. The usual imaging schemes apply a linear gradient G to frequency encode the data. Applying an inverse Fourier transform maps the spin density as a function of frequency linearly to spatial location. The linear relation between frequency (o and position x is: co = yGx

where y is the gyromagnetic ratio for hydrogen. In a gradient free environment, the precessional frequency of the proton of a molecule a decreases by: Ao>a = y<7a£0 This leads to a shift in the image position of the molecule a with respect to that of the protons of water by: Ax a = AcoJyGr

Consequently, the image of molecule a would overlap water in the region of interest and cause an artifact in the image, which might be incorrectly interpreted as actual spatial features. By increasing Gr, the pixel shift due to chemical differences is reduced. However, much valuable information is contained in the

image if the chemical shifts can be sorted out correctly. It is possible to form an image from only a selected portion of the total NMR spectrum. This process is called chemical shift imaging. A particular resonance peak can be selectively excited by r.f. irradiation to the exclusion of others in the chemical shift spectrum. A long, low-power, amplitudeshaped r.f. pulse can be used to excite a narrow range of resonant frequencies distributed about a particular frequency. Such a "soft" pulse is more frequencysensitive than a short, square "hard" pulse. High resolution NMR spectra displaying chemically shifted resonances provide information on the chemical species present in the system and their relative concentrations. The magnetic resonance response can be simultaneously obtained from all regions of a heterogeneous sample by using a four-dimensional Fourier transform technique, where the high resolution spectrum obtained during the data acquisition defines one dimension and the other three dimensions form a Cartesian coordinate system. The application of various spatially resolved MRI techniques for the observation of high resolution spectra has been limited. This is largely due to the mutually exclusive requirements of both the highly homogeneous magnetic field which is necessary for the observation of chemical shift information, and the inhomogeneous field which is applied as a linear magnetic field gradient and is necessary to obtain spatially resolved data. Chemical shift imaging techniques use pulsed magnetic field gradients, which in the standard configuration of superconducting magnets generate sufficiently large eddy currents upon gradient removal to temporarily degrade the field homogeneity. This is one of the reasons why the implementation of high resolution spatial spectroscopy is difficult. Currently, there are several approaches to the problem of the chemical shift effects in NMRI. First of all, one may attempt to construct an image corresponding to a preselected chemical shift of a sample either locally or globally. When different chemical shifts originate from different chemical species, an image taken at a specific chemical shift will provide information on the spatial distribution of the corresponding species while excluding the interference of other species in the image. A local method assumes knowledge of the chemical shift and usually produces an image of the chemical species under consideration. The in-phase and out-of-phase experiments can be used for this purpose [6]. In addition, chemical shift-selective suppression of an unwanted species or selective excitation of the species to be imaged [7, 8] and also a method based on chemical shift-specific slice selection [9] have been proposed as local methods. A global method produces essentially a chemical shift spectrum for each localized region or volume element, and thus creates a stack of chemical shift images. A global deconvolution calculation technique has been proposed [10] utilizing a combination of the Wiener filter and an anodization function. A method of convolution has also been suggested in which the image is deconvoluted by the NMR

spectrum of the sample [ H ] . This latter method shifts the image of each individual resonance such that it is centered about the carrier frequency. No totally adequate method of suppressing the chemical shift artifacts has yet been developed, but all of the methods improve the quality of the images when multiple chemical shifts are present. On the other hand, chemical shift imaging is highly desirable. Selective excitation chemical shift imaging is possible only if the spectrum of the sample is resolvable for the entire imaging volume. It has been suggested that chemical shift-sensitve NMR images can be obtained using spectral simplification by tailoring the excitation pulses [12]. Chemical shift images have been reported for two rubbery polymers, polybutadiene and polydimethylsiloxane [13], and also for polyether polyol with an isocyanate curing agent [14].

6.3 APPLICATIONSOFNMRITOPOLYMERS 6.3.1 DETECTION OF VOIDS IN COMPOSITES The void content of pultruded composite rods have been studied using NMRI [15]. Glass fiber-reinforced nylon rods with fiber contents of 51% by volume were first mixed with different catalyst contents following the reaction injection molding (RIM) process, and then pultruded with a pulling speed of 18 inches per minute. Approximately 4% of the catalyst mixture, containing sodium hydride and phenyl isocyanate, was used. The diameter of the die in the pultruder was 0.90 cm. The rods were then soaked in water at 80 0 C for 25 weeks before imaging. The uptake in water was 3.7%, as measured by the increase in weight of the composite rods. The images were recorded on a Bruker MSL 300 spectrometer using a spine-echo pulse sequence. The slice thickness was 1.0 mm and the slices were taken transverse to the fiber axis. With the rods standing in 1.5 cm diameter vials containing water, the two images shown in Figure 6.4 are taken 0.5 cm apart through the pultruded rod. The light areas in the image represent void areas filled with water. The marker in the upper left hand portion of the image is 1 mm in diameter. Comparison of the sizes of the voids in the pultruded rod intidcates that some of the voids approach the magnitude of the marker. A comparison of the corresponding edge-enchanced images show that some of the voids in the images occur in the same location, which indicates that the voids are connected or tubular in shape. Thus, a channel-like void region is suggested over a length of 0.5 cm. From the computer conparison of the two images taken 0.5 cm apart, it is possible to identify a tubular shaped void running from one image to the other within the nylon rod. Such a void could be obtained if an air bubble was trapped in the matrix during the pultrusion process. It appears that water diffuses by following the fabers in the composite.

Image of water in pultruded nylon rodsreinforcedwith glass fibers

Contour plot of image showing presence of tubular void

Figure 6.4 Image of water in pultruded nylon rods reinforced with glass fibers and a contour plot of image showing the presence of a tubular void

6.3.2 DETECTION OF N O N U N I F O R M DISPERSION O F FILLER The improvement in mechanical properties by inorganic fillers is considerably reduced if there is a nonuniform dispersion of particles in the polymer matrix by formation of agglomerates. NMRI can produce visual pictures of the spatial variation of the organic phase distribution. This is accomplished by observing the proton images of the elastomers as a function of proton density and spin-spin, T2, relaxation times. These NMR parameters provide a measure of the molecular mobility, which in turn is related to the spatial variation of the polymer and the filler in the sample. Samples of poly(dimethylsiloxane) (PDMS) which were reinforced by in situ precipitated silica were examined by NMRI [16]. The images were obtained with a spin-echo technique, with a slice thickness of 500 |im and a digital resolution of 185 urn, and required a time of 25.6 min. A dark rim was observed around the sample which indicated a reduced mobility of the network chains compared with the sample core. This difference arises from the high concentration OfSiO2 in this region. 6.3.3 NMRI O F PHYSICAL AGING NMRI has been used to study the physical aging of cross-linked cautchouc (vulcanized natural rubber filled with carbon) [17]. The nondestructive character of NMRI provides a method to monitor various changes in the materials properties of a single sample rather than using the usual methods which destroy the sample during the analysis. A cylinder sample (5 mm diameter) of natural rubber filled with carbon black was used. The sample was removed after each measurement and aged for a predetermined period of time in a dry box at 1300 C. The samples were imaged using a conventional multiecho pulse sequence. The gradient strength was 250mT/m and the spatial resolution was 80 x 80 nm with a slice thickness of 1 mm. The images revealed air bubbles resulting from the molding process. When the sample was aged, inhomogerieities of varying size were observed as dark spots with bright shadows around them. The shadows arose from the difference in susceptibility of the inhomogeneities in comparison with the surrounding rubber. A ring in the aged surface layer was observed at the interface of the unaged material in the interior of the sample. This ring may have arisen from the presence of stabilizers such as stearin or paraffin, which diffuse to the reaction front. The onset of aging in the natural rubber can be observed by NMRI after only two hours. The thickness of the aged layer shows the asymptotic behavior expected for a radial protective film. If the aging reaction is modeled (for purposes of NMRI) as U + O2-A

where U is the soft rubber reacting with oxygen at elevated temperature yielding a hardened, aged rubber, A, in NMR terms the sample has only two possible internal states, i.e. soft and hard. These two states have two different T2 values, which are 5.8 ms for the unaged rubber and 0.3 ms for the aged portion. As the relaxation times are different by a order of magnitude, the first echo results only from the unaged rubber U and can be used to determine the concentration. The concentration dependence of the unaged rubber U on the aging time ra can be expressed as [U](O = [U 0 ]exp(-/a a ) and then the amplitude of the echo becomes proportional to the concentration of U, The inverse rate constant k~l is determined to be 8 h ± 30%.

6.3.4 NMRI STUDIES O F D I F F U S I O N IN POLYMERS NMR imaging techniques has been used for the study of sorption and diffusion and of the desorption of multiple chemical substances in polymeric materials [18-28]. NMR imaging can directly provide the diffusion coefficients as a characteristic quantity of a liquid component in a sample, making it possible to map molecular migration on a microscopic scale. NMR imaging also provides additional information on the microdynamic and structural properties of heterogeneous systems, such as subregion diameters, exchange times, and phase boundary resistances [29, 30]. The principal advantage of NMR imaging is the possibility of making spatially localized diffusion measurements [30]. One can examine by NMR imaging the concentration and location of a permeating liquid in a solid sample. A true diffusion parameter image is obtained, where calculated diffusion coefficients are encoded into an intensity scale. One of the obvious advantages of NMR imaging for the study of diffusion is the visual presentation of the data in the form of images. Such a presentation allows one to view directly the concentration and location of the penetrant and to ignore extraneous factors influencing the diffusion. Another advantage of NMR imaging is that it allows the study of samples of virtually any shape, and allows the detection of initial imperfections in the sample being studied. It is generally difficult to interpret liquid sorption measurements in solids because the samples being examined are not perfect, that is, they initially contain cracks and voids which increase both the diffusion and the uptake of the liquid. Also, the induced volumetric changes, though small, can cause microcracking or void formation. The NMR imaging technique also allows the system to be studied dynamically, as measurements can be made on the solid sample immersed in the penetrant. The measurements are rapid. Using the FLASH techniques [22], an image can be obtained in a few minutes. In this fashion, it is possible to study the dynamics of

the diffusion process. Of course, the sample-penetrant system can be studied under isothermal conditions. Finally, a primary advantage of NMR imaging is the fact that all of the NMR parameters of the sample can be measured and used to interpret the diffusion or sorption process [30]. Images obtained utilizing different pulse sequences and interrupt times can be used to calculate the spin-lattice T1 and spin-spin T2 relaxation times and the spin density. These additional parameters relate to the bonding and environment of the penetrant in the polymer system. These types of measurements have been useful in understanding the morphological changes which are observed [22]. NMR imaging techniques have been used for the study of sorption, diffusion and chemical reactions as well as the desorption of chemical substances in polymeric materials [23]. NMR imaging can directly provide the diffusion coefficient as a characteristic quantity of the fluidity of a component in a sample, making it possible to map molecular migration on a microscopic scale. The diffusion coefficients have been quantitatively evaluated from a series of images recorded with different gradient field strengths [22]. Analysis involved the simulation of the effects of diffusion using the dynamic magnetization equations to calculate the magnetization for each pixel, which ultimately yielded an image whose intensities represented the spatially resolved diffusion coefficients. Finally, a true diffusion constant image was obtained in which the calculated diffusion coefficients were encoded into an intensity scale [22]. In this scale, high intensities corresponded to fast diffusion. In this manner, the spatial diffusion of a liquid into a solid material was characterized in a quantitative fashion. NMR imaging has been used for methanol diffusing into PMMA [22]. Figure 6.5 shows the image from the PMMA in methanol after 48 h. The diffusion coefficient can be calculated by measuring the thickness of the sorbed layer as a function of time. With data processing techniques, it is possible to simplify the measurements by giving the images a three-level gray scale and then drawing a profile across the sample as shown in Figure 6.6. The results are shown in Figure 6.7, where the thickness of the layer is plotted versus time. The linearity of this plot with time confirms that case II diffusion is occurring. The nonzero intercept at time zero is indicative of an initial Fickian diffusion process followed by case II diffusion. The constant level of methanol in the penetrant front is also reflective of case II diffusion. NMR relaxation parameters are useful probes of molecular motions in polymers. Each correlation time represents the average value of the system, with some distribution around that average. NMR imaging permits the determination of the spatial distribution of NMR relaxation times. This distribution provides information concerning the local motions of the system. In this case, the polymer is partially swollen with solvent, and the spatial distributions of relaxation times reveal the interactions between the solvent and the polymer in the diffusion process.

Figure 6.5 The proton NMR image of a 30 mm PMMA sphere initially submersed in methanol (left) and the image taken after 48 h of exposure to methanol at 300C. Reprinted with permission from John Wiley & Sons Inc. Journal of Polymer Science 1989

Figure 6.6 The intensity profile of the image on the right side of Figure 6.5. The features are: (a) bulk methanol; (b) equilibrium methanol volume in PMMA; (c) sharp concentration front; and (d) glassy PMMA. Reprinted with permission from John Wiley & Sons Inc. Journal of Polymer Science 1989 Acetone swells PMMA to a greater extent than methanol, and the selfdiffusion coefficients of the system are about two orders of magnitude greater than those of the methanol/PMMA system. This is apparently due to the increased volume available to the acetone molecules. The self-diffusion coefficients decrease by 35% from equilibrium in the outer regions to the region near the glassy core. The decreasing motions of the polymer chains as the core is

Diffusion distance (mm)

Time (hours)

Figure 6.7 The plot of diffusion distance measured with NMR imaging vs. exposure time for the PMMA shere in methanol at 300C. Reprinted with permission from John Wiley & Sons Inc. Journal of Polymer Science 1989 approached reduce the solvent mobility, as reflected in the self-diffusion coefficients [22].

6.3.5 DESORPTION OF LIQUIDS FROM POLYMERS Desorption is one diffusion process that has been given little attention, primarily because of the lack of adequate analytical techniques. Desorption measurements above the glass transition temperature of an unswollen polymer are expected to follow Fickian characteristics. Likewise, a polymer swollen so that the Tg is below the experimental temperature initially exhibits Fickian desorption. The solvent is thought to desorb rapidly from the surface of the polymer and raise the Tg of the surface layer. After the surface T8 is above the experimental temperature, the desorption process slows, and the process is controlled by the diffusion through the glassy surface layer. NMR imaging provides the spatial distribution of solvent in the polymer and also the spatial distribution of the rate of desorption [23]. The desorption process can be related to Td, which is the inverse of the rate of net solvent loss for a given pixel through the equation: M = Moexp(-exp7/7d) A nonlinear least-squares fit of the experimental data is used to calculate a Td image on a pixel-by-pixel basis [23]. We have reported some results on the NMR imaging of the desorption process [23]. Images of the desorption of methanol from swollen rods of PMMA were obtained [23]. The methanol volume fraction was 0.26. The rods were then placed in fully deuterated cyclohexane. The first image acquisition began 6min after initial submersion. Images were collected in Ih increments over a 104 h period. The signal intensity decreased with time, the maximum intensity of the

Figure 6.8 A Td image calculated from 20 images at 5 h increments over a 100 h interval. Reprinted with permission from [22]. Copyright 1990 American Chemical Society

last image being only 50% of that of the initial image. The diameter of the rod decreases by 816 ±68 mm over the 10Oh period as measured from the images. A Td image calculated from 20 images taken at 5 h intervals over 100 h is shown in Figure 6.8. In this image, the light portion represents the largest Td and dark represents the smallest T6, which corresponds to the slowest and the fastest intensity decreases, respectively. This image shows that the faster intensity decreases are near the surface of the rod and the slower intensity decreases are near the glassy PMMA core. The Td at the surface is 58 h and that at the glassy core is 450 h, as determined from this image. This agrees with the Fickian characteristics, and indicates that imbibed solvent near the surface desorbs quickly, with the desorption rate decreasing toward the sample core. However, for this system there is no evidence of a glassy skin developing on the polymer surface [23].

6.3.6 MULTICOMPONENT DIFFUSION AS STUDIED BY NMRI It is possible to use NMRI to study multicomponent diffusion in a number of different ways, utilizing differences in chemical shifts, relaxation times or by isotopic labeling. We have chosen the last method [26]. We studied the simultaneous diffusion of acetone and methanol into polycarbonate by completely deuterating one of the components and recording the images of the other component in the PC. Using perdeuterated methanol (MeOH-J4) and acetone (AC), the FLASH images show the movement of the acetone diffusion front within the PC rod. These images show that the 75:25 ACrMeOH-J4 mixture diffuses more rapidly than the 50:50 AC:MeOH-J4. Perdeuterated acetone :hydroxy-deuterated methanol (AC-J6: MeOD) mixtures of 75:25,65:35 and 50:50 volume ratios AC-J6: MeOD were also studied. From these images we can monitor the solvent front movement of acetone and methanol into the PC rods. The movement of the solvent front of acetone into PC versus the square root of time is shown in Figure 6.9(a) for the 75:25,65:35 and 50:50 AC .MeOH-J4 mixtures. The diffusion into PC increases as the acetone content of the mixture increases. In addition, there is a linear dependence between the solvent front movement and the square root of time. This indicates that the diffusion of AC: MeOH-J4 into PC is Fickian [26]. This result was anticipated, as the diffusion of both pure methanol' and pure acetone has previously been determined to be Fickian [33]. (Note, however, that the diffusion of pure acetone was found to be Fickian after an initial period in which the diffusion was reported to be anomalous [33]). This may seem contrary to what is usually found for the diffusion of solvent into a glassy polymer which is below its glass transition temperature Tr Instead, either case II or anomalous diffusion is most often encountered in this temperature region. This is because, below the Tg, the polymer chains are in the glassy state, and are therefore not mobile enough to accommodate the solvent. In contrast, Fickian diffusion is prevalent above the 7^ because the polymer chains are in the rubbery state and can therefore accommodate the solvent more readily. Although the T% of dry PC is 149 0 C, acetone and methanol diffuse into PC in a Fickian manner because the 7^ is reduced to « —9 0 C by the solvent ingress [31]. In this way, PC is able to relax and accommodate the solvent almost immediately, allowing the solvent movement not to be inhibited by the rate of polymer relaxation. The solvent front was also monitored for the AC-J6: MeOD mixtures. For the mixtures of 75:25,65:35 and 50:50 AC-J6: MeOD into PC, similar behavior was also seen in Figure 6.9(b), where the methyl resonance of methanol was monitored. There is an increase in the rate of the front movement as the acetone content increases, and also a linear dependence of the front movement with the square root of time. This linear dependence indicates Fickian diffusion.

Millimeters Millimeters

Square root time (h1/2)

Square root time (h1/2)

Figure 6.9 Solvent front movement of (a) acetone into PC for the 75:25,65:35, and 50:50 v/o AC/MeOH-^ mixtures and (b) methanol into PC for the 75:25,65:35, and 50:50 v/o AC-
behavior is also found when comparing the 50:50 AC:MeOH-^4 and the 50:50 AC-d 6 :MeOD mixtures. It may be proposed that this joint diffusion through PC is the result of the formation of a weak "complex", possibly a weak hydrogen bonding interaction [22] between acetone and methanol. The 65:35 v/o AC:MeOH mixture has approximately a 1:1 molar ratio, and thereby all the acetone may be complexed with methanol. This would account for the overlap of the front movement plots within error. In the 50:50 v/o AC:MeOH mixture, the molar ratio is « 35:65 AC: MeOH. If all the acetone complexes with methanol, that leaves approximately equal amounts of ACMeOH complex and free methanol which would diffuse together. As shown by the 65:35 v/o AC:MeOH mixture diffusing at a greater rate than the 50:50 v/o AC:MeOH mixture, the "complex" may have a greater interaction with PC than the free methanol would in the 50:50 v/o mixture. The complex may be able to reduce the T% further than the free methanol, allowing an increased rate of penetration of slovent.

6.3.7 A B S O R P T I O N - D E S O R P T I O N CYCLING O F LIQUIDS IN POLYMERS We have studied the absorption-desorption cycling of water and methanol into and out of the PMMA rods to determine its effect on the diffusion characteristics. There is an increase in the rate of weight gain with cycling. The increase in the rate of weight gain becomes even more evident as the initial water content in PMMA increases. This may be caused by the increased plasticization of PMMA by the water for higher water contents followed by higher methanol contents. This may have created increased porosity within the PMMA as the solvent contents were increased. A similar effect can be seen for the cyclic diffusion of methanol into watersoaked PMMA with water contents of 0.6 and 0.75 wt%. The percentage weight gain versus time of diffusion is linear with time except for an initial lag time, which is anomalous. The lag time may be attributed to methanol desorbing a thin layer of water from the PMMA, which causes the layer to be in tension from the shrinkage back to the unswollen state. This descreases the mobility of the polymer in this layer and makes the polymer less accommodating to methanol diffusion [27]. For polymers which are in the glassy state, the removal of diluents or small molecules may cause an increase in sorption and mass transport properties of the polymer [32]. It has been found that the removal of liquids from a polymer below its Tg can increase the porosity within the polymer [32]. This would therefore result in an increase in the rate of diffusion of diluents such as water and MeOH into PMMA. It should be noted that there was no reduction in dry weight with each successive absorption-desorption cycle of water and MeOH, which would

indicate initially that unreacted monomer and other small molecules were not leaching out. This would also indicate that the initial drying was sufficient to remove unreacted monomers and other small molecules from the PMMA rods, and none were further released by the absorption-desorption of methanol and water. In a sense, this conditioning of the PMMA rods allows the uptake of increased amounts of solvent with each successive cycle [33]. These increased uptakes may be attributed to reduced packing or lack of reconsolidation when the solvent is removed from the swollen polymer in the glassy sate [32,33]. It may be suggested that increases in uptake are due to an increase in free volume [33], although no increase in dry volume was observed. It is possible that not all the methanol was removed in the drying process, and there may have been some loss of other low molecular weight materials, such as unreacted monomer, from the PMMA sample. It has been well established that it is difficult to remove solvents or monomers from polymers [34]. The PMMA rods were kept in a vacuum at 60 0 C until no further weight loss was apparent. It has been shown in previous experiments [32] that, when PMMA is exposed to solvents such as MeOH, unreacted monomer present within the material will leach out. It is expected that, after drying the polymer to remove the solvent that has diffused into PMMA, the zero weight of the sample should decrease. However, the zero weight of the samples analyzed in this experiment remained the same. This indicates that not all of the methanol that diffused into the PMMA is removed during the drying periods between the absorption cycles. In addition to using weight gain measurements to describe the effects of cycling on the diffusion characteristics of water and methanol in PMMA, NMRI was used to observe the solvent front movements within the PMMA rods [27]. The proton NMR images were obtained for the diffusion of MeOD into three different PMMA samples. These three samples had previously been subjected to no, one and two cycles of the absorption and desorptuon of MeOD. The FLASH images were obtained, and show the movement of the MeOD diffusion front within the PMMA rods after 5.92,18.75, 23.70 and 31.2Oh. The images showed that the diffusion of MeOD increased with an increase in the number of cycles. This corresponded to our previous weight gain experiments. The rate of MeOD diffusion increased with cycling. A linear dependence of the solvent front movement with time was seen for the PMMA samples subjected to no and to one cycle. This indicated that case II diffusion occurred after an initial time period of anomalous diffusion. However, the MeOD front movement for the second cycle was not linear with time, but rather was linear with the square root of time. After an initial lag period of anomalous diffusion, the front movement for the second cycle behaved in a Fickian manner. This indicates that the diffusion characteristics of the PMMA are altered with absorption-desorption cycling. The solvent front velocities were determined for case II diffusion as being 12.6 and 14.5 nm/s, respectively. These values are more than twice the magnitude of

those found by Thomas and Windle [35] and by Weisenberger and Koenig [22, 23] for methanol diffusion in PMMA. This can be explained by the fact that the water content and the drying treatment of the PMMA were never taken into account in their experiments. The removal of water and the leaching out of unreacted monomer were also not considered. The increases in diffusion of MeOD may be accounted for by the plasticization by water of PMM A, which can be demonstrated between the samples exposed to zero and one cycle. The increased plasticization allows for the increased rate of relaxation of the polymer chains and a greater solvent front velocity. The translational diffusion coefficient was determined to be 4.0 x 10" Vs. This compares with a value of 2.4 x 10" Vs for the diffusion of methanol into PMMA at the elevated temperature of 60 0 C reported by Weisenberger and Koenig [22] for as-received PMMA rods. This shows that, even at a low concentration, the cyclic absorption-desorption of water and MeOD has a more significant effect on the characteristics of the methanol diffusion into PMMA than does the temperature at which diffusion occurs. The value of 4.0 x 10" Vs for the diffusion of MeOD after two cycles of absorption-desorption of water and MeOD appears to be comparable with that of MeOD diffusion in PMMA for a high water content (.25 wt% of polymer).

6.4 ACKNOWLEDGEMENTS The author acknowledges the support of ALCOM (Advanced Liquid Crystalline Optical Materials) DMR 8920147 and the students whose work was responsible for the citations in this paper.

6.5 REFERENCES [1] P. Mansfield and P.G. Morris, NMR Imaging in Biomedicine, Academic Press, New York, 1982. [2] J. Liu, A.O. Nieminen and J.L. Koenig, J. Magn. Reson., 1989,85, 95. [3] D.G. Cory, Solid State Imaging, Annu. Rep. NMR, 1992, 25. [4] J.L. Koenig, Spectroscopy of Polymers, ACS, Washington, DC, 1992, Chapter 11. [5] A.O.K. Nieminen and J.L. Koenig, J. Adhes., 1989,30,47. [6] W.T. Dixon, Radiology, 1984,153,189. [7] L.D. Hall, S. Sukumar and S.L. Talagala, J. Magn. Reson., 1984,56, 275. [8] L.D. Hall and V. Rajanayagam, J. Magn. Reson., 1987,74,139. [9] A. VoIk, B. Tiffon, J. Mispelter and J.M. Lhoste, J. Magn. Reson., 1987,71, 168. [10] J. Liu, A.O.K. Nieminen and J.L. Koenig, Appl. Spectrosc, 1989,43, 1260. [11] D.G. Cory, A.M. Reichwein and W.S. Veeman, J. Magn. Reson., 1988,80, 259. [12] P. Bornert, W. Creher, A. Gossler, G. Klee, R. Peter and W. Schneider, J. Magn. Reson., 1989,81, 167. [13] L. Garrido and J.E. Mark, Polym. Repr., 1989,30, 217.

[14] A.O.K. Nieminen and J.L. Koenig, Appl. Spectrosc, 1989,43, 153. [15] K.P. Hoh, B. Perry, G. Rotter, H. Ishida and J.L. Koenig, J. Adhes., 1989, 27, 245. [16] L. Garrido, J.E. Mark, CC. Sun, J.L. Ackerman and C. Chang, Macromolecules, 1991,24,4067. [17] P. Bliimler and B. Blumich, Macromolecules, 1991,24, 2183. [18] S. Blackband and P. Mansfield, Solid State Phys., 1986,19, L49. [19] W.P. Rothwell and P.P. Gentempo, Bruker Rep., 1985,1,46. [20] J.L. Koenig, Appl Spectrosc., 1989, 43,1117. [21] C. Chang and R.A. Komoroski, Macromolecules, 1989, 22, 6000. [22] L.A. Weisenberger and J.L. Koenig, Macromolecules, 1990, 23, 2445. [23] L.A. Weisenberger and J.L. Koenig, Macromolecules, 1990, 23, 2454. [24] B. Blumich, P. Bliimler, E. Gunther, and G. Schauss, Bruker Rep., 1990, 2, 22. [25] S.R. Smith and J.L. Koenig, Macromolecules, 1991,24, 3496. [26] R.A. Grinsted and J.L. Koenig, Macromolecules, 1992, 25,1229. [27] R.A. Grinsted and J.L. Koenig, Macromolecules, 1992, 25,1235. [28] P. Maffei, L. Kiene and D. Canet, Macromolecules, 1992, 25, 7114. [29] B. Bluemich and W. Kuhn (Eds.), Magnetic Resonance Microscopy, VCH, Basel, 1992. [30] P. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Claredon Press, Oxford, 1991. [31] R.A. Ware, S. Tirtowidjojo and C. Cohen, J. Appl Polym. ScL, 1981, 26, 2975. [32] E.E. LaBarre and D.T. Turner, J. Polym. Sci.f Polym. Phys. Ed., 1982, 20, 557. [33] A.R. Barens and H.B. Hopfenberg, J. Polym. ScL, Polym. Phys. Ed., 1979,17, 1757. [34] L. Mandelkern and F.A. Long, J. Polym. ScL, 1951, 6, 456. [35] N.L. Thomas and A.H. Windle, Polymer, 1978,19, 255.

7 FOURIER TRANSFORM INFRARED AND RAMAN SPECTROSCOPIES IN THE STUDY OF POLYMER ORIENTATION P. J. HENDRA and W. F. MADDAMS Department of Chemistry, University of Southampton, Highfield, Southampton, SOU IBJ, UK

7.1 INTRODUCTION Infrared and Raman spectroscopy can be used to detect the presence of orientation in polymer specimens and also to quantify it. The use of infrared methods for films has a long history, but more recently the technique has been extended to bulky specimens. Raman scattering can in principle provide a more detailed insight into molecular anisotropy, but is dogged by experimental difficulties. To review the field in its entirety would be quite impossible, but it is feasible to introduce the subject and through examples to explain its scope. Orientation measurements based on infrared or Raman methods can be applied to static samples or more recently, to those exposed to sinusoidally varying stress. We will consider first the principles governing the effect that orientation has on the observed vibrational spectra, review some of the applications and then move on to the dynamic studies, and conclude with an account of the effect of large strain on elastomers. Any molecular property which is anisotropic, i.e., that shows a direcional dependence, is per se capable of providing information on orientation both in solids and in appropriate melts or liquids. Such properties include optical birefringence, infrared polarization, anisotropic Raman scattering, broad line NMR and X-ray diffraction, each of which has been exploited in the study of polymers. These various approaches yield differing amounts of information, for fundamental reasons; in order to appreciate why this is so it is necessary to consider their theoretical basis, and also to have a convenient mathematical framework by which to quantify degrees of orientation. These two topics will now Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

be considered, first in the case of infrared spectroscopy, which provides a comparatively simple introduction, and then for Raman spectroscopy which, in principle, provides more detailed information at the expense of complexity of interpretation of the experimental measurements.

7.1.1 THE BASIS O F ORIENTATION MEASUREMENTS BY INFRARED SPECTROSCOPY The absorption of infrared radiation occurs to a maximum degree when the direction of the electric vector of the radiation is parallel to the direction of the dipole moment changes involved in the various vibrational modes of the absorbing molecule. If the direction of the electric vector lies at an angle to the direction of the dipole movement change, the component of the former resolved along the latter direction is involved in the absorption process, which thus occurs less strongly. This is the directional property that makes infrared spectroscopy useful for orientation studies. This directional property is not usually a pertinent factor in determining the intensities of the bands in an infrared spectrum, because the radiation is not polarized and the direction of the electric vector is random in the plane perpendicular to the propagation direction. Furthermore, in solutions, and in many solid samples, the absorbing molecules are randomly oriented. In the situation where the incident light is plane polarized, so that the electric vector lies in a fixed direction, and the sample is partially or completely orientated, as is often the case with polymer specimens, changes in peak intensity will usually occur. This is readily understood by reference to Figures 7.1 (a), (b) and (c). The first shows the simple situation of a group of molecules, which are conveniently taken to be polymer chains in the present context, lying parallel to each other. This type of orientation is known as uniaxial, and it often occurs as the result of stretching or rolling in the direction along which the chains are lined up. Consider a molecular vibration in which the direction of the dipole movement change lies along the chain, or the principal orientation direction. Consider further the situation when the electric vector is plane polarized parallel to this direction. In these circumstances maximum absorption will occur, and its magnitude will be determined by the rate at which the dipole moment changes with changes in bond length during the vibration. Complete uniaxial orientation seldom occurs in practice, and the typical situation is that of a range of orientations about the direction of complete orientation. One such chain is shown in Figure 7.1(b). The component of the electric vector resolved along this chain, lying at an angle 9 to the complete orientation direction, is cos 6. Then, since the absorption intensity is proportional to the square of the dipole moment change, it follows that, if the intensity of absorption is / along the direction of complete orientation, it will be / cos 2 0 for

Direction of dipole moment change 1a

1b

1c

Figure 7.1 The relationship between the directions of incidence and the vibrator in a polymer the chain at angle 0. It is evident that for 0 = 90°, zero intensity will be observed. The converse is that in the situation shown in Figure 7.1(a), with complete uniaxial orientation, if the direction of the electric vector is perpendicular to the chain direction, / will be zero. If these two intensities are denoted by J1 and J1, their ratio, which is known as the dichroic ratio Z), will tend to infinity. If the dipole moment change lies perpendicular to the chain direction it follows that for complete uniaxial orientation the dichroic ratio will be zero. In both situations the dichroic ratio will be unity for random orientation, so measurements on the way in which it changes during a process such as stretching or rolling, which frequently induce orientation, will yield useful information. Figure l(c) shows the situation which is common in practice, a range of orientations which, in the uniaxial situation, will be symmetrical about the direction of maximum orientation. The average value of cos 2 0, denoted by , will then define the overall orientation of this system. It may be shown that = /„//, + 2I1 and, therefore, that = D/(D + 2). Thus, may be determined by measuring D. The situation considered in Figures l(a)-(c) is simplistic in that, in general, the direction of dipole moment change in the polymer molecule will not lie precisely along the chain axis, but at some angle <j>. If is known it then becomes possible to determine in the general situation. In practice is often hard to locate for two reasons. Although detailed crystallographic studies and molecular vibrational calculations have been undertaken for most of the better known addition polymers, this is not the case for some newer materials, and <j> for some vibrational modes is not known. Secondly, for amorphous polymers, and indeed for the amorphous component of partially crystalline polymers such as polyethylene, the chains may occur in more than one conformational form, so that perpendicularity becomes rather indeterminate. Nevertheless, the examination of D as a function of processing operations will often yield very useful comparative information which is unobtainable from X-ray diffraction studies, which are specific for crystalline regions only. In

particular, it is worth noting that X-ray diffraction applies only to crystalline fragments, but infrared dichroism is indicative of orientation throughout the system.

7.1.2 THE BASIS O F ORIENTATION MEASUREMENTS BY RAMAN SPECTROSCOPY The information provided by the Raman spectrum of an oriented polymer differs from its infrared counterpart because of the fundamentally different processes involved in the generation of the spectra. In the infrared absorption process, as already noted, the absorption intensity is dependent on the angle between the electric vector and the direction of the dipole moment change. The Raman spectrum results from inelastic photon scattering, details of which are determined by changes in the polarizability of the chemical bonds involved. Polarizability is a tensor quantity, which results in complications but, in principle, provides additional information. As we have seen, infrared spectroscopy involves only one beam of polarized radiation, and the fraction of the radiation absorbed by a molecule depends only on the orientation of the molecule with respect to the polarisation vector of the radiation. However, Raman scattering involves two beams of radiation, those of illumination and collection, and the scattered intensity depends on the orientation of the molecule with respect to the polarisation vectors of both beams, which may, of course, be different. This necessitates more detailed measurements in order to obtain the relevant information. It may be shown that the Raman measurements are capable of yielding information on both < cos 2 0 > and < cos 4 6 >. The availability of < cos 4 6 > data can be valuable is distinguishing between the differing types of stress deformation mechanisms that have been proposed. However, an interpretation of the band intensities in terms of and is possible only when the principal components of the derived polarisability tensor are known. This information is often not available and assumptions must then be made; these then render the method non-absolute. Examples of this approach will be considered briefly below. The interpretation of detailed orientation measurements by Raman spectroscopy has led to the use of various abbreviated procedures. However, unlike the use of infrared dichroic ratios for comparative purposes, simplified Raman procedures present pitfalls for the unwary and must be used with due care and attention. It is useful at this juncture to note the capabilities of the other major methods for assessing orientation in polymers. Birefringence measurements yield values for and broad line NMR provides and , together with in certain favourable circumstances. X-ray diffraction measurements define orientation uniquely, and so give values for , where n takes on all even values. Infrared spectroscopy and birefringence measurements yield the

least detailed information, but are by far the simplest methods from the experimental point of view, and this is often the decisive factor. There is no difficulty in making infrared measurements on polymer specimens having some degree of biaxial orientation, but the interpretation of the results may not be straightforward. It is possible in principle to express the results in terms of a more generalized type of mathematical orientation function. However, the approach that has tended to be used in practice, so far as is possible, is to utilize bands arising from vibrations for which the direction of the dipole moment change is well established, and is presumably either parallel or perpendicular to the chain axis. The complexity of interpretation of the Raman spectra of biaxially oriented specimens has discouraged work in this area.

7.2 7.2.1 EXPERIMENTAL T E C H N I Q U E S O N STATIC SAMPLES In the infrared, plane polarized radiation is required, and is provided by passing the radiation through a polarizer transparent in the wavelength domain of interest. A variety of these devices has been used over the years, but today the use of a fine wire grid on a KRS-5 (thallium bromoiodide) support is pre-eminent. The device is usually in the form of a disc 25 mm in diameter mounted in a metal holder, but the devices are very fragile because only the slightest accidental contact with the face coated with the gold grid is fatal to its efficiency. It is normal to study polymers as films in transmission, having identified a reference direction in the specimen. To remove polarization effects arising from the interferometer, the polarizer should lie in a fixed orientation and the sample should be rotated, rather than the reverse. Where orientation has been introduced by processing operations such as drawing or rolling, visual inspection of the specimen usually reveals the processing directions, widely known as the 'machine' directions, and can be uniaxial or biaxial. The major experimental limitation in infrared transmission measurements is the requirement for films to be thin enough to obtain adequate results. In practice, this requires film thicknesses in the range 25-100/mi depending on the type of polymer involved. See Figure 7.2. Measurements have been successfully made using polarized infrared radiation in attenuated total reflectance (ATR) and specular reflectance. In the ATR experiment the conventional prism is replaced by a 'pent roof device and the polymer is clamped to its surfaces with the machine direction parallel to one of the sides. The experiment is then carried out through two adjacent faces, i.e. with the polarized radiation passing along or normal to the machine direction. See Figure 7.3. Comparison of the two spectra is as for transmission. Specular reflection has a much more complex theoretical background and is not considered here.

Absoitoance

Wavenumber v (cm~1)

Figure 7.2 Dichroic infrared measurements on a film of biaxially oriented polyethylene terephthalate

Sample

AT. R. Crystal

Sample oriented Pent roof A.T.R. prism Il Position Rotation about axis G produces 1 Position Beam enters face A

Figure 7.3 ATR carried out with polarised light. The method was developed by the late

Micrometer

Figure 7.4 The optical arrangements typical of a FT Raman spectrometer operating anisotropically. The laser is turned by prism P1 to the left and brought to a focus in plane S. Samples in this plane scatter light collected by lenses L2 and L3 and pass it to the interferometer, which lies to the right

Confining our attention to FT Raman experiments and to polymers makes the experimental arrangements involved far simpler than they might otherwise be. In FT instruments backscattering is almost invariably used. See Figure 7.4. The radiation, which is from a laser source and almost always plane polarised, irradiates the sample. The scattered light leaving the sample in the reverse direction to the incident beam is collected with a large lens or mirror and passed to the interferometer and detector. The collected radiation is analysed with an analyser in the optical train (frequently between the interferometer and the detector). Several experiments can be attempted by rotating the sample as required and also by rotating the polarization analyser. In theory, correction should be made for the polarization effect of the interferometer itself, but this is usually ignored. The various experiments are too disparate to describe as || or 1 and so a nomenclature originally devised by the late S.P.S. Porto is normally involved. It is defined in Figure 7.5. In principle, samples of any reasonable thickness can be studied with FT Raman spectroscopy and the sampled volume can be located from the surface back into the bulk at will. However, a high degree of optical clarity is essential if the polarization sense is not to be scrambled. With care, convincing measurements can be made on opalescent materials, e.g., ultrahigh-modulus polyethylene, which is milky and non transparent. See Figure 7.4. If study in the bulk phase of an inhomogeneous specimen, e.g. a transparent moulding in, say, polymethyl methacrylate or poly-4-methyl-lpentene is planned, a word of caution is pertinent. As the laser passes through the

Crystal axes

Direction of View Direction of Illumination

Analyze Laser Polarisation

Figure 7.5 The experimental nomenclature defined by the late Dr S.P.S. Porto

surface of the specimen and then the anisotropic bulk on its way to the volume viewed by the spectrometer, the plane of polarization will be rotated. The scattered light will also be affected, so the conclusions reached about the orientation within the specimen may be unreliable.

7.2.2 INFRARED SPECTROSCOPIC STUDIES ON ORIENTED POLYMERS The purpose of this section is to give readers an indication of the type of information that may be obtained, not to provide a detailed literature survey. It covers both the use of dichroic ratio measurements, the more common approach, and the formal use of orientation functions. The value of dichroic ratio measurements, taken in conjunction with polymer processing variables, is demonstrated excellently by a study on cold drawn linear polyethylene, made a quarter of a century ago by Glenz and Peterlin [ I ] . The results are shown in Figure 7.6. Consider first the results for the band at 1894 cm " l . The dichroic ratio decreases rapidly with increasing draw ratio and asymptotically approaches zero as the draw ratio exceeds « 5 . The 1894 cm" 1 band is a combination mode of the Raman active methylene rocking mode at 1170 cm ~ * and the methylene rocking mode at 720 cm " *, and is characteristic for crystalline regions of the polymer. Its dipole moment is perpendicular to the

Draw ratio Figure 7.6 Dichroic ratio D vs. draw ratio for cold drawn linear polyethylene [1] c axis, i.e., the long chain direction of the polymer. Hence, the early decrease in the dichroic ratio with increasing draw ratio shows conclusively that there is rapid orientation of the c axes of the crystallites parallel to the draw direction as the sample is deformed. The peak at 1368cm" x arises from the symmetric CH 2 wagging mode for the CH 2 —CH 2 group, where the C—C band is at the centre of a gauche-transgauche sequence. It differs from the behaviour of the band at 1894 cm" x in two obvious respects: namely, that the approach to the limiting value with increasing draw ratio occurs decidedly more slowly as deformation increases, and the ultimate value indicates that there is only partial orientation of this structural unit. This was interpreted as evidence for a clear segregation of the crystalline and amorphous phases. The corresponding asymmetric wagging vibration gives rise to the band at 1303 cm" 1 , and the polarized intensity of this is virtually dependent on draw ratio, showing that substantial orientation is not occurring, although a knowledge of the direction of dipole moment change is required in order to interpret the results more fully. The peak at 1078 cm" 1 comes from a gauche C—C stretching and some CH 2 wagging. Its behaviour is intermediate in that it reaches its ultimate dichroic ratio of «0.7 at relatively low draw ratios, but the final value is a reasonable indication of partial orientation only, as would be expected for methylene units in amorphous regions.

The value of the approach using dichroic ratios coupled with a knowledge of the assignments of peaks is further illustrated by measurements on plain polyethylene films [2]. The production process leads to a rather complex orientation pattern. The molten polymer is extruded as a thin, hollow cylinder, in what may be termed the machine direction. It is simultaneously expanded in a plane perpendicular to the machine direction by the application of internal pressure. Additional variables are the extrusion temperature and the rate at which the blown film has been cooled. The resulting orientation behaviour is best studied by x-ray diffraction pole figure measurements [3,4,5] but the infrared approach provides a relatively simple means for obtaining a useful amount of information, particularly for the behaviour of chains in amorphous regions. Dichroic ratios were measured for the bands at 1080, 1303, 1352 and 1368 cm" 1 . The first of these is associated with tie chains between crystalline lamellae in amorphous regions, and the remaining three involve methylene group vibrations of loose chain folds in amorphous domains. It was possible to correlate the results with the occurrence of two types of orientation that had earlier been characterized by X-ray diffraction measurements. They are termed high- and lowstress orientation, whose occurrence depends on the blowing conditions and those during film production. The first type of orientation is analogous to that found in cold drawn polyethylene, discussed above, in having the c axis distribution of the crystalline regions substantially along the machine direction. The low-stress orientation, which occurs the more frequently, is the result of the type of crystallization process described by Keller and Machin [6]. The a and c axes are inclined at an angle to the plane of the film, with a strong tendency for the greater concentration of a axes to lie near to the machine direction. The three peaks at 1303,1352 and 1368 cm" * show appreciable orientation in the high-stress type of films but very little with the low-stress materials. Conversely, the extended tie chains, characterized through the 1080 cm" i band, are appreciably oriented in the low-stress films but not so in their high-stress counterparts. These results, together with those from X-ray diffraction measurements, proved to be of appreciable value in selecting the best blowing conditions to manufacture films having optimum tear strengths. The more formal approach, involving values of , has been used by Purvis et al. [7] to study uniaxially oriented specimens of polyethylene terephthalate). These measurements were part of a wider study involving birefringence and Raman studies, and the results are more conveniently considered in the following section. 7.2.3 RAMAN SPECTROSCOPIC STUDIES O N ORIENTED POLYMERS The ability of Raman spectroscopic studies on oriented polymers to yield values for both and has led to its use with polyethylene, atactic

poly(methyl methacrylate), poly(ethylene terephthalate) and poly(vinyl chloride). Some results that have been obtained will be considered briefly. Despite the problems of Raman spectroscopic studies when working with polyethylene specimens, Maxfield et al. [8] obtained spectra of adequate quality by immersing thin drawn films of low density polyethylene in silicone oil to minimize surface scattering. They used the 1170cm" 1 band, characteristic for chains in crystalline regions, and one at 1081 cm" \ specific for the amorphous ones, to obtain values for and . The former agreed well with those deduced from infrared measurements. Both sets of values are reasonably in line with theoretical estimates obtained from the Roe and Krigbaum [9] crosslinked rubber network model, and the crystalline orientation factors are as expected on the basis of the phenomenological theory of Yoon et al. [10]. The major workers in the field have been Professor LM. Ward and his colleagues at the University of Leeds. The technique was first applied to poly(ethylene terephthalate) [T]9 abbreviated to PET for convenience, using uniaxially oriented tape specimens. Measurements were confined to the benzene ring mode band at 1616cm" x and only three independent intensities, in terms of possible orientations, were measured. Nevertheless, some interesting results were forthcoming. Values of were plotted as a function of birefringence, and a straight line was obtained. Extrapolation to = 1 permitted a value for the maximum birefringence to be obtained, and this agreed well with that suggested by Kashiwagiet al. [ H ] . Plots of and as a function of draw ratio were compared with the predictions from the affine rubber elasticity model and the pseudo-affine aggregate deformation model. There is moderately good agreement with the rubber model for draw ratios less than « 3 , and some indication that for those in excess of 4.5 the pseudo-affine aggregate model becomes more appropriate. Purvis and Bower [12] subsequently extended the work, using four additional Raman peaks, all of which predominantly involve motion of the terephthalyl moiety, to a first approximation. The results suggested that there is no preferred orientation of the plane of the ester group with respect to the plane of the benzene ring in the amorphous phase. They also concluded that the drawing of PET occurs in a similar manner to the extension of a rubber-like network. Purvis and Bower [13] also examined drawn specimens of amorphous poly(methyl methacrylate), using four peaks in the Raman spectrum. They were not able to distinguish between two plausible structural models, one essentially linear and the other helical, but they were able to show that their results are consistent with the affine deformational model. The success of these measurements prompted a study on drawn specimens of plasticized PVC [14]. This poses problems because of the complexity of the spectrum, which shows overlapping peaks arising from configurational and conformational isomers. In this first study, attention was confined to peaks at 608 and 638 cm" 1 specific for long planar syndiotactic sequences, the type of unit

INTENSITY

W A V E N U M B E R

( C m-1)

Figure 7.7 FT Raman measurements on ultra high-modulus polyethylene. Spectra recorded in two ways-analyzer vertical or horizontal polarised vertically. involved in the crystalline regions of the polymer. All possible orientation and polarization combinations were used, giving a total of eight intensity measurements per peak. The results, including a comparison of < cos 2 6 > values with those from birefringence measurements, showed that the crystalline regions are more highly oriented than the non-crystalline ones in samples containing the larger amounts of plasticizer and drawn at the higher temperatures. In a continuation of this work, Bower et al. [15] used the intensity of the 616 cm" * band, specific for short syndiotactic sequences probably present in amorphous regions. The results support the earlier tentative conclusion that amorphous chains behave in a rubber-like way during orientation. The results described above all refer to Raman measurements made prior to the introduction of FT methods and near-infrared sources. More recent work shows that anisotropic measurements are far easier than they were, and can be made at room temperature on heated or cooled specimens with consummate ease. The measurements on highly oriented polyethylene shown in Figure 7.7 are simple to produce both at room temperature and at — 1800C. An analysis is available [16]. Several very preliminary reports have appeared in the recent literature, where a 'dichroic' measurement has been attempted, in that spectra have been recorded with no polarization analyser and with the machine direction of the sample set

parallel or perpendicular to the electric vector of the laser. They are, of course, in each case the sum of several of the spectra shown in Figure 7.7. Further, the polarization of ingoing and outgoing radiation may be rotated as described in Section 7.2.1. The results indicate the orientation and variations thereof but cannot be used to give quantitative data. We find the approach useful but it has to be used with caution.

7.3 TIME RESOLVED MEASUREMENTS As we have seen, the changes to a vibrational spectrum as orientation is induced are ones of intensity. Application of stress is well known to induce frequency shifts. However, both effects only subtly change a well developed spectrum characteristic of the specimen itself. One obvious way to study these subtle changes is to apply force sinusoidally and to discriminate electronically between the DC component of the signal (the invariant) and the AC (that of interest). Further, in several practical situations polymers are regularly subjected to variable loads, and their behaviour under these situations is critical. In addition, their deformations under quasi-static stresses are very different from those under alternating ones. Polymers behave to varying degrees as viscoelastic materials, and this has considerable consequence for their response to loading at moderately high frequencies. Their behaviour under such conditions has been studied by a variety of methods that come under the general heading of dynamic mechanical testing. However, until comparatively recently, spectroscopic methods have not been applied to the problem. The work in this area will be considered and, in order to provide the foundation for this discussion, the basic theory for the response of a viscoelastic system to sinusoidal stress will be given first.

7.3.1 THE RESPONSE O F A VISCOELASTIC SYSTEM TO S I N U S O I D A L STRESS Consider an applied stress varying as a function of time according to the relationship (T = (T0 sin co, where co is the stress frequency. If the material were wholly elastic, and obeyed Hooke's law, the strain would then vary as e = e0 sin cot. However, for a viscoelastic material the strain lags behind the stress. Let this lag be denoted by S9 which may be called the phase angle or the phase lag, and is the relative angular displacement of the stress and strain. The appropriate equations then become G = a0 sin cot

and e = e0 sin ((Dt — S)

Hence e = e0 sin cot cos 3 — e0coscot sin S

(1)

The strain can therefore be considered in terms of two components, one of which, e0 sin cot cos <5, is in phase with the strain, and the other, e0 cos cot sin <5, is out of phase with the strain by n/2. It is therefore possible to define two dynamic moduli, E1 in phase with the stress and E2, which is n/2 out of phase with the stress. E1 = (cr Je0) cos d and E2 = ((T0Ze0) sin S. E1=(V0Ze0)COsS

+ E2 =

{<70/e0)sin8

Substitution into (1) then gives e=

E^I/GQ

sin cot — E2e\/a0cos

cot

(2)

and tan S = E2/EX

(3)

tan S is frequently used as a measure of viscoelastic character. For a given temperature, E1^E2 and tan S are functions of the frequency of the applied stress. In general, tan 5 and E2 are usually small at very low and very high frequencies and their values pass through maxima at some intermediate frequency. On the other hand, E1 is high at high frequencies in the case of glassy polymers and low at low frequencies for rubbery polymers. One of the main reasons for studying the frequency dependence of the dynamic mechanical properties is that it is often possible to relate peaks in E2 and tan S to particular types of molecular motion in the polymer, via what may be regarded as a 'resonance' effect. For example, there are particularly strong 'resonances' at the glass transition. Peaks in E2 are also often found at the melting temperature in semi-crystalline polymers, a consequence of the greater freedom of molecular motion that is possible when the molecules are no longer arranged into a regular crystalline structure. Other types of molecular motion, such as those involving the rotation of branches, often give detectable but smaller peaks in E2 and tan <5, and these are usually referred to as secondary transitions. If a series of such transitions occurs over a range of temperature, the peak which occurs at the highest temperature is termed a, and the subsequent ones are called /?, etc. Hence, dynamic mechanical measurements are usually made over a range of temperature and frequencies in order to cover the various types of molecular motion that may occur. The oscillatory strain amplitudes used are very small, typically below 1.0% of the total sample dimension, to ensure a linear viscoelastic response. Molecular motions in polymers, particularly those types that involve some reorganization of functional groups such as branches, should be amenable to study by vibrational spectroscopy. The spatial movement of functional groups involves a change in the directions of dipole moment and polarizability changes during molecular vibrations. Hence, the measurement of linear dichroism using

polarized radiation should prove useful as a complement to dynamic mechanical measurements, or as a characterizational technique in its own right. Because the oscillatory strain amplitudes involved are very small, it is easier to measure the difference between A1 and A19 the absorbances measured for a particular peak for light polarized in planes parallel and perpendicular to a fixed reference direction of the sample, than to measure their ratio A^fA19 as is commonly done in making orientation measurements on appreciably deformed polymers. A1 — A1 is termed the dichroic difference and is usually denoted by AA, or AA(t) in the case of a time dependent signal. It is then easy to show, using the type of reasoning involved in obtaining Equation (2), that the dynamic dichroism signal AA(t) can be separated into two orthogonal components given by the equation AA(t) = AA' sin ot + AA" cos cot 11

(4)

1

and tanS = AA JAA , where tan<5 is termed the dichroic dissipation factor, analogous to the mechanical dissipation factor considered above. The terms AA' and AA" are known as the in-phase spectrum and the quadrature spectrum respectively of the dynamic infrared linear dichroism. They represent components of dynamic optical anisotropy caused by the re-orientation of electric dipole transition moments. The in-phase spectrum is a measure of the instantaneous strain and the quadrature spectrum characterizes the component of re-orientation proportional to the rate of strain which is n/2 out of phase with the stress. The applied oscillatory stress provides a mechanism for perturbing the system and stimulating individual functional groups into the specific reorientational responses, which are then characterized by the resulting dichroic measurements.

7.3.2 EXPERIMENTAL The equipment required to measure in-phase and quadrature linear dichroic spectra consists of two components, the transducer necessary to provide the small amplitude oscillatory strain and a suitably modified infrared spectrometer. So far as the former is concerned, it is desirable that the transducer system is capable of operating over a range of frequencies, in order to provide the flexibility that may be required in probing a change of re-orientational responses. The transducer may either form part of a dynamic mechanical analyzer, as described by Noda et al. [17] or may be a simple unit used solely as part of an infrared spectrometer system. The majority of the measurements reported hitherto have been made on modified dispersive spectrometers, and the system of Noda et al. [17] is typical. This involves three successive modulations of the infrared beam as it passes through the spectrometer, which is custom designed and built. The first stage of

modulation is via a mechanical light chopper, in order to eliminate background radiation and sample emission. The beam is then polarization modulated using a combination of a wire grid polarizer and a photoelastic modulator, whereby the plane of polarization of the light alternates rapidly between directions parallel and perpendicular to a fixed reference axis, conveniently the direction along which the strain occurs. Two photoelastic modulators were used, having modulation frequencies of 37 and 84 kHz, with corresponding time resolutions of 14 and 6 ^s. The dynamic dichroism of the sample leads to the third modulation of the beam. In view of this triple modulation process, a rather complicated demodulation scheme has been employed in order to extract the required information from the signal from the detector. This involved a set of five lock-in amplifiers. A full mathematical analysis of this system has been provided by Noda et al. [17]. In addition to the fine time resolution performance already noted, the sensitivity of the instrument is such that it will detect a signal as small as 10"4 absorbence unit at a resolution of 4cm" *. Chase and Ikeda [18] have also described a dispersive instrument of this type. More recently, and predictably, Fourier transform infrared spectrometers have been used to measure dynamic linear dichroic spectra. However, substantial modifications to the conventional type of FTIR spectrometer have been necessary in order to overcome a basic problem. This arises from the fact that it is necessary to separate the time dependence of the sample response from that of the spectral multiplexing, because the interferogram itself is a cosine function of time. For example, if the moving mirror has a velocity of 0.5 mm per second at 3000 cm" 1 the radiation is frequehcy modulated at 300Hz. Until recently the almost universal approach to the problem has been the use of step-scanning FT interferometers. Such instruments avoid the problem of the separation of two time dependent variables by creating the interferogram point by point. At each retardation position of the interferometer mirrors, data are collected for as long as is required to obtain the desired signal-to-noise ratio, and a single interferogram is recorded for Fourier transformation. By this means the spectral multiplexing is uncoupled from the time domain. The essential difference between conventional FT instruments and the stepscan devices is that, for successful operation, it is necessary to control the retardation (mirror) velocity in the case of the former and the retardation (mirror) position for the latter. In both cases, the method used to control the retardation involves a collinear or parallel helium/neon laser interferometer. In continuous scan operations the laser interference fringes are used to generate feedback signals to maintain constant mirror velocity, and in the step-scan mode the laser interferogram provides the means for the control of the mirror position via a feedback signal. Several methods are available for setting the retardation and the stepping. An early approach was that of Manning et al. [19,20] for use with an IBM IR-44

spectrometer. The control signal is generated by path difference modulation or 'dithering' of the moving mirror via an AC voltage applied to the drive mechanism. The resulting 'phase modulation' in the control laser detector signal is used in a lock-in feedback circuit to the drive mechanism system. This step-scan instrument has a retardation position uncertainty of +15 nm and a minimum stepping rate adjustable over the range 0-100 Hz, although data are normally collected near to the bottom of this range. Gregoriov et al. [21], in a subsequent development, used either complete digital control of the position and stepping or a combination of analogue and digital control, with phase modulation available as an optional extra, in converting a Nicolet System 800 into a step-scanning instrument. They were able to achieve a positional uncertainty of « ± 1 nm. This type of control has been used by Bruker in their IFS 88 instrument and the more recent Bio-Rad Digilab FTS 70A. Fuller details of step-scan instruments are given in the excellent review article by Palmer et al. [22] Marcott et al. [23] have made comparative dynamic measurements on a thin film of atactic polystyrene, using their dispersive spectrometer described above in comparison with a Bio-Rad FTS 60A instrument operating in the step-scanning mode. They concluded that, although the dispersive approach produces higher signal-to-noise ratios over small spectral regions, the multiplex advantage makes the FT approach attractive when broader spectral coverages are required. Block Diagram of Dynamic Infrared System Based on Rapid Scanning FTIR Spectrometer

to ADC

90'Phase Shifter

ADC trigger

S/H Control

Osc

25Hz Reference

Amp

SYS2000 FTIR Polariseir Sample MCT Stretcher Detector

S/H

S/H

Low Pass Filter

S/H

Multiplex

Infrared beam

S/H

Sample & Hold

Figure 7.8 Block diagram of the Perkin-Elmer 2000 system for studying time resolved phenomena.

MODULATION FREQUENCY

ARB. UNITS

RAYLEIGH LINE

ALIAS OF 2ND HARMONIC RAMAN SPECTRUM

WATER ARTEFACTS

UPPER SIDE-BAND SHIFTED BY 5260 CM-1

D.C. SPECTRUM

WAVENUMBER/cm1

Figure 7.9 Bennett's experiment on heated polystyrene. He applies a modulation to the laser source at 540 Hz. This shifts the Fourier transformed spectrum by ± 5260 cm " ! . The shifted spectrum labelled 'upper side-band' is that of the polymer, the unshifted one, the DC spectrum, that of polystyrene over the black body emission

Turner and Hoult [24] have demonstrated recently that very satisfactory results may be obtained from a conventional scanning FTIR system, using synchronous lock-in detection. Their system has a photoelastic polarization modulator operating at 74 kHz. A reference signal is taken from this modulator and fed to the lock-in amplifier and sampled at the same time as the infrared signal at the detector. There are, therefore, two associated data points for each optical path difference of the interferometer, namely the modulated interferogram signal and the photoelastic modulation signal. The data are demodulated and then accumulated with an appropriate software routine. See Figure 7.8. This approach has also been successfully exploited by Bennett [25] for the removal of thermal backgrounds from Raman spectra using a modulated laser source in conjunction with a conventional scanning FT Raman spectrometer; see Figure 7.9. There are therefore now proven methods for obtaining dynamic linear dichroic infrared spectra. This has already prompted a range of studies and more will doubtless follow. In the early studies the in-phase and quadrature spectra were examined by conventional interpretational techniques, and useful information was forthcoming. However, the value of correlation analysis quickly became evident, as the result of the pioneering activities of Noda [26, 27], and this had led to the use of

so-called two dimensional infrared (2D IR) spectroscopy to display graphically the results of correlation analysis. As noted above, the in-phase and quadrature spectra represent components of dynamic optical anisotropy caused by the re-orientational behaviour characteristic of the type and local environment of each group. Reorientation processes tend to synchronize if there is a specific chemical interaction or connectivity between them, and herein lies the value of correlation analysis, in that it provides a valuable method for studying the time dependent variation of infrared dichroism signals. If dichroic differences are measured at two wavenumbers V1 and v2, two orthogonal correlation spectra may be defined as follows: 0(V1, v2) = IAAXv1)AAXv2) + A^l"(v1)A^'/(v1)A^//(v2)]/2

(5)

*(vi, v2) = IAA-(V1)AAXv2) - AAXv1)AAXv1)AA-(V2W

(6)

They are respectively referred to as the synchronous and asynchronous 2D infrared spectra. The synchronous spectrum characterizes the degree of coherence between the dynamic fluctuations of signals measured at two wavenumbers, and the correlation intensity becomes significant only if the reorientation rates of dipole transition moments are similar to each other. The asynchronous spectrum, however, characterizes the independent, uncoordinated out-of-phase fluctuations of the signals. Hence the asynchronous correlation intensity becomes non-vanishing only if the signals vary at different rates. Peaks along the diagonal position of a synchronous 2D spectrum are referred to as autopeaks. They indirectly represent the local mobility of chemical groups contributing to the molecular vibrations at that wavenumber. Peaks located at off-diagonal positions of a 2D spectrum are known as cross peaks. They appear when the dynamic vibration of infrared dichroism at two different wavenumbers are correlated with each other because the two signals are fluctuating more or less in phase with each other. As long as the normal modes of vibrations correspond to reasonably pure group frequencies, the cross peaks in a synchronous 2D spectrum may be used to map out the degree of intra- and inter-molecular interaction of various functional groups. Cross peaks in an asynchronous 2D spectrum provide complementary information. They appear if the signals are out of phase with each other. Even if the characteristic band frequencies are similar and absorption peaks in the conventional infrared spectrum overlap an asynchronous 2D spectrum can differentiate them, because their time dependent intensity fluctuations differ slightly. Spatial and temporal information about the re-orientation processes of transition moments and their associated chemical groups can be obtained from the sign of cross peaks. If the sign of a synchronous cross peak is positive, the corresponding pair of dipole transition moments reorients in the same relative direction. If the sign is negative the re-orientation directions are perpendicular to each other. A positive

Wavenumber, V2 Wavenumber, V1

Figure 7.10 A schematic representation of synchronous 2D correlations. For details see text. Diagram due to Noda et al. [44]

peak in an asynchronous spectrum indicates that the transition moment with vibrational frequency V1 re-orients before v2. This may be appreciated more readily by reference to Figure 7.10, which shows schematic synchronous 2D correlations for two pairs of peaks A and C, and B and D. The shaded areas represent negative intensity correlations. A cross peak is negative if the changes are in opposite directions, as in the case with bands A and C. To summarize, 2D spectra are capable of revealing rather detailed information, as will emerge clearly below when typical examples are considered.

7.3.3 SOME EXAMPLES OF DYNAMIC LINEAR DICHROIC INFRARED STUDIES A detailed review of the published work is not possible in the available space. Selected examples will therefore be used to illustrate the information that may be obtained from the inspection of in-phase and quadrature spectra, and from the use of correlation analysis. Studies on polystyrene provide a very convenient introduction. Noda et al. [17] have measured the in-phase and quadrature spectra of thin films of polystyrene supported on a Teflon film, concentrating on the spectral regions 1425-1525 cm~* and 2800-3200cm" 1 . The former contains two peaks of particular interest, at «1450 and 1490 cm" 1 . The first of these is made up of overlapping bands from two uncoupled vibrations: a CH 2 scissoring motion in

the polymer backbone and an aromatic ring stretching vibration that is locally polarized along the bond between the phenyl group and the polymer backbone. The 1490 cm" l band is assigned to the coupling of an aromatic CH deformation with another aromatic ring stretching mode, locally polarized in the plane of the ring, perpendicular to the bond between the phenyl group and the backbone aliphatic chain. The 1490 cm" 1 band has a significant signal in the quadrative component, which is shifted to higher wavenumbers, whereas the 1450 cm" 1 peak is closer to being in phase with the applied stress. This difference suggests that there may be some fraction of the aromatic side chains which is responding to the applied stress at a rate different from that of the polymer backbone. Unlike the situation at 1450 cm " x , where there is clear separation between the aromatic and aliphatic C-H stretching bands, the specific band assignments in the aromatic C-H stretching region are not wholly certain. There are two clear, positive peaks at 3028 and 3058 cm" 1 in the in-phase spectrum, and this could indicate that the relevant transition moments are locally polarized in the plane of the phenyl ring, perpendicular to the band between the phenyl group and the backbone aliphatic chain. However, this does not prove that this is universally the case; in a non-crystalline polymer such as atactic polystyrene, individual functional groups can be oriented in a variety of directions relative to the reference strain axis. The aliphatic CH 2 symmetric stretching mode giving the band at 2854 cm" 1 is also interesting. This band is quite strongly negative in CH2-stretchtng

Symmetric

Wavenumber, v2

Asymmetric

Cross peak Autopeak

Wavenumber, V1

Figure 7.11 The infrared spectrum of polystyrene shown in a 2D presentation. For details see text. Diagram due to Noda et al. [17]

the in-phase spectrum and is consistent with the polymer chains tending to align in the direction of the applied stress. Noda et al. [28] have interpreted measurements on atactic polystyrene using the correlation technique, and the two groups of C-H stretching bands are again of interest. Figure 7.11 shows the synchronous 2D correlation spectrum over the aliphatic C-H stretching region. The large autopeak on the diagonal represents the re-orientational motions of dipole transition moments assignable to the symmetric and antisymmetric methylene CH 2 stretching vibrations. The appearance of synchronous cross peaks at the corresponding spectral coordinates indicates that the dipole transition moments for these two bands re-orient at a similar rate, as might be expected. The sign of the synchronous cross peaks is positive, suggesting that the transition moments of the two vibrations are both realigning in the same direction, namely perpendicular to the direction of applied stress. As both dipole transition moments are known to lie perpendicular to the polymer backbone, it is reasonable to conclude that the chain of polystyrene must be aligning in the direction of applied stress, even in the glassy state. The re-orientation dynamics of the side group phenyl rings is more complex. Figure 7.12 shows the asynchronous spectrum involving the phenyl side groups and the backbone methylene groups, and strong cross peaks are present. This suggests that the re-orientational motion of the phenyl groups under strain is quite different from that of the backbone. This, in turn, requires that there must be

Wavenumber, v2

Backbone methylene

Side-group phenyl

Wavenumber, V1

Figure 7.12 The infrared spectrum of polystyrene shown in an asynchronous form. Diagram due to Noda et al. [17]

Wavenumber

substantial freedom for the side groups to realign independently of the main polymer chain. Consequently, it is impossible to characterize the main chain dynamics of polystyrene simply by studying the re-orientation of phenyl groups. However, 2D correlation spectra in the ring stretching modes region are more productive, because the dipole transition moment directions are well established. Such spectra show that, in the glassy state, side group phenyls tend to re-orient along the direction of the main chain backbone. This is somewhat unexpected, as such re-orientational motions require highly distorted local conformations of chain segments. As the temperature is raised well above the glass-to-rubber transition point, the asynchronous relationship between side groups and the main chain of polystyrene decreases considerably. It is therefore reasonable to conclude that the anomalous re-orientation behaviour of phenyl groups of glassy polystyrene results from highly localized and constrained motions of functional groups in a molecular environment with limited free volume at temperatures below Tr Polymer blends have proved another fruitful field for study, with considerable technological implications. Particularly simple, but commercially important, is the behaviour of a blend of low density polyethylene (LDPE) and high density polyethylene (HPDE); a 50:50 blend of these two materials is semi-crystalline. In

Wavenumber

Figure 7.13 The asynchronous correlation map for low and high density polyethylenes. Diagram due to Gregoriou Noda et al. [29]

view of the spectral similarity of these two materials, Gregoriou et al. [29] used a blend of perdeuterated HDPE and conventional LDPE. A portion of the asynchronous correlation map is shown in Figure 7.13. There are clearly two components within the 1088 cm" 1 band, at 1085 and 1091cm" 1 , as is evident from the appearance of the corresponding cross peak. Additionally, a negative cross peak exists between the transition dipole moments at 730 and 1091 cm" \ suggesting that the crystalline component of rf-HDPE of the blend re-orients faster than the crystalline LDPE portion under a positive cross peak between the dipoles at 721 and 1085 cm ~ l and also that, in the corresponding synchronous plot, the corresponding peak is also positive. It has been suggested [30] that, when a melted blend of HDPE and LDPE cools, HDPE crystallizes first because of its higher melting temperature, resulting in a volume-filling superstructure of HDPE crystals forming a skeletal network. When the LDPE begins to crystallize it forms disjointed crystallites filling the interstitial space of the HDPE network. If such a system is deformed, the initial observable response will result from the deformation of the HDPE crystalline network. The stress will then transfer to the interstitial spaces, and there will be a secondary orientation of LDPE crystallites. The interpretation of the 2D spectra of the polyethylene blend is in good agreement with this model. The miscibility of some polymer blends is of considerable technological importance although, fundamentally, the reasons for the miscibility are not completely understood. Polystyrene (PS) and poly(2,6-dimethyl-l,4-phenylene oxide) (PPO) is one such system. 2D correlation studies have been made on a blend of 80% of the former and 20% of the latter by Palmer et al. [31]. The results suggest a different dynamic behaviour for the PS and PPO portions of the blend, depsite their compatibility, with the PS chains responding to the perturbing force faster than those of PPO. Some asynchronous cross peaks develop between the constituents, indicating the possible existence of submolecular level microheterogeneity. Atactic polystyrene and poly(vinyl methyl ether) provide another case of miscibility of two very different polymers, the latter being water soluble. Although the conventional infrared spectrum shows a single peak for the C-H stretching mode of the methoxyl group, the asynchronous 2D spectrum of the blend reveals two separate peaks assignable to this mode. Strong synchronous cross peaks exist between one of these two methoxyl peaks and some phenyl group modes of the polystyrene, indicating the possible existence of a specific intermolecular interaction between the phenyl and methoxyl groups. The tri-block polymer styrene-butadiene-styrene, with a weight ratio of 78/28 in favour of butadiene, has also been studied [32]. The in-phase and quadrature spectra over the region 2700-3100Cm"1 show that, at room temperature, the styrene portion of the copolymer displays negligible dynamic response when butadiene forms the continuous matrix. This is not unexpected, as PS is in the glassy form whereas PB is a rubbery phase. The interesting feature of the two

spectra is the appearance of incipient fine structure centred at « 2920 cm l. The 2D correlation spectra prove revealing. The synchronous map indicates the existence of peaks at 2933 and 2915Cm - Mn the asynchronous correlation map there are several peaks in the vicinity of the asymmetric C-H stretch at 2920cm" 1 . There are a positive cross peak between 2936 and 1915cm" 1 , a positive cross peak between 2936 and 2930 cm " \ a negative one between 2930 and 2922 cm" 1 and a positive cross peak between 2922 and 2915 cm" *. Interestingly, Fourier self-deconvolution failed to resolve these features under the broad asymmetric C-H stretching peak. This ability to enhance spectral resolution has also been demonstrated in the case of atactic poly(methyl methacrylate). This has three very overlapped peaks in the C-H stretching region, whose presence has been revealed by studies on polymers with varying degrees of deuteration [33], a useful but not particularly convenient approach. The three peaks are specific for the ester methyl groups, the a-methyl groups and the backbone methylene groups. The 2D correlation approach yields equally specific information without resort to deuterated polymers. Strong synchronous cross peaks occur at spectral coordinates specific for ester methyl groups, and the a-methyl group is clearly differentiated from the ester methyl group on the basis of cross peaks appearing in the asynchronous spectrum. Furthermore, analysis based on the signs of cross peaks provides detailed information on submolecular reorientation mechanisms that occur with small strains. The technique has also been used to study the dynamic behaviour of a polymer-dispersed liquid crystal subjected to an electric field [18]. The liquid polymer used was the commercially available nematic liquid crystal mixture E7, which contains four nitrile and ethyl substituted bi- and tri-phenyls. It was blended with a polymer precursor consisting of a mixture of an acrylate monomer, an acrylate oligomer and a UV curing agent. The 2D correlation analysis showed that the rigid core of the liquid crystal molecules re-orients as a unit, and suggests that the polymer side chains existing in the interface between the polymer and the liquid crystals may re-orient in phase with the liquid crystal re-orientation by interaction with the liquid crystal molecules. The work discussed hitherto has been concerned solely with polymers subjected to sinusoidally varying stress. The use of stress with this simple wave form is not a necessary condition for the production and use of 2D infrared correlation spectroscopy. Noda [35] has shown that signals fluctuating as an arbitrary function of time may be dealt with and, in some circumstances, offer advantages over sinusoidal signals. He has provided the necessary mathematical framework for this more general approach, and the method has been used to study the photopolymerization of acrylic and epoxy monomers [36]. By this approach, features associated with spectral intensity changes and peak shifts arising from the polymerization reactions were clearly observed. It is reasonable to predict that the method will find further applications in this field.

7.4 ELASTOMERS UNDER STRESS Unlike thermoplastics, elastomers are capable of supporting massive reversible strains and yet recovering their original dimensions, i.e., they behave as 'classic' springs recovering their dimensions elastically and reversibly after deforming to three and even six times their original length. Examination of the stress: strain curve shows, however, that many rubbers do not obey Hooke's law, their modulus rising with strain. This comes about because they partially crystallize at higher strains, the micelles of crystalline order lying parallel to the stress direction. Since crystalline polymers show molecular vibrational characteristics different from the non-crystalline materials (because the vibrations are sensitive to the rotational isomerism of the backbone and the intermodular interactions), the spectrum of the highly strained polymer will differ from that of the relaxed state. In addition, of course, the spectrum will reflect the onset of orientation in the otherwise random matrix and in the crystallites as they form. To demonstrate these points, we offer in Figure 7.14 spectra of vulcanized natural rubber, both stressed and relaxed [37]. The vibrational changes that occur on orientation and crystallization have been used to research the origin of the residual orientation frequently found in blown or extruded film. These materials frequently show quite well developed orientation, and hence are useful as shrink wrapping. As the flowing melts from which they are formed are optically dichroic, it seems reasonable to propose a model involving flow-orientation-crystallization and solidfication in an oriented manner. It has been shown, however, that the orientation of a flowing polyethylene melt (as measured by infrared, Raman diffraction and X-ray diffraction) is very small [38]. This can only mean that the few longer chains present are oriented under flow, and these nucleate oriented crystallization. The thesis has been confirmed by examining the virbational spectra of polyethylene rubber [39] (linear polyethylene cross-linked and kept above its melting point). The material shows hardly any orientation when highly extended, but cooling the film without relaxation produces highly oriented and crystalline material. Although most of the investigation of the effect of strain on the vibrational spectrum of elastomers has been confined to the infrared spectrum of natural rubber films, more recently FT Raman results have appeared. Again see Figure 7.14. An analysis of the bands which alter under strain is in hand [40]. Similarly, work on butyl rubber (polyisobutylene) containing a small concentration of a diene and cross-lined shows that the spectrum changes dramatically as the rubber is strained. See Figure 7.15. There is, however, a persistent experimental problem in this type of investigation. FT Raman study is far more convenient and relevant than infrared because the sample does not have to be restricted to a thin film, and any stretching rig can simply and easily be mounted in the sample area of the instrument. Unfortunately, however, the near-infrared laser radiation

Stretched

intensity /arbitrary units

Relaxed

Frequency /wavenumber

Stretched

Intensity/arbitrary units

Relaxed

Frequency /Wavenumber

Figure 7.14 The FT Raman measurements on crosslinked natural rubber stretched and relaxed and recorded in two ways as illustrated. Laser polarised vertically.

Intensity

(i) Butyl Rubber, unstretched

(ii) Butyl Rubber, stretched

Raman shift / wavenumbers

Figure 7.15 Raman spectra of butyl rubber focused into the specimen causes heating and hence atypical stress: strain patterns around the sampled point. The problem is simply illustrated in that changes to the spectrum induced by strain may be apparent only if low laser powers are used. Although experimentally most restricting, one excellent method of avoiding the problem is to stretch and then cool in a cold cell. Clearly, novel cold cell/stretching facilities need developing, but fortunately pioneering work in this field was completed many years ago by Downes [42], who recorded conventional Raman spectra on elastomers strained near their Tg. The proceedures used have been refined and are reported in Ref. 40.

7.5 CONCLUSION Quite clearly, the advent of Fourier transform infrared and Raman methods and the extension to dynamic or time resolved processes have already produced a whole raft of new results and will certainly continue to do so. The measurement of orientation and the structural changes that occur to specimens when stressed in a variety of ways are bound to be studied in detail, if for no other reason than that both FTIR and Raman spectroscopies are versatile, simple to apply and rapid.

At a conference held recently, Everall [43] described a newly developed Raman system involving fibre optical coupling between the optical system and the spectrometer, and showed how it could be used to monitor and control on-line the commercial production of polyethylene terephthalate film. Thus, the extension of these methods into commercial control is upon us.

7.6 REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]

W. Glenz and A. Peterlin, J. MacromoL ScL, Phys., 1970, B4,473. M.A. McRae and W.F. Maddams, J. Appl. Polym. ScL, 1978, 22, 2761. W.F. Maddams and J.E. Preedy, J. Appl. Polym. ScL, 1978, 22, 2721. W.F. Maddams and J.E. Preedy, J. Appl Polym. ScL, 1978,22, 2739. W.F. Maddams and J.E. Preedy, J. Appl. Polym. ScL91978, 22, 2751. A. Keller and MJ. Machin, J. MacromoL ScL Phys., 1967, Bl, 41. J. Purvis, D.I. Bower and LM. Ward, Polymer, 1973,14, 398. J. Maxfield, R.S. Stein and M.C. Chen, J. Polym. ScL, Polym. Phys. Ed., 1978,16,37. RJ. Roe and W.R. Krigbaum, J. Appl. Phys., 1964,35, 2215. D.Y. Yoon, C. Chang and R.S. Stein, J. Polym. ScL, Polym. Phys. Ed., 1974,12,209. M. Kashiwagi, A. Cunningham, AJ. Manuel and LM. Ward, Polymer, 1973,14,111. J. Purvis and D.I. Bower, J. Poly. ScL, Polym. Phys. Ed., 1976,14, 1461. J. Purvis and D.I. Bower, Polymer, 1974,15, 645. M.E.R. Robinson, D.I. Bower and W.F. Maddams, J. Polym. ScL, Polym. Phys. Ed., 1978,16,2115. D.I. Bower, J. King and W.F. Maddams, J. MacromoL ScL Phys., 1981, B20, 305. PJ. Hendra and P. Bentley, Spectrochim. Ada, Part A, 1995, in press. I. Noda, A.E. Dowrey and C. Marcott, Appl. Spectrosc, 1988, 42, 203. B. Chase and R. Ikeda, Appl. Spectrosc, 1993, 47, 1350. MJ. Smith, CJ. Manning, R.A. Palmer and J.L. Chao, Appl. Spectrosc, 1988,42,546. CJ. Manning, R.A. Palmer and J.L. Chao, Rev. ScL Instrum., 1991,62,1219. V.G. Gregoriou, M. Dawn, M.W. Schauer, J.L. Chao and R.A. Palmer, Appl. Spectrosc, 1993,47,1311. R.A. Palmer, J.L. Chao, R.M. Dittmar, V.G. Gregoriov and S.E. Plunkett, Appl. Spectrosc, 1993,47,1297. C. Marcott, E.A. Dowrey and I. Noda, Appl. Spectrosc, 1993, 47,1324. AJ. Turner and R.A. Hoult, Poster presented at the 9th International Conference on Fourier Transform Spectroscopy, Calgary, August 1993. R. Bennett, Spectrochim. Ada, Part A, 1994,5OA, 1813. I. Noda, J. Am. Chem. Soc, 1989, 111, 8116. I. Noda, Appl. Spectrosc, 1990, 44, 550. I. Noda, A.E. Dowrey and C. Marcott, Makromol. Chem., Makromol. Symp., 1993, 72,121. V.G. Gregoriou, I. Noda, A.E. Dowrey, C. Marcott, J.L. Chao an R.A. Palmer, J. Polym. ScL, 1993, B31.

[30] H.H. Song, D.Q.Wu, B. Chu, M. Satkouski, M. Ree, R.S. Stein, and J.C. Phillips, Macromolecules, 1990,23, 2380.

[31] R.A. Palmer, V.G. Gregoriou and J.L. Chao, Polym. Prepr., 1992, 33(1), 1222. [32] K. Saijo, S. Suehiro, T. Hashimoto and I. Noda, Polym. Prepr. Jpn., 1989,38,4212. [33] S.K. Dirtikov and J.L. Koenig, Appl. Spectrosc, 1979, 33, 555.

[34] [35] [36] [37] [38] [39]

R. Hasegawa, M. Sakamoto and H. Sasorki, Appl. Spectrosc, 1993, 47,1386. I. Noda, Appl Spectrosc, 1993,47,1329. T. Nakano, S. Shimada, R. Saitoh and I. Noda, Appl Spectrosc, 1993,47,1337. C. Jones, Spectrochim. Ada, Part A, 1991, 47A, 1313. PJ. Hendra, M.A. Taylor and H.A. Willis, J. Polym. ScL, 1986, 24, 83. PJ. Hendra, T.H. Stevenson, W.F. Maddams, V. Zichy and M.E.A. Cudby, Plast. Rubber, Process. Appl, 1990,14, 7.

[40] [41] [42] [43]

A.M. Healey, PJ. Hendra and Y.D. West, Spectrochim Ada, 1995, 51A in press PJ. Hendra and P. Bentley, Spectrochim. Acta, in press. J.B. Downes, MPhil Thesis, University of Southampton 1972. N. Everall, ICI Wilton Research Centre, Personal communication; J. Andrews, Spectrosc Eur., 1995,7(8), 8.

[44] I. Noda, A.E. Dowrey and C. Marcott, Appl Spectrosc 1993,47, 1317.

8

DEFORMATIONSTUDIESOF POLYMERS USING RAMAN SPECTROSCOPY R. J. YOUNG Manchester Materials Science Centre, UMIST/University of Manchester, Manchester Ml 7HS, UK

8-1 INTRODUCTION Developments in the area of the application of Raman spectroscopy of polymers have been covered elsewhere in this book [1] and this chapter is concerned with a specific application, the use of Raman spectroscopy for the characterization of the deformation of a wide range of both polymers and polymer-based composites. It is found that the wavenumbers Av of the bands in the Raman spectra of some of these materials change under the action of stress a or strain e. This change in the band position is characterized by either dAv/d(T or dAv/de, which can be related directly to the deformation of the individual bonds in the materials. There are several reasons for the upsurge of interest in the use of Raman spectroscopy for deformation studies. There have recently been significant improvements in the hardware available for Raman spectroscopy. The introduction of array detectors has enabled a particular region of a spectrum to be acquired simultaneously rather than stepping through single points. This reduces drastically the time required to obtain a spectrum. A significant development in this area has been the introduction of highly sensitive charge coupled device (CCD) cameras [2], Using a typical Raman microprobe system incorporating a CCD detector, the spectrum of a Kevlar fibre consisting of a single band in the region of 1580-1640Cm"1 can be obtained from areas of the order of 2jim in diameter in a few seconds using a low-power 10 mW He-Ne laser [3]. A typical full spectrum for a fibre of Kevlar 49, made up by joining several such single-band spectra, is shown in Figure 8.1. More recently there have been reports [1,4, 5] of the development of Fourier Transform (FT) Raman systems which have certain advantages over conventional dispersive systems. FT Raman systems have been described in Chapter 7, and are potentially highly efficient, with a high calibration accuracy. One particular advantage for polymers is that the use of IR excitation wavelengths Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

Intensity (Arbitrary Units)

Wavenumber / cm"1

Figure 8.1 Raman spectrum for a single filament of Kevlar 49 in the region 11001700cm"* obtained using a low-power He-Ne laser (after [38]) greatly reduces the problems of fluorescence. Unfortunately, however, the intensity of the Raman scattering is reduced by an order of magnitude by the use of IR radiation rather than excitation in the visible region because the scattering intensity depends on the fourth power of the excitation frequency, vjj. The choice between the use of a dispersive or a FT system depends upon the scattering characteristics of the material under investigation and the type of information being sought. Another significant advance is the development of the Raman microprobe into a true Raman microscope, reported recently by Batchelder and coworkers [6,7], whereby images of the Raman scattered light may be obtained and spectra may be recorded under confocal conditions. There is clearly plenty of scope for the use of these new systems in the analysis of polymers, and there is no doubt that there will be many such reports in the years to come. 8.1.1 POLYDIACETYLENE SINGLE CRYSTALS The first reported and one of the best examples of the use of Raman spectroscopy to follow deformation in polymers is the case of substituted polydiacetylene single crystals [8-12]. The macroscopic polymer crystals are produced by the solidstate polymerization of substituted diacetylene single crystal monomers. The reaction is a topochemical solid-state polymerization [13], and the crystals produced have a high degree of perfection [14]. Cottle et al. [15] reported in 1978 that the imposition of hydrostatic pressure caused an increase in frequency of the four Raman-active vibrational modes in

Wavenumber /cm*1

poly(2,4-hexadiyne-l,6-bis(p-toluenesulphonate) (polyTSHD) [14]. They related these shifts to the decrease in the separation between the carbon atoms on the polymer backbone. A perhaps more significant discovery had been reported a year earlier by Mitra et al. [8], who found that there was an approximately linear decrease in two vibrational frequencies of single crystal fibres of poly(bisphenylurethane-2,4-hexadiyne-l,6-diol) (polyPUHD) [14] subjected to a tensile stress. They showed that this decrease could be explained in terms of the anharmonicity of the bonds between the carbon atoms on the chain. This study has been followed by a series of measurements of the dependence of the vibration frequencies upon stress and strain for several different substituted polydiacetylenes [9-12]. Batchelder and Bloor [9] performed an elegant series of experiments upon cleaved single crystal fibres of polyTSHD fixed to the aluminium jaws of a small micrometer-driven straining rig by an epoxy resin adhesive. They showed that care had to be taken to obtain an accurate estimate of the strain in relatively short fibres during deformation, and suggested that the exact values of strain reported by Mitra et al. [8] may be in error. The dependence upon strain of the wavenumbers for the Raman modes of several different substituted polydiacetylene single crystal fibres has been measured by various groups of workers [10,12,14]. Most attention has been paid to the behaviour of the V1 mode which is essentially the symmetrical stretching mode of the C = C triple bond, as this is the most sensitive to applied strain. The dependence of the wavenumber of this band upon applied strain for a polyTSHD single crystal [11] is shown in Figure 8.2, and the dependence of the position of this Raman band upon strain for four polydiacetylenes [14] with different

Strain (%)

Figure 8.2 Dependence of the wavenumber of the C = C Raman band upon strain for a polyTSHD single crystal (after [H])

Table 8.1 Values of the strain-induced Raman band shifts for the C = C stretching band of different substituted polydiacetylene single crystals Polymer [14] dAv/de(cm" 7%) Reference polyPUHD ^20 [8] polyTSHD -20.3 ±0.5 [9] polyDCHD -19.7±0.4 [18] polyEUHD -18.8 ±0.4fl [10] -19.0 ±0.3» "Phase 1 fc Phase 2.

side-groups is summarized in Table 8.1. It is important to note that the rate of change of the wavenumber of the band with applied strain, dAv/de, for the C=C stretching V1 mode is « — 20 cm " 7 % and is virtually identical for all polydiacetylene single crystals, even though they may have different modulus values [14]. This is because the structure of the backbone is very similar in each case and the shift of the Raman band wavenumber with applied strain is a function only of the backbone structure, whereas the Young's modulus depends upon both the properties of the backbone and the size of the side-groups [12,16, 17]. 8.1.2 EXTENSIONOFTHETECHNIQUETO OTHER MATERIALS Over the 15 years since the original Raman deformation studies upon polydiacetylene single crystals, the technique has been developed and refined to involve the study of a wide range of different high-performance polymers and other materials. These have included rigid-rod polymer fibres [19-21], carbon fibres [22-24] and ceramic fibres [25-27]. This present chapter will concentrate upon recent research concerning the use of Raman spectroscopy to follow the deformation of aramid fibres and gel-spun polyethylene fibres and the possibility of the extension of the technique to isotropic polymers, and also the important and developing application of the method to the study of the deformation of fibres within composites.

8.2 HIGH-PERFORMANCEPOLYMER FIBRES 8.2.1 AROMATICPOLYAMIDEFIBRES Aromatic polyamide (aramid) fibres are produced by spinning from liquid crystalline solutions using solvents such as sulphuric acid [28,29]. The properties

of the fibres can be improved by a brief heat treatment under tension at elevated temperatures [29]. Fibres of aramids with high levels of stiffness and strength have been available commercially for several years and they are now used, under trade names such as Kevlar (Du Pont) and Twaron (Akzo), in a variety of applications, particularly in the areas of fibre-reinforced composites, protective clothing, tyre cord and ropes [30]. Original materials such as Kevlar 49 were produced with values of filament modulus of the order of 120 GPa, but recent developments have led to fibres with higher degrees of crystallinity such as Kevlar 149, which has a modulus of 170GPa [29]. The first report of the Raman spectrum of an aramid fibre was made in 1979 by Penn and Milanovich [31], and a typical spectrum for a single filament of Kevlar 49 was given in Figure 8.1. Aramid fibres generally give strong Raman scattering with little fluorescence, and well-defined spectra can be obtained from single filaments using low-power laser beams [32-38]. The structure of the most widely used aramid, poly(p-phenylene terephthalamide) is shown below.

It has been pointed out [30] that the C-N bond has considerable double bond character which, along with the para-substituted phenyl group, leads to a resonance conjugated system giving restricted rotation about the bond. These factors help to give rise to liquid crystalline solutions, which allows the formation of highly oriented fibres. They also lead to the characteristic yellow coloration of aramid fibres and probably increase the intensity of the Raman scattering due to resonance enhancement [ H ] . Penn and Milanovich [31] were able to assign some of the Raman bands to vibrations of structural groups in the poly(pphenylene terephthalamide) molecule by comparison with model compounds, and the strong band at «1610cm" 1 has been assigned to stretching of the p-phenylene ring. Penn and Milanovich [31] looked at the effect of deformation upon the Raman spectrum of Kevlar 49 and, although they found that stress caused a change in the relative band intensities and depolarization ratios, they did not find any measurable shift in the band wavenumbers with stress [31]. This finding is completely at odds with the findings of Young and coworkers [32, 33], who have shown that significant and measurable frequency shifts of several Raman bands in Kevlar take place on the application of stress or strain. It is found that the position of the Kevlar 1610cm"1 Raman band shifts to lower frequency under the application of a tensile stress, as shown in Figure 8.3. The peak position of the band is plotted as a function of strain in Figure 8.4 for

Intensity (Arbitrary Units)

Wavenumber / cm*1

Peak Position, Av / cnv1

Figure 8 3 Shift in the position of the 1610 cm ~~ * Raman band for Kevlar 49 at different levels of tensile strain (indicated) (after [38])

Fibre Strain, e / %

Figure 8.4 Variation of the peak position of the 1610cm"1 Raman band with tensile fibre strain for the five different aramid fibres (after [38]) two different commercial fibres and three experimental fibres [38], and it can be seen that there is an approximately linear shift in peak position Av with strain e up to failure at « 3 % strain. The slope of the line is given by dAv/de, and it is normally found [33, 37, 38] that for different aramid fibres the slope is propor-

Rate of Band Shift, dAv / de cm 1 / %

Fibre Modulus, E 1 /Gpa

Figure &5 Dependence of the rate of shift per unit strain for the 1610cm * Raman band upon fibre modulus for the five different aramid fibres shown in Figure 8.4. The symbols have the same meaning as in Figure 8.4 (after [38]) tional to the fibre Young's modulus £ f , i.e. dAv/deocEf

(1)

Figure 8.5 give a plot of dAv/de versus fibre modulus £ f , and it can be seen that there is an approximately linear relationship consistent with Equation (1). This is an indication that the Raman technique is probing molecular stretching directly [37] and is consistent with the theoretical work of Northolt and coworkers [39-41]. They suggested that, for the deformation of aramid fibres such as Kevlar, the total strain is the sum of the strains due to two deformation processes, stretching and rotation, such that ^total =

^stretch + ^rotation

w

It has been shown [37] that the Raman technique follows only the crystal and molecular stretching and, moreover, that the change in the peak position dAv is a measure of the molecular stress rather than the molecular strain [37]. The rate of shift per unit strain in the higher modulus fibres is a reflection of the higher levels of molecular stress in such fibres. Penn and Milanovich [31] expressed surprise that they did not find any frequency shifts during the deformation of aramid fibres, bearing in mind the earlier polymer deformation studies using infrared [42] and Raman spectroscopy [8] and wide-angle X-ray scattering (WAXS) studies of deformed aramid fibres [39]. The situation was confused further by the publication by Edwards and Hadiki [34], who reported that no Raman band shifts were found when Kevlar

fibres were deformed. They claimed that their work supported the findings of Penn and Milanovich [31] and disputed the findings of Young and coworkers [32, 33]. The situation was eventually sorted out by a careful study by Young etal. [35], who repeated the experiments of both groups. One significant difference was that Penn and Milanovich [31] and Edwards and Hadiki [34] had both used a relatively high-power argon ion laser, whereas Young and coworkers [32,33] had used a low-power He-Ne laser. It was demonstrated that the 488 nm line of argon ion lasers caused significant radiation damage to Kevlar fibres and led to the fibres fracturing at very low stresses and strains [35]. Hence the groups using argon ion lasers [31,34] had damaged their fibres, and careful inspection of their data showed that they had not been able to apply very high strains, at least not large enough to cause significant Raman band shifts. In contrast it was shown that the 632 nm line of the He-Ne laser produced virtually no radiation damage, and so high strains could be applied and significant band shifts obtained [35]. Hence the dispute was resolved.

8.2.2 POLYETHYLENE FIBRES There has been considerable interest recently in preparing highly oriented fibres of polyethylene with very high values of stiffness and strength [43-45]. The techniques employed to achieve this end include ultra-drawing [43], solid-state extrusion [44] and gel drawing or spinning [45]. It has been possible by gel processing of ultra-high molar mass polyethylene to produce fibres with Young's modulus values of up to 200 GPa and strengths in the range 2-5 GPa, and such materials are now available commercially under the trade names of Spectra from Allied Signal in the USA and as Dyneema from DSM in the Netherlands. These values of stiffness and strength are close to the theoretical limits for polyethylene, which are about 300GPa for the modulus [46] and 20-30GPa for the strength [47]. Although real materials rarely have mechanical properties so close to their theoretical limits, it is of considerable interest to know how structural features control the mechanical properties of these high-modulus fibres and what factors lead to this shortfall in properties. For example, it is found that fibres produced under different conditions may have the same levels of orientation and degrees of crystallinity but very different levels of stiffness and strength [45]. There must clearly be structural differences in the fibres which lead to a difference in the molecular deformation processes in the fibres. It has been relatively difficult to devise experiments to follow the deformation of these high modulus fibres on the molecular level. Wide-angle X-ray scattering experiments upon fibres subjected to stress have been used extensively to monitor strains in the crystalline regions of high-modulus polyethylene fibres [48, 49]. Such experiments can be relatively tedious, requiring long data-collection times (unless synchrotron radiation sources are employed [50,51]), and the interpreta-

tion of the data often requires assumptions to be made about the state of stress in the materials. It has been known for many years that the vibrational modes of polyolefin molecules are affected by the application of stress, particularly in the oriented state [42,52,53], and considerable effort has been put into studying the effect of stress upon the infrared spectra of such materials. In general it has been found that some infrared bands shift to lower frequency and increase in width, often also accompanied by the development of an asymmetric tail. However, difficulties are often encountered in obtaining infrared spectra from fibres, and it has been recognized recently that the measurement of Raman spectra during the stressing of highly oriented polyethylene fibres offers a unique opportunity to follow the deformation of these materials on the molecular level [50-60]. It is found that well-defined Raman spectra can be obtained from highly oriented polyethylene fibres when the polarization direction of the laser beam is parallel to the fibre axis. Figure 8.6 shows a Raman spectrum in the region of 1080-1150 cm ~ l for a high-modulus gel-spun polyethylene fibre before and after deformation [59]. It can be seen that there is a change in the position and shape of the 1128 cm ~ * Raman band, which has been assigned to the symmetric stretching of C-C single bonds [55]. It can be seen that, following deformation, the band develops a low-frequency tail, and it is possible to fit the band to two Gaussian curves. In fact, it has also been found that even before deformation the asymmetry of the band can be fitted to two peaks [59,60]. The variation in the position of the two peaks with strain is shown in Figure 8.7, and it can be seen that they both move to lower frequency, although the smaller peak moves most rapidly. This type of behaviour for polyethylene has been interpreted as being due to the presence of two populations of molecules in the microstructure of the gel-spun material. During deformation they experience different levels of stress. It is found [59, 60] that the size of the rapidly moving peak and the rate of shift per unit strain scale with the Young's modulus of the fibre, and hence it appears that the changes in the Raman spectra are related to the presence of microstructural features which give rise to the impressive mechanical properties of the fibres. There has been some controversy in the literature concerning the exact form of the stress-induced Raman shifts in polyethylene fibres. Some workers reported non-linear peak shifts with significant broadening of the bands and the development of a low-frequency tail [53, 55], whereas others apparently found linear peak shifts with little broadening [54, 56]. There is no doubt that, in some instances, the differences stem from differences in fibre structure due to variations in manufacturing route and testing conditions. Band splitting is certainly more apparent in the gel-spun polymer deformed rapidly and obtaining spectra using a CCD camera. However, it appears that there is also a difference in the methods of data interpretation. If the Raman band is fitted to a single function (e.g. Gauss-Lorentz sum function [55]) then it is difficult to deal with any band asymmetry. For example, Prasad and Grubb [55] reported that, although the shift of the band peak fitted to a symmetrical function is not linear with applied

Intensity (Arbitrary Units) Intensity (Arbitrary Units)

Wavenumber/cm 1

Wavenumber/cnr1 Figure 8.6 Raman spectrum in the region 1080-1150Cm"1 for an experimental highmodulus gel-spun polyethylene fibre (after [59]). The Raman band has been fitted to two Gaussian curves, (a) Fibre undeformed; (b) at a strain of 4.06% stress, the shift of the centre of gravity of the full band is linear. Such problems are overcome if the shifting Raman band is fitted to more than one function, i.e. if it is assumed that the band splits into several components as in Figure 8.6. This clearly implies that either the fibres must have a two-phase structure or there must be different stresses on certain molecules in the structure. Prasad and Grubb [55] interpreted the low-frequency tail of the 1063 cm" 1 C-C asymmetric stretching band of their spectra as non-crystalline overstressed tie molecules, as they did not observe the development of any tail in their WAXS peaks. However, recent WAXS studies [57] has indicated that the Bragg peaks in gel-spun

Wavenumber/cm*1

NARROW PEAK BROAD PEAK

Strain %

Figure 8.7 Variation in the position of the two peaks in the Raman spectra of the high-modulus gel-spun polyethylene fibre in Figure 8.6 with strain (after [59])

polyethylene may also split into two during deformation. Clearly more work is required to ascertain the relationship between Raman band movement and the behaviour of WAXS peaks under stress, since this may enable a better insight to be obtained concerning the relationship between crystalline and molecular deformation processes. Several models have been proposed to explain the mechanical properties of high-modulus polymer fibres [54, 61-63], and they all assume that the fibres contain some highly stressed molecules or crystals contributing to the high level of modulus, with other molecules or crystals taking lower levels of stress. Wong and Young [61] have shown that there is a bimodal distribution of stress in the crystalline regions of gel-spun polyethylene fibres due to their two-phase microstructure, and have demonstrated that the molecular deformation behaviour can be interpreted quantitatively using a parallel-series Takayanagi model. They have shown that the Young's modulus of the crystalline regions increases with the degree of chain extension, and that for the highest-modulus fibres may be close to the theoretical modulus of polyethylene crystals. It appears that for the first time Raman spectroscopy allows the deformation of the different components in the structure to be determined directly [60, 61].

8.3 ISOTROPIC POLYMERS Fina et al. [64] found that significant shifts in the wavenumbers of the Raman bands in poly(ethylene terephthalate) with moderate degrees of orientation could be obtained, and so the question arises as to whether or not measurable shifts in Raman bands could be obtained using isotropic polymers which contain little or no molecular orientation. In a little-quoted letter published in 1976, Evans and Hallam [65] reported measurable shifts to lower frequency in the wavenumbers of the bands in the Raman spectra of polymers such as polypropylene, polycarbonate, polystyrene and nylon 66 from samples which were presumably unoriented (although they did not give any details of specimen preparation). Shifts of the order of 1 cm" * were obtained for specimens deformed up to the point of specimen necking, but the exact values of shift were found to depend upon the band in question [65]. They did not give any values of stress but, assuming a yield stress of their polypropylene of % 30 MPa, then the shifts they measured approach — 30 cm ~ VGPa, which is quite significant. However, the relatively low yield stress of the material means that the magnitudes of the shifts will always be relatively small. Their data for polypropylene showed that between the point of yield and eventual specimen fracture the behaviour of the Raman bands is relatively complex, and that the wavenumber increases, decreases or stays the same for different bands. Unfortunately, they did not give sufficient detail of their measurements to explain this effect. Evans and Hallam [65] pointed out the significant advantages of the Raman technique over similar infrared measurements; although a full publication of their work was promised, no record of its publication has been found. Over recent years a completely different approach has been adopted by Hu, Day, Stanford and Young [66-69], who have shown that, through the synthesis of specially designed copolymers, it is possible to prepare isotropic polymers for which the deformation can be followed using Raman spectroscopy. They have demonstrated that such materials can be used for the study of polymer surface and interface deformation [68,69] and their work in this area is reviewed below.

8.3.1 U R E T H A N E - D I A C E T Y L E N E COPOLYMERS The approach that was adopted [66-69] was to prepare a series of urethanediacetylene copolymers in which polydiacetylene units are incorporated into segmented copolyurethanes. It was shown in Section 8.1.1 that large straininduced Raman band shifts can be obtained during the deformation of polydiacetylene single crystal fibers [8-12]. In fact, it is found that the largest shift measured so far ( — 20 cm"7% strain) is for the C = C triple bond stretching band of polydiacetylenes (Table 8.1).

Polyurethanes constitute a versatile class of materials ranging from soft elastomers to glassy resins, and are readily produced by a variety of processes in many different forms. Fibres, films, bulk sheets and surface coatings can all be formed either from solution or in bulk. Segmented copolyurethanes, because of their phase-separated structures, are particularly attractive, as they enable the combination of disparate polymer properties to be obtained within a single material. Polydiacetylene single crystals are formed by the rapid solid-state polymerization [13, 14] of substituted diacetylene monomer crystals on the application of heat or radiation. It is possible to induce similar solid-state reactions known as "cross-polymerization" in the diacetylene groups of repeat units in certain copolyurethanes and copolyesters [70-72]. Cross-polymerization within the crystalline diacetylene regions produces a network structure in which the chains connecting the polydiacetylenes are analogous to the substituent side-groups in the polydiacetylene single crystals[13,14]. In this way, linear copolyurethanes containing phase-separated, diacetylene-containing domains can be crosslinked in situ and transformed into insoluble and infusible materials [73-75]. These previous studies were concerned only with elastomeric materials formed via a two-stage solution process [73-75] at only one composition. The more recent studies [66-69] have been concerned with the development of more rigid copolymers formed by a relatively simple one-shot bulk polymerization route. The reactants used to prepare the copolyurethanes were 4,4'-methylenediphenylene diisocyanate (MDI), 2,4-hexadiyne-l,6-diol (HDD) and a polypropylene glycol (PPG400). It is possible to vary the structure and consequent properties of the materials by varying the relative proportions of HDD and PPG400. The exact details of the reaction conditions are give elsewhere [67], and linear polymers can be produced with molar masses of the order of 10000 gmol" 1 . These linear segmented urethane copolymers are soluble in a variety of solvents, and can therefore be processed into a variety of forms such as surface coatings [68]. The structure of the material consists of diacetylene-urethane hard segments A and polyether-urethane segments B. The development of this alternating segmented structure results in phase separation owing to the incompatibility of the chemically distinct segments A and B. Thermodynamic incompatibility depends primarily on the interaction parameter between the diacetylene- and polyether-based segments (determined by their intrinsic solubility parameters) and their sequence lengths (degrees of polymerization). The development of hydrogen bonding and potential crystallinity of the hard segments further enhances the driving force for phase separation. The linear copolyurethanes thus form as essentially a two-phase morphology consisting of rigid, highly hydrogenbonded hard segment domains (with a distribution of sizes) dispersed in a ductile polyether-urethane phase. The formation of linear diacetylene-containing copolyurethanes provides the distinct advantage, in subsequent applications, of

enabling the copolymers to be processed from solution. During or after removal of solvent, the phase-separated copolymers can be rapidly crosslinked in situ using heat or radiation, either of which causes cross-polymerization of diacetylene units within the hard segment domains. In practice, however, the solid-state topochemical reaction involves many chains packed within the hard segment domains, and the resulting crosspolymerization occurs three-dimensionally as depicted in Figure 8.8. The diacetylene-urethane hard segments are assumed to be crystalline and have fully extended conformations in which the HDD unit is alUtrans, and the chains are

Figure 8.8 Schematic representation of the solid-state topochemical polymerization of the diacetylene-urethane hard segments: (a) linear segmented block copolymer; (b) crosspolymerized material (after [67])

staggered so that adjacent chains are linked by straight C = C • • • H — N hydrogen bonds in both directions perpendicular to the urethane chain axes. It is found [68] that these hard segment domains are organized in the form of spherulitic entities, which are seen to be of the order of 1 ^m in diameter using transmission electron microscopy. The idealized structure in Figure 8.8, however, is unlikely to be totally representative of the overall structure actually obtained for the hard segment domains, although regions of such three-dimensional order must exist within domains dispersed throughout the copolyurethanes in order to achieve overall cross-polymerization. The formation of fully conjugated polydiacetylene (PDA) chains within the phase-separated copolyurethanes produces dramatic colour changes (white -• red -* deep purple) and transforms the copolymers into completely insoluble and infusible materials. The extent of cross-polymerization that is achieved depends upon a number of factors such as the time and temperature of heating, the concentration of hard segment domains and the degree of order within the domains [67]. The relationship between chemical composition, structure and properties for the copolymers has been described in detail elsewhere [68, 69]. In general it is found that the glass transition temperature Tg and the Young's modulus E increase with hard segment content and heat treatment temperature. It was found that the material with the optimum composition and properties had a value of T% of %80°C and a Young's modulus (isotropic) of « 1.7GPa, both of which are typical of a conventional glassy polymer.

8.3.2 DEFORMATION STUDIES A Raman spectrum for a sample of the cross-polymerized copolyurethane is shown in Figure 8.9 and it can be seen that it has four main scattering bands [67, 68]. The spectrum is remarkably similar to that obtained from a polydiacetylene single crystal fibre [ H ] . For the fibres, a strong spectrum is obtained only when the fibre axis is parallel to the direction of polarization of the laser beam, whereas it is found that the spectrum from the copolymer is identical for all orientations of the sample [67,68]. This shows clearly the isotropic nature of the copolymer. It was found [67,68] that the intensities of the bands in the Raman spectrum varied with both the hard segment content and the heat treatment temperature and, moreover, it was demonstrated that this variation could be used to follow the cross-polymerization reaction. In particular, the C = C triple bond stretching band at « 2090 cm ~ l is not present before cross-polymerization and is indicative of the formation of the polydiacetylene chains in the structure. Figure 8.10(a) shows the position of the C = C stretching Raman band for one of the copolymers in the undeformed and deformed states [68]. Upon deformation there is a pronounced shift to lower frequency and a slight broadening of the

lntensity

Wavenumber

Figure 8.9 Full Raman spectrum for the cross-polymerized diacetylene-urethane copolymer (after [67,68]) Raman band. This shift is a clear indication of stress transfer from the polyetherurethane matrix to the diacetylene-urethane hard segments, and shows that this stress is translated into direct deformation of the polydiacetylene chains. Broadening of the bands suggests that a distribution of stresses is developed within the non-uniform hard segment domains during deformation. The dependence of the band position upon tensile strain is shown in Figure 8.10(b). It can be seen that it is approximately linear up to %1% strain with a slope dAv/de of the order of - 5 c m " 7% strain, and is also completely reversible on both unloading and reloading. The slope of the line in Figure 8.10(b) is significantly lower than that for polydiacetylene single crystal fibres (Table 8.1) but is comparable with that of high-performance fibres such as those based upon aromatic polyamides [37, 38] or rigid-rod polymers [19-21]. It has been found that the relationship shown in Figure 8.10(b) can be used to measure strain in a wide variety of situations. It is known that polydiacetylenes absorb visible light very strongly, and so for the bulk copolyurethane the spectrum is obtained only from material in the surface regions. Hence any strain measurements will be only for surface material. Moreover, since it is possible to focus the laser beam in the spectrometer to a spot of the order of 2 jim in diameter, it is possible to obtain considerable spatial resolution. Various examples of using these materials for surface strain mapping have been presented in a recent publication [69]. The determination of stress concentrations around defects such as holes or notches in a deformed plate of the copolyurethane is shown in Figure 8.11. A circular hole and a notch of predetermined dimensions were accurately machined into a 3 mm thick specimen of the copolymer. The specimen was deformed in tension in the Raman spec-

Intensity Wavenumber/cnv1

Wavenumbor cm"1

Strain % 1

Figure 8.10 (a) Shift of the 2090 cm " Raman band with strain for the cross-polymerized urethane-diacetylene copolymer (after [68]); (b) dependence of the peak position of the 2090 cm"1 Raman band upon strain; •,first loading; • ; unloading, O, reloading (after [68]) trometer and the change in position of the C = C stretching band at 2090 cm" l with copolymer strain (measured remotely with a resistance strain gauge) was determined at different positions around the defects, as shown schematically (inset) in Figure 8.11. The slope (dAv/de) of each line, relative to that for the remote applied deformation data (open O) is proportional to the stress concentration at each position. For the hole, the stress concentration, as expected, is highest at the equator (solid • ) and is essentially zero at the pole (solid • ) . For the notch,

Wavenumber / cm*1

Overall strain/%

Figure 8.11 The effects of stress concentrations on the peak position of the C = C Raman band for a 3 mm thick cross-polymerized diacetylene-urethane plate deformed in tension. The data were obtained from spectra obtained at the different positions indicated (after [69]) the stress concentration (open O) increases sharply depending on the notch tip radius and the distance from the tip. The results obtained for the various defect geometries [69] show the stress concentration values measured by Raman spectroscopy to be very similar to those determined from conventional stress analyses [76]. The good solubility and adhesive characteristics of the diacetylene-containing copolyurethanes make them attractive materials for use as surface coatings that can be applied with controlled thickness to a variety of substrates. Subsequent cross-polymerization, in situ, would then convert the coatings into crosslinked materials with strain-sensitive properties that can be determined quantitatively, in conjunction with the substrate, using Raman spectroscopy. To illustrate this use [68], a solution of the copolyurethane was applied as a 0.05 mm coating to the following substrates: (a) a sheet of highly crosslinked (non-diacetylene- containing) polyurethane resin, (b) an inorganic glass filament (% 25 ^m diameter) and (c) a sheet of aluminium. The solvent was removed by evaporation and the coatings were thermally treated at 1000C for 4Oh. The coated substrate specimens were deformed in tension in a Raman spectrometer and the shift in the position (Av) of the C=C triple bond stretching band was monitored as a function of the overall specimen strain e. Excellent linearity between Av and e was obtained in each case. The strain sensitivities of the three coated substrates determined from the slopes of the plots are given in Table 8.2; the values near — 5 cm " 7% strain for dAv/de

Table 8.2 Strain sensitivities of the Raman frequencies of the C = C triple bond stretching band for the diacetylene-urethane copolymer and for the copolymer coated on different substrates (after [68]) Substrate dAv/de (cm " 7%) Pure copolymer 5.3 ± 0.4 Polyurethane 5.5 ± 0.4 Glass fibre 5.7 ±0.4 Aluminium 5.5 ± 0.4 are almost identical to that of the bulk sheet material. Clearly, these results demonstrate that the copolymers can be used as coatings to monitor accurately the deformation of a substrate, which is particularly useful if the substrate is of complex geometrical shape or is not readily accessible for direct measurements. As such, the polydiacetylene- containing copolyurethanes are shown to behave as optical strain gauges.

8.4 COMPOSITES The shifts in the peak position of the 1610cm" * aramid Raman band, shown in Figure 8.4, can be used as calibration curves to monitor the deformation of fibres in a composite under any state of stress or strain. Previous studies have shown [77-81] that it is possible to map out the distribution of stress or strain along a single short, discontinuous fibre in a low-modulus epoxy resin. This is described in detail next.

8.4.1 SINGLE-FIBRECOMPOSITES Figure 8.12 shows the distribution of strain along a single Kevlar 149 fibre in a model single-fibre epoxy composite [38] calculated from the point-to-point variation of the shift of the 1610cm" * aramid Raman band. Measurements were taken at 20 \im intervals along the fibre for different levels of matrix strain em ranging from 0% to 2.0% in intervals of 0.4%, and the curves drawn are best fits to the experimental data. It can be seen that in the unstrained case (em = 0%) there is no strain in the fibre. As em increases the strain in the fibre increases from the fibre end up to a plateau value along the middle of the fibre. It is shown that the strain in the central region of the fibre is approximately equal to the matrix strain em for matrix strain levels up to 1.6%. This behaviour is qualitatively identical to the distribution of fibre stress and strain predicted by classical shear-lag theory [82,83], where it is found that, following the shear-lag analysis

Fibre Strain, e f / %

Distance Along Fibre, x / pm

Figure 8.12 Derived variation of fibre strain with distance along the Kevlar 149 fibre in a single-fibre composite tensile specimen at different indicated levels of matrix strain em (after [38]) of Cox [ 8 3 ] , the variation of tensile stress a in the fibre with distance along the fibre x is given by

1

_

T

'- ^-L

cosh

fli/2-x)1

cosh/?//2 J

where

where E1 is the Young's modulus of the fibre, em is the matrix strain, Gm is the shear modulus of the matrix, A1 is the cross-sectional area of the fibre, r0 is the fibre radius and R is the radius of the cylinder of resin around the fibre. This behaviour is shown more clearly in Figure 8.13, in which the data points from Figure 8.12 are fitted to theoretical curves calculated from Equation (3) at matrix strain levels of 0.4%, 0.8% and 1.2%. The value of R was assumed to be the half-width of the matrix resin bar, and the matrix shear modulus Gm was calculated from the matrix tensile modulus and Poisson's ratio at the relevant

Fibre Strain, ef / %

Distance Along Fibre, x / fim

Figure 8.13 Derived variation offibrestrain with distance along the Kevlar 149fibrein a single-fibre composite tensile specimen at different indicated levels of matrix strain em. The curves arefittedusing Equation (3) (after [38]) matrix strains. It can be seen that, while the data points are a good fit to the theoretical curves in the central region of the fibre, there is a slight deviation at the fibre ends. This is due in part to the geometry of the cut fibre ends [84] and the fact that some of the assumptions of the Cox analysis [83], such that the strain at the end of the fibres is equal to zero, are not appropriate. It can be seen from Figure 8.12 that at 2.0% matrix strain, when the failure strain of the fibre is exceeded, fibre fracture occurs, with the fibre breaking into three fragments. The strain increases from the fibre ends in each of the fragments to a value equal to or less than the failure strain of the fibre, at which point the fibre strain decreases. The distance from the fibre end to the point of maximum strain defines the region IJl where the maximum length of a fibre fragment is given by [85]:

where xy is the shear yield stress of the fibre-matrix interface, o> is the failure stress of the fibre, /c is the critical length of the fibre, and d is the fibre diameter (2r0).

The fibre fragments initially over a large distance of between 200 and 500 ^m, with the crack running at an angle to the fibre axis [86]. In this region the distribution of strain is mapped along a fibrillar section of the fibre which is still bonded to the matrix. The points of minimum strain along the fibre are recorded where the laser is focused on the propagating crack at the surface of the fibre. The use of Raman spectroscopy to study the fragmentation of aramid fibres in a resin matrix has the advantage that the strain can be mapped at intervals of 20 jim or less in order to define the fragmented regions. This may be compared with conventional polarized light experiments [87], which do not clearly define the fibrillar fractured regions associated with aramid fibres [86].

8.4.2 INTERFACIAL MICROMECHANICS It will be shown finally that Raman spectroscopy may be used to compare the interfacial properties of Kevlar fibres with different surface treatments [38]. Figures 8.14(a) and 8.14(b) show the variation of fibre strain with distance x along the left-hand end of a sized and de-sized Kevlar 49 fibre respectively for matrix strains ranging from 0% to 2.4%. The solid lines are a fit of the experimental data using either asymmetric or logistic sigmoid functions with correlation coefficients greater than 98%. The distribution of fibre strain, at matrix strain levels up to 1.2%, is similar to that shown in Figure 8.12 for the Kevlar 149 fibre, and is in qualitative agreement with that predicted by classical shear-lag theory [83]. At matrix strain levels greater than 1.6%, the fibre strain increases from the fibre end at a slower rate than at lower matrix strains. This effect is clearly more pronounced in Figure 8.14(b) for the de-sized fibre, where it is seen that the transfer of stress from the matrix to the fibre is greatly reduced at the fibre end, when em = 2.4%, compared with the strain in the sized fibre at the same level of applied matrix strain. It is possible to derive the variation of interfacial shear stress T with distance x along the fibre from the data in Figures 8.14(a) and 8.14(b) using the relationship [88]:

where T is the interfacial shear stress and (de/dx) is the differential of the variation of fibre strain with position along the fibre. Figures 8.14(a) and 8.15(b) show the derived variation of interfacial shear stress with distance x along the sized and de-sized Kevlar 49 fibres respectively. At matrix strains up to 1.2% the interfacial shear stress is a maximum at the fibre end (x = 0), decreasing to zero at a distance x along the fibre equal to IJl. At matrix srains greater than 1.6%, the epoxy resin exhibits plastic deformation, which leads to a reduction in the transfer of stress from the matrix to the fibre. This is clearly shown in Figure 8.15(b), where the

Fibre Strain, ef / % Fibre Strain, ef / %

Distance Along Fibre, x / urn

Distance Along Fibre, x / urn

Figure 8.14 Derived variation of fibre strain with distance along the left-hand end of a Kevlar 49 fibre in a single-fibre composite tensile specimen at different indicated levels of matrix strain em: (a) sized fibre; (b) de-sized fibre (after [38])

ISS1 T/MPa ISS, x / MPa

Distance Along Fibre, x / ^m

Distance Along Fibre, x / |im

Figure 8.15 Derived variation of the interfacial shear stress (ISS) T with distance along the left-hand end of a Kevlar 49 fibre in a single-fibre composite tensile specimen at different indicated levels of matrix strain em using the data from Figure 8.14: (a) sized fibre; (b) de-sized fibre (after [38])

Maximum ISS9 rmtx/MPa

Matrix Strain, em/% Figure 8.16 Dependence of the maximum interfacial shear stress upon matrix strain for the sized and de-sized Kevlar 49 fibres in an epoxy resin matrix (data taken from Figure 8.15). The horizontal dashed line represents the shear yield stress of the epoxy resin, along with the scatter band of the measurements (after [38]) iterfacial shear stress at the fibre end is only of the order of 3-4MPa for an applied matrix strain of 2.4%, compared with « 4 3 MPa for an applied matrix strain of 1.2%. The maximum interfacial shear stress values for the sized and de-sized Kevlar 49 fibres are shown in Figure 8.16 as a function of applied matrix strain. It is clearly shown that the values of maximum interfacial shear stress rmax for the de-sized fibres are less than those for the sized fibres at all levels of applied matrix strain. It is shown that the interfacial shear stress for the de-sized fibres reaches a maximum value of 43 MPa, which is close to the shear yield stress of the epoxy resin matrix [77] indicated by the dashed line in Figure 8.16.

8.5 CONCLUSIONS It has been demonstrated that Raman spectroscopy is not only a very powerful technique for following the deformation of high-performance fibres and composites but is also of use in the study of the deformation of isotropic polymers. It has been shown that the shifts in the Raman bands is related directly to deformation of the bonds in the polymers, and so the technique offers a unique method of following molecular deformation in polymers. The relationship between the shift

in a particular Raman band and stress or strain can be used to map deformation in a wide variety of systems. For example, the point-to-point variation of strain in high-performance fibres in a composite can be determined with a spatial resolution of the order of 2 ^m, which enables the micromechanics of composite deformation to be studied with a resolution and precision which were hitherto unobtainable. Smart polymer coatings have been developed which allow strain mapping in the substrates with a similar level of resolution. It is clear that the use of Raman spectroscopy to follow deformation is in its infancy, and over years to come there will be significant developments in instrumentation and in its application to different materials which will allow further significant advances to be made.

8-6 ACKNOWLEDGEMENTS The author is grateful to a large number of colleagues and research workers in Manchester who have helped with his work on the development of Raman spectroscopy for the study of mechanical properties in materials. He is also grateful to the Royal Society for support in the form of the Wolfson Research Professorship in Materials Science.

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[15] A.C. Cottle, W.F. Lewis and D.N. Batchelder, J. Phys. C, 1978,11,605. [16] C. Galiotis and RJ. Young, Polymer, 1983,24,1023. [17] C. Galiotis, R.T. Read, P.H.J. Yeung, RJ. Young, LF. Chalmers and D. Bloor, J. Polym. ScL, Polym. Phys. Ed., 1984, 22,1589. [18] C. Galiotis, RJ. Young, P.HJ. Yeung and D.N. Batchelder, J. Mater. ScL, 1984,19, 1640. [19] RJ. Day, LM. Robinson, M. Zakikhani and RJ. Young, Polymer, 1987, 28, 1833. [20] RJ. Young, RJ. Day and M. Zakikhani, J. Mater. ScL, 1990, 25,127. [21] RJ. Young and P.P. Ang, Polymer, 1992,33, 975. [22] LM. Ribinson, M. Zakikhani, RJ. Day, RJ. Young and C. Galiotis, J. Mater. ScL Lett., 1987, 6, 1212. [23] C. Galiotis and D.N. Batchelder, J. Mater. ScL Lett., 1988,7, 545. [24] Y. Huang and RJ. Young, J. Mater. ScL, 1994,29,4027. [25] RJ. Day, V. Piddock, R. Taylor, RJ. young and M. Zakikhani, J. Mater. ScL, 1989, 24, 2998. [26] X. Yang, X. Hu, RJ. Day and RJ. Young, J. Mater. ScL, 1992, 27,1409. [27] X. Yang and RJ. Young, J. Mater. ScL, 1993, 28, 536. [28] J.R. Schaefgen, Chapter 8, A.E. Zachariades and R.S. Porter (Eds.), The Strength and Stiffness of Polymers, Marcel Dekker, New York, 1983. [29] S.L. Kwolek, W. Memeger and J.E. Van Trump, in M. Lewin (Ed.), Polymers for Advanced Technologies, VCH Publishers, New York, 1988, p. 421. [30] D. Tanner, J.A. Fitzgerald, P.G. Riewald and W.F. Knoff, in M. Lewin and J. Preston (Eds.), High Technology Fibers—Part B, Marcel Dekker, New York, 1989. [31] L. Penn and F. Milanovich, Polymer, 1979,20, 31. [32] C. Galiotis, LM. Ribonson, RJ. Young, B.E J. Smith and D.N. Batchelder, Polym. Commun., 1985, 26, 354. [33] S. Van der Zwaag, M.G. Northolt, RJ. Young, LM. Robinson, C. Galiotis and D.N. Batchelder, Polym. Commun, 1987,28, 276. [34] H.G.M. Edwards and S. Hadiki, Br. Polym. J., 1989,21, 505. [35] RJ. Young, D. Lu and RJ. Day, Polym. Int., 1991,24, 71. [36] RJ. Day, LM. Robinson, M. Zakikhani and RJ. Young, in PJ. Lemstra and L.A. Klientjens (Eds.), Integration of Fundamental Polymer Science and Technology—2, Elsevier Applied Science, London 1988, p. 571. [37] RJ. Young, RJ. Day, L. Dong and W. Knoff, J. Mater. ScL, 1992,27, 5431. [38] M.C. Andrews and RJ. Young, J. Raman. Spectrosc, 1993,24, 539. [39] M.G. Northolt and JJ. Van Aartsen, J. Polym. ScL, Polym. Symp., 1978,58, 283. [40] M.G. Northolt, Polymer, 1980,21,1199. [41] M.G. Northolt and R. Van der Hout, Polymer, 1985, 26, 310. [42] D.K. Roylance and K.L. Devries, J. Polym. ScL, Polym. Lett, 1971,9, 443. [43] G. Capaccio, A.G. Gibson and LM. Ward, in A. Ciferri and LM. Ward (Ed.), Ultra-High Modulus Polymers, Applied Science, London, 1979. [44] A.E. Zachariades, WT. Mead and R.S. Porter, A. Ciferri and LM. Ward (Eds.), Ultra-High Modulus Polymers, Ed. Applied Science, London, 1979. [45] P. Smith and PJ. Lemstra, J. Mater. ScL, 1981,15, 505. [46] L. Holliday and J. W. White, Pure Appl. Chem., 1971, 26, 545. [47] AJ. Kinloch and RJ. Young, Fracture Behaviour of Polymers, Applied Science, London, 1983. [48] J. Clements, R. Jakeways and LM. Ward, Polymer, 1978,19, 639. [49] K. Nakamae, T. Nishino and H. Ohkubo, J. Macromol. ScL, Phys., 1991 B30,1. [50] DT. Grubb and JJ.-H. Liu, J. Appl. Phys., 1985,58, 2822. [51] K. Prasad and DT. Grubb, J. Polym. ScL: Part B: Polym. Phys., 1990, 28, 2199.

[52] R.P. Wool and W.O. Station, J. Polym. ScL, Polym. Phys. Ed., 1974,12,1575. [53] R.P. Wool, R.S. Bretzlaff, B.Y. Li, CH. Wang and R.H. Boyd, J. Polym. ScL, Polym. Phys. Ed., 1986, 24,1039. [54] K. Tashiro, G. Wu and M. Kobayashi, Polymer, 1988, 29,1768. [55] K. Prasad and D.T. Grubb, J. Polym. ScL, Polym. Phys. Ed., 1989,27, 381. [56] BJ. Kip, M.C.P. Van Eijk and RJ. Meier, J. Polym. ScL: Part B: Polym. Phys., 1991, B29,99. [57] J.A.H.M. Moonen, W.A.C. Roovers, RJ. Meier and BJ. Kip, J. Polym. ScL, Polym. Phys. 1992,30,361. [58] D.T. Grubb and Z. Li, Polymer., 1992,30, 2587. [59] W.F. Wong, Ph.D. Thesis, Victoria University of Manchester, 1992. [60] W.F. Wong and RJ. Young, J. Mater. ScL, 1994, 29, 510. [61] W.F. Wong and RJ. Young, J. Mater. ScL, 1994, 29, 520. [62] PJ. Barham and R.G.C. Arridge, J. Polym. ScL, Polym. Phys. Ed., 1977,15, 1177. [63] A.G. Gibson, G.R. Davies and LM. Ward, Polymer, 1978,19, 683. [64] LJ. Fina, D.I. Bower, and LM. Ward, Polymer, 1988, 29, 2146. [65] R.A. Evans and H.E. Hallam, Polymer, 1976,17, 838. [66] J.L. Stanford, RJ. Young and RJ. Day, Polymer, 1991,32,1713. [67] X. Hu, J.L. Stanford, RJ. Day and RJ. Young, Macromolecules, 1992, 672. [68] X. Hu, J.L. Stanford, RJ. Day and RJ. Young, Macromolecules, 1992, 684. [69] X. Hu, RJ. Day, J.L. Stanford and RJ. Young, J. Mater. ScL, 1992, 27, 5958. [70] G. Wegner, Makromol. Chem., 1970,134, 219. [71] D. Day and J.B. Lando, J. Polym. ScL, Polym. Lett. Ed., 1981,19, 227. [72] A.O. Patil, D.D. Deshpande, S.S. Talwar and A.B. Biswas, J. Polym. ScL, Polym. Chem. Ed., 1981,19, 1155. [73] M.F. Rubner, Macromolecules, 1986,19, 2114. [74] R.S. Liang and AJ. Reiser, J. Polym. ScL, Polym. Chem. Ed., 1987, 25, 451. [75] R.A. Nallicheri and M.F. Rubner, Macromolecules, 1991, 24, 517. [76] J.G. Williams, Stress Analysis of Polymers, Longman, London, 1973. [77] M.C. Andrews, RJ. Day and RJ. Young, Comp. ScL and Tech., 1993,48, 255. [78] RJ. Young, C. Galiotis, LM. Robinson and D.N. Batchelder, J. Mater. ScL, 1987,22, 3642. [79] RJ. Young and P.P. Ang, in I. Verpoest and F.R. Jones (Eds.) lnterfacial Phenomena in Composite Materials '91, Butterworth-Heinemann, Oxford, 1991, pp. 45-52. [80] H. Jahankhani and C. Galiotis, J. Compos. Mater., 1991, 25,609. [81] M.C. Andrews, RJ. Day, X. Hu and RJ. Young, J. Mater. ScL Lett., 1992,11,1344. [82] M.E. Cates and S.F. Edwards, Proc. R. Soc. Lond. A, 1984,395, 89. [83] H.L. Cox, Br. J. Appl. Phys., 1952,3, 72. [84] CF. Fan and S.L. Hsu, Macromolecules, 1989,22, 1474. [85] A. Kelly, Strong Solids, Clarendon Press, Oxford, 1966, p. 130. [86] A.N. Netravali, Z.-F. Li, W. Sachse and H.F. Wu, J. Mater. ScL, 1991,28,6631. [87] L.T. Drzal, MJ. Rich and P.F. Lloyd, J. Adhes., 1982,16,1. [88] A. Kelly and N.H. Macmillan, Strong Solids, 3rd edn., Clarendon Press, Oxford, 1986.

9

SPIN-LABELSTUDIESOF HETEROGENEOUS POLYMER SYSTEMS G. G. CAMERON and L G. DAVIDSON Department of Chemistry, University of Aberdeen, Old Aberdeen AB9 2UE, Scotland, UK

9.1 INTRODUCTION The spin-label and spin-probe techniques have been used to study a wide variety of polymers, both in bulk and in solution, and several reviews of the subject have been published [1-3]. The object of this article is to provide a brief outline of the theoretical background, with particular, reference to spin-labelling, before discussing some recent applications of the technique to polymers in heterogeneous systems. The shape and width of the electron spin resonance (ESR) spectrum of a spin label or probe is sensitive to the mode and rate of rotation of the radical. Thus, examination of the ESR spectrum of the labelled or probed polymer can yield information on the dynamics and relaxations of the polymer and is therefore complementary to such techniques as mechanical, NMR and dielectric relaxation measurements. In the spin-probe experiment the free radical is simply dispersed in the polymer matrix. However, as any interaction with the polymer is only by secondary valence forces, the motion of the probe may not directly reflect the motion of the polymer. Spin-labelling, where the radical is covalently attached to the polymer chain, does give information on the dynamics of that part of the polymer to which it is joined. It is possible to label polymers specifically at either inner or terminal segments, and thus, provided that the label does not rotate independently or perturb the motion of the polymer, specific information about the dynamics of these particular sites can be obtained. An advantage of the ESR technique is its high sensitivity, so that, in favourable circumstances, spin concentrations as low as 10"6 M may be used. In practical terms, this relates to approximately one spin label per polymer chain. Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

9.1.1 SYNTHESIS OF SPIN LABELS Spin labels are almost invariably di-t-alkyl-substituted nitroxide (nitroxyl or aminoxyl) free radicals. These are used because they are quite stable to heat and light, and nitroxides with a wide variety of structures and functional groups can be readily synthesised, so facilitating the labelling of a range of polymers [4]. Many labels are functionalised piperidine and pyrroline derivatives (Table 9.1), although other types are also sometimes used. The simplest method of spin labelling is to utilise a functional group on the polymer to attach the label, usually via a condensation reaction (Scheme 1). Labels can also be introduced by less direct methods. For example, the Keana synthesis [6] (Scheme 2) has been used to label polyethylene that had been copolymerised with a small amount of carbon monoxide [7]. Polystyrene has been labelled by reacting the lightly lithiated polymer with either 2-methyl-2nitrosopropane or nitrosobenzene (Scheme 3) [8]. Direct ionic or radical copolymerisation of vinyl-substituted nitroxides is not usually feasible, as either the initiators or the growing polymers can react with the nitroxide. However, if the spin label is converted into the amine or hydroxylamine such a polymerisation is possible, the nitroxide being subsequently generated by oxidation. In most spin-label experiments, the label is attached as a pendent group. It is possible to place a spin label directly into the polymer backbone using either radicals [9] or ionic [10] polymerisation (Scheme 4). Such labels have no rotational freedom independent of the polymer, and so their motion directly reflects that of the polymer segments. Table 9.1 Some nitroxides used for spin-labelling

Scheme 1

Scheme 2

Scheme 3

AU of these methods produce randomly labelled polymers with the labels on in-chain segments. End-labelled polymers are generally prepared by anionic polymerisations. The living chain end is terminated with a suitably functionalised spin label, usually an acid chloride [11]. A different method was used to prepare end labelled poly(w-butyl isocyanate) [12]. Here the spin label 2,2,5,5- tetramethyl-l-pyrrolidinyloxy-3-carboxamide was used as an initiator in competition with cyanide ion (Scheme 5). This produced a spin concentration of one label per three polymer chains.

9.2 THEORETICAL BACKGROUND The ESR spectrum of a nitroxide free radical consists of three lines arising from the interaction of the unpaired electron with the 1 4 N nucleus (nuclear spin quantum number / = 1). The spectra are anisotropic, as the position of the centre of the spectrum—g tensor—and the splitting of the lines—hyperfine coupling tensor A—depend on the orientation of the nitroxide with respect to the applied magnetic field (Figure 9.1). In bulk polymers, or at low temperatures, where the motion of the label is restricted, a powder average or slow-motion spectrum is observed (Figure 9. l(d)). When the nitroxide is rotating freely, e.g. in dilute solution or at high temperatures, the anisotropies are averaged out, giving a motionally narrowed or fast-motion spectrum (Figure 9.1(e)) whose centre is defined by 0iso = l(0xx + 9yy + 0zz)

and which has a splitting given by <*N = ^iso = i(^xx + ^yy +

A

zz)

where gxx, gyr gzz and Axxi Ayr Azz are the principal values of the g and hyperfine coupling tensors respectively.

9.2.1 C O R R E L A T I O N T I M E S The ESR spectra of nitroxides can be characterised by the rotational correlation time TC, which is inversely proportional to the rate or frequency of rotation of the radical. The correlation times for nitroxides can be divided into three distinct regions, designated fast (10" 1 MO" 9 s), slow (10" 9 -10" 7 s) and very slow (10" 7 10"3 s). The limits to these regions are determined by the anisotropies of the magnetic interactions of the radicals, and different methods of calculating TC are required for each region.

Scheme 4

Scheme 5

Figure 9.1 Idealised ESR spectra of nitroxide radicals: (a), (b) and (c) single crystal spectra with the applied magnetic field along the x, y and z principal axes; (d) slow-motion spectrum; (e) fast-motion spectrum

9.2.1.1 Fast Motion The line widths (W) of a motionally narrowed or fast-motion spectrum depend both on the correlation time and on m7, the component of the nuclear spin along the direction of the applied magnetic field. For 14 N, m7 = 1,0, — 1, corresponding to the low, middle and high field lines in the ESR spectrum. In general the dependence of W upon m7 is given by [13] W(Yn1) = A + Bm j + Cm] where A% B a n d C are coefficients which depend o n the correlation time a n d the principal values of the g a n d hyperfine coupling tensors. T h e A term includes factors arising from homogeneous broadening independent of mj, b u t as W{0) = A the equation can be rearranged t o W(mj) _

Bm1

Cm]

For nitroxide spin labels, assuming isotropic rotational diffusion a n d near axial symmetry of the coupling tensor, i.e. A x x % Ayy9 B a n d C are given by B=

^bAyHoic

where * = y [ ^ - 0.5(Axx + A y y )] a n d Ay = J [g 2 2 - 0.5(g xx + g yy )] H 0 is the applied magnetic field a n d ft is t h e Bohr magneton. T w o values of the correlation time can then be calculated: 4>W \5W t . ( D - - ^ C * + r - -2)andr c (2) = ^ ( r

+

-r_)

(1)

It is usual to obtain accurate values for r± from peak to peak intensities Y of the relevant lines, thus: _ ^(±1) = 1

^(O)

r

(Q)

{1\

J

L (±i)J

If the two TC values are not in close agreement, then the assumption that the rotation of the spin label is isotropic must be suspect. A more rigorous approach based on the assumption of axially symmetric rotation of the spin label must then be used [14]. It should be noted that the lines of the ESR spectrum of a spin-labelled polymer are broadened by unresolved hydrogen couplings. This inhomogeneous broadening is not accounted for in the above equations, but there are several methods of overcoming this problem [I].

9.2.1.2 Slow Motion

As the motion of the spin label is slowed, the lines gradually broaden. When the correlation time is « 3 x 10"9 s the spectrum suddenly changes from a motionally narrowed to a slow-motion one. The spectrum then remains essentially the same except that the distance between the low and high field extrema increases with increasing correlation time until the rigid limit is reached. The most rigorous method of determining TC in this region is by computer simulation [15,16]. The variable input parameters of correlation time and line width are varied until a good match between the computed and the observed spectra is obtained. Anisotropic rotation and various rotational diffusion models can be accommodated by this method. In many cases, however, simpler methods based on analysis of the outer extrema, either their inward shift from the rigid limit or their line width, are adequate. Such methods have been extensively reviewed elsewhere [1,15, 17,18]. It is important for all of these methods to choose an appropriate diffusion model for the system. It has been shown that the ratio of the shifts of the high and low field extrema (AHJAH1) with change in AH1 is sensitive to the mode of reorientation of the nitroxide, and so can be used in the choice of diffusion model [19]. For correlation times longer than «10 7S, the technique of saturation transfer (ST) ESR spectroscopy must be used [20]. In this technique, either the first harmonic of the dispersion or the second harmonic of the absorption signal, as opposed to the usual first derivative ESR espectrum, is observed. The shapes of these spectra are sensitive to changes in the correlation time in the range 10" 7-10~3 s. As for the slow-motion spectra, correlation times are calculated by computer simulation of the STESR spectra. 9.2.2 THE GLASS TRANSITION AND T 50G As was noted above (Section 9.2.1.2), as a spin-probed or labelled polymer is cooled, the fast-motion spectrum of width « 30 G reaches a point where it rapidly changes into a slow-motion spectrum of width 65-70 G (Figure 9.1(d),(e)). The temperature at which this transition occurs is taken as the temperature at which the spectrum is 50G wide, the 7 50G [21] (Figure 9.2).This change occurs over a narrow temperature range (i.e. it is a guasz-discontinuity) and is usually associated with the glass transition temperature Tg of the polymer. However, T5QG is generally higher than T g because the frequency of rotation of the nitroxide at 7 50G is ^10 7 Hz, whereas Tg is measured at ^ IHz. Thus, T50G is often considered as a high frequency T r although it must be noted that it is possible for a probe to exhibit a T50G with the polymer still in its glassy state. The T50G for a particular polymer increases with the molecular volume of the probe, as the mobility of the probe is associated with the free volume of the

Extrema separation / G

Temperature

Figure 9.2 Plot of extrema separation versus temperature showing T50G

polymer [22]. This increase has a limiting value where the volume of the probe is comparable with the volume of the polymer segment undergoing relaxation. Thus, spin labels can be regarded as large probes, and reflect the relaxation volume of the segment to which they are attached [ I ] . It has been shown that the correlation time of a spin probe is related to the temperature T of the system by [23]

lnT =lnT

-[1303C11C21I

' " +4r-rg;c;J

(3)

where T00 is the high temperature limit of TC, C l g and C 2g are constants for a given polymer, as defined by Williams et al. [24], and / is the ratio of the activation volume of the probe to the activation volume of the polymer segment. Thus, a plot of In t c against 2.303 Cl%C2J{T — T1 + C2g) is linear, with a slope o f / and intercept T00. A simpler but less exact method of evaluating / assumes that T00 = 1.1 x 10~ 12 s and, at T 5 0 0 , TC = 10"8 S, giving on rearrangement of Equation (3) [I]:

T

T-C

P°3Ci»/

jl

(4)

It must be noted that there is no general correlation between / and probe volume. This is because no account is taken of any differences in probe flexibility or any

polymer-probe interactions which will depend on the chemical structure of both polymer and probe [23].

9.3 HETEROGENEOUSSYSTEMS The above discussion has considered the spin-label or spin-probe to be in a homogeneous system with a single correlation time. In some cases, however, the observed ESR spectrum is of neither the fast- nor the slow-motion type but is a mixture of the two (Figure 9.3). Such composite spectra arise when the spin-labels or probes simultaneously occupy two motionally distinct environments, one of which is significantly more restricting than the other. This behaviour may occur in situations such as adsorption of a polymer onto a solid [9], phase separations of polymers or polymer blends [25], polymer networks [26] or any other system where more than one phase is present. Analysis of composite spectra can be achieved by computer simulation of the fast and slow components, yielding the relative proportions of the label or probe in the different environments. It must be noted that a few percent of fast motion in an otherwise slow-motion spectrum is readily detected, whereas this is not true of the reverse situation. This is because the peak-to-peak intensity of an ESR line is proportional to the inverse of the square of the linewidth (see Equation (2)) and fast-motion lines are much narrower than slow-motion lines. Among the first heterogeneous systems involving polymers to be studied by the spin-label technique were solids suspended in polymer solutions [5, 9, 27-29]. The aim of these studies was to obtain new and complementary information on the nature and mechanism of polymer molecule adsorption at the solid-solution interface. In most of these studies the labelled polymer adsorbed from solution on the surface of adsorbents, such as silica, yielded composite ESR spectra compris-

Figure 93 Composite ESR spectrum

ing a slow- and a fast-motion component. These spectra were interpreted as showing that the polymer molecules in the adsorbed state, but still in contact with solvent, had some regions of their chains in a hindered state, probably fiat on or very close to the surface ('trains'), and other regions in a relatively unhindered state more distant from the surface ('loops' and 'tails'). The former gave the slow-motion and the latter the fast-motion component in the ESR spectra. By deconvolution or spectral simulation, it is possible to calculate the relative proportions of hindered and mobile nitroxides, and hence the proportions of the adsorbed polymer chains in the 'train' mode and the 'loop'/'taiF mode. The proportions of the hindered and free segments are dependent on the nature of the surface and the thermodynamic quality of the solvent for the polymer. The adsorption isotherm may be obtained by measuring the intensity of the ESR spectrum before and after shaking the solution with the solid adsorbent [9]. A good example of this application concerns poly(vinyl acetate) (PVA), which was labelled both in the in-chain position (Scheme 4) [9] and with a pendent nitroxide (Scheme 1) [5]. The ESR spectra of these labelled polymers both in solution and in the adsorbed state reflect the greater motional freedom of the pendent label. Thus, the correlation times TC for the in-chain and pendent nitroxide groups were 0.6 and 0.04 ns respectively in chloroform solution and 0.8 and 0.06 ns respectively in toluene solution [9]. With silica as adsorbent, it was observed that the adsorption capacity diminished with decreasing surface silanol content. Furthermore, the adsorption capacity was greatest when toluene, a thermodynamically poor solvent, was employed, and least with the good solvent ethyl acetate [9]. The ESR spectra of in-chain labelled PVA adsorbed on a silica sample of relatively high silanol content (Microsil GP) from toluene, chloroform and ethyl acetate solution are shown in Figure 9.4. The spectra of the polymer adsorbed from toluene and chloroform solutions (Figure 9.4(a) and (b)) are almost identical and are of the slow-motion type, with only a hint at most of fast motion. This suggests rathet-strong adsorption and a relatively flat polymer conformation on the surface. The ESR spectrum of the labelled polymer adsorbed from the good solvent ethyl acetate (Figure 9.4(c)) is clearly a composite one with a well-defined fast-motion component. In this case, some of the segments at the surface are motionally quite free, probably in the form of loops or tails. The above observations are physically quite reasonable. One would expect relatively stronger adsorption from solution when polymer-solvent interactions are energetically rather unfavourable. Interestingly, when most of the surface silanol groups are trimethylsilylated, adsorption still occurs and the ESR spectrum (Figure 9.4(d)) again shows a fairly strong polymer-surface interaction. However, the ESR spectrum of the polymer on the modified silica surface is quite distinct from its spectrum on the unmodified substrate. There appears to be a change in the type of motion, as opposed to facility of motion, when the surface is altered. The change is probably associated with a change in the anisotropy of

Figure 9.4 ESR spectra of PVA adsorbed on Microsil GP: (a) from toluene solution, equilibrium cone. 0.077 gdl" *; (b) from chloroform solution, equilibrium cone. O.llOgdl"1; (c) from ethyl acetate solution, equilibrium cone. 0.076gdl"1; (d) on trimethylsilylated Microsil GP from toluene solution, equilibrium cone. 0.084 g dl"i probe tumbling which could, in turn, indicate a change in the mode of adsorption at the surface [9]. This is a subtlety which requires a more detailed spectral analysis for clarification. In experiments of this type it is important to establish that there is no strong or preferred affinity between the nitroxide label and the surface. This can usually be ascertained by checking a small-molecule analogue of the label. In the study described above, experiments with the free label 3-carbamoyl-2,2,5,5-tetramethylpyrrolidine-1-oxyl established that only with toluene as solvent was the nitroxide group adsorbed on the silica surface in detectable quantities. Thus, the PVA segments in general have a stronger affinity for the surface than the nitroxide label. The principles applied in studying polymers adsorbing on to solid surfaces from solution can be applied to other types of interactions involving polymer solutions and solid surfaces. A recent example of such an application concerns polymers containing suitable sequences of methylene units which interfere with the crystallisation of a straight-chain hydrocarbon from solution. In the presence of ppm quantities of such polymers, the crystallisation temperature is depressed

and the n-alkane crystals which eventually form are much smaller and usually needle-shaped rather than plate-like [30]. Much remains to be learned about the precise mode of interaction of the polymer with the w-alkane crystals.

The problem was approached by preparing the spin-labelled fumarate-VA copolymer shown above. To a solution comprising 2% dotriacontane in dodecane was added 0.1% w/w of this polymer [31]. Above the cloud point of this homogeneous mixture, the ESR spectrum of the polymer is of the fast-motion type, with three rather broad but clearly defined lines typical of a spin-labelled polymer in solution (Figure 9.5(a)). As the temperature of the solution is lowered, crytallisation of the dotriacontane commences at the cloud point (20 0C), which is well above the temperature (6 0C) at which the polymer itself precipitates from dodecane solution. Just below this temperature (Figure 9.5(b)) the ESR spectrum of the polymer shows the beginnings of a broad-line slow-motion spectrum which can be ascribed to polymer interacting with the solid crystalline dotriacontane. As the temperature is lowered further, the slow-motion spectrum increases in intensity at the expense of the fast-motion spectrum (Figure 9.5(c)) as increasing quantities of polymer are incorporated with the progressively crystallizing n-alkane, and by 10 0 C very little fast-motion character remains. Simulation of the spectra allows the proportion of fast- and slow-motion spectra shown in Figure 9.5 to be calculated. However, infrared spectral examination of the precipitated dotriacontane shows that the proportion of incorporated polymer is greater than the proportion of slow-motion in the composite spectrum. In other words, some of the polymer associated with the crystalline dotriacontane shows a fast-motion spectrum, rather in the manner of labelled PVA adsorbed on silica [9]. Clearly, a proportion of the polymer is not 'locked up' or cocrystallised and must reside on the surface of the growing crystals. It seems probable that further growth is inhibited at the crystal face where the polymer molecule is located.

9.4 POLYMER BLENDS Applications of the spin-label technique to polymer blends have been relatively recent. Shimada et al. have studied blends of end-labelled polyethylene oxide)-

Figure 9.5 ESR spectrum of 0.1% (w/w) fumarate-vinyl acetate copolymer, 2% dotriacontane in dodecane: (a) 23 0C, above the cloud point; (b) 190C, just below the cloud point; (c) 150C (PEO) with isotactic poly(methyl methacrylate) (PMMA) [25, 32] and labelled (both random and chain-end) PMMA with poly(vinylidene fluoride) (PVDF) [33, 34]. These are complex systems because they show partial miscibility and because in each case one of the components is capable of crystallising. Nevertheless, these authors obtained fundamental information on the morphology of the blend and phase separation. In the PEO-PMMA blends, the spectra were of the composite type, and they ascribed the fast- and slow-motion spectra to nitroxides located in PEO-rich regions and PMMA-rich regions respectively. In our own work [11, 35] we have studied blends of polystyrene (PS) and ris-l,4-polyisoprene (PIP), the former labelled either at random in the m-site of the benzene ring, as in Scheme 3, or at chain ends, as in Scheme 5. This pair of polymers was chosen because they are immiscible, amorphous and have widely different Tg values. Thus, any significant interaction of the two should lead to

Bulk PS

1:1 (w/ w) Blend with cis -1,4 PIP

Figure 9.6 ESR spectra of in-chain labelled PS and its 1:1 (w/w) blend with cis- 1,4-PIP: (a)-(d) temperature increased progressively from 292 to 453 K. Reproduced from [35] by permission of the publishers, Butterworth-Heinemann Ltd. plasticisation of the PS, which could then influence the ESR spectrum of the label. Figure 9.6 shows the temperature dependence of the ESR spectrum of the in-chain labelled PS both in the pure (bulk) state and in a 1:1 w/w blend with PIP [35]. The spectra of the pure and the blended PS are identical and remain essentially of the slow-motion type up to « 450 K, above which decomposition of the nitroxide group is fairly rapid. In both systems the slight spectral changes observed on heating are completely reversed on cooling. There is no evidence of even limited miscibility in these spectra. However, the behaviour of the end-labelled PS is quite different (Figure 9.7). The spectrum of the blend shows a motionally narrowed component at «420 K (Figure 9.7(c)) where the spectrum of the pure PS is still of the slow-motion type. At 433 K the differences between the spectra of the two samples are very marked, the 1:1 blend showing an intense narrow-line component in its composite spectrum and the pure PS a gradual shift to line-narrowing. On cooling from 433 K to room temperature, the spectra of the pure PS are identical to those recorded during heating, i.e. there is complete reversibility. In the blend, by contrast, the changes in the ESR spectrum on heating are not exactly reversed on cooling. Thus, the motionally narrowed component persists and is clearly visible at temperatures well below the temperature at which it was first detectable during the heat-up procedure. On cooling to room temperature after heating to 433 K, the spectrum of the blend closely resembles the spectrum at 423 K in Figure 9.7(c).

PS2

1:1 (w/ w) Blend with cis -1,4 - PIP

Figure 9.7 ESR spectra of end-labelled PS and its 1:1 (w/w) blend with cis- 1,4-PIP: (a)-(d) temperature increased progressively from 292 to 433 K; (e) samples heated to 433 K, cooled to room temperature then reheated to 343 K. Reproduced from [35] by permission of the Publishers, Butterworth-Heinemann Ltd. The fifth pair of spectra (Figure 9.7(e)) was obtained by reheating to 343 K, and underlines the contrasting behaviour of the pure labelled PS and its blend with PIP: the spectrum of the pure PS maintains the slow-motion shape but that of the blend contains a sharp fast-motion component. After storing the heat-treated blend at room temperature under vacuum for one week, the motionally narrowed component reappears on heating again to 343 K, though at a somewhat reduced intensity. It is clear from these observations that, on heating to «430 K, the blend, originally prepared by freeze-drying a co-solution in benzene, is reorganised in such a manner that more nitroxide chain ends reside in a region relatively rich in PIP. We have concluded that these groups are in fact located in the interphase between the PS and PIP domains, where they experience increased motional freedom because of the plasticising influence of PIP in the interphase [35] and possibly also because of a concentration of free volume in this region. Similar results were obtained with a blend of chain-end labelled PMMA (prepared by group transfer polymerisation) and an immiscible partner, poly(2ethylhexyl methacrylate), of low Tg (263 K) [36]. These observations are in accord with Helfand's general theory that at thermodynamic equilibrium the interphase in a blend of immiscible polymers

EXTREMA SEPARATION / G

contains more than the statistical concentration of chain ends [37-39]. Indeed, spectral simulations have indicated that composite spectra of the type in Figure 9.6(c) comprise « 2 5 % nitroxide groups in the fast-motion regime [40]. These spin-label experiments on polymer blends appear to be the first experimental verification of Helfand's theory. With heterogeneous polymer blends such as those under discussion here, it is strictly speaking not possible to obtain an accurate value of the parameter T 500 . However, if the temperature is noted at which the motionally narrowed spectrum (with an extrema separation of « 30 G) becomes just visible, a value of T 50G may be estimated [ H ] . The extrema separations for pure labelled PS and PS-PIP blends are plotted in Figure 9.8, from which estimated values of T 50G for the three systems were calculated to be 425, 405 and 400K for blends comprising a PS weight fraction of 1.0,0.5 and 0.025 respectively. These figures re-emphasise the

TEMPERATURE/K

Figure 9.8 Extrema separation vs. temperature for pure PS, O; 1:1 blend of PS and PIP, D; 1:39 blend of PS and PIP, A. Reproduced from [11] with permission of Pergamon Press Ltd., Headington Hill Hall, Oxford 0X3 OBW, UK

W1

Figure 9.9 T50G vs. composition for PS and blends with PIP. W1 = wt fraction of PS. Reproduced from [11] with permission of Pergamon Press Ltd., Headington Hill Hall, Oxford 0X3 OBW, UK plasticising influence of the PIP on the labelled PS chain ends, and the T 50G values may be regarded as pertaining to the labels with the least hindered motion in each of the three systems. If it is assumed that these T 50G values refer to labels in a homogeneous environment—the interphase—the composition of this environment may be calculated from the relationship [41]

VT500 = WJT5001+ W2ZT5001 = W 1 (T 5 0 Q 2 — ^5OG|)/^5OG, ^SOG2 + 1/T 5 0 Q 2

(5)

where W refers to a weight fraction and the subscripts 1 and 2 to the components. Setting PS as component 1, at W1 = 1, T 50G is 425 K, and at W1 = O, T 50G2 is very close to 400 K (see Figure 9.9). With T 50G = 405 K for the 1:1 blend, Equation (5) yields W1 =0.21. Thus, in the 1:1 blend the labelled PS chain ends which first show evidence of being plasticised appear to be in a PIP-rich environment, i.e. 79% by weight of PIP. Notwithstanding the approximations and assumptions in this calculation, it does show that a proportion of the PS chain-end labels is in a region well removed from the pure PS phase [ H ] . In the above calculation the labelled PS is being treated as a macromolecular spin probe—in pure PS when W1 = I and in pure PIP when W1 = 0. By substituting the values of T 50G (425 and 400 K for W1 = 1 and W1=O respectively) and those of the other parameters T^C1% and C 2g into Equation (4), the value of the parameter / may be calculated. For pure, bulk PS / = 0.62; this approximates to the ratio of the volume of the labelled PS chain end to the effective volume of an inner segment. For the spin-probed PIP / = 1.01, which approximates to the ratio of the volume of the

labelled PS chain end to that of an inner PIP segment. Thus, an in-chain PS segment is about 1.6 times bulkier than an in-chain PIP segment. These figures are qualitatively reasonable, and are consistent with the generalisation that, in a series of polymers, the effective volumes of segments involved in the glass-torubber transition increases with increasing Tg [42]. The results of these experiments show that the spin-label technique is capable of providing detailed information at a molecular level on the structure and composition of polymer blends.

9.5 REFERENCES

[1] G.G. Cameron, in C. Booth and C. Price (Eds.), Comprehensive Polymer Science, Vol. 1, Pergamon Press, Oxford, 1989, p. 517. [2] LJ. Berliner (Ed.), Spin Labelling Theory and Applications, Academic Press, New York, 1976. [3] LJ. Berliner and J. Reuben (Eds.), Biological Magnetic Resonance 8: Spin Labelling Theory and Applications, Plenum Press, New York, 1989. [4] E.G. Rosantsev, Free Nitroxyl Radicals, Plenum Press, New York, 1970. [5] T.M. Liang, P.M. Dickenson and W.G. Miller, Am. Chem. Soc. Symp. Ser., 1980, 142,1. [6] J.F.W. Keana, S.B. Keana and D. Beetham, J. Am. Chem. Soc, 1967,89, 3055. [7] AT. Bullock, GG. Cameron and P.M. Smith, Eur. Polym. J., 1975,11,617. [8] AT. Bullock, G.G. Cameron and P.M. Smith, J. Phys. Chem., 1973, 77, 1635; Polymer, 1973,14, 525. [9] AT. Bullock, G.G. Cameron, I. More and LD. Robb, Eur. Polym. J., 1984,20, 951. [10] C. Friedrich, C. Noel, R. Ramasseul and A. Rassat, Polymer, 1980,21, 232. [11] G.G. Cameron, M.Y. Qureshi, E. Ross, LS. Miles and J. Richardson, Eur. Polym. J., 1991,27,1181. [12] R. Olayo, M.A. Patron and W.G. Miller, Macromolecules, 1990,23,1680. [13] A. Hudson and G.R. Luckhurst, Chem. Rev., 1969,69,191. [14] S.A. Goldman, G.V. Bruno, CF. Polnaszek and J. H. Freed, J. Chem. Phys., 1972,56, 716. [15] J.H. Freed, in LJ. Berliner (Ed.), Spin Labelling Theory and Applications, Academic Press, New York, 1976. [16] DJ. Schneider and J.H. Freed, in LJ. Berliner and J. Reuben (Eds.), Biological Magnetic Resonance 8: Spin Labelling Theory and Applications, Plenum Press, New York, 1989, p. 1. [17] G.G. Cameron, in R.F. Boyer and S.E. Keineth (Eds.), Molecular Motions in Polymers by E.S.R., MMI Press, Symposium Series Vol. 1, Harwood, Chur, 1980. [18] T.N. Khazanovich, A.D. Kolbanovsky, A.I. Kokorin, T.V. Medvedeva and A.M. Wasserman, Polymer, 1992, 33, 5208. [19] A.N. Kuznetsov and B. Ebert, Chem. Phys. Lett., 1974, 25, 342. [20] M.A. Hemminga and P.A. de Jager, in LJ. Berliner and J. Reuban (Eds.), Biological Magnetic Resonance 8: Spin Labelling Theory and Applications, Plenum Press, New York, 1989, p. 131. [21] G.P. Rabold, J. Polym. ScL, Part A-I, 1967,7, 1203. [22] N. Kusumoto, in R.F. Boyer and S.E. Keineth (Eds.), Molecular Motions in Polymers by E.S.R., MMI Press, Symposium Series Vol. 1, Harwood, Chur, 1980, p. 223.

[23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]

AT. Bullock, G.G. Cameron and LS. Miles, Polymer, 1982, 23,1536. M.L. Williams, R.F. Landel and J.D. Ferry, J. Am. Chem. Soc, 1955,77, 3701. S. Shimada, Y. Hori and H. Kashiwabara, Macromolecules, 1990, 23, 3769. R. Harvey and S. Schlick, Polymer, 1989,30,11. K.K. Fox, LD. Robb and R. Smith, J. Chem. Soc, Faraday Trans. 1,1974,70,1186. LD. Robb and R. Smith, Polymer, 1977,18, 500. LD. Robb and M. Sharpies, J. Colloid Interface ScL, 1982,89, 301. K. Lewtas, R.D. Tack, D.H.M. Beiny and J.W. Mullin, in J. Garside, R. Davey and A. Jones (Eds.), Advances in Industrial Crystallisation, Butterworth-Heinemann, Oxford, 1991, p. 166. LG. Davidson and G.G. Cameron, Polymer International, 1994, 34, 443 and 449. S. Shimada, Y. Hori and H. Kashiwabara, Macromolecules, 1992,25, 2771. S. Shimada, Y. Hori and H. Kashiwabara, Macromolecules, 1988, 21, 2107. S. Shimada, Y. Hori and H. Kashiwabara, Macromolecules, 1988, 21, 3454. G.G. Cameron, M.Y. Qureshi, E. Ross, LS. Miles and J. Richardson, Polymer, 1993, 34, 25. G.G. Cameron, D. Stewart, R. Buscall and J. Nemcek, Polymer, 1994,35, 3384. E. Helfand and Y. Tagami, J. Chem. Phys., 1972,56, 3592. T.H. Weber and E. Helfand, J. Chem. Phys., 1980,72,4017. E. Helfand, in K. Sole (Ed.), Polymer Compatibility and Incompatibility, Harwood, Chur, 1982. E. Ross, Ph.D. Thesis, University of Aberdeen, 1990. G.G. Cameron, LS. Miles and AT. Bullock, Br. Polym. J., 1987,19,129. AT. Bullock, G.G. Cameron and LS. Miles, Polymer, 1982,23,1536.

10 THE USE OF ESR SPECTROSCOPY FOR STUDYING POLYMERIZATION AND POLYMER DEGRADATION REACTIONS T. G. CARSWELL, R. W. GARRETT, D. J. T. HILL, J. H. O'DONNELL, P. J. POMERY and C. L. WINZOR

Polymer Materials and Radiation Group, Department of Chemistry, University Queensland, Brisbane, QLD 4072, Australia

10.1 INTRODUCTION Electron spin resonance spectroscopy offers a unique technique to study the role of radical species as intermediates in both polymerization and polymer degradation processes. The technique has been developed significantly since its introduction to chemical applications in the 1950s [1], with major advances in the stability of the magnetic field, in the sensitivity to low radical concentrations— and hence the limit of detection and measurement—and in data collection and manipulation. ESR spectrometry enables both the identification of radicals and the measurement of their concentration. It is a non-destructive technique and spectra can be recorded both during polymerization, and, in suitable circumstances, during degradation of polymers [2]. New quantitative studies of free radical polymerization kinetics are currently being undertaken by a number of researchers using pulse laser techniques [3,4]. However, the pulsed laser methods cannot be used for crosslinking systems. There has also been development of a number of new theoretical models for polymerization [5-7]. The experimental information available comprises monomer concentration and polymer molecular weight. ESR spectroscopy offers the possibility of an additional piece of information—the radical concentration during polymerization. There is increasing interest in polymerization to high conversion, which is of great practical importance, and ESR spectra can be Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

obtained readily under these conditions when other methods can be difficult to apply [8]. Degradation of polymers is often understood from a practical viewpoint as a deterioration in the properties of polymer materials leading to failure in service. Changes in the molecular structure, and particularly the molecular weight, of the polymer is the fundamental degradation process. High-energy radiation, e.g. gamma-rays and electron beams, is an important cause of controlled polymer degradation [9]. The degradation reactions usually involve free radical intermediates, and therefore ESR spectroscopy is a valuable technique for investigating the chemical mechanism of degradation. We have studied the degradation by high-energy radiation of a number of families of polymers by using a variety of techniques, including ESR spectroscopy [10, H]. In this paper we show the similarities and differences in the role of free radicals in the radiolysis of poly(methyl methacrylate), polystyrene, and random copolymers of methyl methacrylate and styrene.

10.2 EXPERIMENTAL The ESR spectra were recorded using a Bruker ER200D spectrometer fitted with a liquid nitrogen dewar for measurements at 77 K, and with a variable temperature cavity having a heated supply of cold nitrogen for temperature control from 100 to 400K. Methyl methacrylate (MMA) was distilled under a reduced pressure of nitrogen; ethylene glycol dimethacrylate (EGDMA) was purified by passage through an alumina column. Polymerization mixtures containing azobisiso- butyronitrile (AIBN) as initiator were sealed in 3 mm i.d. quartz tubes under vacuum. Some measurements were also made in 1 mm i.e. tubes in order to minimize increases in the temperature of the polymerization which could result from the exothermic heat of polymerization during the Norrish-Trommsdorff region. The conversion of monomer ( C = C concentration) was measured by near-infrared Fourier transform spectroscopy using the C = C H vibration at 6152cm" l . CH3 I CH2=C COOCH3 MMA

CH3 CH3 I I CH2=C C=CH 2 CO CO I I 0-CH2-CH2-O EGDMA

Poly(methyl methacrylate), polystyrene and their random copolymers were prepared by free radical polymerization in vacuum using AIBN as initiator.

Samples of the polymers were evacuated with heating and sealed in high-purity quartz tubes. Cobalt-60 gamma-irradiation was carried out in liquid nitrogen (77 K) and at ambient temperature (300 K) at a dose rate of « 1 kGy/h.

10.3 RESULTS AND DISCUSSION 10.3.1 FREE RADICAL POLYMERIZATION 10.3.1.1 Identification of the Radicals in the ESR Spectrum

The ESR spectrum is recorded in the first-derivative form as shown in Figure 10.1. A number of characteristics of the spectrum of a radical can be predicted from its structure and used to identify the presence of the radical in an ESR spectrum. These characteristics are illustrated in Figure 10.1, which is the ESR spectrum of the methyl radical at 77 K. They include: (1) g value—the centre of the spectrum—corresponding to the proportionality between the magnetic field H and the microwave frequency, expressed in the relationshipfcv= gfiH; (2) the number of lines in the spectrum—resulting from interactions between the unpaired electron spin on the radical and the nuclear spins of adjacent atoms, particularly hydrogen;

Linewidth

Intensity

Lines

Figure 10.1 ESR spectrum of the methyl radical (CH3') showing the characteristic features of g value, number of lines, relative intensities of the lines, hyperfine splitting (hfs), line width, and line shape

(3) the relative intensities of the component lines of the spectrum of the radical—frequently described by a binomial distribution of intensities; (4) the hyperfine splitting, hfs, between the lines—this separation of the lines depends on the electron spin on the radical site, the magnitude of interacting nuclear spins and the conformation of the radical; (5) the line widths—usually measured between the positive and negative peaks of the derivative spectrum, or the width at half height of the absorption spectrum. (6) the line shape—usually represented by a Gaussian or Lorentzian expression, or a combination, depending on the curvature of the wings of the absorption spectrum, reflecting the environment of the radical. 10.3.1.2 Measurement of Radical Concentration

ESR spectra are obtained as first-derivative spectra of signal intensity versus magnetic field because of the method of observation of the absorption of microwave power. Integration of the experimental spectrum gives the corresponding absorption spectrum and a second integration gives the area of the spectrum, which is proportional to the radical concentration provided that microwave power saturation is avoided. Saturation of the upper energy level of the unpaired spins can occur at high microwave powers, the actual power depending on the relaxation time and hence on the nature of the radical. Therefore for quantitative measurements of radical concentrations the power dependence of the spectrum must be examined. Deviation from linearity in a plot of spectrum area versus the square root of the microwave power indicates the onset of microwave power saturation and the upper limit for quantitative measurements of radical concentrations. Microwave power saturation measurements for methacrylate propagation radicals during polymerization is shown in Figure 10.2. The area of the absorption spectrum does not yield an absolute value for radical concentration. This must be obtained by calibration with a sample containing a known concentration of radicals using standardized conditions of measurement. A sample of pitch/KCl provided by Varian was used in the present study, and this sample was calibrated with a measured concentration of recrystallized diphenylpicrylhydrazine (DPPH) in benzene. 10.3.1.3 Monomer Concentration during Polymerization

We have utilized a variety of techniques for determination of the conversion of monomer to polymer, by measurement of the concentration of C = C bonds at different times during the polymerization of vinyl and allyl monomers. The 1 H NMR spectra of samples quenched and dissolved in deuterated solvent showed resonances due to the different H atoms of the monomer and polymer, and 1 H NMR was a very good method for determination of conversion. However,

Area of ESR spectrum

1/2

(Microwave power) Figure 10.2 Microwave power saturation plot of the area of the ESR spectrum versus the square root of the microwave power: (•) (experimental values; ( ) linear relationship assuming no saturation, S is the maximum power level that can be used without saturation occurring Fourier transform near-infrared spectroscopy, using the C = C H band at 6152 cm" 1 for methacrylates, enabled the conversion to be followed in a single sample throughout the polymerization to high conversion. Parallel experiments were performed for near-infrared spectroscopic determination of monomer concentrations and for ESR measurements of radical concentrations. A further advantage of the near-IR method is its applicability to insoluble crosslinked systems. A typical conversion curve for the polymerization of methyl methacrylate is shown in Figure 10.3. The three regions in the conversion curve correspond to (1) the pre-gel region, (2) the Norrish-Trommsdorff region between the gel point and the glass point, and (3) the glass region. The steep rise in the polymerization rate above the gel point is attributed to a marked decrease in the termination rate parameter, kv and the decrease in polymerization rate to near zero above the glass point is attributed to a decrease of several orders of magnitude in the apparent propagation rate parameter, kp. 10.3.1.4 Radical Concentration during Polymerization

Typical plots of radical concentration versus time during the polymerization of methyl methacrylate are shown in Figure 10.4. The lower limit of sensitivity of

% Conversion

glass point

gel point

Time / min

Figure 103 Typical conversion curve for polymerization of methyl methacrylate showing the gel and glass points and the (1) pre-gel, (2) Norrish-Trommsdorff, and (3) glass regions. Polymerization temperature 45 0C; [AIBN] = 0.1 M

current ESR spectrometers is « 1 0 " 7 M, which is not sufficient to enable measurement of the concentration of propagating radicals during the polymerization of most monomers below the gel point. An ESR spectrum of propagating radicals can be obtained below the gel point by quenching the polymerization system in liquid nitrogen and accumulating spectra at 77 K, which also utilizes the favourable Boltzmann distribution at this temperature. Radical concentrations obtained below the gel point by the quenching technique are also shown in Figure 10.4. In favourable circumstances, the radical concentration below the gel point may be obtained by accumulation of spectra in situ. However, the limited time available for accumulation and the changing nature of the spectrum with conversion militate against this procedure. Radical concentrations obtained above the gel point by the quenching and in situ methods (without accumulation) were in good agreement. Comparison of the monomer concentration (Figure 10.3) and the radical concentration (Figure 10.4) during the polymerization shows that, whereas the rate of conversion decreases very suddenly at the glass point, the radical concentration continues to increase, but at a steadily decreasing rate. At long polymerization times the radical concentration reaches a maximum and then decreases due to the depletion of initiator, indicating that termination reactions continue above the glass point, although more slowly.

[FT)/ mol dm3

Time/ min

Figure 10.4 The variation of the radical concentration [R#] with time during the polymerization of methyl methacrylate at 45 0C for different concentrations of AIBN initiator: (A) 0.2 M; (o) 0.1 Af; (•) 0.05 Af, spectra obtained in situ during polymerization in the ESR spectrometer. (•) 0.05 M AIBN, spectra obtained by quenching to 77 K, enabling accumulation of scans

103.1.5 Correction for Changing Sensitivity of the Spectrometer

The dielectric constant of the polymerizing system decreases during the polymerization owing to changes in the molecular mobility of the polar ester groups and the conjugation between C=C and C = O . This effect will be greatest in the Norrish-Trommsdorff region, between the gel and the glass point. The changes in the dielectric constant cause changes in (1) the frequency of resonance, and (2) the sensitivity, or Q value, of the spectrometer, i.e. in the area of the spectrum which would be obtained from a constant radical concentration. A procedure which can be used to measure the change in sensitivity of the spectrometer during polymerization is to record the spectrum of a reference unpaired spin species with an ESR spectrum which does not overlap the spectrum of the methacrylate propagating radical. We have found that the Mn 2+ species (conveniently found in MgO) provides a suitable spectrum [12]. The Mn 2+ (in MgO) was coated on the outside of the ESR tube as an external standard by

Time / min

Figure 10.5 Simultaneous measurement of the ESR spectra of Mn2+ and methacrylate propagating radicals during the polymerization of methyl methacrylate: Mn area, sensitivity of the spectrometer; Mn field, conversion: [R*], corrected concentration of MMA radicals

exposing the tube to the flame from burning magnesium metal. The variation in sensitivity is shown in Figure 10.5 as the area of one peak in the spectrum of Mn2 + . The increase in sensitivity occurs mainly in the Norrish-Trommsdorff region and corresponds to a factor of % 3 in the area. The measured area of the spectrum of the methacrylate propagating radical can then be corrected according to the change in area of the Mn2 + peak. An additional aspect of using Mn2 + to measure the changing sensitivity of the spectrometer during the polymerization of methyl methacrylate was found to be that the field position of the Mn 2+ peak also varied, and this variation could be correlated with the C = C conversion. The position of the propagating radical showed an identical variation in resonance frequency. Thus, the concentrations of both R* and C = C can be obtained throughout the polymerization from the ESR spectra. Typical data obtained for the polymerization of MMA at 600C with AIBN initiator are shown in Figure 10.5. 10.3.1.6 Kinetic Analysis

The mechanism of polymerization of methyl methacrylate initiated by AIBN involves the three kinetic steps:

Initiation I—>2Y Propagation P;+M^P; + 1 Termination

The instantaneous rate of polymerization and the net rate of formation of radicals are given by the following equations -d[M]/df = fcp[F][M] d[P]/dr = 2fc d /[I]-2fc f [P-] 2 where [M], [P'] and [I] are the concentrations of monomer, propagating radicals and initiator, respectively, / is the initiator efficiency and kd is the rate of decomposition of the initiator. The values of fcp and kt can be obtained directly from these equations using the experimentally determined values for [M] and [P - ], provided that / remains constant. We have shown that a suitable manipulation of the second equation enables the values of / and kt to be derived for incremental increases in conversion. Good agreement is obtained with current theories of free radical polymerization for the polymerization of methyl methacrylate at 60 0C [13].

10.3.1.7 Crosslinking Methacrylate Monomers

A major objective of the current research programme is to extend the treatment of polymerization kinetics based on direct measurements of monomer and radical concentrations to crosslinking systems. Conventional methods for measurement of monomer concentrations are not suitable, as they require soluble polymer. We have been able to apply our procedure for utilizing the near-infrared spectrum of the C = C bond in methyl methacrylate to systems containing ethylene glycol dimethacrylate (EGDMA) [14]. Figure 10.6 shows the variation of the concentration of C = C bonds during the polymerization of a MMA-EGDMA mixture containing 36% of EGDMA. The initial rate of polymerization is much higher than for MMA, and this can be attributed to the absence of a pre-gel region. However, the plateau region of the conversion is lower. This results from the crosslinking reaction, with the radicals and C = C bonds immobilized in the network.

% Conversion

Time / min

[R*]x10- 6 /moldnrr 3

Figure 10.6 Dependence of C = C concentration on polymerization time for (a) MMA and (b) a MMA-EGDMA mixture (36% EGDMA): polymerization temperature 600C; initiator 0.05 M AIBN

Time / min

Figure 10.7 Dependence of radical concentration [R#] on polymerization time for (a) MMA and (b) a MMA-EGDMA mixture (36% EGDMA): polymerization temperature 600C; initiator 0.05 M AIBN. Note that the concentration scales differ by a factor of 40 The radical concentration in MMA-EGDMA mixtures might be expected to be higher than in MMA owing to the retardation of the termination reaction by the network. In Figure 10.7 the absence of a pre-gel region is indicated by the increase in radical concentration from the beginning of the polymerization. The

most significant difference between the MMA-EGDMA mixture and MMA is the radical concentration in the plateau region. It is approximately 40 times greater in the mixture, and is almost millimolar. Kinetic analysis of the propagation and termination rate constants in the polymerization of MMA-EGDMA mixtures is more difficult than for MMA. An understanding of the polymerization depends on knowledge of the individual concentrations of C = C bonds that are (1) in monomer molecules and (2) attached to polymer molecules. This information may be obtainable for NMR spectra utilizing differences in the relaxation times of the two types of C=C environments. However, it is likely that the polymerization is heterogeneous with a non-spatially random distribution of crosslinks. 10.3.2 POLYMER DEGRADATION BY HIGH-ENERGY RADIATION The effects of high-energy radiation, principally y-rays and electron beams, on polymers have been studied extensively for many years. The main interest has been in the changes in material properties, such as strength and elongation. These changes in properties have been related to changes in molecular weight of the polymer molecules, either by main-chain scission or by chain crosslinking, frequently with the formation of an insoluble gel fraction. The applications of radiation effects on polymers have been two-fold: (1) the use of polymer materials in radiation environments, such as nuclear reactors, and more recently in space, (2) modification of the properties of polymer materials by reduction in molecular weight or crosslinking, especially in the microelectronics industry as electron beam resists, and perhaps in the future as X-ray resists. Fundamental understanding of the mechanism of degradation of polymers by high-energy radiation has been based mainly on structural changes observed in the polymers, and to a much smaller extent on measurements of small molecule products. ESR has been used since 1960 to observe radicals produced in irradiated polymers, and hence to provide evidence for intermediate species in the radiolysis. However, recent improvements in the stability and sensitivity of ESR spectrometers and in computer manipulation of the spectra have enhanced the use of this technique. The capabilities of the ESR technique for providing fundamental information about the mechanism of radiation degradation of polymers are shown in observations on gamma-irradiated poly(methyl methacrylate), polystyrene and their random copolymers. 10.3.2.1 Poly(methyl methacrylate)

The ESR spectrum of poly(methyl methacrylate) at 300K, shown in Figure 10.8(a), is well known. This characteristic 13 line (9 + 5) alternating spectrum

Figure 10.8 ESR spectra of poly(methyl methacrylate) after y-irradiation in vacuum: radiation dose 1 kGy; radiation temperature (a) 300 K, (b) 77 K

has been the subject of much debate, but it is now generally accepted to be due to the methacrylate propagating radical with two conformations. The ESR spectrum after irradiation at 77 K, shown in Figure 10.8(b), is quite different from the spectrum after irradiation at 300K. It is evidently due to a number of radicals; the propagating radical is not a significant component at this temperature, and must be formed by subsequent reactions of the radicals produced at 77 K.

Analysis of spectra A variety of techniques can be used to analyse for the component radicals in an ESR spectrum. They include: (1) dose saturation—spectra are obtained after irradiation to a series of radiation doses. The yield of trapped radicals does not increase linearly with dose above certain doses which are characteristic of particular radicals. In particular, radical ions show 'dose-saturation' at low doses;

(2) microwave power saturation—the observation of an ESR spectrum depends on the relaxation of the radicals (which are excited into the higher energy level by the microwave radiation) back to the lower energy level in accordance with the requirements of the Boltzmann distribution. Some radicals, and particularly radical ions, have a slow relaxation and hence they will not be observed at high microwave powers; (3) Photobleaching—radical ions can be distinguished from neutral radicals by irradiation with visible light above a critical wavelength, which is usually «500nm. The radical ions are bleached and disappear, whereas the neutral radicals are unaffected. The efficiency of this technique does depend on the interaction of the light with the radicals and hence requires a transparent or finely powdered sample; (4) Fourier transform masking—the ESR spectrum can be converted to its Fourier transform in the frequency domain. Lines in the original spectrum with different line-widths can be separated by masking of different parts of the spectrum and then conversion back into the original domain; (5) accumulation of spectra—the signal to noise ratio must be high to enable separation of different radicals in a spectrum, especially if some of the radicals are present in small proportion of the total spectrum. Accumulation of the spectra, possible with high stability of the magnetic field, enables the signal to noise ratio to be enhanced. The effect of spectral accumulation is illustrated in Figure 10.9 for poly(a-methylstyrene);

Figure 10.9 ESR spectrum of poly(a-methylstyrene) after y-irradiation in vacuum at 300 K (dose 6 kGy): (a) one scan of 200 s; (b) 150 scans

(6) thermal annealing—when a number of different types of radicals are trapped in a polymer during irradiation at a particular temperature, they will react in different ways at different temperatures on subsequent heating. The process of radical disappearance is known as thermal annealing, and can be used to distinguish different radicals present at a lower temperature. The greatest number of radicals will be produced by irradiation at the lowest possible temperature. Usually, liquid nitrogen is used to enable irradiation at 77 K for this reason, and the procedure is known as cryogenic trapping; (7) subtraction techniques—recording of ESR spectra by computer enables a variety of computational procedures to be used to identify and quantify the component radicals and their reactions. In particular, subtraction of spectra obtained after progressive stages of warming (thermal annealing after cryogenic trapping) will frequently show a triplet or other spectrum characteristic of a particular radical which has disappeared. The effectiveness of this procedure is enhanced if the sample is cooled back to the same reference temperature to record the spectrum after each warming step; (8) simulation—confirmation of the presence of different types of radicals and estimates of their proportions, and hence of their concentrations, can be obtained by simulation of the ESR spectrum. This procedure requires values for the parameters of the spectrum, Le. g value, number of lines, relative intensities of the lines, hyperfine splittings, line-widths, line shape (Gaussian or Lorentzian or a mixture). Simulated spectra can be computed for a wide variety of values for the different parameters, the simulated ESR spectrum being matched to the experimentally observed spectrum. We have utilized all of these techniques to analyse the ESR spectrum of poly(methyl methacrylate) at 77 K after y-irradiation. The progressive disappearance of different types of radicals, and the formation of the chain scission radical (which is the same radical as the propagating radical), eventually as the only species, during thermal annealing after cryogenic trapping, are shown in Figure 10.10. We have identified seven different radical species A-G, including the polymer radical anion G, in the ESR spectrum of poly(methyl methacrylate) at 77 K after y-irradiation in vacuum (the spectrum shown in Figure 10.8(b)), as follows: CH3

I

I

I

1

.

CH3

1 I

CH3- -CHO -COOCH3 - C H 2 - C -C—CH-C—CH2-CCOOCH^ I ' COOCH2 A B C D E F The progressive disappearance of these radicals, based on the spectra shown in Figure 10.10, is shown in Figure 10.11. The five regions shown in Figure 10.11 correspond to the disappearance of different radicals as follows: stage (1) A, B and

C; stage (2) C and D; stage (3) E; stage (4) propagating radical (F) is the only species present and is stable; (5) F. The mechanism of the degradation of poly(methyl methacrylate) by y-radiation can be deduced on the basis of the disappearance of radicals shown in Figure 10.11. This mechanism (Scheme 1) is consistent with the formation of molecular products, as previously reported.

^ C H

2

CH 3 I - C ^ C=O O

CH 3 O I Il - - C H 2 C - C H 2 - + - C - O — C H 3 + OTHERS #CH 3 -CHO

(LjJ3 CH 3 I -CH2C-CH2-

-CO-O-CH2

SCISSION

CH 3 CH 3 I I • -CH2-C+ CH2=C-CH2C=O O I CH 3

-CO-O-CH3

CO + CO 2 + CH 4 + CH 3 OH

Scheme 1 Mechanism of degradation of poly(methyl methacrylate) by y-radiation deduced from ESR studies of radical intermediates

10.3.2.2 Polystyrene The ESR spectrum of polystyrene after y-irradiation in vacuum at 77 K is shown in Figure 10.12(a). The spectrum is quite different from that of poly(methyl methacrylate). It can be assigned to three species: (1) the oc-carbon radical, (2) the cyclohexadienyl radical, and (3) a radical anion. The proportions of cyclo-

a-carbon

cyclohexadienyl

Figure 10.10 ESR spectra of poly(methyl methacrylate) after y-irradiation at 77 K and progressive wanning to 300 K. All spectra (except that at 77 K) were recorded on cooling back to 140K after 10 min at the specified temperature hexadienyl radicals and of radical anions are strongly dose-dependent, which provides a method for their assignment. The two neutral radicals are consistent with crosslinking being the major effect of radiation on polystyrene, in contrast to main-chain scission in poly(methyl methacrylate). The ESR spectrum after irradiation at 300K, shown in Figure 10.12(b), is similar to the spectrum at 77 K except that the centre line is reduced, owing to the absence of the radical anion, and the large outer peaks of the 'triplet' show greater resolution into subsidiary peaks. 10.3.2.3 Random Copolymers of Methyl Methacrylate and Styrene The effect of high-energy radiation on random copolymers of styrene and methyl methacrylate provides an excellent system for testing hypotheses for intra-

Btfrel

T / K

Figure 10.11 Decrease in radical concentration in poly(methyl methacrylate) after 1 kGy of y-irradiation at 77 K on progressive warming to 360K. The numbers refer to stages of radical reactions during wanning molecular and inter-molecular interactions of energy transfer and radical reactions. The ESR spectra of a series of copolymers of styrene and methyl methacrylate across the composition range between the two homopolymers are shown in Figure 10.13 after irradiation at 300K. The spectra show a progressive change between the spectra of the homopolymers, but it is apparent, e.g., considering the copolymers containing 20% and 50% of styrene, that the proportions of'styrene' radicals in the spectra are greater than the proportions in the compositions of the copolymers. Thus, there is a preference for the formation of styrene radicals. This effect has one component occurring during irradiation at 77 K (attributed to energy transfer) and another component occurring during warming to 300 K (or occurring during irradiation at 300K), which we have attributed to radical transfer reactions. This preference for the formation of styrene radicals is a manifestation of a protective effect by styrene units on the degradation of methacrylate units in the copolymer. The protective effect is also shown by the variation in the yield of radicals, G(R"), with the composition of the copolymer. Figure 10.14 shows how the value of G(R*) in the copolymers is always much less than the value which would be obtained from the additivity of the electron densities of the two monomer units. The protective effect is even greater at 300 K than at 77 K, which is consistent with the additional mechanism of protection which occurs above 77 K. 10.3.2.4 ESR and the Mechanism of Radiolysis

The number of different types of radicals observed in the ESR spectra of irradiated polymers is always greater after irradiation at 77 K than at 300 K. The

Figure 10.12 ESR spectra of polystyrene after y-irradiation in vacuum. Radiation dose 10OkGy; radiation temperature: (a) 77 K, (b) 300K

Scheme 2 ESR procedure of cryogenic trapping and thermal annealing to provide an understanding of reactions which occur rapidly during the irradiation of polymers at

0%STY

8% STY

20% STY

50% STY

100% STY

Figure 10.13 ESR spectra of random copolymers of styrene and methyl methacrylate after y-irradiation in vacuum at 300K. Radiation dose 3kGy. The compositions of the copolymers are specified in mol% styrene

G(R) G(R-)

% STYRENE

Figure 10.14 Protective effect against degradation by y-radiation provided by styrene units in random copolymers of styrene and methyl methacrylate, shown by the radical yields G(R#) derived from the ESR spectra, (a) Experimental values for y-irradiation at 77 K; (b) experimental values for y-irradiation at 300 K. The lines correspond to the G(R*) values for the copolymers calculated from the G(R') values for poly(methyl methacrylate) and polystyrene based on the additivity of electron densities

ESR spectra are usually similar after irradiation at 300K or irradiation at 77 K and warming to 300 K, although the concentrations of radicals may be different. A model for the mechanism of the radiolysis can then be deduced from the radicals which are observed at 77 K and the reactions which they undergo on warming. The procedure is outlined in Scheme 2.

10.4 CONCLUSIONS ESR provides a powerful technique for developing a fundamental understanding of the mechanism and kinetics of free radical polymerization and of the mechanism of degradation of polymers by high-energy radiation. The assignment of ESR spectra to component radicals and the measurement of the concentrations of these radicals require a variety of experimental and computational procedures, which have been greatly enhanced by improvements in spectrometer performance and computer capabilities.

10.5 ACKNOWLEDGEMENTS The authors are grateful to the Australian Research Council and the Australian Institute of Nuclear Science and Engineering for supporting this research, and to the Australian Nuclear Science and Technology Organization for the provision of irradiation facilities.

10.6 REFERENCES [1] P.B. Ayscough, Electron Spin Resonance in Chemistry, Methuen, London, 1967. [2] D.J.T. Hill, J.H. O'Donnell and PJ. Pomery, in Electron Spin Resonance, Royal Society of Chemistry Specialist Periodical Reports, Vol. i3A, Cambridge, 1992, p. 202. [3] O.F. Olaj, I. Bitai and F. Hinkelman, Makromol. Chem., 1987,188,1689. [4] T.P. Davis, K.F. O'Driscoll, M.C. Piton and M.A. Winnik, Macromolecules, 1989, 22, 2785. [5] S.K. Soh and D.C. Sundberg, J. Polym. ScL, Polym. Chem. Ed., 1982,20,1345. [6] MJ. Ballard, R.G. Gilbert, D.H. Napper, PJ. Pomery, P.W. O'Sullivan and J.H. O'Donnell, Macromolecules, 1986,19,1303. [7] G.T. Russell, D.H. Napper and R.G. Gilbert, Macromolecules, 1988, 21, 2141. [8] R.W. Garrett, DJ.T. Hill, J.H. O'Donnell, PJ. Pomery and CL. Winzor, Polym. Bull, 1989,22,611. [9] M. Dole (Ed.), The Radiation Chemistry of Macromolecules, Academic Press, New York, 1972. [10] R.W. Garrett, DJ.T. Hill, TT. Le, J.H. O'Donnell and PJ. Pomery, Radiat. Phys. Chem., 1992,39,215.

[11] DJ.T. Hill, S.Y. Ho, J.H. O'Donnell and PJ. Pomery, Radiat. Phys. Chem., 1990,36, 467. [12] T.G. Carswell, DJ.T. Hill, D.S. Hunter, PJ. Pomery, J.H. O'Donnell and CL. Winzor, Eur. Polym. J., 1990, 26, 541. [13] T.G. Carswell, DJ.T. Hill, D.I. Londero, J.H. O'Donnell, PJ. Pomery and CL. Winzor, Polymer, 1992,33,137. [14] T.G. Carswell, DJ.T. Hill, R. Kellman, D.I. Londero, J.H. O'Donnell, PJ. Pomery and CL. Winzor, Makromol. Chem., Macromol. Symp., 1991,51,183.

11 DYNAMICS OF BULK POLYMERS AND POLYMERIZING SYSTEMS AS STUDIED USING DIELECTRIC RELAXATION SPECTROSCOPY G. WILLIAMS, C. DUCH, J. FOURNIER and J. R. HAYDEN Department of Chemistry, University College of Swansea, Singleton Park, Swansea SA2 SPP, UK

11.1 INTRODUCTION

Dielectric relaxation spectroscopy (DRS), with its wide frequency range 10~6 to 1011 Hz, has been used for over fifty years as a leading method for studying the reorientational motions of molecules in the liquid, amorphous solid, crystalline and liquid-crystalline states [1-6]. Most of these studies involved point-by-point measurements of permittivity ef(co) and loss factor e"(a>) at chosen frequencies using different apparatus for each frequency range, e.g. transient current recorders, LCR impedance meters, microwave transmission lines and cavity resonators. Such difficult and tedious procedures hindered the progress of DRS in comparison with that made by other methods such as NMR, ESR, dynamic quasi-elastic light scattering in the time and frequency domains, quasielastic neutron scattering and time-resolved fluorescence depolarization (for accounts of such techniques applied to polymer science see ref. [7]). However, during the past eight years or so modern DRS equipment has appeared in the form of automatic-measuring LCR meters, transient equipment and time-domain reflectometry for microwave frequencies, which together with computer control and modern data-processing methods now provide techniques for the fast, accurate determination of permittivity and loss over the range 10 " 6 1010Hz. In addition to allowing conventional DRS studies of polymers to be made more conveniently, the new techniques allow studies to be undertaken that Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

were not practical hitherto, e.g. (i) for reasons of experimental time and (ii) for systems that change with time where manual point-by-point measurements are inappropriate. As a result, broad-band DRS now provides a powerful method for studying new problems in polymer science and takes its place alongside the other methods for studying polymer dynamics mentioned above [3, 8-10]. The present account summarizes briefly selected aspects of earlier DRS studies of polymers and of recent development, especially those concerning short- and long-range motions of chains and systems undergoing polymerization.

11.2 AMORPHOUS POLYMERS: PHENOMENOLOGICAL AND MOLECULAR ASPECTS The phenomenological theory of the dielectric relaxation behaviour of linear systems is well-established [1-5]. The fundamental relationship joining the frequency-dependent complex permittivity e(a>) measured at frequency / = o)/2n and the transient step-response function <j>(t) is the Fourier transform relationship

where e((o) = e'(co) — ie"{a>), e0 and S00 are the limiting low and high frequency permittivities and 3 indicates a one-sided Fourier transform; i = -y/—1. Thus measurements of e(a)) give information on (t) and vice versa through the inversion relationships [11] that follow from Equation (1). For a polymer material exhibiting multiple relaxation regions, multiple peaks will be observed in e"((o) and corresponding multiple decays will occur for (f>(t). For amorphous solid polymers, multiple relaxations have been observed and analysed in great detail [3, 12-17]. For T< Tr where Tg is the apparent glass transition temperature, a single broad /? process is observed. For T>Tg the OL process emerges from low frequencies, so that in a limited range both a and /? relaxations are observed in plots of e" vs. log/. As temperature is further increased, the a and fi processes tend to coalesce to form at high temperatures a single <xfi process, which is a continuation of the a process to higher frequencies, only now all of the relaxation strength is contained within the single process. This is the pattern of behaviour exhibited by all amorphous polymers, including the acrylates, methacrylates, halogen polymers, oxide polymers and polyesters, as we have described and discussed [12-17], including the effects of temperature and applied pressure [18-20]. Such behaviour is well-represented by the relaxation function [16-17]

№ = a(t)LAa + Afi0(tn where Aa + Afi=l

(2)

and <j>a(t) and <^(f) are normalized decay functions for the

a and /J processes respectively. For T< Tg, a(t) is approximately constant in the time-scale of interest, so only a part, A0Ae9 of the total relaxation strength Ae is relaxed through the /? process. For T ^ Tg, two relaxation regions occur of relative strengths Aa:Afi. At still higher temperature a(t) begins to decay faster than p(t\ and is this continues to the range where a(t) decays much faster than (f)p(t) the a and P process coalesce so that all the relaxation strength Aa is relaxed through a(t), which corresponds to the a/? process. In the range where a and P coexist and are observed as two processes in the time or frequency domains, this phenomenological description requires that the conservation rule [ 12,13,15-17] holds A£ = A£a + Ae,

(3)

Thus, if an increase in pressure decreases the strength of the P process, then there will be a consequent increase in the strength of the a process in order to conserve AE, as we and others have observed [12,17, 20]. A further feature of dielectric relaxations in amorphous polymers is that the a (or a/?) relaxations are well-described by the 'stretched-exponentiaF or 'Kohlrausch-Williams-Watts' function [21-23] 0(t) = e x p [ - ( t / t o n

(4)

0 < / ? ^ 1 and T0 = T0(T5P) is the effective correlation time. For the dielectric a-relaxation in such polymers as poly(vinyl acetate), poly(methyl acrylate), polypropylene oxide and polyethylene terephthalate the loss curves are wellfitted by the KWW function, with p values being in the range 0.4-0.6. The calculated curves for the KWW function with different values of P have been described [21-23] and tables of ef and e" values are available [24]. The a process observed in the time or frequency domains for amorphous polymers using dynamic-mechanical, NMR, ESR, light-scattering and fluorescence depolarization methods is also well-fitted using the KWW function with similar /lvalues. In addition, glass formation is small molecule liquids (molecular and ionic) gives relaxation phenomena that are entirely similar to those found for amorphous polymer [6, 25]. This observation, that the KWW function is ubiquitous in relaxation phenomena in all glass-forming materials, has been a focus of attention in condensed matter physics and chemical physics in recent years, and many models have been proposed to rationalize behaviour [6,12,25, 26]. Notable among recent developments are those due to Ngai [27] and by Goetze [28,29] and Mazenko [30]. In the works of Ngai [27,31-33], the starting point for applications of theory to diverse relaxation phenomena is the first time-derivative of the KWW equation (4) in which T0 is given, through a second relationship, a dependence on a primitive relaxation time and the P parameter. In the works of Goetze and Mazenko, a 'mode-mode coupling theory' is proposed which is formally equivalent to Mori-Zwanzig continued fraction representation of a relaxation function in which the frequency-dependent relaxation function

<j>((o) is related to a higher-order memory function K(a>), thus closing the problem and allowing both (co) and K((o) to be determined. The results of^such a theory depend entirely on the assumed form of interrelationship between K(o) and (co). One difficulty with these approaches is that they do not specify the particular molecular property whose relaxation behaviour is being considered. Thus (t) is simply a relaxation function from any of the relaxation experiments. However, the molecular origins of such relaxation phenomena have been well-established for dielectric, NMR, quasi-elastic light and neutron scattering experiments and for fluorescence depolarization through the time-correlation function representation for molecular reorientations and translations and theories (linear-response theory, field-perturbation theories) that connect the observable (a vectorial or tensorial quantity) to such time-correlation functions. For the special case of dielectric relaxation of an amorphous material composed of dipolar polymer molecules, linear-response theory gives the following result [34-36] for e(co)

r^^T^J^l-icoSWr)]

(5)

L £ o-£oo J where p(co) is an internal field factor, and O(f) is a time-correlation function for the fluctuations in the macroscopic dipole moment M(t) of a spherical volume V in the dielectric. <M(0)-M(t)> 11 (6) ^M(O)-M(O)) For flexible polymer chains having no persistent dipole moment along the chain contour, we may show that [34-36, 8]

XZM(QY »j(t)>

^'

1,-ZM(O) /*,-(0)>

l

7

'

where /x,(0 is the dipole moment of group i along the chain at time t. The terms (/X1(O)^(O)) express the equilibrium angular correlations between dipoles i and j along a chain, and the magnitude of such terms decreases rapidly in magnitude for \i—j\ increasing [12, 34]. The terms are autocorrelation functions for the motions of dipole i, and are cross-correlation terms between dipoles i and j . For a bulk polymer or for a polymer in solution, it is normally assumed that the contributions to O(f) are dominated by intra-chain terms and that inter-molecular contributions are negligible. We may rewrite Equation (7) for the case of chains containing equivalent dipole groups as

W-W+frW

(8)

where atJ = / and , „, . , M Xii{t)= Xi t)=

<»?> ' + WO)-^m

, Qa w (9a b)

'

Equations (8) and (9) give a clear physical insight into the molecular quantities that determine the dielectric properties of flexible chains in solution and in the bulk amorphous state. The autocorrelation functions XH(t) are equal for all i and dominate (t). The cross-correlation terms make a contribution weighted by the equilibrium factors a^ that are determined by average chain conformation. It has been reasoned [34, 37] that X{j(t)« A11-(O for amorphous polymers, so in this approximation ] 2 /;

A, = { - [<(iI>]2}/

(IQa, b)

Thus the mean moment that is not relaxed by local motions (p process) is relaxed by the a process, which is an alternative statement of the conservation rule. Quite recently, Smith and Boyd [40] used a theory to describe the p process (in vinyl acetate copolymers) that is formally equivalent to that described above. The single dipole theory that leads to Equation (10) has been extended by Williams [12] to include cross-correlation terms in the general expression for O(t) in Equation (8). Thus, the experimental facts regarding multiple dielectric relaxation processes in amorphous polymers are well-established, and phenomenological theory is able to rationalize their occurrence and their dependence upon temperature and applied pressure. The actual forms of a(t) and <j>fl) still await adequate descriptions using molecular theory, and this is a continuing challenge not only for the DRS of polymers but also for related relaxation and scattering phenomena in such systems. It may transpire that analytical models will not be successful, and that progress in understanding will come from simulations using molecular dynamics or Monte Carlo methods. In an attempt to deduce the form of dielectric a and P relaxations in amorphous polymers, Rosato and Williams [41] evaluated a multi-site barrier model which developed the early models of Bueche to the dynamical situation. Their theory gave (i) a cluster of 'fast' modes for the P process and (ii) a single mode at low frequencies for the a process. Although two relaxation regions are predicted, the low frequency process is not in accord with the experimental result, which gives a broad asymmetrical process of KWW type with j8«0.5. Jernigan [42] considered the model of conformational tran-

sitions for a flexible polymer chain involving a master equation in time of the form ^=TpW

(11)

where p(f) is a generalized probability of obtaining the different conformations at time t(f(t) is a vector of elementary probabilities) and T is a transition matrix that expresses the transition probabilities between conformational states. T involves the local energy barriers and energy differences between conformational states. The dielectric properties were calculated as , where P(t) is the dipole moment of a whole chain at time t. Jernigan deduced the dielectric properties of oc,co dibromide chains and found that was given by a weighted sum of exponential decay terms plus a constant value. The latter quantity has a value that is dependent on the choice of reference coordinates, and this is a basic problem with this theory. Jernigan [42] multiplied by a correlation function ov(t) for motions of the chosen reference coordinates, thus giving a decay to zero for the total correlation function, but this is artificial. Beevers and Williams [43] showed how changed when the reference coordinates were changed, demonstrating the inadequacy of this approach. The origin of the problem is clear: Equation (11) is a scalar equation but measured properties such as dielectric permittivity, Kerr constant, nuclear magnetization and fluorescence emission are related to time-correlation functions for the motions of molecular axes—which are vectorial or tensorial quantities. Although the Jernigan approach is inapplicable to the motions of chains in the bulk amorphous state or in solution, it would be applicable where the reference coordinates are well-defined, e.g. for a chain tethered to a surface.

11.3 CRYSTALLINEPOLYMERS Numerous account of the dielectric properties of partially crystalline polymers are available [3,12,14,17,44,45]. Two classes of partially crystalline polymers are important, those of high crystallinity, such as polyethylene, i-polypropylene and polyoxymethylene, and those having only a medium degree of crystallinity, such as the nylons and polyethylene terephthalate (up to « 50% crystallinity). Multiple relaxations are observed, e.g. lightly oxidized and lightly chlorinated polyethylenes have, in descending order of temperature, ac, /?a and yc relaxations. These have been documented by Ashcraft and Boyd [46] and others [3,4,5]. The <xc process in polyethylenes was first explained by Frohlich [47] using a chaintwist-assisted rotational model in an alkane crystal. Subsequently Hoffman et al. [44] and Williams et al. [48] extended the theoretical model and applied it successfully to polyethylenes and alkanes of different chain lengths. Further development of the chain-twist-assisted rotation and model was made by Mans-

field and Boyd [49], who carried out a computer simulation for a realistic model of a chain moving in the crystal. In all cases it is predicted that the average relaxation time for the ac process increases linearly with chain length for short chains, and that a plateau level is reached for long chains when chaintwisting becomes an essential part of the chain rotation mechanism. The /?a absorption in polyethylenes is generally accepted as being due to large-scale motions in the disordered phase [44,45,46], while the yc process is thought to be due to local motions in the amorphous phase [46] or to local motions in both amorphous and crystalline phases [44]. While many dielectric studies have been made of oxidized and chlorinated polyethylenes, we note that pure polyethylene would not give any dipole relaxation owing the low polarity of the methylene group. For polymers of medium degree of crystallinity, again motions in both amorphous and crystalline phases are observed [3,12,14,17, 23]. Polyethylene terephthalate (PET) is an interesting case, as samples can be obtained in the amorphous state by quenching from the melt or in the partially crystalline state by melt crystallization or quench annealing. Since partially crystalline samples are entirely composed of spherulites, it follows that the amorphous regions (up to 50% of polymer) are contained within the spherulites. Thus this is an 'abnormal amorphous phase', whose relaxation behaviour would be expected to be qualitatively different from that for a wholly amorphous polymer. This has been demonstrated to be the case from the dielectric measurements of Ishida (see [3,45] and subsequently of Tidy and Williams (see data reported in [12]). The amorphous PET exhibits a well-defined a dielectric relaxation, but the partially crystalline sample exhibits a broad a' relaxation whose frequency location is removed to lower frequencies when compared with that for the oc relaxation. Tidy and Williams followed the evolution of the a and a' relaxations in time as an amorphous material was annealed, leading to crystallization, above its T%. As the normal a process disappeared the a' process emerged, and grew as crystallization proceeded. This demonstrates that the 'amorphous' regions within the spherulites suffer a range of constraints imposed by the crystalline regions, giving a slower, broader a process than that for a normal amorphous phase. Thus real time dielectric studies are able to give information on the dynamics of the amorphous regions within spherulites that cannot be readily obtained through NMR and dynamic mechanical relaxation studies. For accounts of DRS studies of other crystalline polymers, including polyoxymethylene, polyvinylidene difluoride, polyvinyl fluoride and the nylons, the reader is referred to the text by McCrum et al. [3], the reviews [12-14,17,23,44, 45] and references therein. In all cases multiple dielectric relaxations are observed, arising from motions within crystals, on crystal surfaces and in the constrained amorphous regions within crystals. These processes are also observed in NMR and mechanical relaxation studies of such polymers.

11.4 LIQUID CRYSTALLINE (LC) POLYMERS Liquid-crystal-forming (mesogenic) groups may be incorporated into main chain, side chain or main chain and side chain, giving MCLC, SCLC and MCSCLC polymers respectively [50]. MCLC polymers show promise as high modulus, high melting thermoplastics, whereas SCLC polymers show promise as electroactive and electrooptical materials for optical data storage and non-linear optics [51]. For MCLC polymer the long stiff chains have only slight reorientational freedom in the LC or 'glassy' LC states, as has been shown from DRS studies [52,53]. Araki et al. [53] studied the following MCLC polymer where m is 2 or 3. For m = 3 a well-defined dielectric a process was observed having an apparent activation energy of 290 kJ mol ~ *. This material could not be aligned in directing electric fields [53].

Dielectric studies of SCLC polymers are more numerous (see [14], [54-60] and references therein). The dielectric behaviour of unaligned SCLC polymers gives little information on the underlying motions since the observed loss curves correspond to a superposition of several components. Alignment may be achieved using directing electric (E) or magnetic (B) fields or by surface forces.The alignment process in directing E fields is a dielectric phenomenon [58] and depends on the dielectric anisotropy Ae{a)) at the frequency / = a>/2n at which the E field is applied. Homeotropic (n\\Z) and planar ( n i Z ) alignments may be obtained by choice of the frequency of the directing E field. Here n is the LC director axis and Z is the laboratory axis defined as the normal to the parallel plates that confine the LC material. The two-frequency-addressing principle that leads to homeotropic (H) and planar (P) alignments for LC polymers has been reviewed [58]. Studies have been made of LCSC polymers of the following generic structures

where m denotes a spacer group; m typically lies in the range 2 < m < 12. R1 is H (for acrylates) or CH 3 (for methacrylates) and R2 is typically an alkylcyanobiphenyl group or an aromatic ester group, as follows

For such materials, which may be smectic or nematic liquid crystals, the dielectric properties of the LC phase are anisotropic. For a uniaxial LC phase, the dielectric tensor is diagonal such that

e((o) = diag [E1(O)), E1(G)), E1(O))]

where, for a material for which Ae(co) is positive at low frequencies, we find that S11(O)) and E1(O)) are measured for H-aligned and P-aligned samples respectively [58]. The permittivity E'(CO) and loss factor E"(O)) change markedly when a SCLC polymer is aligned in directing E fields or B fields [54-60]. As one example, Figure 11.1 shows plots of our recent results [61] for a carbon chain polymer having m = 2 and an alkyl cyanobiphenyl mesogenic head group in the side chain. The plot shows dielectric loss G/co = E"C0, where G is the equivalent parallel conductance of the sample and C 0 is its geometrical electrode capacitance, as a function of log(//Hz) and temperature for an unaligned sample (Figure 1 l.l(a)) and for the same sample that was aligned homeotropically using a low frequency E field (30Hz, 50 V across a 70 urn thick sample) (Figure ll.l(b)). For the unaligned sample one broad loss peak is observed, which moves rapidly to higher freqencies with increasing temperature. Only a slight change in property is observed when the material transforms from the LC state to the isotropic liquid at 89 0 C. Figure 1 l.l(b) shows data for the H-aligned sample. The loss peak in the LC state is nearly twice the height of that for the unaligned sample and much narrower, being only slightly broader than that for a single relaxation time process. As the clearing temperature Tc = 89 0 C is approached in the LC state there is a marked fall in the peak height to the level of that for the isotropic liquid. A part of the fall is due to the decrease in local order parameter S(T) as Tc is approached, and the remainder is due to the onset of the biphasic region, which in this case is restricted to « 2 0 C. These data serve to illustrate the anisotropic nature of molecular motions in LCSC and show (compare Figures 11. l(a) and (b)) that it is necessary to align samples macroscopically in order to reveal this property. DRS provides a particularly useful means of monitoring the nature and extent of macroscopic alignment in SCLC samples that have been subjected to E fields, B fields, surface forces or are aligning/disaligning after electrical and/or thermal treatments. As we have shown [56], the complex permittivity of a uniaxial sample of intermediate alignment is given, to a good approximation, by the linearaddition relationship E{O)) = (1 4- 2S d ) £|) M/3 + 2(1 - S6)E1(O))P

(12)

Here, S6 is a macroscopic director order parameter Sd = O c O S 2 ^ 2 - l > / 2

(13)

where 6nZ is the angle between a local director n and the laboratory Z axis (Z is

(GZo))ZpF

UNSUBTRACTED DATA FOR UNALIGNED LCP95

(GZ(O)/pF

UNSUBTRACTED DATA FOR HOMEOTROPIC LCP95

Figure 11.1 Plots of G/co = e"C0 as a function of log frequency/Hz and temperature for (a) unaligned and (b) homeotropically aligned SCLC polymer. Note the marked change in loss on melting the H-aligned material (Tc« 89 0C) and the lack of change on melting the unaligned material [61]

normal to the plane of the parallel electrodes, as described above). Thus Sd = 1,0, - 0 . 5 for H-aligned, unaligned and planarly aligned samples respectively. Application of Equation (12) using both its real part e'(ca) and/or its imaginary part s"(co) allows Sd to be determined for a sample of intermediate alignment if e\(co), s'^G)), e'±((o)9 and e'[(a>) are known. Two crossover frequencies occur at /', say, when s[((o) = ei(co), and at /", say when ej[(co) = el(cw). (Insertion of these conditions in Equation (12) show that e'((o) is independent of Sd for s'^co) = e'L(a>) and s"(co) is independent of Sd for ej,'(co) = £^(co)). The accuracy o the method for determining Sd can be checked via the consistency of Sd values determined at different frequencies through the spectral range, and this has been shown to be very successful in practice for siloxane polymers [54, 56, 57, 62]. Thus DRS provides a direct unambiguous means of determining the extent of macroscopic order, through Sd, in SCLC samples. We note that optical microscopy and infrared and Raman spectroscopy may not be used easily to monitor alignment in SCLC samples owing to the scattering of light by LC materials, but NMR provides a further method. Furthermore, DRS may be used to monitor the kinetics of alignment of SCLC polymers, as we have described [62, 63]. In our studies of a chiral nematic LC polymer, the changes of loss spectra with time as a sample realigned from P to H alignment in the presence of a steady d.c. E field were monitored, and were fitted using a continuum theory first described by Martins et al. [64] and further developed by Esnault et al. [65]. An important consequence of this theory is that it predicts that Sd reaches a plateau determined by the balance between dielectric forces (involving Ae £ 2 ) and elastic forces (involving elastic constants of the LC phase). It has been shown [58] that the ease of alignment in SCLC polymers is strongly dependent on chemical structure and the thermal/electrical treatments given to samples. In most cases it is difficult to align SCLC polymers in the LC state using directing E fields [56-58,66], so cooling from the melt with an a.c. E field of chosen frequency and amplitude may provide an alternative route— although dielectric breakdown is then a problem because E fields of 100 V/50 ^m are required, typically, in order to achieve full H of P alignment. An 'electrical cleaning' method may be used to reduce the extrinsic conduction of melt samples and hence to allow the sample to sustain higher aligning E fields in the melt before breakdown occurs (see [58] and references therein for a review). In addition to providing a method for determining the alignment of SCLC samples, DRS data also give information on the anisotropic reorientational dynamics of the dipolar mesogenic groups in a LC polymer. As we have shown [57,67], the generalization of the earlier theories [68,69] of dielectric relaxation of low molar mass liquid crystals can be achieved in the following way. The field-free orientation distribution function /°(Q 0 ) a f l d the field-perturbed orientation distribution function fE(Cl0) of mesogenic groups may be written as

expansions involving the Wigner rotation matrix elements DQ 0 as follows QO / 9 J

- L i X

-

AQ 0 ) = A Z - J V pJooDoo("o) j=0\

™

(14)

/

AOo) = *(l+^+-)AQo)

(15)

where A and B are normalization constants, D 0 0 are order parameters and D 00 (Q 0 ) describes the orientations of mesogenic dipolar groups (each of dipole moment fi) in Euler space with respect to the laboratory frame. When the dipolar units reorientate in the LC potential, the conditional probability of finding the dipole group in the orientation around Q at time t given that it was around the orientation Q0 at t = O is given formally by the further expansion

f(0,t/Qo,0) = S I Z DUO 0 )DL(O)GLW

<16)

J mn

where the G^n(O are time-correlation functions of the motion of the group, and are defined by the relationship <„(')=[

f/(Q,t/Q 0 ,0)D^ n (Q 0 )DU")dQ o dQ

(17)

The dipole moment in the laboratory frame (X, Y, Z) following the step withdrawal of the measuring electric field is then determined from the relationship [57]

W W ) = f f /E(Qo)/(ar/Qo,0)^P)dQodQ

(18)

JnoJn where P = O, ± 1 and relates to the laboratory axes. Insertion of Equations (14)—(16) into Equation (18) and using standard relations for integrals of triple products of the rotation matrix elements leads to expressions for (fifab(t)} and <ji£b(f) > ( = <^£b(f) >) in terms of weighted sums of Clebsch-Gordan coefficients. Relating these quantities to dipole polarization and hence to permittivities sfah(t) and s^h(t), then Fourier transformation into the frequency domain, gives the important result that [57] e,(co) = S0011 + ^ [ ( 1 + 2S)tiF{(co) + (1 - S)Ai12FJ(CO)] « » = Sooi + 3^r [(I + S)^1(W)

+ (1 + SWrfF^o)-]

(19a) (19b)

where G is a constant involving internal field factors, S0011 and S001 are limiting high frequency permittivities, S is the local order parameter in the LC and /z, and /*t are

the longitudinal and transverse components of the dipole moment of the mesogenic group. The different F)(O)) are given by F)(Co)- 1 — io>3[£j(r)] where 3 indicates a one-sided Fourier transform and the Cj(O are (real) time-correlation functions which correspond to certain linear combinations of the different O^in(0 as follows

^W = Oj0W; CJ(O = Oj1(O + 0^ 1 (O CiW = OL10W + *io(0 CiW = ol. x _ , w + ol. xx(t) + 0 ^ 1 W + Oi1W

(20a-d)

Thus, four active dielectric relaxation 'modes' are predicted, corresponding to the reorientational motions of /i( = (/^,/if)) with respect to the reference frame defined by the LC potential, giving two modes for e^o) and two for E1(O)). The strengths of these modes are governed by \i{j\iK and the magnitude of the local order parameter S (and hence depend on sample temperature). When a SCLC polymer is aligned macroscopically, then e^co) and e±(o)) are unchanged, as these are quantities that relate to local regions in the LC material and are defined in terms of molecular properties (see Equation (19)). However, the macroscopic dielectric properties change with macroscopic alignment as Sd is changed, as we have discussed above in connection with Equation (12) and Figure 11.1. For H alignment (Sd = 1), E,,(CO) is measured, and is usually dominated by F^1(O)), which is the S process (or W mode), and this is the case in Figure 11.1. The correlation function for this process is given by OJ0(O = 0(O)> =

(21)

where O is the polar angle between the molecular z axis and the laboratory Z axis. In many cases samples initially in an unaligned state may be aligned homeotropically but not planarly, owing to experimental difficulties of two kinds: (i) that the frequency required to prepare P alignment is too high for practical generators in the temperature range where P alignment is possible, and (ii) that Ae is too small to allow realignment to the P state to occur in practical time-scales for applied fields below breakdown levels. In these cases, if data for unaligned (U) and H-aligned samples have been obtained, then ^1(a>) may be calculated as follows. For the unaligned sample Sd = O, so Equation (12) gives £uM

= [IS1(Oi) + 2 e » ] / 3

(22)

£xM = [3%M-e (l (a>)]/2

(23)

thus Thus, the permittivity and loss spectra for P-aligned material may be calculated from the permittivity and loss spectra of U- and H-aligned material. We note that the above treatments consider only the anisotropic dielectric properties arising from the anisotropic motions of dipolar mesogenic groups in

the LC phase. However, it has been emphasized by Haase that isotropic motions, e.g. of a dipole unit in the main chain removed from the dipolar mesogenic head group will give an additional term in each of Equations (19) which is independent of S, the local order parameter. This is important for acrylate and methacrylate polymers with mildy polar mesogenic groups but of lesser importance for siloxane polymers with strongly polar mesogenic groups of the kind we have investigated [54-58].

11.5 REAL-TIMESTUDIESOFCHEMICAL AND PHYSICAL CHANGES The speed of operation of modern measuring equipment now allows measurements of e(co) to be made in real time as a system undergoes chemical or physical transformations such as polymerization or crystallization, respectively. This capability greatly extends the applications of DRS in polymer science and poses new challenges for theoretical interpretations of the observed dielectric phenomena, as we shall mention below. One subject presently receiving much attention is that of the bulk step polymerization of epoxides with amines. Dielectric spectroscopy of such systems has been studied for many years, notably by Lane and Seferis [70], and has been reviewed by Senturia and Sheppard [71,72]. In a series of recent papers, Mangion and Johari [73-78] have given extensive data for permittivity e'(co,t,TK) and loss factor e"(a),t, TR) for the diglycidyl ether of bisphenol-A (DGEBA) reacting with diaminodiphenylmethane (DDM) and/or diaminodiphenylsulphone (DDS) as a function of reaction time t for fixed measuring frequencies ( / = l/27ico) and fixed reaction temperatures TR. Samples of different compositions of DGEBA/DDM and DGEBA/DDS and DGEBA/DDM/DDS were investigated in real time; also, post-cured materials were studied over a wide range of temperature, including the glassy state at low temperatures, in order to detect changes in sub-Tg processes resulting from cure and post-cure. It was found that, as a reacting mixture transformed from a liquid to a (thermoset) glass, e'((o, t> TK) showed dispersion and s"((o, f, TR) showed an absorption peak. Thus, the DRS method detects 'vitrification' of the thermosetting material, but this is a relaxation phenomenon whose interpretation relates to the measuring frequencies used. As one example of the dielctric behaviour of a thermosetting system Figure 11.2 shows real-time e\ a" data obtained recently by us [79] for a 1:2 molar mixture of DGEBA with an alicyclic diamine diaminodicyclohexylmethane (DDCM)

In Figure 11.2(a), s'(co,t, TR) is plotted against time for different measuring

(a) Variation of e' as a function of time for the thermoset (DGEBA/DDCM) at Tcure= 60 0C

e1

note: the frequency step between the curves is 0.4 in Iog(f/Hz)

Log(F)=5

Log(F)=3

time / s (b) Variation of e" as a function of time for the thermoset (DGEBA/DDCM) at 1=60 0C

e"

Log(f)=5

Log(f)=3

time / s

Figure 11.2 Plots of e' and e" against reaction time at different measuring frequencies for a 1:2 molar mixture of DGEBA with DDCM at 60 0C [79] frequencies, and dielectric dispersion is seen to occur and move to longer times as the frequency is lowered. Figure 11.2(b) shows the complementary data for fi"(co, U 7R)> and a well-defined loss peak is seen to occur that moves to longer times as / is lowered. Such data were obtained by continual measurements of e\e" at chosen frequencies and recording the time of each measurement. Post-processing

of these data allows values of s\ e" to be calculated for chosen times, thus enabling plots of e\e" to be made as a function of frequency, as shown Figure 11.3, where dispersion and absorption are now seen in a familiar representation. An instructive representation of these data is provided by the 3D plots of permittivity and loss as a function of both log / and t, as shown in Figure 11.4. These data show that an a process, far broader than the 'normal' a process described above for conventional amorphous polymers, is observed, which moves rapidly to lower frequencies as reaction time increases. Evidently, when the frequency of maximum loss e'n occurs below, say, 10" 2 Hz, we would regard the material to be a glass operationally; extrapolation of such dielectric data to lower frequencies thus provides a method of dielectrically monitoring the 'effective cure-time' of a given reaction mixture, and this is useful for practical thermosetting systems. Mangion and Johari [73-78] have made quantitative analyses of their data. For example, they found that plots of logr cure vs 1/TR for a fixed measuring frequency were linear. Here, fcure is defined as the time at which s" = e^ for the given measurement frequency and given reaction temperature. They derived an apparent activation energy which was 47 kJ mol" 1 and 44.51CmOl"1 for their DGEBA/DDM and DGEBA/DDS mixtures, respectively. With regard to the time-temperature variation of e' and s", they write ^cure) = £oo(^cure)+[^cure)~£ao(tc«re)](

eXP - k J

^

~

d

* ( 24 )

where rcurc is the reaction time, £(*curc) = S(Q)9 tcurc). A difficulty with this equation is that a Fourier transform relationship between the frequency-dependent permittivity e((o) and a relaxation function 4>(t) is valid only for a stationary system: i.e. one whose thermodynamic properties are independent of time. (t) necessarily has the meaning of the relaxation function [3] for the decay of polarization following a step withdrawal of a steady applied d.c. E field. For a non-stationary system, and that includes a thermosetting polymer, this experiment cannot be performed, as the chemical and physical properties evolve in time. It is said [73] that tmn(t) is the dielectric decay function at the instant of tcure, but this confuses two time variables fcure and t and therefore has no physical significance. It is also clear that the Fourier integral in Equation (24) cannot be performed in practice. Therefore there are basic difficulties with Equation (24) that cannot be overcome. Alternative descriptions that relate the measured e\co) and e"(co) to time-dependent polarization processes are required. Mangion and Johari show that the Argand diagrams ('Cole-Cole plot') of e"{a), t, TR) against ef(co, t, TR) for fixed co and TK is asymmetric and may be fitted with a KWW function with parameter j8 in the range 0.2 < ft < 0.4. However, care should be taken in assuming that such plots actually correspond to the KWW form, whose origins lie in stationary systems where t and co are Fourier-paired variables. It appears that, as cure proceeds, the a process moves rapidly to low frequencies (see Figure 11.2(b)) with approximately constant shape and that at each reaction time t the plots of s" vs. sf

e1

(a) Variation of e' with the frequency of measurement for the thermoset (DGEBA/DDCM) at 7 = 60° C measurements every 6 mins, 4 ^ 0 , « 25 min

Logf/Hz

eM

(b) Variation of e" with the frequency of measurement for the thermoset (DGEBA/DDCM) at 7 = 60° C

Logf/Hz

Figure 113 Plots of ef and e" against log frequency/Hz for different reaction times for a 1:2 molar mixture of DGEBA with DDCM at 600C [79]. Curves 1-10 correspond to 25 min to 225 min in increments of 6 min

e'

(a) Evolution of the permittivity 7 = 6 0 0C

e"

(b)Evdlution of the loss factor T=60°C

Figure 11.4 3Dplotsofe' ande" against reaction time for a 1:2 molar mixture of DGEB A with DDCM at 600C [79] are fitted approximately by the KWW function. Thus, fixing the frequency f=co/2n and constructing the Argand diagram for e' and e" variations as t changes would lead to a skewed arc of KWW type. However, the variations of the KWW parameter with reaction time need to be investigated.

In many studies of polymerizing systems, low frequency conductivity-related processes are large and may obscure the dipole relaxation process. Some evidence of these processes is seen in Figures 11.2-11.4 at low reaction times and low frequencies, but in other systems they may dominate the overall behaviour, e.g. as in the case of phase-separating elastomer-epoxy resins described by Pethrick and coworkers [80, 81] and by Maistros et al. [82]. In such cases the apparently dominating conductivity processes may be represented alternatively by the modulus representation [73] M = [1/e], which gives M' = ^

;

A*" = ^

(25a,b)

Such a duality of representations is well-known in dynamic mechanical relaxation [3] for compliance and modulus. The apparent correlation times Compliance a n d Modulus a r e related through the ratios (E0/EJ = [JJJ0), where subscripts 0, oo refer to limiting low and high frequencies respectively and E and J are modulus and compliance respectively. In the view of the author, the permittivity representation should be used for the dipolar relaxations in cure-monitoring data. The M representation may be useful where it is known that conductivity processes are involved, but in this numerical representation space-charge and electrode processes appear to have less importance than their true contributions. Finally, we note that present applications of DRS to polymerizing systems have emphasized epoxy-amine thermosetting mixtures. Clearly much information could be obtained for photosetting and thermosetting addition polymerizations. We have conducted such studies recently using dimethacrylate monomers, which are photopolymerized using blue light (480 nm) and a camphoroquinone-amine initiator [83]. The dielectric data obtained during photoreaction are qualitatively different from those shown in Figures 11.2-11.4 for a thermosetting system. Analysis of our data show that the a process in the unreacted liquid monomer transforms into two processes as reaction proceeds, and that a /? process remains at low frequencies when polymerization is essentially completed. It is anticipated that DRS will be applied to real-time studies of phaseseparating polymer-polymer mixtures and to crystallizing polymers (see the data of Tidy and Williams in [12] for early results for isothermal crystallization of amorphous polyethylene terephthalate). Although such measurements are entirely feasible in the usual low frequency region 10-10 7 Hz, it would be highly desirable to develop experimental dielectric cells and fast measuring methods for the high frequency range 10 8 -10 1 0 Hz, thus providing the wide frequency range necessary to document and define the multiple dielectric relaxations that arise from dipole motions in the different phases.

11.6 CONCLUSIONS AND FUTURE PROSPECTS It is apparent that DRS provides an important method for studying the reorientational dynamics of polymer chains in bulk amorphous, crystalline and liquid-

crystalline polymers and in polymerizing, phase-separating and crystallizing systems. The merits of DRS include small sample size (typically 1 cm 2 x 50 jim), wide frequency range (typically 10"3 to 107 Hz) and its sound theoretical basis both in phenomenological and molecular terms. Difficulties with DRS include (i) low frequency conductivity-related processes, which may obscure the dipole relaxation processes, and (ii) the present limited access to high frequency (10 8 10 10 Hz) techniques. It is anticipated that DRS studies of polymers will be extended to more complicated systems, e.g. where two phases may be present and electrical-field-induced processes occur. One example is polymer-dispersed liquid crystals (PDLC), which may be formed in several ways, in which liquid-crystal droplets are dispersed in a polymer matrix. Such PDLC materials as films 50-500 ^m in thickness may be switched optically using moderate E fields, and the required voltage depends both on the response of the liquid crystal and the dielectric properties of the host polymer. In such cases a knowledge and control of the dielectric properties of guest and host materials will enable the optical switching properties to be optimized, especially in regard to the lowering of the E field required for switching. A further example where DRS properties are useful is non-linear-optical (NLO) films, which show promise for second- and thirdharmonic generation of laser light [84]. It is generally observed that the nonlinear susceptibility for second-harmonic generation of E-poled films decays with time, and this may be due partly to the intrinsic motions of the electroactive molecules in the glassy amorphous or glassy LC state of the poled material. Such motions can be characterized using DRS, and this provides direct information on such electro-optical phenomena which may not be readily obtained by other methods such as NMR and quasi-elastic light scattering.

11.7 ACKNOWLEDGEMENTS The author acknowledges the support of the SERC and AFOSR and the Erasmus scheme for studies of the dielectric properties of polymers, and thanks Prof. CIi ve Bucknall for information regarding the 'Axum' programs used for the 3D plots shown in this paper.

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[5] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics Press, London, 1983. [6] J. Wong and CA. Angell, Glass; Structure by Spectroscopy, Marcel Dekker, Basel, 1976. [7] G. Allen and J.C. Bevington (Eds.), Comprehensive Polymer Science, Vol. 1, Polymer Characterization, Pergamon Press, Oxford, 1989. [8] E. Riande and E. Saiz, Dipole Moments and Birefringence of Polymers, Prentice Hall, New Jersey, 1992. [9] F.I. Mopsik, Rev. ScL Instrum., 1984,55, 79. [10] J.M. Pochan, JJ. Fitzgerald and G. Williams, in B.W. Rossiter and R.C. Baetzold (Eds.), Determination of Electronic and Optical Properties, Physical Methods of Chemistry Series, 2nd edn., Vol. VIII, Wiley, New York, 1993, Ch. 6, p. 392. [11] G. Williams, Chem. Rev., 1972,72, 55. [12] G. Williams, Adv. Polym. ScL, 1979,33,60. [13] G. Williams and D.C. Watts, in NMR Basic Principles and Progress, Vol. 4, NMR of Polymers, Springer Verlag, Heidelberg, 1971, p. 271. [14] G. Williams, in G. Allen and J.C. Bevington (Eds.), Comprehensive Polymer Sciences, Vol. 2, Polymer Properties, Pergamon Press, Oxford, 1989, p. 601. [15] M. Cook, D.C. Watts and G. Williams, Trans. Faraday Soc, 1970,66, 2503. [16] G. Williams, M. Cook and PJ. Hains, J. Chem. Soc, Faraday Trans, 2,1972,69,1045. [17] G. Williams, in R. Pethrick and R.W. Richards (Eds.), Dynamic Properties of Solid Polymers, NATO ASI, Reidel, Dordrecht, 1982. [18] G. Williams and D.A. Edwards, Trans. Faraday Soc, 1966,62,1329. [19] G. Williams, Trans. Faraday Soc, 1964,60,1548,1556. [20] G. Williams, Trans. Faraday Soc, 1966,62, 2091. [21] G. Williams, D.C. Watts, Trans. Faraday Soc, 1970, 66, 80. [22] G. Williams, D.C. Watts, S.B. Dev and A.M. North, Trans. Faraday Soc, 1971,67, 1323. [23] G. Williams, IEEE Trans. Electr. Insul., 1982, El-17, 469. [24] N. Koizumi and Y. Kita, Bull Inst. Chem. Res. Kyoto Univ., 1978,56, 300. [25] G. Williams in M. Davies (Ed.), Dielectric and Related Molecular Processes, Vol. 2, Chemical Society, 1975, p. 151. [26] G. Williams, IEEE Trans. Electr. Insul., 1985, El-20, 843. [27] K.L. Ngai, in T.V. Ramakrishnan and M. Raj Lakshmi (Eds.), Non-Debye Relaxation in Condensed Matter, World Scientific, Singapore, 1987, p. 1. [28] W. Goetze, Rep. Progr. Phys., 1992,55, 241. [29] W. Goetze, Ferroelectrics, 1992,128, 307. [30] G.F. Mazenko, J. Non-Cryst. Solids, 1991,131-133,120. [31] A.K. Rajagopal, K.L. Ngai, and S. Teitler, J. Non-Cryst. Solids, 1991,131-133,282. [32] K.L. Ngai, Commun. Solid. State Phys., 1979,9,127, 141. [33] K.L. Ngai, A.K. Rajagopal and S. Teitler, J. Chem. Phys., 1988,88, 5086. [34] G. Williams and M. Cook Trans. Faraday Soc, 1971,67,990. [35] R.H. Cole, J. Chem. Phys., 1965, 42, 637. [36] U.M. Tituiaer and J.M. Deutch, J. Chem. Phys., 1974,60,1502. [37] G. Williams in E. Wyn-Jones (Ed.), Chemical and Biological Applications of Relaxation Spectroscopy, Reidel, Dordrecht, 1975, p. 515. [38] G. Williams and D.C. Watts, in Dielectric Properties of Polymers, Plenum Press, 1971, p. 17. [39] G. Williams and D.C. Watts, Trans. Faraday Soc, 1971, 67, 2793. [40] G.D. Smith and R.H. Boyd, Macromolecules, 1991, 24, 2725, 2731. [41] V. Rosato and G. Williams, Adv. MoL Relax. Processes, 1981, 20, 233.

[42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84]

R.L. Jernigan, in Dielectric Properties of Polymers, Plenum Press, 1971, p. 99. M.S. Beevers and G. Williams, Adv. MoL Relax. Processes, 1975, 7, 237. J.D. Hoffman, G. Williams and E. Passaglia, J. Polym. ScU Part C, 1966,173. Y. Ishida, J. Polym. ScU 1969,7,1835. CR. Ashcraft and R.H. Boyd, J. Polym. ScU Polym. Phys. Ed., 1976,14, 2153. H. Frohlich, Proc. Phys. Soc. (London), 1942,54,422. G. Williams, J.D. Hoffman and J.I. Lauritzen, J. Appl. Phys., 1967,38,2503. M. Mansfield and R.H. Boyd, J. Polym. ScU Polym. Phys. Ed., 1978,16,1227. Adv. Polym. ScL, 1984,60/61. CB. McArdle, (Ed.), Side Chain Liquid Crystal Polymers, Blackie, Glasgow, 1989. F. Laupretre, C Noel, W.N. Jenkins and G. Williams, J. Chem. Soc, Faraday Discuss, 1985, 79,191. K. Araki, M. Aoshima, N. Namiki, S. Ujiie, N. Koide, K. Imamura and G. Williams, Makromol. Chem. Rapid Commun., 1989,10, 265. G.S. Attard, K. Araki, JJ. Moura-Ramos and G. Williams, Liq. Cryst., 1988,3,861. A. Kozak, JJ. Moura-Ramos, G.P. Simon and G. Williams, Makromol. Chem., 1989, 190, 2463. G.S. Attard, K. Araki and G. Williams, Br. Polym. J., 1987,19,119. K. Araki, G.S. Attard, A. Kozak, G. Williams, G.W. Gray, D. Lacey and G. Nestor, J. Chem. Soc, Faraday Trans. 2,1988,84, 1067. A. Nazemi, G. Williams, G.S. Attard and F.E. Karasz, Polym. Adv. TechnoL, 1992,3, 157. W. Haase, H. Pranoto and FJ. Bormuth, Macromolecules, 1985,18,960. FJ. Bormuth and W. Haase, MoL Cryst. Liq. Cryst., 1987,148,1. G. Williams and J. Hayden, manuscript in preparation. A. Kozak, G.P. Simon and G. Williams, Polym. Commun., 1989, 30,102. A. Kozak, G.P. Simon, J.K. Moscicki and G. Williams, MoL Cryst. Liq. Cryst., 1990, 193,155. A.F. Martins, P. Esnault and F. Volino, Phys. Rev. Lett., 1986, 57,1745. P. Esnault, J.P. Casquilho, F. Volino, A.F. Martins and A. Blumstein, Liq. Cryst., 1990,7,607. G.S. Attard, G. Williams and A.H. Fawcett, Polymer, 1990,31, 928. G.S. Attard, MoL Phys., 1986,58,1087. W. Maier and G. Meier, Z. Naturforsch., 1961,162,1961. P.L. Nordio, G. Rigatti and U. Segre, MoL Phys., 1973,25,129. J.W. Lane and J.C Seferis, J. Appl. Polym. ScL, 1986,31,1155. S.D. Senturia and N.F. Sheppard Jr., Adv. Polym. ScL, 1986,80,1. N.F. Sheppard, Jr. and S.D. Senturia, Polym. Eng. ScL, 1986, 26, 354. M.B.M. Mangion and G.P. Johari, J. Polym. ScL, Polym. Phys., 1990,28, 71. M.B.M. Mangion and G.P. Johari, J. Polym. ScL, Polym. Phys., 1990, 28,1621. M.B.M. Mangion and G.P. Johari, J. Polym. ScL, Polym. Phys., 1991, 29,1117. M.B.M. Mangion and G.P. Johari, J. Polym. ScL, Polym. Phys., 1991,29, 1127. M.B.M. Mangion and G.P. Johari, Polymer, 1991, 32, 2747. M.B.M. Mangion and G.P. Johari, Macromolecules, 1990,23, 3867. C Duch, J. Fournier and G. Williams, manuscript in preparation. AJ. MacKinnon and R.A. Pethrick, Macromolecules, 1992,25, 3492. D. Lairez and R.A. Pethrick, Macromolecules, 1992, 25, 7208. G. Maistros, H. Block, CB. Bucknall and LK. Partridge, Polymer, 1992, 33,4470. G. Williams and J. Fournier, manuscript in preparation. D.S. Chemla and J. Zyss (Eds.), Nonlinear Optical Properties of Organic Molecules and Crystals, VoIs. 1 and 2, Academic Press, Orlando, 1987.

12

LIGHTSCATTERING FROM POLYMER SYSTEMS R, W. RICHARDS Department of Chemistry, University of Durham, Durham DHl 3LE, UK

12.1 INTRODUCTION Light scattering from dilute polymer solutions has long been used by polymer scientists to determine the molecular weights, the radii of gyration and the second virial coefficients of polymers [1,2]. Such information has been instrumental in the development of two-parameter theories [3] of polymer solutions, and classical intensity light scattering has been exhaustively discussed. In addition to two of the parameters mentioned (mean molecular weight and second virial coefficient), classical intensity light scattering has also been used to obtain information on the compositional dispersity in copolymers, and depolarised light scattering can provide information on molecular anisotropy in rod-like polymerss such as the main chain liquid crystal polymers [4,5]. Both of these applications have attendant difficulties. For copolymers, light scattering measurements have to be made in at least three solvents with different refractive indices to obtain compositional heterogeneity, although the judicious choice of solvents can considerably simplify the calculation process [6]. Depolarised light scattering intensity is often low and the signal-to-noise ratio can also be low. These aspects of light scattering have been plentifully discussed and will not be reviewed here. A more recent development has been quasi-elastic light scattering [7,8], which is often used to obtain diffusion coefficients of polymers in dilute solution. Quasi-elastic light scattering has been applied to solvent-swollen cross-linked networks and to semi-dilute solutions of polymers in an effort to investigate scaling theories and reptation theories. Additionally, the possibility of obtaining the viscoelastic properties of spread films of polymers at the air-water interface by quasi-elastic light scattering has also been discussed. Both of these aspects will be reviewed here. Light scattering from solid polymer films and melts was first reported some 40 years ago [9]. The experimental difficulties have been considerably simplified by newer technology, and the increased power of computing has eased the process of Polymer Spectroscopy. Edited by Allan H. Fawcett © 1996 John Wiley & Sons Ltd

data analysis. Much simpler experiments than implied in the original theory are capable of producing information on the kinetics of phase-separating blends and the thermodynamics of the systems. An overview of small angle light scattering applied to semi-crystalline polymers and phase-separating blends will also be given here. All of these different types of experiment are united by a common source for the light scattering observed, that is, the existence of fluctuations in polarisability, and hence refractive index, at microscopic length scales in the material upon which the light is incident. The cause of these fluctuations may differ markedly from thermal fluctuations (surface quasi-elastic light scattering), concentration gradients (quasi-elastic light scattering), density variations due to packing (crystallinity) etc., but such fluctuations scatter light efficiently, so that light scattering provides a convenient non-perturbative probe of the structure and dynamics of polymer systems.

112 SMALL ANGLE LIGHT SCATTERING (SALS) 12.2.1 SEMI-CRYSTALLINEPOLYMERS The pioneering work in SALS was done by Stein and his collaborators [10] some 30-40 years ago, and it is a relatively simple technique for investigating spherulite growth and size in nearly transparent polymers. The original equations derived by Stein and Rhodes [10] sought to explain the 'four leaf clover' pattern of scattered light intensity observed in the Hv scattering experimental set-up shown schematically in Figure 12.1. (Hv implies vertically polarised incident light, horizontally polarised scattered light.) Spherulites are optically anisotropic, and originally Stein and Rhodes explained the disposition of the scattered light as lobes along the azimuthal angle of n/4 as being due to the orientation of dipoles in the spherulite with respect to the plane of polarisation of the incident light. Much interesting work has been analysed on the basis of the original equations (e.g. influence of deformation [12], size distribution of spherulites [13], influence of chain branching [14]). However, this explanation has been shown to be fundamentally incorrect by Meeten and co-workers [15-17], although the extraction of parameters such as spherulite size etc. from SALS data using the original equations is not altered. Meeten and Navard [16] used Mie theory, RayleighGans-Debye theory and anomalous diffraction theory on isotropic spheres and the latter two theories on anisotropic spherical scatterers. For all theories, both types of particles produced 'four leaf clover' scattering patterns for Hv scattering. The dependence of scattered intensity on azimuthal angle (f> and scattering angle 0 can be calculated from the dimensionless angular gaing (which is approximately the ratio of the intensity of the scattered light to the incident

Potariser

Laser

Sample Analyser

Detector Plane

Figure 12.1 Schematic of small angle light scattering experiment: scattering angle = 0; the azimuthal angle <j> is measured from the plane of polarisation of the incident light light intensity). G^ = ( I A V ) I S 1 - S 2 I 2 sin 2 20 GVv = (4AV)IS 1 Sm 2 + S2COs2 \2 and k = 2nlk (Vv, vertically polarised incident light, vertically polarised scattered light). The Rayleigh-Gans-Debye approximations are the most easily handled expressions for S1 and S2. Isotropic sphere 2/fcV 5 1 = — — Ox— l)(sinu —MCOSM)

5 2 = S1COsO V = wm/ns with nm and ns being the refractive index of the matrix and the sphere respectively.

Anisotropic sphere 2ik3r3 51 =

3

{3(/x— l)(sinw —MCOSW) + A / * [ u c o s K - 4 s i n u + 3Si(u)]}

2ifc3r3 52 =-^~3-{3(/I- I)(sinu-Mcosw)cos0- A^(I + cos2(0/2))(wcosw-4sinwSi(u))} where jx = (nr + 2nt)/3nm, Afi = (nr — nt)/nm, nT is the radial refractive index, nt the tangential refractive index, and Si(u) is the sine integral of u. For both cases r is the radius of the sphere and u = An/X r sin(Q/2), with A being the wavelength of light in the scattering polymer film. Figure 12.2 shows the form of the scattering for both isotropic and anisotropic spheres and Hv scattering. Note that both show a maximum scattering disposed in lobes at azimuthal angles of n/4. Figure 12.3 shows the intensity variation with u along one such lobe; again both have the same qualitative features, i.e. a maximum at a defined value of u. For

Figure 12.2 (Continued)

Figure 12.2 Contour plots of Hv scattered light intensity from (a) optically anisotropic spheres (b) optically isotropic spheres; x = r sin <£, y = r cos <£, where r is the radius of the sphere anisotropic spheres wmax = 4.09, for isotropic spheres wmax = 2.74 for the first order maximum. Over the years the method of detecting the scattered light has improved; originally photographic methods were used, followed by high speed cameras, vidicons and optical multichannel analysers. Nowadays CCD cameras are able to record scattering patterns digitally, and fast shutter speeds mean that the data can be recorded in real time. A typical apparatus as constructed at Durham [18] is shown in Figure 12.4; a description of similar equipment has recently appeared [19]. Typically, the fastest shutter speed may be «20/xs and the time needed to refresh the detector area and store 4K pixels each with 18 bit dynamic range is « 2 s. One system on which this apparatus has been used is the crystallisation

10 Intensity

Intensity 4

Figure 12.3 Variation of Hv scattered light intensity at <j> = 45° for (a) optically anisotropic spheres, (b) optically isotropic spheres; in each case u = (4nnr/Ao)sin(0/2). (a) Reprinted with permission from Macromolecules, 1982, 15, 1004; (b) reprinted with permission from [53]. Copyright 1982 and 1993 American Chemical Society kinetics of linear diblock copolymer of methyl methacrylate and ethylene oxide [20]. A copolymer with 76 mol % of ethylene oxide was quenched to a temperature of 308 K from 400 K and the Hv SALS pattern was recorded as a function of time; the variation of intensity obtained is shown in Figure 12.5. From the maxima in such curves, the radius of the spherulite was obtained, and was used in an Avrami analysis of the crystallisation kinetics [21]. This provides a parameter proportional to the rate of crystallisation and the Avrami exponent. From the latter parameter it is sometimes possible to infer something about the growth mechanism and geometry (Table 12.1). For this block copolymer the Avrami

Fibre optic link

CCD Camera

Marata plate

analysor

hot stage+ sample

polariser

ND filters

beam expander

Figure 12.4 Block diagram of a small angle light scattering instrument exponent obtained was 1.8; the equivalent homopolymer blend had an Avrami exponent of 1.5. A word of caution is appropriate here. Meeten's analysis shows that the value OfU1114x depends on the anisotropy of the spherulite; thus in the early stages the observed growth rate may appear to be smaller than the actual growth rate.

Intensity

PEO-b-PMMA (76% w/w PEO) Block Copolymer, 7C=35 0C

Polar scattering angle

Figure 123 Variation of Hv scattered light intensity at <j> = 45° for a linear diblock copolymer of methyl methacrylate and ethylene oxide. The copolymer was quenched from 1000C to a crystallisation temperature of 350C and the time lapse between each curve is 2.1s

Table 12.1 Avrami exponents predicted for a variety of growth geometries and growth control mechanisms Exponent Nucleation" Growth geometry Growth control* 0.5 Instantaneous Rod Diffusion 1 Instantaneous Rod Interface 1 Instantaneous Disc Diffusion 1.5 Instantaneous Sphere Diffusion 1.5 Homogeneous Rod Diffusion 2 Homogeneous Disc Interface 2 Homogeneous Disc Diffusion 2 Homogeneous Rod Interface 2.5 Homogeneous Sphere Diffusion 3 Instantaneous Sphere Interface 3 Homogeneous Disc Interface 4 Homogeneous Sphere Interface 'Instantaneous: nuclcation on existing heterogeneities. Nuclei form simultaneously at beginning. Homogeneous: sporadic formation of nuclei. Nucleation continuous in the untransformed material. ^Diffusion controlled: kinetics are controlled by the rate of diffusion of molecules to the nuclei. Interface controlled: kinetics controlled by rate of attachment of molecules to the nuclei.

12.2.2 PHASE-SEPARATING POLYMER MIXTURES Generally, compatible polymer mixtures display a lower critical consolute (or coexistence curve), and the variation of the Gibbs free energy change on mixing with composition shows a pair of inflection points above a particular temperature defined by the thermodynamics of the system and the mixture composition. At these inflection points (d2AGJd<j>2)TtP = 0, and they define the locus of the spinodal curve. This curve is the limit of stability of the mixture, i.e. within the curve the mixture is unstable to any fluctuation and demixing (spinodal decomposition) takes place spontaneously. Between the coexistence curve and the spinodal curve there is a metastable region wherein large fluctuations are necessary to initiate demixing, usually via a nucleation and growth process (Figure 12.6). Both curves meet at the critical temperature where (d2AG/d2)Tp = (d3AG/d3)Tp = 0. If a compatible blend is quenched into the spinodal region, phase separation takes place and the kinetics of the demixing are describable by the linearised Cahn-Hilliard theory of spinodal decomposition, which gives the time dependence of the composition variation as [22] (d/dt)TtP = M(d2Ald2)T%pV24> - 2 M X V 4 0 where M is the mobility of the polymer and KV2<j> is the free energy density

Temperature (K)

binodal spinodal

Figure 12.6 Schematic phase diagram for polymer-polymer mixtures

gradient due to composition gradients. The solution to this equation is a Fourier series describing the compositional fluctuations in the system, i.e. the local compositional deviations from the average value, and these fluctuations are the source of the scattered light intensity. Since light scattering is described in Fourier space terms, the solution to the Cahn-Hilliard equation is also needed in Fourier space, Le. in terms of a wave vector, where the wave vector is (In/X) and X is the concentration fluctuation wavelength. The intensity of light scattered from the phase-separating mixture is proportional to the square of the fluctuation amplitudes and is given by: / ( a 0 = /(Q^ = 0)exp[2R(Q)r] where Q is the scattering vector = Ann sin(0)/Ao, with n the refractive index of the sample, 20 the scattering angle and X0 the wavelength of light in vacuo. The term R(Q) is known as the amplification factor and R(Q) = - M(d2A/d2)TtPQ2 - 2MKQ* In the phase-separating system, there will be a most probable composition

10- 3 Q(Cm- 1 )

Figure 12.7 Scattered light intensity (Vv conditions) as a function of angle for different times for a phase-separating mixture of polystyrene and polyvinyl methyl ether. Times after start of phase separation (seconds) A 2 +20 D40 O60 V 10 x 30 O 50 • 70

10ln(I(Q max )

Time (S)

Figure 12.8 Exponential dependence of scattered light intensity for a phase separating mixture of polystyrene and poly vinyl methyl ether at Qmmx fluctuation wavelength which will grow preferentially as phase separation proceeds. This leads to a maximum in the observed scattered intensity at a finite value of Q. The position of this intensity maximum does not alter as in the early stages of phase separation but increases in intensity as phase separation proceeds. At late stages in the phase separation, there is a coalescence of particles via Ostwald ripening and the maximum will shift to lower Q values. During the early stages, at a fixed value of Q, the scattered light intensity from a spinodally decomposing system should increase exponentially with time, and from this relationship the amplification factor can be obtained. A set of light scattering data for a demixing polystyrene/polyvinyl methyl ether (PVME) mixture collected at discrete time intervals is shown in Figure 12.7 [23]; the dependence of the scattered intensity on time at the Q value (Qmax) where the maximum intensity is seen is shown in Figure 12.8. From values of R(Qn^x) the effective diffusion coefficient De, can be obtained, as Dt = 2R(QmAX)/Qliax. At the spinodal curve Dt = 0, and thus if Dc is obtained for a series of composition and over a range of temperatures, the spinodal curve can be obtained. Figure 12.9 shows values of Dc as a function of temperature obtained for the mixture of polystyrene and PVME referred to earlier, and the spinodal curve predicted from these data is given in Figure 12.10. Light scattering investigations of other demixing polymers have been reported elsewhere [24, 25] and recently a very sophisticated instrument for such studies has been described [26].

1O10C-D9)Cm2S'1

PS(2)/PVME

Temperature (K) Figure 12,9 Effective diffusion coefficient as a function of temperature

B

PS(2)/PVME

TEMPERATURE (K)

cloud point curve

WEIGHT FRACTION PS

Figure 12.10 Spinodal curve (•) predicted from temperature dependence of Dc for polystyrene/polyvinyl methyl ether mixtures

123 QUASI-ELASTIC LIGHT SCATTERING (QELS) 12.3.1 DILUTE POLYMER SOLUTIONS Light scattering by polymers in solution is not a perfectly elastic process, small amounts of energy being transferred between molecules and photons. This energy transfer leads to a broadening of the frequency of the scattered light relative to the incident light, and the intensity variation of the scattered light over a frequency range from — oo to + oo is the spectral density or power spectrum, which is given by I((o) = 1/2« I °° < E*{t)E{t + T) > exp iojTdt where <£*(r)£(t+T)> is the electric field autocorrelation function gt(t). In quasi-elastic light scattering (QELS) what is actually obtained as the output from the photomultiplier tube is the unnormalised intensity autocorrelation function G2(t\ and G2(t) = A + [Bg 1 (O] 2 (homodyne) where A is a constant background intensity to which the correlation function decays after a suitably long delay time f, and B is a constant close to unity. If we have a single species in the solution, e.g. a monodisperse polymer, and there are only concentration gradient relaxation processes, then ^1(O = exp(-Ff) and F l is the relaxation time of the diffusive process of the polymer down the concentration gradients; F = DQ2 with Q = (4nn/Xo)sin(0/2) and D is the translational diffusion coefficient. For polymer solutions, D is concentration dependent D = D 0 (l + fcDc) where D 0 is the infinite dilution value of D and c is the concentration of polymer. The term kD is composed of thermodynamic and factional parameters for the polymer in the particular solvent conditions investigated. Polymers are not often monodisperse, and each different relaxation time will make a contribution to the observed average F. A popular method of obtaining the diffusion coefficient is to use the cumulants approach outlined by Koppel [27] and the algorithm of Pusey et al. [28] In Q1(Z) = - T11 + (F2/2!)r2 - (F3/3!)r3 + • • • Generally only the first two cumulants can be extracted from the correlation functions with any confidence, and TJQ2 = D29 the z-average diffusion coefficient. About 12 years ago, Burchard et al. [29] showed that r JQ2 = D(I+

CR2Q2)

Hq 2 XiO 8 (Cm 2 S 1 )

Cj 2 XiO- 10 ^kC(Cm 2 )

Figure 12.11 Dynamic Zimm plot for polystyrene in toluene. Reproduced with permission of the American Chemical Society from ref. [29] where R9 is the radius of gyration of the polymer molecule and C is a parameter related to the molecular architecture and the thermodynamic environment. Incorporating the concentration dependence of D, TJQ2 = D0(I + kDc)(l + CRlQ2) Thus, as c->0 and Q->0, TJQ2 = D 0 and D 0 , kD and C can be obtained from a 'dynamic' Zimm plot (Figure 12.11). The slope of the line dependent on Q2 alone is CR2, whereas the slope of the line dependent on c only is DokD. Thus method has not been widely used; however, it has been applied to naturally occurring polymers to extract C and thus to enable something to be said about their structure. We noted earlier that each relaxation time will contribute to T and hence influence the shape of the correlation function. Consequently, all the information on polymer polydispersity is contained within the intensity correlation function because D is proportional to (molecular weight)"0. The extraction of the molecular weight distribution from the correlation function is an 'ill posed problem', as there are an infinite number of solutions to the Laplace inversion of the data that is required to obtain the distribution. Several attempts have been made at developing suitable computational methods to derive a distribution from a correlation function. Perhaps the most widely known and used is the constrained regularisation programme CONTIN [30,31]. In many cases the programme works well, but care has to be taken in choosing the right range of D to explore for a solution, and the original data must be of high quality, as 'noisy' data can lead to artefacts in the analysis. A comparison of CONTIN with maximum entropy methods has recently been published [32].

Relative Contribution

Diffusion Coefficient (cm 2 s'x)

x1

°

Figure 12.12 Distribution in diffusion coefficients for an aromatic terpolyester in a mixed solvent of trifluoroacetic acid and dichloromethane obtained by CONTIN analysis of quasi-elastic light scattering data Obtaining molecular weight distributions by this means has two benefits. Firstly, with a high power laser light source on the correlator and with fast data links to a work station, a full molecular weight distribution can be obtained in «2min. The second benefit is when only ferocious solvents are available, ones which would destroy size-exclusion chromatography (SEC) column packings; quasi-elastic light scattering then becomes a highly suitable method to obtain a molecular weight distribution. An example of this is the aromatic terpolyester prepared from hydroxybenzoic acid, isophthalic acid and hydroquinone [33], which is soluble in a mixture of trifluoroacetic acid and methylene chloride. The low refractive index of the solvents and the high refractive index of the polymer make the solutions extremely strong scatterers of light and ideal for CONTIN analysis, even with only a modest laser. An example of the distribution in diffusion coefficients (and hence molecular weight) is shown in Figure 12.12.

12.3.2 GELS A cross-linked polymer swollen by a solvent constitutes a gel, and if swollen sufficiently the concentration of polymer in the gel is that of a semi-dilute

solution, i.e. it is between c* and c** as defined by de Gennes. The gel has continual local fluctuations in the degree of swelling (equivalent to polymer concentration) which lead to variations in the local osmotic pressure. The analysis of the intensity correlation function obtained from the scattering of light by these fluctuations produces a co-operative diffusion coefficient. The first QELS experiments on gels and the theoretical analysis of the data were reported over 20 years ago by Tanaka et al. [34]. They showed that at a delay time of zero (i.e. extrapolating the correlation functiion to t = 0), the scattered light intensity above the background was equal to the osmotic moldulus Mos (= Kos + 4Gos/3 where Kos is the bulk osmotic modulus and Gos is the shear osmotic modulus), also known as the longitudinal modulus. The co-operative diffusion coefficient is given by DC = (KOS + 4GOS/3)(1 -p)/f where cf)p is the volume fraction of polymer in the gel and / is the total friction of the polymer against the solvent per unit volume / = CeNAc/m where c is the polymer concentration in gml" 1 , m is the monomer molecular weight, and £c is the monomeric friction coefficient at concentration c. Since the first report there have been many papers published on light scattering from polymer gels, the work of Geissler and Hecht on polyacrylamide gels [35-39] being noteworthy. Measurements [40, 41] obtained on radiation cross-linked polystyrene gels subsequently swollen in cyclohexane at different temperatures exemplify the type of results obtained. A typical correlation function is shown (Figure 12.13) in which the ordinate axis was calibrated directly in terms of osmotic modulus using data obtained by Scholte [42] from ultracentrifugation analysis of polystyrene solutions. Scaling relationships can be used to interpret the dependence of Mos

and Dc o n p. The dependence of Dc on the volume fraction of the polymer in the gel varied markedly with the temperature (Figure 12.14), whereas the osmotic modulus for these same gels could be fitted by the same scaling relationship Mos = 4.7 x 1 0 6 ^ 6 N m - 2 Scaling laws predict that the exponent of 0 p for Mos should vary from 2.25 in good solvents to 3 in theta solvent conditions; for the concentration dependence of diffusion coefficients the same exponents are 0.75 and 1 respectively. At 308 K an exponent of 1.17 was observed, which within the experimental error agreed with predictions. However, at 333 K, the exponent was 0.46, much lower than theory predicts. This observation and the high exponent observed for Mos were attributed to the presence of dangling chains in the network, since the correlation functions were observed to become more non-exponential as the temperature

Intensity (a.u.)

T = 308K Solvent C6H12

Baseline

Time (jus) Figure 12.13 Intensity autocorrelation function obtained for a randomly cross-linked network of polystyrene swollen in cyclohexane at 308 K was increased. Increased non-exponential behaviour has been identified with the overlapping of molecules and appears to be possible only when there are many loose dangling chains.

12.3.3 SEMI-DILUTE S O L U T I O N S A N D TRAPPED CHAINS The broad outlines of reptation theory are well known, and the detailed theory is available elsewhere [43,44]. Essentially, a polymer molecule in a melt is confined to a tube which is defined by the surrounding molecules, and can only move along the tube axis. The time dependence of the various dynamic modes of the molecule in the tube has been discussed by Doi and Edwards [45]. Additionally, de Gennes [46] has set out equations which relate the translational diffusion coefficient of a probe polymer to its molecular weight (Mp), the entanglement molecular weight of the matrix (MJ and the molecular weight between cross-links (AfJ. Three regimes are predicted: 1. Free draining (A/p < Afc, Afp > AfJ, D = D0M; K

DJm2S'1)

Figure 12.14 Co-operative diffusion coefficient as a function of volume fraction of polymer in cyclohexane swollen polystyrene networks; (o) 308 K, (o) 318 K, (•) 333 K 2. Simple reptation (M p > Me, M c > Mc), D = D0M tM; 2. 3. 'Strangulation' regime (Me > Mc, M p > Mc), Dt = D0M0M;

2

.

Attempts have been made at observing these regimes using semi-dilute solutions of a matrix polymer with a chemically identical probe of a different molecular weight incorporated in the solution. The conclusion of these experiments was that the reptation theory was inappropriate for such semi-dilute solutions [47,48]. A possible explanation for the failure of reptation theory may be in the recent analysis of Wang [49-51]. He shows that the quasi-elastic light scattering from a semi-dilute solution has contributions from both concentration fluctuations and density (pressure) fluctuations, and consequently the long time viscoelastic relaxation spectrum, usually observed by dynamic mechanical means, will also contribute to the autocorrelation function. The extent to which both contributions are seen depends on the frequency distribution of the stress relaxation modulus and a coupling parameter j8 (proportional to the partial

log[D t <M x >/M x ]

log M Figure 12.15 Diffusion coefficient of polystyrene tracer in polyvinyl methyl ether gels as a function of tracer molecular weight. Diffusion coefficients normalised by ratio of molecular weight between crosslinks of gels. Reprinted with permission from [52]. Copyright 1992 American Chemical Society

specific volume of the polymer minus the partial specific volume of the solvent). Very recently, QELS investigation of reptation predictions has been made using randomly cross-linked networks containing chemically distinct trapped chains. Rotstein and Lodge [52] prepared polyvinyl methyl ether gels containing trapped polystyrene chains, and obtain tracer diffusion coefficients for the toluene-swollen gels. Values of M c were calculated from swelling data, and 4 x 103 ^ Mc ^ 14 x 103. Figure 12.15 shows the diffusion coefficient data normalised by the ratio of the M c values for the three networks involved. There appears to be little or no influence of Mc even when M p » Me; furthermore, the probe molecular weight dependence of D (DocM~2S) is much stronger than predicted by reptation theory. Pajevik et al. [53] prepared randomly cross-linked polymethyl meth'acrylate gels containing polystyrene probe molecules. Their results are shown in Figure 12.16. When M p < Mc («80000) then D scales as Mp ° 6; above this molecular weight the influence of M p is marked and D scales as M~ l'*±°-29 i.e. almost exactly in agreement with reptation theories, CONTIN or an equivalent program was used in both investigations, and the isorefractivity of toluene with polyvinyl methyl ether and polymethyl methacrylate aids the

D*/D0

Mp

Figure 12.16 Ratio of polystyrene tracer diffusion coefficient (D1) in toluene swollen PMMA gel to diffusion coefficient of polystyrene in dilute toluene solution (•); (A) values for PS tracer in PMMA solutions. Reproduced with permission from the American Chemical Society from Ref. [53] process of extracting the probe diffusion coefficient. However, about 14 years [54] ago it was noted that, when polystyrene was dissolved in a semi-dilute benzene solution of polymethyl methacrylate, the value of D decreased as the polymethyl methacrylate concentration increased, i.e. rather similar to the molecular weight dependence seen by Pajevik et al, and this may be due to polymer-polymer interactions. To overcome these possible complications, polystyrene networks with trapped polystyrene molecules have been prepared [55] and are currently being investigated.

12.3.4 SURFACE QUASI-ELASTIC LIGHT SCATTERING (SQELS) A liquid surface is continually roughened by thermal excitations, which give rise to the hydrodynamic modes known as capillary waves. The r.m.s. amplitudes of the waves are small ( « 2A) but they are efficient light scatterers. The displacement of the liquid surface from its equilibrium position by a wave propagating in the x direction is: C(x,r) = C 0 exp(/ex-ho)0 where Q is the surface wavenumber or the scattering vector parallel to the liquid surface. The wave frequency o is a complex quantity given by a>0 + iT, where co0 is the capillary wave frequency and F is the decay rate of the waves. A dispersion equation relates co and Q, and for pure liquids the controlling factors (for fixed Q)

are the kinematic viscosity and the surface tension [56]. For most instruments the accessible range of Q is 100-2000Cm"1 and hence the wavelengths probed are « 600-30 /mi. If a polymer film is spread on the surface of the liquid, additional hydrodynamic modes modify the dispersion equation. Only the transverse modes (capillary waves) scatter light, but there is coupling with the longitudinal or dilational modes, and hence in principle some information is obtainable on both modes from the power spectrum of the scattered light. The parameters obtainable are the surface tension y and the dilational modulus e; both of these are viscoelastic properties, as energy dissipation takes place in the relaxation processes, and thus y = y0 + icoy' e = 6 0 + icoe'

where y0 and £0 are the static surface tension and dilational modulus I — I, \ A aA J y' is the transverse shear viscosity and e' is the in-plane dilational viscosity. Although direct measurement of the frequency broadening of the scattered light by the capillary waves has been used, the frequency shifts are rather small, and a more direct means of observing the frequency of the capillary waves is to use heterodyne quasi-elastic light scattering [57,58]. The experimental arrangement to collect such data is shown in Figure 12.17; the diffracted beams produced

Laser

rough

PM Tube

Figure 12.17 Schematic diagram of surface quasi-elastic light scattering apparatus. Ll, L2 = lenses, T = transmission grating, F = neutral density filter, Ml, M2, M3, M4 = mirrors

Normalised correlation function

Time (us)

Figure 12.18 Heterodyne correlation function for syndiotactic polymethyl methacrylate spread on water at a surface concentration of 1.7mgm~2 by the transmission grating act as the reference beam of zero frequency shift, and this beats with the scattered light at the photocathode to produce the typical correlation function shown in Figure 12.18. From these data the capillary wave frequency co and the decay constant F can be obtained. By assuming that y and e! are zero, y0 and e0 can be obtained from these values by solving the dispersion equation. Extracting the viscous moduli requires a non-linear least squares fit of the Fourier transform of the power spectrum equation to the data. A computational method for this process has been developed by Earnshaw et al. [59] and exhaustively justified [60]. Wider aspects of light scattering from liquid surfaces are discussed in the book edited by Langevin [61]. To date much of the work published on SQELS from spread polymers has emanated from Yu and colleagues [62-65], but assumed that the viscous moduli are zero. We have reported [66] a limited study of spread polymethyl methacrylates and polyethylene oxide. Figure 12.19 shows the variation in surface tension, shear viscosity and dilational modulus obtained from SQELS data as a function of surface concentration. The viscoelastic moduli both show maximum values at finite values of the surface concentration. As the capillary waves generate oscillatory stress and strain, these are related via the complex dynamic modulus of the surface a* =y*[G'(co) +iG"(co)]

Surface tension (mN nrr1) Shear viscosity (mN s rrr1)

Surface concentration (mg nrr2)

Surface concentration (mg m*2) Figure 12.19

(Continued)

Dilational modulus (mN nrr1)

Surface concentration (mg nrr2)

Figure 12.19 Derived parameters from surface quasi-elastic light scattering as a function of concentration of polymethyl methacrylate spread on water: (a) surface tension; (b) surface shear viscosity; (c) dilational modulus

where <x* is stress, y* is strain, G'(co) is the storage modulus (surface tension) and G"(a>) is the loss modulus (a>yf). Using volume fraction composition data obtained from neutron reflectometry on the spread polymer films, it is evident that the surface film loss modulus is linearly dependent on the volume fraction of polymer in the film. If we presume that the relaxation process in the surface film is described by a Maxwell model, then G'(co) = Ge + GCO2T2/(1 + CO2T2)

where Ge is the elastic modulus at co = O, i.e. the static surface tension. Further, if there is only one relaxation process in the spread film, then T = A7c/co2y' where An is the difference in the surface tensions measured by SQELS and from static (Wilhelmy) plate methods. The dependence of relaxation time on the volume fraction of the polymer shows an exponential increase, Figure 12.20. To obtain further insight into the relaxation mechanism requires the frequency dependence (i.e. different Q values) of the transverse shear viscosity to be known.

Relaxation time (s)

SYN PMMA SQELS DATA

VoI fraction of polymer

Figure 12.20 Relaxation time for spread polymethyl methacrylate as a function of volume fraction of polymer in the spread film

12.4 CONCLUSIONS An overview of some of the areas where light scattering has made contributions to polymer science has been given. The emphasis has been on dynamics, either by using light to follow a process (crystallisation or phase separation) or using dynamic light scattering per se. A broad range of polymer types and situations has been covered and the discussion has by no means been exhaustive. Evidently, despite its maturity as a laboratory technique, light scattering is still capable of providing much information on polymer systems. Furthermore, the development of newer applications such as surface quasi-elastic light scattering will enable investigations of surface gelation and surface ordering in polymer solutions, areas which have yet to be investigated.

12.5 REFERENCES [1] M.B. Huglin (Ed.), Light Scattering from Dilute Polymer Solutions, Academic Press, London, 1972. [2] P. Kratochvil, Classical Light Scattering from Polymer Solutions, Elsevier, Amsterdam, 1987.

[3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44]

H. Yamakawa, Modern Theory of Polymer Solutions, Harper, New York, 1971. GC. Berry, J. Polym. ScL, Polym. Symp., 1978,65,143. W.R. Krigbaum and G. Brelsford, Macromolecules, 1988, 21, 2502. Z. Tuzar, P. Kratochvil and D. Strakova, Eur. Polym. J., 1970,6,1113. BJ. Berne and R. Pecora, Dynamic Light Scattering, Wiley, New York, 1976. K.S. Schmitz, An Introduction to Dynamic Light Scattering by Macromolecules, Academic Press, San Diego, 1990. R.S. Stein and JJ. Keane, J. Polym. ScL, 1955,17, 21. R.S. Stein and M.B. Rhodes, J. Appl. Phys., 1960, 31,1873. R.S. Stein, P. Erhardt, JJ. van Aartsen, S. Clough and M. Rhodes, J. Polym. Sci. C, 1965,13,1. RJ. Samuels, J. Polym. Sci. C, 1965,13, 37. G.E. Wissler and B. Crist, J. Polym. Sci., Polym. Phys. Ed., 1985, 23, 2395. M. Ree, T. Kyu and R.S. Stein, J. Polym. ScL, Polym. Phys., 1987, 25,105. J.V.Champion,A.KilleyandG.H.Meeten,J.Polym.ScL,Polym.Phys.Ed., 1985,23, 1467. G.H. Meeten and P. Navard, J. Polym. ScL, Polym. Phys., 1989, 27, 2023. M. Desbordes, G.H. Meeten and P. Navard, J. Polym. ScL, Polym. Phys., 1989, 27, 2037. P.H. Richardson and R.W. Richards, unpublished work. WT. Culberson and M.R. Tant, J. Appl. Polym. ScL, 1993,47, 395. P.H. Richardson, ubpublished results. J.C. Schultz, Polymer Materials Science, Prentice-Hall, New Jersey, 1974. J.W. Cahn and J.E. Hilliard, J. Chem. Phys., 1958,28, 258. J.G. Connell, Ph.D. Thesis, University of Strathclyde, 1989. H.L. Snyder and P. Meakin, Macromolecules, 1983,16, 757. T. Hashimoto, M. Itakura and N. Shimidzu, J. Chem. Phys., 1986,85,6773. A. Cumming, P. Wiltzius, F.S. Bates and J.H. Rosedale, Phys. Rev. A, 1992, 45, 885. D.E. Koppel, J. Chem. Phys., 1972,57,4814. P.N. Pusey, D.E. Koppel, D.W. Schaefer, R.D. Camerini Otero and S.H. Koenig, Biochemistry, 1974,13, 952. W. Burchard, M. Schmidt and W.H. Stockmayer, Macromolecules, 1980,13,1265. S.W. Provencher, Comput. Phys. Commun., 1982,27, 213. S.W. Provencher, in E.O. Schulz-DuBois (Ed.), Photon Correlation Techniques in Fluid Mechanics, Springer, Berlin, 1983. S.W. Provencher, in S.E. Harding, D.B. Sattele and V.A. Bloomfield (Eds.), Laser Light Scattering in Biochemistry, Royal Society of Chemistry, Cambridge, 1992. A.D.W. McLenaghan, Ph.D. Thesis, University of Strathclyde, 1990. T. Tanaka, L.O. Hocker and G.B. Benedek, J. Chem. Phys., 1973,59, 5151. E. Gleissler and A.M. Hecht, J. Phys. (Paris) Lett., 1979,40, L173. A.M. Hecht and E. Geissler, J. Phys. (Paris), 1978, 39, 631. A.M. Hecht, E. Geissler and A. Chosson, Polymer, 1981,22, 877. E. Geissler and A.M. Hecht, J. Chem. Phys., 1982, 77,1548. EJ. Amis, P.A. Janney, J.D. Fery and H. Yu, Macromolecules, 1983,16,441. N.S. Davidson, Ph.D. Thesis, University of Strathclyde, 1984. N.S. Davidson, R.W. Richards and E. Geissler, Polymer, 1985, 26,1643. T.G. Scholte, J. Polym. ScL A2, 1970,8, 841. W.W. Merrill and M. Tirrell, in G.R. Freeman (Ed.), Kinetics of Nonhomogeneous Processes, Wiley, New York, 1987. T.P. Lodge, N.A. Rotstein and S. Prager, Adv. Chem. Phys., 1990,79,1.

[45] M. Doi and S.F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, Oxford, 1986. [46] P.G. de Gennes, Macromolecules, 1986,19,1245. [47] W. Brown and P. Zhou, Macromolecules, 1989, 22, 3508. [48] T. Nicolai, W. Brown, S. Hvidt and K. Heller, Macromolecules, 1990,23, 5088. [49] CH. Wang, J. Chem. Phys., 1991,95, 3788. [50] CH. Wang, Macromolecules, 1992, 25, 1524. [51] CH. Wang and X.Q. Zhang, Macromolecules, 1993,26, 707. [52] N.A. Rotstein and T.P. Lodge, Macromolecules, 1992, 25,1316. [53] S. Pajevic, R. Bansil and C Konak, Macromolecules, 1993, 26, 305. [54] AJ. Hyde, J. Hadgraft and R.W. Richards, J. Chem. Soc. Faraday Trans II, 1979,75, 1495. [55] D.A. Davison, University of Durham, work in progress. [56] J.C Earnshaw and R.C McGivera, J. Phys. D, 1987,20, 82. [57] S. Hard and R.D. Neuman, J. Colloid Interface ScL, 1981,83, 315. [58] J.C. Earnshaw, in CA. Croxton (Ed.), Fluid Interfacial Phenomena, Wiley, New York, 1986. [59] J.C Earnshaw, R.C McGivern, A.C McLaughlin and P. J. Winch, Langmuir, 1990, 649. [60] J.C. Earnshaw and R.C. McGivern, J. Colloid Interface ScL, 1988,123, 36. [61] D. Langevin (Ed.), Light Scattering by Liquid Surfaces and Complementary Techniques, Dekker, Basel, 1992. [62] M. Kawaguchi, M. Sano, Y.-L. Chen, G. Zografi and H. Yu, Macromolecules, 1986, 19, 2606. [63] M. Kawaguchi, B.B. Sauer and H. Yu, Macromolecules, 1989, 22,1735. [64] B.B. Sauer, M. Kawaguchi and H. Yu, Macromolecules, 1987, 20, 2732. [65] K.-H. Yoo and H. Yu, Macromolecules, 1989, 22,1989. [66] J.A. Henderson, R.W. Richards, J. Penfold and R.K. Thomas, Macromolecules, 1993, 26,65.

13 NEUTRONSCATTERING FROM POLYMERS A. R. RENNIE Polymers and Colloids Group, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 OHE, UK

13.1 INTRODUCTION In the space of a few pages it would be impossible to provide a full description of the different investigations of polymers that can be made, or even have already been made, using neutron techniques. The intention is rather to provide an introduction to the methods. Those readers who may wish to exploit the special advantages of neutrons will be able to assess the feasibility of experiments and find some guide to the recent literature. The description of published work will necessarily be selective and will try to reflect some of the wide range of studies that are now in progress. There are several reviews of both the technique of neutron scattering and its application to the study of polymers. Although both provide little information about work on polymers, readers interested in a thorough description of the theory of neutron scattering should refer to the books by Lovesey [1] and Squires [2]. Reviews and books concerning neutron studies of polymers can be divided into those that are concerned with the technique [e.g. 3-5] and those that describe results, often in particular areas of the topic such as copolymers [6], networks [7], polymer motion [8-11], semi-crystalline polymers [12], polymer colloids [13] and biopolymers [14].

13.2 THE PRINCIPLES OF NEUTRON SCATTERING The scattering of neutrons can be treated formally as an inversion problem: the scattered intensity from a plane incident beam of wavelength A into a solid angle dQ, in the energy range d£, at a scattering angle 6 can be expressed as the Fourier transform in space and time of the pair correlation function of scattering length density. In this respect the theory of neutron scattering is identical to that of weak scattering of any other form of radiation. The advantages of neutron scattering Polymer Spectroscopy. Edited by Allan H. Fawcett © 19% John Wiley & Sons Ltd

arise from the magnitudes of the quantities mentioned above and their interrelationships. For example, the large mass of the neutron when compared with electrons or photons is important in providing good coupling between molecular motion and the energy of the scattered beam. In the next few paragraphs some of the formalism associated with the description of scattering will be presented. Further details of the principles of scattering and the properties of neutrons will be found in books on atomic physics such as that by Born [15]. Many people will not be concerned with such fundamentals of the theory, and the interpretation of many experimental results can be adequately performed using the simple relationships that derive from appropriate integrations of the wave equations. Some of these are described in the next section. It is first useful to recall that the neutrons can be considered as either particles or waves; the connection between the two descriptions is provided by the de Broglie relationships: E = hv p = hk/2n

(1) (2)

where E is the energy, p is the momentum (product of mass and velocity v), v is the frequency and k is the wave vector of the neutron. The magnitude of the wave vector is given by |k| = 2n/h where X is the wavelength. A schematic diagram of a general scattering experiment is shown in Figure 13.1. We can distinguish two general cases. First, the situation in which the energy and wavelength of the scattered neutron are equal to those of the incident beam. This is known as elastic scattering, and gives the simple result that the momentum transfer | Ql is (An/X) sin (0/2). More generally, there will be some energy transfer between the neutron and the sample. The experiment is then said to involve inelastic scattering or, if the energy transfer is small and corresponds only to a broadening of the incident wavelength distribution, quasi-elastic scattering. Advantages of neutrons over other types of radiation for studies of polymers arise both from the relationship of energy to wavelength and from the mechanism of scattering by nuclei. The calculation of scattering patterns is based on the summation of amplitudes or intensities scattered from all components. The intensity I of a wave described in the usual notation of complex variables is given by I = AA*

(3)

where A is the amplitude and the star represents a complex conjugate. The addition of wave amplitudes from different scattering centres must take account of the phase of each wave if the incident beam is a coherent wave front. Coherence in the context of neutrons will be discussed further below. The amplitude A scattered by a single nucleus at a position r from an incident plane wave of amplitude A0 is given by:

A = Aobc-^/\r\

(4)

Sample

Detector

Sample

Figure 13.1 (a) Schematic diagram of a scattering experiment; (b) the wave vectors that describe the scattering process. Q is the difference between the incident and scattered wave vectors

This is known as the Born approximation for scattering from weak potentials. It is seen that the scattered wave is spherically symmetric and decreases in intensity as l/|r| 2 , which is the usual inverse square law. For a distribution of scattering lengths described by a density p(r) the resulting amplitude is

A = A0^tp(r)e-^/\rndr3

(5)

and thus the scattered intensity / is / = AA* = Al f [p(r)e- fQr p(r')e^7|r| 2 ]d(r - r')3

(6)

The quantity p{r)p{r') is the spatial correlation function of the scattering length density, and the integral with e" lQ(r " r) is equivalent to a Fourier transform. It would be out of place to develop this formalism at great length. The results for elastic scattering are well described by Hukins [16].

It is possible to include the angular frequency co or energy E of the neutrons and the time variation of the scattering length density in Equation (4) to device related results for inelastic or quasi-elastic scattering. A more formal treatment would first treat this general case and then simplify the results for elastic scattering. These will not be derived but it is sufficient to quote the result:

dL/dodQ = I/Al

= I Mr,t)e-i(Qr+cor)p(^tV(Qr'+
- r'fdt

(7)

Details of the theory of inelastic scattering can be found in the books of Lovesey [1] and Squires [2]. The intensity or the differential scattering cross-section dZ/dcodfi can be calculated for various models of structure and dynamic behaviour using Equation (7). The models of particular importance to the study of polymers are similar to those relevant to quasi-elastic light scattering [17,18]. In practice, the calculation of such integrals is often simplified by recognising that they are Fourier transforms and that several theorems are available to describe their properties, and are included in textbooks on mathematical methods [20,21]. Very few polymers are completely crystalline, and so the present description differs from that of most scattering experiments, which are concerned with diffraction or inelastic scattering from a regular lattice. The problems of predicting scattering patterns can generally be reduced to integrals, results for many of which can be derived readily or calculated numerically. For the case of structural studies by elastic scattering, many of these results are available in the literature [22-24], even for amorphous or random structures. Most were originally derived for X-ray or light scattering. An important feature of neutron scattering is the neutron scattering length, designated b9 which describes the probability of scattering. Unlike photons or electrons the neutron is scattered by the atomic nucleus. Some values for elements commonly found in synthetic polymers are listed in Table 13.1. The scattering lengths are not correlated with atomic number and can change between isotopes of a single element. This allows isotopic labelling of individual molecules or parts of molecules without perturbing the chemistry, and has proved of particular value in the study of polymers, which often consist largely of atoms such as carbon, hydrogen, oxygen and nitrogen with low electron densities and thus poor contrast for other radiation. Of particular significance is the ability to label individual molecules among other chemically identical polymers to determine their size or investigate their mobility in the bulk. Most readers will be familiar with the idea that structural studies of materials carried out by light scattering can be performed only within the limits of coherence of the source. This is usually explained in terms of the finite time over which a wave is emitted from a source. Similar considerations apply to neutrons;

Table 13.1 Neutron scattering cross-sections [19] Element Hydrogen 1 H Deuterium 2 H Carbon Nitrogen Oxygen

Coherent scattering lengh/fm -3.74 6.67 6.65 9.21 5.9

Incoherent scattering cross-section/10"28 m 2 79^9 2.04 0.0014 0.49 0.015

there is, however, a further constraint on the condition for coherent addition of amplitudes. A neutron possesses the property known as spin, and must retain the same spin state for coherent scattering. The nuclei of atoms can also have spin, and will in general have two separate probabilities of scattering associated with the preservation and loss of spin coherence. It is usual to quote the coherent scattering length (often written as b) in units of length and the incoherent scattering as a cross-section
13.3 NEUTRON EXPERIMENTS There are many classes of experiment that can be made with neutrons; they cover a wide range of angles, wavelengths and energy transfer and it is not possible to give a full description of them all here. Some experiments are frequently used with polymers, and these will be outlined briefly in three categories after a few general remarks on neutron instrumentation. The description of scattering theory given above has indicated that the important variable is the momentum transfer Q rather than the wavelength or angle of scattering. It is possible to measure over the necessary range of Q values in two distinct ways. The first is to use a fixed wavelength and scan the angle. The second is to use a fixed angle and a range of wavelengths. This second technique can be exploited with advantage at pulsed neutron sources: the source provides a pulse consisting of many wavelengths which can be analysed using measurements of the time-of-flight of neutrons from the source to the detector. This

Table 13.2 Benefits of neutron scattering Advantages Disadvantages Contrast with isotopes Low flux Contrast variation Large, expensive source Measurements in bulk Easy control of sample environment Measurements of molecular motion Can be surface specific approach can exploit a wide range of wavelengths available in a pulse, as it avoids the need to provide a monochromatic beam. On continuous sources it is usual to use a monochromator, either crystals used for Bragg diffraction or mechanical velocity selection, and measurement is made at a range of angles. These two techniques are sometimes associated with spallation sources, which are often pulsed, and reactors, which are usually run as continuous sources. Exceptions to both these rules occur, in that pulsed reactors have been built and, even more simply, the continuous beam from a reactor can be pulsed using a rotating chopper. Continuous spallation sources can also be built. The details of design of both neutron sources and the diffractometers and spectrometers associated with them are to be found in the specialist literature [25-27]. A property common to all neutron sources is that of low flux or brightness. Even the best design of nuclear reactors cannot provide a flux of thermal neutrons in the moderator close to the core larger than a few times 10 15 n cm ~2 s ~ *. After selection of wavelength (monochromation) and collimation to define the incident beam, the flux available at the sample on a diffractometer or spectrometer is unlikely to be more than 108n Cm -2 S" 1 and is often much less. This is lower than the flux of photons available from typical laboratory sources of light or X-rays. A consequence of this low flux is the need to use large samples (crosssectional areas of % 1 cm2) and detectors of high efficiency covering a large solid angle around the sample. The combination of large samples and the need to obtain reasonable angular resolution on the detectors will usually lead to physically large instruments. An extreme example is the overall length of 80 m for one small angle scattering instrument known as Dl 1, which has been built at the Institut Laue-Langevin in Grenoble, France [28]. Characteristics of neutron scattering for comparison with other radiation are shown in Table 13.2.

13.3.1 STUDIES O F POLYMER DIMENSIONS: SMALL ANGLE SCATTERING The most frequently encountered use of neutrons in the study of polymers is the measurement of small angle scattering (SANS). Use of neutrons with wavelengths in the range 0.5-2 nm and scattering angles between 0.1° and 10° readily allows

investigation of structures in the size range l-200nm. This class of study can be used to give information about the size and conformation of individual polymer molecules. These may be either in solution or in the bulk. The technique is also used for the study of phase separation in polymer blends or copolymers and in the study of structures of composite materials. The theory of small angle scattering has several simplifications over the more general ideas outlined above. It is concerned only with elastic scattering, although in practice the total intensity measured includes both elastic and inelastic scattering [29, 30], which can give rise to some additional complications to measurements made with time-of-flight instruments. In the most straightforward case, the scattering from isolated objects is measured to determine their size and shape. The integral in Equation (6) is thus performed over a single object such as a polymer molecule in solution. There is no correlation between the positions of nuclei in different objects, and so the total intensity from a solution is found by adding the intensity from each object. Several simple results can be derived for the scattering at small Q. It is useful to write down the result of integrating Equation (6) in the following simplified manner /(Q) = CP(Q) (8) where P(Q) is a function describing the shape of the scattering normalised to unity at Q = 0. The constant C depends on the contrast (square of scattering length density difference), the number density of particles and the incident flux. A general result due to Guinier [23] states that for any object with spherical symmetry, in the limit of small Q9 P(Q) will be approximated by />(G) = exp(-e 2 R g 2 /3) (9) where Rg is the radius of gyration of the object. This is clearly of considerable value in determining the dimensions of polymer molecules, even in the absence of detailed models of the structure. It is trivial to show by way of series expansions that in this condition of QRg < 1 the result can also be written as 1/P(Q)=I-Q2

R2g/3

(10)

which is the result of Zimm [31] frequently encountered in light scattering. It is of course possible to extend the analysis to include virial interactions between molecules in the manner described in light scattering texts [32, 33]. In many circumstances it is possible to extend the range of measurements with neutrons to cover more than this low Q limit, and then more detailed models of the structure must be evaluated. Debye [22] has derived a result for the scattering from a Gaussian distribution of polymer segments appropriate to a random polymer coil which is of the form: P(Q) = (2/Q2Rl)lexp(-Q2R2g)-(l-Q2R2K (11) and can be used to fit data over a much wider range of momentum transfer until the Gaussian approximation for molecular structure fails at short distances.

The constant C describing the absolute intensity is of importance as it permits determination of the molecular weight of polymers. By rearrangement of the constants in Equation (S), it can be expressed as: I/C = ( N A / c M w ) p > p - p s ) 2

(12)

where NA is Avogadro's number, c is the concentration, Mw is the molecular mass, pm is the mass density of the polymer, and p p and p s are the scattering length densities of the polymer and solvent respectively [14, 34]. Measurements of the absolute intensity of scattering at low Q, which can be extrapolated to Q = 0 or fitted using one of the equations above, can thus give information about the weight average molecular mass. The real value of small angle neutron scattering lies in the realisation that the simple theory above, which is essentially identical to that of light scattering, can be extended in two ways. The possibility of isotopic substitution and contrast between chemically identical molecules can lead to measurements of molecular dimensions in the bulk rather than in solution. Some of the early work with SANS or polymers was concerned with the verification of the idea that screening of molecular interactions in the melt gave rise to molecular dimensions that were identical to those found in theta solvents [35-37]. This work has now been extended to a wide range of investigations of molecular conformation in bulk polymers, which can include amorphous glasses [38], melts [39], gels [40-42], elastomers [43-46] and semi-crystalline polymers [47-51]. A major boost to the application of SANS to polymers in the bulk came from the recognition that the screening of molecular interactions in bulk homopolymers could be used to extend the range of concentrations over which measurements can be made. This idea, which is known as the random phase approximation or RPA [52, 53], states that if there are no interactions, i.e. the second virial coefficient is zero, then measurements of molecular dimensions can be made at any concentration. In order to optimise count rates this may often be close to 50% blends of deuterated and protonated polymers. Several experiments have been performed to test this theory [54, 55], which is now widely applied. It should be remembered that there are many cases where the measurement of interactions is of importance. SANS has been widely used for the study of polymer blends. A simple extension of the theory gives the following expression for the scattering from a blend of two miscible polymers with a Flory-Huggins interaction parameter x'. 1/7(0 - 1 / P 1 ( Q ) + 1/P2(Q) -2X

(13)

where P 1 and P 2 are the Debye expressions for separate polymers as given by Equation (11). Other extensions of theory can be made to describe the scattering from copolymers [56,57], branched and star-like polymers [58] and also variety of geometrical shapes that may be appropriate to describe liquid crystalline and semi-crystalline structures [23, 24]. Local structure in polymers such as that

arising from chain rigidity has also been described [59]. It should also be mentioned that the scattering from polymers bound to the interface of colloidal particles has been the subject of several investigations with SANS. 13.3.2 POLYMERS AT S U R F A C E - R E F L E C T I O N Neutrons can be reflected from planar surfaces according to the usual laws of specular optics. The refractive index n for neutrons is given by: n=l-(p№t)

(14)

This equation indicates that for most materials the refractive index will be very close to, but generally slightly less than, unity. The condition in optics known as total internal reflection will thus be replaced by total external reflection [60]. This will occur at low angles, typically about one degree for thermal neutrons. At angles larger than the critical angle, the reflectivity is reduced, and it is this variation that provides information about the structure of the interface. The intensity of a neutron beam reflected from a surface can be calculated exactly using the optical matrix approach of approximating the interface to a series of thin layers and calculating the reflection at each boundary in the manner described by Born and Wolf [61], Heavens [62] or Abeles [63]. It is perhaps more instructive to consider an alternative procedure based on the kinematic theory of scattering [64] which gives the following approximate expression for the reflectivity R(Q) as a function of Q the momentum transfer normal to the interface: R(Q)= I6n2\ H(Q)2 \Q2 (15) where H(Q) is the Fourier transform of the scattering length density distribution normal to the interface p(z). This result is not valid close to critical reflection,but can now be extended [65] to provide analytical forms over the entire range of Q. The experimental arrangements for such measurements are shown schematically in Figure 13.2(a). This technique has emerged only recently but is rapidly growing. Reviews of the experimental technique [66] and the application to polymers [67] have already appeared. The application of neutrons to the study of polymer surfaces or interfaces can be divided into two categories. First, the study of polymers adsorbed or spread at liquid interfaces; secondly, the study of polymers in thin films. This second category provides interesting models for measurements on polymer compatibility and inter-diffusion. Reports of ordering of copolymers at surfaces [68], phase separation [69] and the width of polymer/polymer interfaces during diffusion [70] have been made. The results on adsorbed polymers using neutron reflection provide a useful complement to studies Qf adsorption by small angle scattering and other classical techniques. Measurements of the excess polymer at both solution/vapour [ 7 1 73] and solution/solid [74-76] interfaces have been described. Other studies

Detector

Neutrons

Sample

Solid

Solution Figure 13.2 (a) Neutron reflection experiment; the geometry is arranged so that only specular reflection (angle of incidence is equal to angle of reflection) is observed; (b) observations can be made either at the interface of a sample with vapour (i) or at a solution/solid interface (ii) provided that a material of adequate transparency to neutrons such as silicon or quartz is used to form the bulk of the solid have been made of the structure of polymer monolayers spread at the air/water interface on Langmuir troughs [ 7 7 - 7 9 ] .

13.3.3 POLYMER DYNAMICS—QUASI-ELASTIC SCATTERING The advantage of neutron scattering for studies of polymer dynamics is the direct information that is provided about the molecular correlation functions in time and space by the technique. Other spectroscopic probes such as NMR and dielectric or mechanical response can provide information about the time or frequency of relaxations, but do not directly provide information about the length scale on which the dynamic processes occur. Once again there is an analogy to dynamic light scattering, and most of the theory is similar. The derivation of the scattering laws describing the differential scattering cross-

precession

Figure 133 A schematic diagram of a neutron spin-echo spectrometer. The difference in velocities of the polarised neutron before and after the scattering process can be observed by measuring the precession in the regions of uniform magnetic field H. The difference in the precession is easily determined from the polarisation of the beam reaching the detector D if the fields before and after the sample S are symmetrical and the polarization is inverted with the flipper coil marked as U/2. The coils marked n/4 are used to provide magnetic fields that define the initial and final states of polarisation section for various models of polymeric motion, such as reptation of molecules through entanglements or the hydrodynamic screening described by Zimm, is complex. The main results can be found in the book by Doi and Edwards [80]. For our purposes it is sufficient to recognise that a diffusive process gives rise to a scattering law of the form: /(Q, Q) = DQ2/{Q2 + D2Q2)

(16)

where D is the diffusion coefficient and Q and Q refer to the momentum and the energy transfer in the scattering process. If measurements are made directly in the time domain, then the scattering law will ocrrespond to the Fourier transform of this Lorentzian, which is simply an exponential decay I{Q,t) = exp(-DQ2t) (17) Measurements of the diffusion of polymers in the melt and in solution have been made using neutrons. It is of particular interest that the distance scale over which diffusion is measured depends inversely on Q9 and so it is possible to probe both the regions of internal modes and overall intermolecular diffusion. The technique that has attracted most recent attention is that of neutron spin-echo (NSE) spectrometry. This method of measuring small energy transfers, which was proposed by Mezei [81, 82], cleverly avoids the need to monochromate the beam precisely and thus provides gains in the incident flux. The experiment (see Figure 13.3) measures the energy change of each neutron by observation of the precession of the spin in uniform magnetic fields. Experiments using the NSE technique have been used to verify the microscopic aspects of Rouse and Zimm models of the motion in polymer solutions [83]. They have also shown that the reptation process [84] of self-diffusion along a tube

can be well described by Rouse modes within the tube. The effects of entanglements (topological constraints) can be observed in the long distance (small Q) modes in melts and networks [85-88]. More recently, experiments have looked at the motion of copolymers [89] and of polymers close to the glass transition [90-92].

13.4 SOME EXAMPLES OF RECENT PROGRESS Here a few examples of recent work will be mentioned. The selection naturally reflects the author's interests, but is intended to illustrate those areas of neutron scattering that have particular prominence at present or are growing rapidly. Many of the early experiments with neutrons were concerned with the properties of homopolymers; indeed, physicists were often seeking the simplest systems that could be considered as uniform, flexible macromolecules to test fundamental models of polymer conformation and dynamics. Recent work has been characterised by an increasing complexity in the systems that are investigated to include copolymers, blends and composite materials. In some cases the neutron studies are a minor part of more widespread investigations of the properties of novel polymers, their synthesis or processing. The examples below are intended to provide some insight into the range of studies that can be made and the precision of data that can be obtained. 13.4.1 STUDIES O F COPOLYMERS The study of copolymers with scattering techniques is greatly aided by isotopic contrast variation. Studies of phase separated and homogeneous states have been made on several systems [6]. A description of the static scattering obtained from a diblock copolymer in the homogeneous melt has been given by Leibler [56]. It is characterised by a peak in the small angle scattering arising from the so-called 'correlation-hole'. A volume around a segment of a given type is depleted in that monomer by the constraints of the relative monomer density imposed by the molecular block structure. This is shown in Figure 13.4. Small angle scattering on such materials proves to be an excellent way of measuring the interaction, as the width of the peak seen in the scattering pattern is very sensitive to the interaction parameter xRecently the neutron spin-echo technique has been used in conjunction with isotopic labelling to test theories of copolymer dynamics. The theory has been reviewed in the context of light scattering [93]. Data for a diblock isoprenestyrene copolymer have been presented [89] that are in good agreement with the RPA theories. The findings demonstrate a general feature that is perhaps worthy of comment. The mobility of the more mobile isoprene segment can be characterised by a relaxation time r or characteristic frequency Q. The ratio Q/Q2 is not

Intensity/a.u.

Q/nrrr1

Figure 13.4 Scattering from a diblock copolymer in the homogeneous melt showing the variation with temperature. This data taken from the study of styrene-isoprene diblock polymers described in ref. [89] is measured with X-rays, although the principles are the same as for SANS measurements. If there is sufficient X-ray contrast (electron density difference) it is usually more economic to use X-rays. The width of the peak is a good measure of the interaction between the two components

Q? / nnr2 Figure 13.5 Motion of the polyisoprene block in blends of 50:50 polyisoprene/polystyrene diblock copolymer dissolved in polyisoprene at the different temperatures indicated. The data is displayed as the characteristic frequency O divided by Q2. The relaxation time is seen to tend to infinity at a finite Q vector that corresponds to the peak in the static structure seen in Figure 13.4. Full details of the interpretation of these data are to be found in ref. [89] constant, as might be expected for a normal diffusion process, but varies with Q. This is normal for the 'Rouse' or 'Zimm' relaxation modes of a polymer chain. The significant feature of the data for the copolymer shown in Figure 13.5 is that the ratio Q/Q2 tends to zero at a finite value of Q. This corresponds roughly to peak in the static structure, and demonstrates clearly that a static correlation between monomers of a given type at a given distance or Q-vector must be reflected in hindered diffusion in the same range.

IgR

Q/nnrr1

Figure 13.6 Reflectivity curves for deuterated polystyrene (390000 Mw) adsorbed at an amorphous quartz surface from a 0.1% w/w cyclohexane solution [94]. The scattering length density of the solvent was adjusted (HfD ratio) to match the quartz so that the only signal arises from the adsorbed polymer. The curves for 15 (•) and 350C (+) are shown; the adsorption between these limits was reversible. The continuous lines show approximate fits indicating an exponential polymer segment distribution with a characteristic length increasing from 95 to « 800 A

13.4.2 ADSORPTIONATSURFACES The use of neutrons to study interfaces is still relatively new, but several studies have already been made which demonstrate the scope of the technique. By way of example, some data for polystyrene adsorbing to amorphous silica [94] are shown in Figure 13.6. The curves show a large difference between 15 and 350C, which is associated with a rapid increase in adsorption as the temperature is decreased to 210C, which is the cloud point for the solution of deuterated polystyrene (molecular weight «390000) in a mixture of deuterated and protonated cyclohexane. The large increase in adsorption is substantially reversible in that, on heating, most of the polystyrene will be desorbed. This contradicts the frequently held view that physical adsorption of polymers is usually irreversible. However, it must be remembered that in this case the adsorbed layer really corresponds to a large thickness of concentrated solution. The layer is rather thicker than that of single polymer molecules, and many of the molecules may have no direct interaction with the silica surface. It must not be assumed that this type of

behaviour is typical of polymers in general, as rather few systems have been subject to detailed study, although reports in the literature do refer to polyethylene oxide adsorbing from aqueous solution [74] and to some copolymers [75]. A further point that emerges in such studies on polymers is that isotopic labelling can sometimes significantly alter the behaviour of a polymer solution or blend. Detailed studies of the system polystyrene/cyclohexane have been

Q2/nm- 2

Figure 13.7 (a) Schematic diagram of chain fragment diffusion in polymer glasses and melts; after the initial fragmentation, which can occur rapidly, the polymer segments diffuse apart and at long times will appear as separate smaller polymer molecules; (b) example data [101] for a deuterated polycar bonate/tetramethyl polycarbonate blend containing some tetraethylethane groups that can split readily under moderate heating (three or four per molecule). The data shows the diffusion at 1860C during which the polymer is observed

published [95], showing a variation of several degrees in the cloud point. Other work on deuterated polystyrene/protonated polystyrene has also shown interactions that can be significant in high molecular weight polymers [96,97].

13.4.3 KINETICS A N D POLYMER M O T I O N In recent years it has been possible to extend the use of small angle neutron scattering to study many processes that concern polymers in a variety of complex sample environments. These have included deformation and yield of elastomers and glassy polymers in conditions close to those occurring in processing and service. Other aspects of time dependent behaviour have included the study of polymerisation and observing the growth of polymer molecules during the scattering experiment. An example of the use of time dependent small angle scattering can be found in the chain fragment diffusion experiments described by Hellmann and co-workers [98-101]. Polycarbonate molecules with links that can be thermally degraded were included in a matrix of other polymers. As the chain fragments diffuse apart after the degradation, the change in apparent radius of gyration and molecular weight can be observed by SANS. This process is shown schematically in Figure 13.7(a), and some data showing the resulting data for a sample held at 186 0C are given in Figure 13.7(b). The times shown on the

Figure 13.8 Results of diffusion measurements over a range of temperatures for the system shown in Figure 13.7. The comparison with the standard WLF equation [102] (dashed line) and the glass transition temperature Tg is indicated

graph of normalised inverse intensity against Q2 indicate that the time scale of the diffusion process over a distance of about a molecular radius is several minutes. At a modern high flux reactor with good instrumentation it is possible to record data at approximately every minute. This has permitted measurements of diffusion coefficients in the range 10"1 4 - 1 0 ~ 1 8 cm2 s" 1 such as those shown in Figure 13.8.

13.5 FINAL REMARKS Neutrons provide a powerful investigative tool to study the structure and molecular motion in materials. Although available in only a few specialist laboratories, they have been widely exploited, and both sample preparation and data analysis are relatively straightforward. It is to be expected that neutron scattering will increasingly become a standard technique available to polymer scientists for characterisation of samples, and also for measurement of the structure of materials to correlate with physical properties. The possibilities of building realistic sample environments permit the study of polymers and their surfaces in conditions that are close to those in service or in polymerisation reactors.

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14 OPTICAL ACTIVITY AND THE STRUCTURE OF MACROMOLECULES F. CIARDELLI Department of Chemistry and Industrial Chemistry, University of Pisa, Italy and CNR, Center for Stereordered and Optically Active Macromolecules, Pisa, Italy

O. PIERONI Department of Chemistry and Industrial Chemistry, University of Pisa, Italy and CNR, Institute of Biophysics, Pisa, Italy and

A. FISSI CNR, Institute of Biophysics, Pisa, Italy

14.1 INTRODUCTION 14.1.1 ORIGIN OF OPTICAL ACTIVITY IN MACROMOLECULES As in low molecular weight compounds, optical activity can be observed only in chiral macromolecules, that is, macromolecules for which all allowed conformations lack reflection symmetry elements. The identification of chiral macromolecules differs from that of low molecular weight molecules because of the substantially linear structure along the chain backbone. Accordingly, analysis of the symmetry properties has been carried out on the basis of three different models: (i) the infinite length chain; (ii) the finite length chain with equal end groups; and (iii) the finite length chain with different end groups. Point symmetry valid for molecules having definite and 'discrete' dimensions in all directions can be used only for the last two models, whereas linear symmetry must be used for the first model, which implies an infinite dimension [I]. In linear symmetry, in contrast to point symmetry, the new symmetry operation 'translation' and the new symmetry element 'translation axis' are introduced. The analysis for aflexiblemacromolecule, which can assume an extremely large number of conformations, is conveniently carried out on the most symmetric of these conformations, which is usually the 'planar zigzag'. The Polymer Spectroscopy. Edited by Allan H. Fawcctt © 19% John Wiley & Sons Ltd

analysis of the derived Fischer projection of an infinite chain indicates that this is chiral when a symmetry plane containing the chain, those perpendicular to the chain and that with translation containing the chain are all lacking [ I ] . For finite length chains, chirality is guaranteed by lack of symmetry in the plane containing the chain and the plane perpendicular to the chain at its central point [I]. Thus, in vinyl polymers, only atactic macromolecules can be chiral in the first model with infinite length chain. The atactic and the syndiotactic macromolecules with an even number of monomer residues are chiral in the finite chain model with identical end groups, whereas all isotactic, syndiotactic and atactic chains have a chiral structure for the last model with different end groups [1,2]. Even in vinyl polymers consisting of chiral macromolecules, extremely low or vanishing optical rotation can be predicted when the molecular weight is high, even if a complete separation of the enantiomeric pair were to be possible. Indeed, in vinyl polymers every stereogenic carbon atom is flanked by two CH 2 groups, and its chirality arises only from the different lengths of the two chain sections attached to it. Thus an appreciable contribution to chiroptical properties is conceivable only for asymmetric centers close to the chain ends, the concentration of which decreases with increasing molecular weight. The same holds for conformational optical activity referred to the presence of secondary structures, involving the macromolecule as whole or a substantial fraction of it, with a predominant handedness. This last is not attributable simply to stereogenic centers (asymmetric centers) with a single absolute configuration in each repeating unit. Indeed, the existence of purely conformational optical activity is not a unique macromolecular requisite, being Well known in low molecular weight atropisomerism. However, in polymers it assumes a very specific characteristic connected with the occurrence of cooperative effects which allow transmittance of molecular asymmetry along the chain to very long distances [3]. Most isotactic vinyl polymers assume helical conformations in the crystalline state [4], but owing to the substantial achirality of the macromolecules both screw senses are found in the lattice cells in equal amounts. This is even more true in a melt or in solution, where left-handed and right-handed helical sections alternate even within the same macromolecular chain. Certainly, an appreciable optical rotation would be observed in the crystalline state provided that crystallization occurred under a chiral field inducing a single screw sense helicity in all chains. Such an optical rotation would promptly be lost on melting or dissolution, as an immediate equilibration between the two opposite helical senses would occur. Isotactic macromolecules derived from achiral monomers have no preference for right- or left-handed screw senses, and the two are perfectly balanced at interand intramolecular level. However, distribution of left- and right-handed helical secondary structures affects markedly the free energy of the system, alternation of the two senses in the same chain being favored for entropic reasons [4,5]. If this last situation takes place, conformational optical activity cannot be obtained

because of intramolecular conformational compensation, which hinders any isolation of chains with a predominant handedness. The above considerations are described in fuller detail in previous papers [6,7] and indicate that macromolecules assuming a single chirality conformation can show chiroptical properties characteristic of the conformation itself. Moreover, if chromophores are present in the side chains specific chiroptical properties can arise from dipole-dipole electronic interactions among these chromophores disposed along the chirally arranged backbone. This situation is clearly shown in poly-a-amino acids, in which specific and typical chiroptical properties are associated with specific and typical conformations (a-helix, /?-structures, random coil) [8]. In order to make one screw sense largely predominant in a single macromolecule, the intramolecular equilibration must be hindered by building very rigid chains. In the limiting case the chains will form rods having helical structure with either left- or right-handed helicity. Even if hindering of equilibration can be considered as a kinetic effect, it cannot be excluded that thermodynamic contributions are involved, particularly when rigidity is due to bulk side chains and conformational reversals have a very high internal energy [5,9]. In other words, bulky side chains in a vinyl type structure, for instance, can favor the formation of longer helical chain sections, as the lower entropy is balanced by the gain in internal energy due to minimization of the number of conformational reversals. Indeed these last have, in the case of macromolecules with bulky and branched side chains, larger internal energy per structural unit than the same unit in the helical conformation [10]. Which mechanism is actually operating cannot be established from primary structure as a general rule, an increase in temperature in both cases favoring the equilibration of the two screw senses within each macromolecular chain. Chiroptical properties (molar rotatory power [ $ ] and molar ellipticity [0]) result from a weighted average of the contributions from different conformers, as shown in the following equations:

where N1 indicates the molar fraction and [O] 1 (or [G]1) indicates the molar rotatory power (or molar ellipticity) of the i-th conformer. In macromolecules the molar entities refer to one residue; thus the chiroptical properties are independent of molecular weight, at least when this is very high. It has been demonstrated that in isotactic polymers of optically active a-olefins the molar optical rotation per monomeric residue can be interpreted in terms of the prevalence of few conformations with very high optical rotation of the same sign, corresponding to those allowed to the structural unit inserted in an one screw sense helix [11].

Moreover, in coisotactic copolymers of optically active a-olefins with vinylaromatic monomers, it was shown that the aromatic groups in the side chains give rise to dichroic bands in the spectral region of the n->n* electronic transitions. In several cases exciton splitting was also observed, corresponding to the strong allowed n-m* electronic transition [12]. This circulardichroism (CD) couplet was confirmed to be connected to the dipole-dipole electronic interaction of transition moments of aromatic moieties disposed in a mutual chiral geometry with a predominant handedness, such as that of a one screw sense helix [13,14]. This clear demonstration that the extrinsic CD bands of side chains are related to main chain conformation indicates their usefulness as 'conformational probes'. A typical case comprises polypeptides with aromatic side chains masking the peptide absorption bands [15].

14.1.2 OBJECTIVE With reference to the concepts summarized in the previous section, optical activity measurements can be particularly effective in providing structural information on polypeptides with side chains absorbing at a wavelength clearly distinct from that of the peptide group. In some favorable cases, moreover, CD spectra can allow the detection of very specific structural features, including non-bonding interactions. On the other hand, the same data can be used for monitoring even subtle structural changes induced by external factors. Accordingly, the evaluation of chiroptical properties allows one to follow crucial conformational changes accompanying such biological phenomena as substrate binding, macromolecule-macromolecule interactions, and so on. In order to substantiate these last considerations, the present paper is devoted to the description of studies, using mainly CD spectra, concerning poly (Lglutamic acid)- and poly(L-lysine)-bearing photochromic side chains. Light irradiation of these polypeptides gives rise to reversible isomerization of the photoresponsive chromophores attached to the macromolecule's backbone, which itself can then undergo reversible conformational changes. These may be accompanied by reversible variations of the polymer's properties, such as viscosity, solubility and so on. The main objective of this paper is to show that the examination of the chiroptical properties during the above mentioned phenomena can allow the correlatation of changes in conformation and properties with the photoresponse of the chromophores. On the same basis, an interpretation at the molecular level can be put forward of the reversible variation of viscosity and the solubility. It is also hoped that these indications may be useful for developing photorecording devices which can be read using their chiroptical properties.

14.2 CHIROPTICALPROPERTIESOF PHOTOCHROMIC POLYPEPTIDES 14.2.1 POLYPEPTIDES PHOTORESPONSIVE TO UV LIGHT 14.2.1.1 Azobenzene-containing Polypeptides

Polypeptides sensitive to irradiation with near UV light can be prepared by introducing photochromic azobenzene units into the side chains of high molecular weight (Mv = 100000-250000) poly(a-amino acid)s, such as poly(L-glutamic acid) or poly(L-lysine). Macromolecules having the structures represented in Figure 14.1, and containing various percentages of azo groups, can be obtained under various reaction conditions [16,17]. The photoisomerization of azobenzene moieties (Figure 14.2) is the event responsible for the photochromic behavior of these macromolecules. At room temperature in the dark all azo groups are in the trans configuration, which is planar and then fully conjugated. Irradiation produces isomerization to the cis configuration which, by contrast, is not planar for steric reasons. At the photostationary state, the relative composition of the two isomers depends only on the incident light. The maximum photoconversion to the cis isomer (85 %) is achieved by irradiating at 350-370 nm, whereas the maximum yield of the back reaction from the cis to the trans isomer (80%) is achieved by irradiating at 450 nm. With a lamp having a power of 100 W, irradiation for 1 or 2 min is enough to achieve the photostationary state. By dark adaptation, the metastable cis chromophores decay again to the trans form. The thermal decay at room temperature in the dark is rather slow for azo-modified poly(L-glutamic acid) and takes more than 20Oh to restore the all-trans isomeric composition; for azo-modified poly(L-lysine) the decay in the

Figure 14.1 Chemical structures of poly(L-glutamic acid) and poly(L-lysine) containing azobenzene units in the side chains

Figure 14.2 Photochromic behavior of azobenzene-containing poly(L-glutamic acid). Reproduced by permission of Elsevier Science S.A. from J. Photochem. Photobiol. B: Bioi 1992,12,125-140

dark takes place so slowly that it cannot be observed under normal experimental conditions. The photochromic cycles are completely reversible and can be repeated at will, without any apparent fatigue. As a consequence of the different electronic situations, the two isomers have markedly different absorption, and the photo-isomerization is accompanied by strong variations in the spectra (Figure 14.2). In particular, the trans-to-cis isomerization is revealed by a strong decrease of the intense band at « 350 nm associated with a n-n* transition and a contemporaneous increase of the band at 450 nm associated with the n-n* transition of the azo-chromophore. 14.2.1.2 Light-induced Conformational Changes

Poly(L-glutamate)s having azobenzene units in the side chains, in organic solvents such as trimethyl phosphate (TMP), show the typical CD curve of the a-helix structure, with two minima at 208 and 222 nm. Above 250 nm, the dark-adapted samples exhibit also a couplet of bands centered at 350 nm, corresponding to the n-n* transition of the azo chromophore in trans configuration. The trans-to-cis photoisomerization completely cancels the side chain CD bands in the region of 35Onm, but does not modify at all the CD spectra in the peptide region. This indicates that, in these solvents, light causes the isomerization of the azo side chains, but the isomerization does not induce any variation of the polypeptide main chain.

Figure 143 CD spectra of poly(L-glutamic acid) bearing 36 mol% azobenzene units, before ( ) and after ( ) irradiation, in aqueous solution at various pH values: A, pH 4.8; B, pH 6.5; C,pH 8.0 The secondary structure in water depends on the molar content of azobenzene units and also on the degree of ionization of the unmodified COOH side chains. Below pH 5, a sample of poly(Glu) bearing 35 mol% of azobenzene units assumes a /^-structure. Irradiation does not induce any variation of the polypeptide conformation. At pH values above 7, the polypeptide adopts a random coil conformation which is again not affected by the photoisomerization of the azo side chains. However, at pH values of 5-7, irradiation produces a remarkable decrease of the ordered structure (Figure 14.3). In this range of pH the trans-to-cis isomerization produces a higher degree of ionization of the unmodified COOH side chains, thus amplifying the first light effect and causing unfolding of the polypeptide. Cationic surfactants are known to affect the conformation of poly(L-glutamic acid). This suggested to us that it might be possible to combine the isomerization of the photochromic side chains with the surfactant effect to obtain an amplification of the photoresponse. The expectation was realized by irradiating azomodified poly(L-glutamic acid) in the presence of dodecylammonium chloride (DAC) at the critical micelle concentration (c.m.c) [18]. Figure 14.4 shows the CD spectra of a 20% azo-modified poly(Glu) both in the absence and in the presence of DAC. In the absence of detergent at pH 7, the polymer is completely in random coil conformation and not affected at all by irradiation. In the presence of detergent at the c.m.c, irradiation at 35Onm (trans-to-cis isomerization) induces

Figure 14.4 CD spectra of poly(L-glutamic acid) bearing 20 mol% azobenzene units, at pH 7.6, before ( ) and after ( ) irradiation: A, in the absence of dodecylammonium chloride (DAC); B, in the presence of DAC, below the c.m.c; C, in the presence of DAC, at the c.m.c. Reproduced by permission of Elsevier Science S.A. from J. Photochem. Photobioi B: BioL, 1992,12,125-140 an evident coil-to-helix transition. The variation is completely reversible when the sample is dark-adapted or irradiated at 450 nm (cis-to-trans isomerization). Thus, in the presence of DAC micelles, the polypeptide conformation can be photomodulated by exposure alternately to light or dark, or by irradiating at two different appropriate wavelengths. The key factor responsible for the photoinduced variations of conformation is the affinity of the azo-polymer for the micelles. Such an affinity, in fact, is likely to be different when the azo side chains are in trans or in cis configuration. When azo-units are in the planar, apolar, trans form, they dissolve within the hydrophobic core of the micelles, forcing the polypeptide chains to assume a coil conformation. Isomerization of the azo units to the skewed, polar, cis form inhibits hydrophobic interactions and causes the azo-units to leave the micelles, thus allowing the polypeptide chains to adopt the a-helix structure (which is favored in the absence of micelles). In other words, the primary photochemical event is the trans ^ cis isomerization of the azobenzene units, but the driving force of the photoresponse should be the different location of the macromolecules relative to the micelles. Dark-adapted (all trans azo groups) poly(L-lysine) bearing 43 mol% of azobenzene groups, in a medium of hexafluoroisopropanol/water/sodium dodecyl sulfate, shows a CD spectrum which can be attributed to the presence of a /?-form. Irradiation at 340 nm causes the disruption of the /!-structure and promotes the formation of an a-helix (helix content % 50%), as revealed by the appearance of the typical CD pattern. Upon irradiation at 450 nm, the spectrum reverses again

to the original one. The photoinduced /J;=± helix conformational change is completely reversible and the two conformations can be obtained by irradiating alternately at the two different wavelengths. This photoinduced fi^± helix change can readily be explained on the basis of the different geometry and hydrophobicity of the trans and cis azobenzene units. The /J-form is stabilized by hydrophobic interactions among the side chains and is favored when the azobenzene units have the planar geometry and the high hydrophobicity of the trans configuration. The interactions are inhibited when the azo units are isomerized to the skewed cis configuration, and thus the /^-structure is destabilized and destroyed. The polypeptide chains then adopt the a-helix form in the helix-supporting solvent hexafluoroisopropanol. The photochromic behaviour of azobenzene-containing poly(L-lysine) has also been reported in the monolayer state [19]. When the polypeptide monolayer is kept at constant area, alternate irradiation with visible and ultraviolet light produces reversible changes (% 25%) of the surface pressure of the monolayer. 14.2.13 Photostimulated 'Aggregation-Dissaggregation' Effects

CD data provided evidence that azo-modified poly(Glu) containing azobenzene units can undergo reversible aggregation-disaggregation processes upon exposure to light or dark conditions [20]. Samples stored in the dark or irradiated at 450 nm (azo groups in the trans configuration) show variations of their CD spectra on aging in a TMP/water solution (Figure 14.5). The time dependence is characterized by the gradual appearance of an intense side chain CD couplet together with a progressive distortion of the a-helix pattern, typical of the effects produced by aggregates of polypeptide chains [21,22]. Irradiation at 361 nm (tran to cis isomerization) produces the full restoration of the initial CD spectra, indicating dissociation of the aggregates. The spectra revert again to the distorted ones on irradiating at 450 nm or by dark adaptation, thus confirming the reversibility of the light-induced effect. Investigation of azo-modified poly(Glu) containing 85 mol% azobenzene units in the side chains has provided confirmation of the occurrence of aggregationdisaggregation processes induced by light, together with the possibility of photoregulating polymer solubility [23]. This polypeptide, when stored in the dark, assumes the a-helix structure in hexafluoroisopropanol (HFP). Addition of a small amount of water (15 vol%) to the HFP solution causes the formation of aggregates, followed by precipitation of the polymer as a yellow material. The precipitation is total and quantitative, as can be seen by recording the absorption spectrum of the filtered colorless liquid. Complete dissolution of the polymer was obtained by irradiation of the suspension for a few seconds at 350 nm; irradiation at 450 nm or dark adaptation of the solution caused the polymer to precipitate. In a HFP/water = 85/15 solvent mixture, therefore, the 'precipitation-dissolution' cycles can be reversibly

Figure 14.5 Poly(L-glutamic acid) bearing 20mol% azobenzene units. CD spectra in trimethyl phosphate/water = 50/50, recorded at various aging times: (1) freshly prepared solution; (2) aged 1 day; (3) aged 2 days; (4) aged 3 days. ( ) Dark-adapted samples; ( ) irradiated at 360 nm, at any aging time. Reprinted with permission from [23]. Copyright 1989 American Chemical Society

repeated by irradiation and dark adaptation, or by irradiating at two different wavelengths. The dependence of the polymer solubility on the cis/trans composition of the azobenzene side chains was investigated by performing irradiation experiments at various wavelengths of the incident light. The considerable amount of photodissolved polymer allowed its determination by evaporating the solutions obtained upon irradiation and weighing the dry residue. The solubility of the polymer, as a function of the cis/trans ratio of azobenzene side chains, is described by a sharp sigmoidal curve. The polymer is fully insoluble when more than 60% of the azo groups is in a trans configuration. By contrast, the maximum amount of

photosolubilization is achieved when 60% of azo groups are in the cis configuration; the solubility then remains unaffected at higher values of cis content [23]. The described photoresponse effects can be well interpreted on the basis of association among macromolecules through hydrophobic interactions and stacking of azobenzene side chains. The planar, apolar, trans configuration gives aggregation and precipitation; when the azo moieties are photoisomerized to the skewed, polar, cis configuration, interactions and stacking between azo-groups are inhibited, so that disaggregation of the macromolecules takes place and polymer dissolution occurs. 14.2.2 PHOTOMODULATION OF POLYPEPTIDE CONFORMATION BY SUNLIGHT 14.2.2.1 Spiropyran-containing Polypeptides Azo-modified polypeptides could be considered as models for photoregulated processes occurring in nature, but the generation of cis and trans photoisomers, and hence photoregulation, requires artificial sources of ultraviolet light. Ideally, one would like to have a model system responding to the presence or absence of sunlight, such as polypeptides bearing spiropyran groups attached to poly(Lglutamic acid) [24] or poly(L-lysine) [25] (Figure 14.6). Spiropyran-modified poly(L-glutamate)s in hexafluoroisopropanol (HFP) exhibit 'reverse photochromism', that is, a photochromic behavior which is

Spiro

Spiro

Spiro

group

Figure 14.6 Chemical structure of poly(L-glutamic acid) and poly(L-lysine) bearing spirobenzopyran units in the side chains

dark light

Figure 14.7 Structure and reverse photochromic reactions in HFP of poly(L-glutamic acid) containing spiropyran units in the side chains opposite to that usually observed in most common organic solvents. Thus, HFP solutions kept in the dark at room temperature show a yellow-orange color which is completely bleached upon exposure to visible light and is reversibly restored in the dark. NMR data confirm that the photochromism in HFP involves the well-known interconversion between the colorless closed spiro structure / and the colored ring-opened merocyanine structure II (Figure 14.7). Accordingly, in the 13C NMR spectra of the colorless solution the resonances of the geminal methyl groups appear as two separate peakes, 27.0 and 21.0 ppm, as a consequence of the presence of the chiral spiro carbon atom. In the colored solution, by contrast, the two methyl group resonances merge to a single signal at 28.7 ppm, analogously to that observed for the proton resonances. The spectra of the colored species kept in the dark do not show nuclear resonances associated with the spiro form, indicating that in HFP the spiropyran ;=± merocyanine equilibrium is fully shifted to the right. The very polar solvent HFP is probably responsible for the reverse photochromism by stabilizing the charged merocyanine species II more than the apolar spiropyran species I. A protonated open structure III might also be formed between the zwitterionic species II and HFP, with the solvent functioning as an acid, as will be described in the following section. The dark-adapted sample shows a spectrum which displays two absorption maxima, at 500 and 370 nm, of about the same intensity (Figure 14.8). Irradiation with visible light (500-550 nm) or exposure to sunlight for a few seconds completely dispels the absorption in the visible region and gives rise to the spectrum of the colorless spiro form, characterized by absorption maxima at 355 and 272 nm. In the dark, the original spectrum is progressively restored. In the colorless indolinospiropyran species, the two halves of the molecule are topologically independent, so the absorption spectrum consists mainly of

light

dark

A

Figure 14.8 Variation of the absorption spectra as a function of irradiation and darkadaptation time for poly(L-glutamic acid) bearing 85mol% spiropyran units in HFP (c = 5.01 x 10"2 g/1; / = 1 cm); 1, dark-adapted solution; 2, irradiated solution

localized transitions belonging to a particular half of the molecule, rather than delocalized transitions belonging to the molecule as a whole [26]. The electronic transition at longer wavelength, which in HFP occurs at 355 nm, has been assigned to the benzopyran, and the second transition, which in HFP is seen at 272 nm, has been assigned to the indoline portion of the molecule [26]. In the colored species, the absorption band at 500 nm can be assigned to a n-n* electronic transition of the extended and conjugated merocyanine chromophore, and the 370 nm band can be attributed to a charge-transfer transition from the oxygen atom of the benzopyran ring to the electron-accepting nitro substituent [27,28].

light dark

Figure 14.9 Reverse photochromic reactions of spiropyran salts (see Fig. 14.7) Considering the acidity of HFP, the band at longer wavelengths should be assigned to the zwitterionic ring-opened form II (Figure 14.9), whereas the band at shorter wavelengths might be assigned to the presence of the ring-opened species III formed between the zwitterionic species and HFP, with this last acting as an acid (pKa = 9.30) [29] (shown in Figure 14.9). In the polymers, protonation of the open form by unmodified COOH side chains may also occur [27], even though this effect cannot play a relevant role in the 85 mol% modified polymer shown in the figure. The presence of a well-defined isosbestic point should indicate only two interconverting species. However, the salt of the spiropyran with trifluoroacetic acid exibits exactly the same isosbestic point (see the following section), so that one cannot exclude the presence of both the zwitterionic and the protonated merocyanine forms. 14.2.2.2 Photomodulation of Conformation

The CD spectra of the dark-adapted samples of poly(Gluj bearing 85 mol% photochromic units are those of random coil polypeptides. CD bands of small intensity are also present in the near UV-visible region, in correspondence with the merocyanine electronic transitions. The solutions bleached after exposure to visible light display the typical pattern of the a-helix, with the two minima at 222 and 208 nm, thus indicating that the isomerization of the side chains produces spiralization of the main chain. The back reaction in the dark is accompanied by a progressive decrease of the helix content and restoration of the original disordered conformation (Figure 14.10). The photoinduced helix content can be only approximately estimated on the basis of the CD spectra. In fact, several polypeptides, all having a-helical

light

dark

Figure 14.10 Effect of irradiation and dark adaptation on CD spectra of poly(L-glutamic acid) bearing 85 mol% spiropyran units in HFP at 250C: 1, kept in the dark; 2, exposed to sunlight; dotted lines are CD spectra recorded during decay in the dark over 8h. Below 250 nm, CD data are expressed in terms of molar ellipticity based on the mean residue molecular weight; above 250 nm, the molar ellipticity is referred to one spiropyranglutamyl residue conformation, were reported [30] to show significant variations of the maximum ellipticities when CD spectra were measured in HFP. On the basis of the literature values [30] of [ G ] 2 2 2 ( - 3 0 0 0 0 — 40000) for 100% a-helix in HFP, the photoinduced helix content can be evaluated as 90-70%. The photochromic reaction involves the reversible conversion of the zwitterionic merocyanine (sample kept in the dark) to the uncharged spiro form (sample exposed to light); the isomerization is thus accompanied by large variations of the electrostatic interactions among the side chains of the polypeptides. Intrachain interactions should produce loops in the macromolecules, whereas intermolecular stacking should produce aggregation phenomena. As

a result, the macromolecules are forced to adopt a disordered structure. When the sample is exposed to light and merocyanines are converted to the neutral spiro form, electrostatic interactions are removed and the polypeptide can adopt the a-helix structure. When spiropyrans are treated with acids they are converted into 'spiropyran salts', which exhibit photochromic behavior differing from that of the parent spiropyran compounds. The gross mechanism proposed is illustrated in Figure 14.9. In the dark at room temperature, the compounds give colored solutions due to the presence of the O-protonated merocyanine species III. The open form is converted by irradiation with visible light to the iV-protonated spiro form IV. As spiropyrans are fairly strong bases in the open form but very weak bases in the closed spiro form, the charged species IV can lose a proton and the neutral species I can be actually formed. Comparison of Figure 14.9 with Figure 14.7 shows that different photoisomers are involved in acidic or non-acidic solution. Therefore we may expect spiropyran-containing polypeptides to be affected by light in a different way depending on whether they are irradiated in the absence or in the presence of acid. Poly(spiropyran-L-glutamate) in HFP solution in the presence of TFA does not give light-induced conformational changes. Actually, the solutions show the typical CD spectra of random coil polypeptides both when they are kept in the dark and when they are exposed to light. The addition of methanol as a cosolvent induces the coil -> helix conformational transition, as for other polypeptides having salified side chains [31]. The most remarkable aspect of this system is that two distinct curves are observed for the dark-adapted sample and for the irradiated one (Figure 14.11). In particular, for the polymer containing 85mol% photochromic units, the concentration of methanol needed to induce the conformational transition is « 10-40% for the sample kept in the dark and « 5-10% for the sample exposed to light. Therefore, at any solvent composition in the range between the two curves, exposure to light produces reversible variations of the helix content (Figure 14.12). The photochromic reactions schematized in Figure 14.9 and the above discussed absorption spectra allow us to explain the conformational behavior. In HFP, in the presence of TFA, the photochromic side chains are protonated by the acid either when the sample is kept in the dark (photochromic units present as open species III) or when the sample is exposed to light (photochromic units present as closed species IV). In both cases the polypeptide is essentially a polycation, so the repulsive forces among the side chains make the macromolecules adopt an extended coil conformation, and no photoresponse is observed. In the presence of methanol (> 10%) the equilibrium between the two colorless species IV and I (Figure 14.9) is shifted toward the neutral spiro structure I. In these conditions the 'folding-unfolding' of the macromolecules is photocontrolled by the isomerization of the photochromic units. In the dark, they are present as charged species, so the macromolecules adopt a disordered conformation.

MeOH,%

dark

light

Figure 14.11 Variation of ellipticity at 222 nm as a function of methanol concentration (v/v) for poly(Glu) bearing 85mol% spiropyran units in HFP/MeOH/TFA solvent system, at 250C: ( ) dark-adapted sample; ( ), irradiated sample

Figure 14.12 Effect of irradiation on CD spectra for poly(Glu) containing 85 mol% spiropyran units at 250C in various HFP/MeOH/TFA solvent mixtures (c = 2.59 x 10"2 g/1; TFA = 1 x 10"3 ml in 2 ml of mixed solvent); MeOH % (v/v): (a) 0-5%; (b) 10%; (c) 20%; (d) 40%. ( ), dark-adapted; ( ) irradiated samples

a-helix v a r i a t i o n , %

merocyanine

form , %

Figure 14.13 PoIy(GIu) bearing 85 mol% spiropyran units. a-Helix relative variation as a function of spiropyran/merocyanine isomeric composition of the side chains, in pure HFP ( ) and HFP/MeOH/TFA = 90/10/5 x 10 " 2 ( ). The a-helix variation in % was estimated as {[@]V[©]°} x 100, where [0]° and [ 0 ] ' are the ellipticity values measured at 222 nm at the beginning and at the time t during decay, at 250C Exposure to light and the consequent photoconversion of the side chains to the apolar spiro form make the macromolecules adopt the a-helix conformation. In order to investigate the dependence of the secondary structure on the isomeric composition of the photochromic side chains, the rate of the helix-tocoil conversion and the rate of appearance of absorbance at the longer wavelength in the dark were measured simultaneously. The helix content was then plotted as a function of the photochromic units present in the merocyanine form (Figure 14.13). In pure H F P (Figure 14.13, dotted line), the helical structure starts to break up rapidly as soon as the merocyanine species begin to be formed, and the helix -* coil conformational change takes place almost entirely following conversion of % 30% of spiropyran to merocyanine groups. A rather different behavior is observed in HFP/MeOH/TFA (Figure 14.13, full line): the helix content decreases slowly with increasing merocyanine percentage, but the helical structure does not collapse until « 50% of the spiro groups are isomerized to the merocyanine form. The different dependence of the helix structure on the percentage of photochromic groups present in the merocyanine form is a confirmation that denaturation of the macromolecules in the dark occurs through different mechanisms in non-acidic and acidic media. In the former case denaturation should be caused by

stacking and aggregation between zwitterionic merocyanine species II. In the latter case, denaturation should be caused by repulsive forces among the cationic side chains III. In both cases, exposure to light removes the electrostatic interactions between side chains, allowing the formation by the polypeptide chains. Also poly(Lys)-containing spirobenzopyran side chains, as well as low molecular weight model compounds, exhibit intense 'negative' photochromism in HFP [25]. In the dark the solutions are orange, with two absorption maxima at «470nm (£mol = 31700) and 370 nm (emol = 32 000). Exposure to sunlight is accompanied by prompt bleaching, with a shift of the absorption maxima to 353 nm (emol = 11200) and 270-272 nm (emol = 16 200). The original spectrum is reversibly restored when the illumination is stopped. Decay in the dark at 25 0 C follows first order kinetics for the model compounds, with a rate constant of 5.7 x 10" 3 min" 1 and a half-life of «122min. For the polymer, the kinetics deviate slightly from monoexponential and biexponential decay; the time necessary to restore half of the original absorbance is « 80 min. The analogy of these reversible processes with those observed in spiropyranmodified poly(Glu) suggests the occurrence of similar photochromic reactions. Accordingly, HFP stabilizes the colored ionic merocyanine structure, while irradiation gives the colorless spiro structure. In pure HFP, the CD spectra are consistent with those of random coil polypeptide chains, and the photoisomerization reaction does not affect the polymer conformation at all. Addition of triethylamine to the HFP solution induces the coil-•helix transition, but the amount of base necessary to induce the transition is different for the dark-adapted sample (15% v/v) than for the irradiated one (30% v/v). Thus, at any composition in the range 3-15% v/v of NEt 3 , exposure to sunlight produces reversible variations of the helix content. Combination of the effects due to the photochromic behavior with appropriate amounts of NEt 3 allows modulation of the extent of the photoresponse. It appears that in pure HFP the conformation for poly(Lys)-containing spiropyran is determined by the unmodified Lys side chains protonated by the acid solvent; as a consequence, the polypeptide assumes a coil conformation which is not affected by the isomerization of the photochromic groups. Addition of a moderate amount (3-15%) OfNEt3 removes protons from Lys side chains, whose basicity depends on isomeric composition of the photochromic moieties. In the range between the transition curves of the dark-adapted and the irradiated sample, the chain folding ;=± unfolding is then controlled by the isomerization of the photochromic side chains: when these are in the charged merocyanine form, the polypeptide chains are in the random coil arrangement, but photoconversion to the apolar spiropyran form causes the macromolecules to assume a helical conformation. At NEt 3 contents above 15%, the high concentration of a NEt 3 • HFP saline complex can probably exert a shielding effect on the charged

side chains, allowing the polypeptide to stay in the helical conformation at any photoisomeric composition. The system described provides a well defined example of the combined action of light and environment on the secondary structure of polypeptides. It can thus be considered as a macromolecular model resembling the behavior of naturally occurring photoreceptors [32]. 14.2.2.3 Photoinduced Variations of Viscosity

a-helix v a r i a t i o n , %

The colored solutions of poly(L-glutamic acid) and poly(L-lysine) containing spiropyran, when kept in the dark, are characterized by very high values of viscosity, typical of those displayed by polyelectrolytes. The viscosity decreases dramatically upon exposure to sunlight and returns to the original value along with the reappearance of the absorption in the visible region. In order to correlate viscosity changes with conformational changes, samples of photochromic polypeptides were exposed to light, then the viscosity and the CD spectra were measured over time in the dark. Viscosity progressively increases with the gradual decrease of the helix content for both spiropyrancontaining poly(L-glutamic acid) (Figure 14.14) and poly(L-lysine) (Figure 14.15). The high viscosity of the solutions in the dark is essentially due to the side chains, which are charged when macromolecules are in disordered conformation. In these conditions the polypeptides are able to coordinate many solvent molecules to give highly solvated an extended macromolecules with a large hydrodynamic

t i m e , mi n Figure 14.14 PoIy(GIu) bearing 85mol% spiropyran units. a-Helix content ( ) and viscosity ( ) variation during decay in the dark at 25 0C. HFP solutions were irradiated, then dark adapted and monitored over time. The percentage of a-helix variation is estimated as indicated in Figure 14.13

a-helix variation,%

t i m e , min Figure 14.15 Helix content ( ) and viscosity ( ) variation during decay in the dark for poly(Lys) bearing 46 mol% spiropyran units, in HFP/NEt3 = 94/6

volume, thus exhibiting high values of viscosity. Aggregation phenomena, through interactions between merocyanine side chains, can also contribute to viscosity increases. From the figures it appears that viscosity keeps on increasing even when the a-helix is completely destroyed. In fact, the helix is fully destroyed by conversions of the spiro to the merocyanine form of « 60%, (Figure 14.13), but the macromolecules go on expanding until conversion to the merocyanine form reaches 100%.

14.3 REFERENCES [1] (a) M. Farina, Chim. Ind. (Milan), 1986, 68, 62; (b) M. Farina, Top. Stereochem., 1987,17,1. [2] P. Pino, Adv. Polym. ScL, 1965,4, 393. [3] F. Ciardelli, M. Aglietto and G. Ruggeri, in M. Fontanille and A. Guyot (Eds.), Recent Advances in Mechanistic and Synthetic Aspects of Polymerization, Reidel, Dordrecht, 1987, p. 409. [4] G. Natta, Makromol. Chem., 1960,35,94. [5] P. Pino, F. Ciardelli and G.P. Lorenzi, J. Polym. ScI, Part C, 1963, 4,21. [6] P. Pino, F. Ciardelli and M. Zandomeneghi, Annu. Rev. Phys. Chem., 1970, 21, 561. [7] F. Ciardelli and P. Salvadori, Pure Appl. Chem., 1985,57,931. [8] E.R. Blout, in F. Ciardelli and P. Salvadori (Eds.), Fundamental Aspects and Recent Developments in ORD and CD, Heyden, London, 1973, Chs. 4 and 5.

[9] P.L. Luisi and F. Ciardelli, in A.D. Jenkins and A. Ledwith (Eds.), Reactivity, Mechanism and Structure in Polymer Chemistry, John Wiley & Sons, New York, 1974, p. 471. [10] P.L. Luisi and P. Pino, J. Phys. Chem., 1968,72,2400. [11] P. Pino, F. Ciardelli, G.P. Lorenzi and G. Montagnoli, Makromol. Chem., 1963,61, 207. [12] F. Ciardelli, P. Salvadori, C. Carlini and E. Chiellini, J. Am. Chem. Soc, 1972, 94, 6536. [13] W. Hug, F. Ciardelli and I. Tinoco, Jr, J. Am. Chem. Soc, 1974,96, 3407. [14] F. Ciardelli, C. Righini, M. Zandomeneghi and W. Hug, J. Phys. Chem., 1977, 81, 1948. [15] F. Ciardelli and O. Pieroni, Chimia, 1980, 34, 301. [16] F. Ciardelli, O. Pieroni, A. Fissi and J.L. Houben, Biopolymers, 1984,23, 1423. [17] A. Fissi, O. Pieroni and F. Ciardelli, Biopolymers, 1987, 26,1993. [18] O. Pieroni, D. Fabbri, A. Fissi and F. Ciardelli, Makromol. Chem., Rapid. Commun., 1988,9,637. [19] B.R. Malcolm and O. Pieroni, Biopolymers, 1990, 29,1121. [20] O. Pieroni, A. Fissi, J.L. Houben and F. Ciardelli, J. Am. Chem. Soc, 1985,107,2990. [21] M.M. Long and D.W. Ury, in E. Grell (Ed.), Membrane Spectroscopy, SpringerVerlag, Berlin, 1981, pp. 143-171. [22] P. Bayley, in S.B. Brown (Ed.), An Introduction to Spectroscopy for Biochemists, Academic Press, London, 1980, pp. 148-234. [23] A. Fissi and O. Pieroni, Macromolecules, 1989,22,1115. [24] F. Ciardelli, D. Fabbri, O. Pieroni and A. Fissi, J. Am. Chem. Soc, 1989, 111, 3470. [25] O. Pieroni, A. Fissi, A. Viegi, D. Fabbri and F. Ciardelli, J. Am. Chem. Soc, 1992,114, 2734. [26] N.W. Tyer, Jr, and R.S. Becker, J. Am. Chem. Soc, 1970,92,1289. [27] T.M. Cooper, K.A. Obermeyer, L.V. Natarajan and R.L. Crane, Photochem. Photobiol., 1992,55,1. [28] A.S. Kholmanskii and K.M. Dyumaev, Russ. Chem. Rev. (Engl. TransL), 1987, 56, 136. [29] WJ. Middleton and R.V. Lindsey, Jr., J. Am. Chem. Soc, 1964,86,4948. [30] (a) J.R. Parrish, Jr., and E.R. Blout, Biopolymers, 1971,10,1491; (b) R.W. Woody, J. Polym. ScL, Macromol. Rev., 1977,12,181. [31] (a) M. Satoh, Y. Fujii, F. Kato and J. Komiyama, Biopolymers, 1991,31, l;(b) R.F. Epand and H. Scheraga, Biopolymers, 1968, 6,1383. [32] B.F. Erlanger, Annu. Rev. Biochem., 1976,45,267.

15 POLYMER LUMINESCENCE AND PHOTOPHYSICS D. PHILLIPS and M. CAREY Department of Chemistry, Imperial College, London SW7 2AY1 UK

15-1 INTRODUCTION Ultra-violet and visible light-absorbing chromophores in synthetic polymers may be present due to adventitious impurities such as oxidation products, termination residues or initiator fragments (type A), or be present in the repeat unit and thus be in high concentration (type B). Many simple synthetic polymers such as poly(ethylene) and poly(propylene) in a pure state will exhibit only o-a* absorptions in the high-energy UV region, where most organic molecules absorb. Such excitations in general lead to photochemical reactions rather than luminescence, and excited states will thus be very short-lived. Here we focus attention arbitrarily on species that absorb in the spectral region from 250 nm to longer wavelengths, where luminescence may be an additional fate of photoexcited species, which are depicted in Figure 15.1, for a typical organic chromophore. The many studies carried out on luminescence in synthetic polymers have been motivated by a wide range of scientific and technological aims. Some of the more obvious are categorized below [1,2]. (a) F undamental interests: these include studies on the nature of photoemission from polymers of type B, in which interchromophoric interactions are of special interest. (b) Luminescence of probe molecules: these studies permit the evaluation of polymer properties. In particular, measurement of the relative intensities of fluorescence of a probe molecule polarized parallel to and perpendicular to the plane of linearly polarized exciting radiation as a function of the orientation of a solid sample yields information concerning the ordering of polymer chains. In soultion, similar polarization studies yield information on the rotational relaxation of chains and the viscosity of the microenvironment of the probe molecule. The study of luminescence intensity of probe molecules as a function of temperature has been used as a method of studying transition temperatures and subgroup motion in polymers. (c) Luminescent species in polymer photooxidation: the problems associated with establishing a mechanism for the photooxidation and weathering of synPolymer Spectroscopy. Edited by Allan H. Fawcett © 19% John Wiley & Sons Ltd

S-S absorption

lntersystem crossing

Fluorescence

Vibrational relaxation

Absorption

lntersystem crossing

lntersystem crossing Vibrational relaxation

Phosphorescence

Vibrational relaxation

T-T absorption

Internal conversion

Internal conversion

Figure 15.1 Jablonskii state diagram depicting the fates of photoexcited polyatomic molecules thetic polymers are great, and any method that provides additional information is useful. In addition to traditional methods such as product analysis, infrared spectroscopy (both conventional and ATR) and U V-visible absorption spectroscopy, luminescence methods have been employed. (d) Identification of polymers: luminescence spectroscopy can provide a convenient method for rapid identification of some synthetic polymers. We will cite here a few classic examples of studies in the various categories, using steady-state measurements.

15.2 PROBES OF ORDER IN POLYMERS Physical properties of polymers are often altered significantly by preferential orientation of structural units by drawing or some other means. The degree of anisotropy thus introduced requires measurement if correlation between structure and physical properties is to be established. There are a number of methods available for the measurement of such anisotropy, including wide-line NMR, optical birefringence, X-ray scattering, light scattering, Raman spectroscopy,

infrared dichroism and fluorescence polarization. The methods are not all equivalent in the type of information they provide, but when used simultaneously on the same sample they can yield complementary data. Thus, for example, birefringence is sensitive to the orientation of both the amorphous and the crystalline units, whereas X-ray scattering reveals the orientation of crystallites only. Raman methods can probe much more local order than X-ray techniques. In principle it is desirable to have knowledge of the complete distribution function in a sample, but X-ray diffraction is currently the only method that can be used for this purpose. However, the majority of physical properties depend only upon the second moment of the orientation distribution, although mechanical properties such as Young's modulus depend also upon the fourth moment. The latter information is available from both wide-line NMR and fluorescence polarization measurements. Experimentally the fluorescence polarization

Figure 15.2 Intensity of parallel component of fluorescence, I, as function of orientation of sample in uniaxially stretched poly(vinyl alcohol) film at draw ratios of (1) 1, (2) 1.08, (3) 1.3, (4) 1.6, (5) 2.0, and (6) 5.0 (after figure in J. Polym. ScI, Polym. Symp., 1970,31, 353

measurements are simple, in that a rigid polymer sample in which fluorescent molecules are dispersed or chemically attached is excited in a spectrofluorimeter with (usually) vertically plane-polarized light. Measurements of the fluorescence intensity of the probe with the analysing polarizer parallel (J1) and crossed (J1) with the excitation polarizer are taken as a function of the orientation of the sample with respect to the vartically polarized excitation radiation; that is, plots are made of the components J11 and J 1 as a function of physical ratation of a sample through 360°. The intrinsic probe, which must be a long molecule, is assumed to align with the fibres in a material. A typical plot is shown in Figure 15.2, in which the anisotropy introduced by drawing is clearly illustrated. [3] The method can be used to distinguish orientations which correspond to different arrays which nevertheless have identical orientation functions.

15.3 PROBES OF SUB-GROUP MOTIONS Phosphorescence may be used as a probe of sub-group motion in synthetic polymers, particularly be studying the temperature dependence of the emission of an intrinsic probe. Using probe naphthalenes (or ketones), a wide variety of polymer films have been studied in which, over the temperature range 3OO-77K, the intensity of phosphorescence from the probe was found to vary by up to four orders of magnitude [4]. This is illustrated in Figure 15.3; for a series of styrene polymers with emitting comonomers, the temperature dependence showed distinct linear regions with at least one common discontinuity (for each polymer type) in the slope within a narrow temperature region. These discontinuities coincided well with the known y-transition temperatures and secondary transition temperatures for each of the polymer types investigated. The conclusion of this study was that the phosphorescence decrease with increasing temperature was not due to temperature dependent intramolecular decay or 'intermolecular deactivation' but could be best explained in terms of the increasing accessibility of the excited chromophore to molecular oxygen. The observed temperatures of discontinuity were explained in terms of the several possible structural relaxations, and in general the observed temperatures were in good agreement with results from other relaxation measuring techniques.

15.4 PHOTOCHEMISTRY IN POLYMERS The vast literature on photopolymerization and cross-linking makes this subject impossible to attempt within the scope of this brief review. Photochemical effects of formed polymers are dominated by photooxidation processes summarized in

Figure 153 Plots of In / p (J? = phosphorescence intensity) against inverse temperature for styrene polymers. Transitions corresponding to Ty and other sub-group motions are visible (after figure in Macromolecules, W)% 7, 233). Figure 15.4, which also depicts the means available to protect polymers against the effect of light. These are the use of UV absorbers, A; quenchers of excited states, B; radical scavengers, C; singlet oxygen scavengers, D; or destroyers of hydroperoxide, E.

QUENCHER UV-ABSORBER

«'•

RADICAL SCAVENGER

*•

RO #

ROO,

MOLECULAR DISSOCIATION

QUENCHER

ROOH

METAL DEACTIVATOR PEROXIDE DECOMPOSER

Figure 15.4 Mechanism of photo-oxidation and stabilisation of commercial polymers

15.5 EXCIMER-FORMING POLYMERS [5] In type B polymers, the structural constraints of the polymer chain tend to confine the chromophores in spatial positions such that they can be expected to exhibit strong mutual interactions. These may depend strongly upon the relative orientation of the interacting chromophores, and the orientations themselves will usually be dependent upon the conformation of the polymer chain. Interaction between the excited state chromophore and a neighbouring ground state can give rise to excimer (excited dimer) formation, which proves to be a powerful diagnostic of interacting molecules. The salient features of excimer formation are represented in Figure 15.5. Aromatic molecules at large separations, that is at separations much greater than 4 A, may be considered as isolated entities. Consequently, if the aromatic molecules are in an excited state, the fluorescence is unaffected by the presence of other molecules. For small separations, less than 4 A, repulsive potentials R(r) and R'(r) will exist between molecules in their ground state and between molecules in the ground and the excited state. In general, the existence of these repulsive potentials prevents the formation of complexes. However, for the interaction between ground and excited state molecules, an attractive potential V(r) may be obtained, owing to configurational interaction between resonance and exciton-resonance states. The combination of repulsive and attractive potentials may form the excimer state shown by the potential well in Figure 15.5. The fluorescence from the 'excimer' state will thus be unstructured (since a corre-

energy fluorescence intensity

Figure 15.5 Energy diagram for excimer formation

sponding ground state complex does not exist) and at a lower energy than the corresponding monomer emission. In general, excimer formation can occur whenever aromatic chromophores adopt a face-to-face coplanar arrangement with a separation of 0.3-0.35 nm, as shown for naphthalene in Figure 15.6. Static measurements of intensities of monomeric fluorescence (here defined as that from an uncomplexed chromophore attached to the polymer chain) relative to that from the excimer can be used to yield information relating to energy transfer and migration, rotational relaxation and segmental motion, and to the heterogeneity of synthetic polymers and copolymers in solution and solid forms. Results of technological importance are available. Thus, in blends of polymers, such measurements have been used to investigate compatibility [6, 7].

Figure 15.6 Excimer formation in a naphthalene-containing molecule

15.6 DYNAMICS OF LUMINESCENCE The processes of depletion of excited-state population in Figure 15.1 lead fo fluorescence decay times which may be 10 " 8 -10 " *2 s or less. Molecules may thus provide a 'clock' over this range with which to time other processes which are

Spontaneous radiative transitions lntersystem crossing (S 1 -T 1 ) Internal conversion (Sn - SnJ Vibrational redistribution and isomerization Field-induced transitions

Coherent exciton Exchange transfer Resonance (Forster) transfer Diff usional encounter (1 cp) Rotational diffusion (1 cp) Vibrational relaxation Geminate recombination Chemical reaction

Typical Q-switched laser, excimer, N 2 pulse duration

Typical picosecond laser pulse duration

Shortest laser pulse yet produced

Limit of photon-counting streak camera detection

Figure 15.7 Some physical and chemical processes which occur on the 10~ 6 -10~ l5 s time scale

Second harmonic generator Second harmonic generator Harmonic separator Cavity dumper

KTP rfout sync Cavity dumper Mode-locker driver out driver sync out

KDP

Sample

Fast photodipde

rfout

Timing filter amplifier

Harmonic separator

Constant fraction timing discriminator CFTD

Filter

MicroChannel plate

CFTD

PC/AT computer

TAC/SCA

Multichannel analyser

X100 Amplifier

Time-to-amplitude converter/single channel analyser

Figure 15.8 Time-correlated single-photon counting spectrometer based on CW modelocked Nd: Y AG laser

subject to environmental influence, such as diffusion, energy transfer and migration, etc., as shown in Figure 15.7 [8,9]. For fluorescence measurements, by far the most versatile and widely used time-resolved emission technique involves time-correlated single-photon counting [8] in conjunction with mode-locked lasers, a typical modern apparatus being shown in Figure 15.8. The instrument response time of such an apparatus with microchannel plate detectors is of the order of 70 ps, giving an ultimate capability of measurement of decay times in the region of « 7 ps. However, it is the phenomenal sensitivity and accuracy which are the main attractive features of the technique, which is widely used for time-resolved fluorescence decay, timeresolved emission spectra, and time-resolved anisotropy measurements. Below are described three applications of such time-resolved measurements on synthetic polymers, derived from recent work by the author's group.

15.7 FLUORESCENCE DECAY IN VINYL AROMATIC POLYMERS Fluorescence in such polymers is dominated by excimer formation, the simplest kinetics for which were described by Birks and co-workers [10,11] (Scheme 1). In

Scheme 1 Birks kinetic scheme

this treatment the influences of diffusion or energy migration are neglected, and only the two chromophores directly involved in the excimer formation process are considered. In Scheme 1, M refers to the ground state monomer species, 1 M* to the monomer in its first excited singlet state and 1 D* represents the excimer; kM is the molecular decay rate, which is the rate of depopulation of * M* by radiative or non-radiative decay in the absence of other chromophores or intra-molecular chemistry; kD is the rate of radiative and non-radiative decay of the excimer;fcDMis the rate of formation of excimer from monomer, and kMD is the rate of dissociation of the excimer to recreate the excited monomer. Equations for the monomer and excimer population are then as follows: [ 1 M*] = -^

^ [ ( A 2 - J 0 e x p ( - A , t ) + (X-A 1 )exp(-A 2 t)]

[»D*] = kD^ll.^*\cxp(-

A l t )exp(- A2t)]

(D (2)

[A2 ~ ^V

where X9 A1 and A2 are functions of the rate parametersfcM,fcD,fcMDand /cDM, viz: X = kM + /cDM[M]

(3) 1

1/2

(4)

2

1/2

(5)

A1 = 1/2(Z + kD + kM - {(kD + fcM - X) + 4fcMD/cDM[M]} ) A2 = 1/2(Z + kD 4- /cM + {(kD + fcM - X) +4fcMD/cDM[M]} )

It can be seen from Equations (1) and (2) that the monomer and excimer decays are both the sum of exactly two exponential decay terms, with the same lifetimes A1 and A2 appearing in both monomer and excimer decays. In addition, the two pre-exponential factors in the excimer decay are of equal magnitude but opposite sign. However, except to a first approximation, neither of these characteristics is usually seen experimentally in polymers [12-14] where, typically, the monomer and excimer decays will give different values OfA1 and A2 and the excimer decay will not have pre-exponential factors of equal magnitude. As real polymer decays do not follow the Birks kinetic scheme, the scheme evidently does not take account of all the photophysical processes which occur in polymers, and efforts to improve the models have been made in two main directions. The first approach

has been to parameterize the deviations from Birks kinetics using a third exponential decay term in both the monomer and excimer decays. The third term can then be interpreted in a number of ways, such as the existence of a third species. In fact, if all the photophysical processes occurring in the polymer are time independent, i.e. can be expressed by a simple rate constant in a kinetic scheme, then the existence of a third species is the only conclusion that can be drawn from a third decay term. Some of the models proposed, and which have been successful in explaining polymer fluorescence decays, are as follows: (1) two monomer species, the first one able to form the second, but only the second one able to form excimers [15,16]; (2) two monomer species, one of which can be formed only by dissociation of excimers, and cannot reform excimers [15,16]; (3) three excimer species, two of which are in equilibrium, the third being formed only from the monomer [17-19]. The multi-exponential approach has been criticized on the grounds that the kinetic schemes are not unique: data which are consistent with two excimers may also be consistent with a second type of monomer [20]. Also, there is rarely supporting spectroscopic evidence for the presence of a third species, which would be expected to have a different emission spectrum. However, except in the case of poly(vinylcarbazoles) [21-24], no such evidence has been found.

15.7.1 D I F F U S I O N A L MODELS The second approach to the study of excimer kinetics has been more theoretical. In experiments on dilute solutions of unlinked chromophores, there has been some success in considering the process of excimer formation as a diffusive process [25]. Nemzek and Ware [26] used an extension of the Smoluchowski equation [27] devised by Collins and Kimball [28], which gives for Jt(^DM k(t) = 4TIDABR'N(

1+

R

)

(6)

The Birks kinetic scheme can then be adjusted to include k(t)DM. Because of the complexity involved, the rate constant /cMD is usually neglected at this stage. The population of the monomer excited state then has the time dependence of Equation (7): [ 1 M*] = [ 1 M^] 0 exp[ -(fcM + 4nDABR'Nt)-

*'

t1'2]

(7)

Consider now the diffusion of excitation through an array of monomers. The excited state moves along the polymer chain from one monomer to another, probably by the Forster dipole-dipole mechanism, but other energy transfer

mechanisms such as the Dexter electron exchange mechanism may also play a part, especially in solid polymers, where the chromophores are very close together. The excitation may be trapped at any chromophore by formation of an excimer. A number of different models have been used to consider the time evolution of an excited state which may migrate to a trap site, and often several different approaches are used to approximate the observable parameters for each model. A review of these complex mathematical models is beyong the scope of this paper, but they can be summarized as follows. 15.7.1.1 Random Walk Migration, Evenly Spaced Chromophores This model has been investigated ]by a number of groups and solved approximately using several different methods. Huber [29] solved the rate equations for the donor (monomer) decay using the t-matrix approximation, resulting in Equation (8) for the one dimensional case. [M*] = A exp(4n2qWt)erfc(2nqW1/2tl/2)

(8)

In the asymptotic limit, i.e. for long times, the decay can be approximated by Equation (9); however, when the number of trap sites is sufficiently small, the decay reduces to an exp — (at + btlf2) dependence similar to Equation (7)

[M

*]=(WW*

(9)

In addition to the Mnatrix approximation, however, a various methods have been used to solve the deep trapping problem which has been solved exactly in the one dimensional case [30]. Movaghar et al. compared the coherent potential approximation (CPA) [31] and the first passage time approach (FPT) [32] results with the exact solution while stating that the Mnatrix approximation used by Huber is less accurate than the CPA under all conditions. Movaghar et al. [30] [31] found that the FPT approach is superior to the CPA at all trap concentrations except for very high concentrations approaching 1, where all chromophores are traps. At long times the FPT approach gives a solution which asymptotes to exp — (ati/2)9 similar to the low trap concentration Mnatrix derived result. By contrast, the exact result asymptotes to exp — (at1/3). 15.7.1.2 Random Walk, Random Distribution Chromophores

A second, more complex model which can approximate energy migration kinetics involves the relaxation of the condition that there must be an even distribution of chromophores. Such a relaxation can involve, say, a random distribution of chromophores in three dimensions interspersed by a random distribution of traps. The GAF [34] and LAF [35] models are of this type and, in addition,

a model has been derived for polymers (FAF) [36] which relates fluorescence decay parameters to the radius of gyration of the polymer. 15.7.1.3 Multiple Trap Energies

A further complication is to consider the disorder of the energies of the monomer excited states as well as positional disorder. In a polymer, the chromophores are in a range of environments, each of which will have different energies. This problem has been treated theoretically [37] and in a Monte-Carlo simulation [38], both giving an approximate relationship of the form of Equation (10): mv* = b + cf-1

(10)

More recently, the problem of energetic disorder has been considered by Stein et al. [39], who treated the combination of energy migration and trapping as part way between donor-donor transfer and direct trapping of the excitation. The theory agreed well with some of their experimental polymer anisotropy decays. 15.7.1.4 Reversible Excimer Formation

In the Birks kinetic scheme, back-transfer is considered simply by the rate constant fcMD. Weixelbaumer et al. [40] used an approximate method to approach this, whereas Sienicki and Winnick [41] derived an exact result, and posed the question, what happens if monomers formed by back dissociation behave differently from those excited directly? The question was answered by Berberan-Santos and Martinho [42], who showed that k(t)DM does not necessarily decrease monotonically but can sometimes increase with time. 15.7.1.5 Diffusion of Energy and Chromophore

Baumann and Fayer [43] considered a two-body problem in which diffusion and energy transfer occurred simultaneously. Frederickson and Frank developed a simpler one dimensional array model [44]. The equation for the rate of monomer fluorescence in the FF model is given by Equation (11): W ) = 4 F M M 1 " q)2 expl(4n2q2W-kM

- *rot)fj crfc(2nqW1^2)

(11)

In Equation (11), iM(r) is the intensity for fluorescence from the monomer, which is related to the monomer concentration by the monomer quantum yield of fluorescence q^ arid the rate of decay of the monomer fluorescence in isolation fcM; q is the pre-formed trap fraction, which is the fraction of dyads which are trap sites at equilibrium; W is the rate of energy transfer between nearest neighbours

on the polymer, which is of course highly dependent on the distance between the chromophores. Tao and Frank [45] found that 2-vinylnaphthalene homopolymer fluorescence decays fit the FF model under conditions of relatively low temperature. However, they noted that at higher temperatures the model breaks down, probably because of the breakdown of one of the assumptions below: (1) that the polymer may be considered as a one-dimensional string of equally spaced chromophores; (2) that the primary excimer forming step is energy migration, and not internal rotation. This requires that there are a number of 'pre-formed trap sites' in the ground state, which just means that there must be a number of sites where chromophores are in high-energy configurations which are very close to the excimer configuration, or else there must be a low-energy conformation very close to the excimer conformation; (3) that the number of these 'pre-formed trap sites' is low. For this concentration of trap sites, the r-matrix approximation becomes poor; (4) that the excimer formation step is irreversible. We have extended the FF model to high trap concentrations using the FPT approximation. In this, the expression for the monomer fluorescence intensity is given by Equation (12), and that for excimer fluorescence by Equation (13): 'M(0 =
-
T

<1T)

Jo

/

(12) 1

2

*E(0 =
I1(HVT)IdT)

-qFEkE(kM-kE)(l-q)2[texp(-u(kE-T-1)Jo V

— -q[t "2W T Jo

x exp(-2WT)lI0(2WT) +I^WTftdTjdu

(13)

We have tested some of the above models using data from careful timeresolved fluorescence measurements on 1-vinylnaphthalene homopolymer, and copolymers with methyl methacrylate, in the following way. The FF model appears to have five variables, the amplitude, the isolated decay ratefcM,the rate of rotation fcrot, the rate of intramolecular energy transfer W, and the number of trap sites q. However, some of the variables cannot be treated independently and the FF function may actually by rewritten using only three variables. This is done by substituting, say, r = l/(feM + krot) and Q = q W1/2 into Equation (11) to give Equation (14), and fitting the data by varying only the amplitude, t and W. In fact,

if an attempt is made to fit the function while varying all of fcM, krov q and W simultaneously, all solutions with the same t and Q will fit the data equally well. So the FF model actually has only three variable parameters, which is one fewer than the sum of two exponential decay terms. iM(0 = A exp[(4jT2<22 - t)r] erfc(27rQt1/2)

(14)

The efficacy of the FF model was investigated over the range of naphthalene mole fractions. At 290 K, fluorescence from the 25% 1-vinylnaphthalene polymer fits the FF model, whereas neither the 50% 1-vinylnaphthalene polymer nor the homopolymer does so. Obviously the model fits only for low naphthalene concentrations and low temperatures. The breakdown of the FF model at high temperatures and high naphthalene concentrations could be explained by the breakdown of any one of the assumptions outlined above. Tao and Frank also found that the FF model does not adequately fit 2-vinylnaphthalene fluorescence decay profiles at high temperatures [45]. The FPT model should be appropriate for high trap concentrations, but in Figure 15.9 the FPT model produces very similar results to the FF model and was unable to fit any of our data which did not fit the FF model. In the interpretation of fluorescence data, models as complex as the FF model are seldom employed. Commercially available programs for fitting time-resolved fluorescence data generally cover exponential decay, the exponential of a t* function, or sums of these functions, but rarely anything more complex. It would be useful to know when simpler approximations, for which fitting routines are

homopolymer

copolymer

Temperature /K

Figure 15.9 Comparison of fitting parameters from the FF model and the FPT model (see text)

available, are adequate to fit data actually obeying a more complex theory, so that information about a complex model can be inferred from the fit of the experimental data to a simple function. It would consequently be useful to know when the FF model can be successfully approximated by a simpler function. If q2 W stays within certain limits, then fcDM in the FF model can be accurately approximated by a constant term plus a term dependent on t1/2. On integration of the rate equations, the fluorescence decay will then follow Equation (15), which is commonly available in fluorescence decay fitting software.

[

AQ

-(kM + krJt—^-J

/Wt~~\

(15)

Table 15.1 shows reduced x2 test, fcM + ferot and qW112 values obtained from fits of some of the experimental data presented earlier to the FF model and to Equation (15). The last two columns of Table 15.1 consists of values of 4(1 — 2/n)q2W and feM + krov The chi-squared values are equally good for both functions, but the kM + krot and qW1/2 parameters do show some deviations which may be not be explained by experimental error. The FF model consistently finds a slightly less 'exponential decay', indicating that small inaccuracies in the approximation have shown up. Tao and Frank [45] presented data consistent with the FF model without any reference to fitting the exp — (at + bt1/2) approximation. We tested this by simulation; thus, Tao and Frank's data were simulated with the same amplitude as shown in their paper, from their published parameters, and with Gaussian noise added. When our simulated curves were analysed with our FF fitting program, they gave chi-squared values of 1.00 ± 0.05. They were subsequently fitted to Equation (15). The x2 values from the FF fit were then subtracted from the x2 values from the t1'2 fit to give a measure of the difference in the quality of the fit. These results are presented in Table 15.2, along with parameters extracted from the paper. At low temperatures, Equation (15) is well satisfied, and #2(*1/2) —X2(FT) is also very low. As the temperature rises, however, qW1/2 increases faster than Table 15.1 Quality of fit and some fitting parameters for 27% l-vinylnaphthalene/72% methyl methacrylate copolymer

Temp (K)

*2(FF)

290 270 250 230 210

U5 1.11 1.09 0.99 1.26

2 112 x (t )

1.11 1.05 1.09 1.06 1.30

Tw (FF)/

Tw (r 1/2 )/

kM +1/2kTOt 4(1-2/7T)(r )/ q2W/

10 7 S" 1

10 7 S- 1

(xlO" 4 )

10 7 S" 1

O20 0.12 0.049 0.041 0.053

019 0.12 0.047 0.038 0.046

115 116 114 1.95 1.71

O30 0.18 0.07 0.06 0.08

/cM + /crot (FF)/ 10 7 S" 1 236 130 118 1.99 1.76

Table 15.2 Fitting parameters for actual and synthesized data of Tao and Frank; 2-vinylnaphthalene homopolymer Temperature/K 293 273 253 233 213 193 173 153 133 113

* 2 (FF)

* 2 (' 1/2 )-X 2 (FF)

4(1-2/Tr)^2WyIO7S-1

ikM +Jk n ^lO 7 S" 1

L29 1.18 1.10 1.10 1.08 1.05 1.06 1.05 1.02 1.03

017 0.11 0.05 0.03 0.02 0.01 <0.01 <0.01 <0.01 <0.01

15 1.9 1.0 0.62 0.44 0.24 0.09 0.08 0.02 0.02

11 3.1 2.8 2.4 1.9 1.6 1.5 1.5 1.4 1.4

fcM + kTOV until the condition that 4(1 — 2/^)9 W < WkM + fcrot is no longer satisfied above 193 K. At the same time, x2(f1/2) - X2(ff) increases until, at « 293 K, the two models should easily be differentiated. However, by 293 K, the experimental x2(FF) value has also increased to a stage where the data no longer fit the FF model. So at 293 K the exp - (at + bt1/2) function may possibly fit the data better than the FF model. In fact, nothing so far has contradicted the premise that Tao and Frank's data can fit Equation (15) as well as the FF model. This means that the polymer could actually be undergoing any set of processes which approximates sufficiently well to an exp — (at + bt1/2) function. 15.7.1.6 Fluorescence Anisotropy Measurements

The fluorescence decay times of excited states are such that the fluorescence depolarization technique may only be used to examine relatively high frequency relaxation processes of polymers. Consequently fluorescence depolarization has been primarily limited to the study of relaxation processes of polymers in solution. The anisotropy of a system, r(t\ is derived from measurements of the fluorescence decays with polarizations parallel and perpendicular to the polarization of excitation: Ht) = [Z1W - IAt)WiIt)

+ 2Z1(O] = D(t)/S(t)

Time-resolved fluorescence anisotropy measurements [47] can provide detailed information on the reorientation dynamics of molecules in solution. Until recently, however, this information has been limited to single rotational correlation times, which are only strictly appropriate for the diffusion of spherically symmetric molecules. Improvements in instrumentation and data analysis techniques during the last decade have led to increasingly accurate measurements of fluorescence lifetimes, with parallel improvements in determinations of fluorescence anisotropies.

The advances in time-resolved techniques have fostered a reexamination of theories of the rotational motions of molecules in liquids. Models considered include the anisotropic motion of unsymmetrical fluorophores; the internal motions of probes relative to the overall movement with respect to their surroundings, the restricted motion of molecules within membranes (e.g., wobbling within a cone), and the segmental motion of synthetic macromolecules [8]. Analyses of these models point to experimental situations in which the anisotropy can show both multi-exponential and none-exponential decay. Current experimental techniques are capable in principle of distinguishing between these different models. It should be emphasized, however, that to extract a single average rotational correlation time demands the same precision of data and analysis as fluorescence decay experiments which exhibit dual exponential decays. Multiple or non-exponential anisotropy experiments are thus near the limits of present capabilities, and generally demand favourable combinations of fluorescence and rotational diffusion times [48]. An example is cited below of study on the copolymers (a) methyl methacrylate/ acenaphthylene (PMMA/ACE), (b) methyl methacrylate/1-vinylnaphthalene (PMMA/1-VN), (c) methyl acrylate/acenaphthylene (PM A/ACE), and (d) methyl aery late/1-vinylnaphthalene (PMA/l-VN). The results are summarized in Table 15.3. Averaging all the determinations for the initial anisotropy for each polymer sample leads to the following values for excitation at 300 nm: PMMA/ACE, Table 153 Fluorescence anisotropy parameters for labelled acrylic polymers

PMA/ACE

PMA/VN

PMMA/ACE

PMMA/VN

T/K

Tf/ns

To

TR

298 ±2 260±2 245±2 230±2 289±2 275±2 260±2 245±2 230±2 298±2 275±2 260±2 245±2 23O±2 298±2 275±2 260±2 245±2 23O±2

17.4 ±0.2 17.4±0.3 17.4±0.3 17.5±0.3 15.1 ±0.1 14.9±0.1 14.8±0.1 14.9±0.1 14.9±0.1 15.5±O.l 15.7±O.l 15.4±0.2 15.5±0.2 15.6±0.1 15.9±0.02 15.6±0.2 15.5±O.l 15.4±0.1 15.4±0.1

0.10 ±0.01 0.10±0.01 0.11 ±0.01 0.12±0.02 0.13±0.01 0.13±0.01 0.14±0.01 0.14±0.01 0.15±0.01 0.13±0.01 0.13±0.01 0.13 ±0.01 0.13±0.01 0.11 ±0.02 0.15±0.01 0.16±0.01 0.14±0.01 0.15±0.01 0.16±0.01

0.8 ±0.3 1.3±0.2 1.8±0.3 2.5±0.3 0.5±0.1 0.8±0.1 1.0±0.2 1.3±0.3 1.7±0.3 1.3±0.1 2.2±0.2 3.2 ±0.5 4.5±0.7 5.6±0.7 1.3±0.2 2.2±0.5 2.7±0.3 3.6±0.5 4.9±0.7

Direction of independent motion Polymer backbone

backbone

Figure 15.10 Alignment of the transition dipoles and the direction of the independent motion of the 1-vinylnaphthalene chromophore relative to a polymer backbone r0 = 0.13 ±0.01; PMA/ACE, r0 = 0.11 ±0.01; PMMA/1-VN, r0 = 0.15 ±0.01; PMA/l-VN, r0 = 0.14 ±0.02. These results are in excellent agreement with values obtained for polymers with similar compositions. Initial anisotropies are expected to have the value of 0.4. However, the first and second excited states of naphthalene and its derivatives are, in the Platt notation, designated 1L1, and 1 L 3 respectively. The transition dipole moments for absorption into these bands are directed along the long (1L1,) and short ( 1 LJ axes of the aromatic rings. Irradiation at 300 nm produces excitation of both absorption bands, and so naphthalene, when excited at this wavelength, can be considered to have a planar rather than a linear absorption oscillator. The 1-vinylnaphthalene chromophore, unlike the acenaphthylene chromophore, would appear to be capable of motion independent of the polymer backbone by rotation about the single bond [Fig. 15.10]. However, such rotation cannot lead to depolarization. Consequently for the 1-vinylnaphthalene labelled polymers, as with the acenaphthylene labelled polymers, it is only segmental motions which lead to depolarization. For the poly(methacrylates) and poly(acrylates), the a and /? relaxations are associated with segmental motions of the polymer and independent motions of the ester substituents respectively. The merging of these transitions at high frequencies or temperatures corresponds, at the molecular level, to the incidence of co-operative motion between the substituent and the polymer backbone. Consequently, it is to be expected that, in solution, the high frequency motions of both polymer chain and fluorescent label will assume a co-operative form characterized by a single relaxation process/time. The activation energies derived from the results at different temperatures (Table 15.3) show that in poly(methyl methacrylate) and poly(methyl acrylate) the segmental motions are largely controlled by solvent flow.

15.8 CONCLUSION Time-resolved luminescence measurements have still unrealized potential for the study of energy migration, rotational motion and surface effects in polymers in solution and in the solid state.

15.9 ACKNOWLEDGEMENTS This paper has drawn upon the work of AJ. Roberts, G. Rumbles, R.C. Drake, C.F.C. Porter and R.L. Christensen, of Imperial College, London, and of Professor Ian Soutar and his group at the University of Lancaster. All are thanked for their contributions. Financial support from SERC and The Royal Society is gratefully acknowledged.

15.10 REFERENCES [1] D. Philips (Ed.), Polymer Photophysics: Luminescence, Energy Migration and Molecular Motion in Synthetic Polymers, Chapman Hall, London, 1985.

[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

S.W. Beavan, J.S. Hargreaves and D. Phillips, Adv. Photochem. 1979,11, 207. Y. Nishijima, J. Polym. ScL Polym. Symp., 1970, 31, 353. A.C. Somersall, E. Dan and J.E. Guillet, Macromolecules, 1974,7, 233. D. Phillips, Br. Polym. J., 1987,19,135. W.C. Tao and CW. Frank, in J.-P. Fouassier and J.F. Rabek (Eds.), Lasers in Polymer Science and Technology: Applications, Vol. 1, CRC Press, Boca Raton, 1990 p. 161. M.A. Winnick, in J.-P. Fouassier and J.F. Rabek (Eds.), Lasers in Polymer Science and Technology: Applications, Vol. 1, CRC Press, Boca Raton, 1990, p. 197. G. Rumbles and D. Phillips, in J.-P. Fouassier and J.F. Rabek (Eds.), Lasers in Polymer Science and Technology: Applications, Vol. 1, CRC Press, Boca Raton, 199 p. 91. D. Phillips, in CE. Hoyle and J.M. Torkelsen (Eds.), Photophysics of Polymers, ACS Symp. Ser., 1987, (358), 308. J.B. Birks, Photophysics of Aromatic Molecules, Wiley-Interscience, London, 1970, pp. 322-335. J.B. Birks, DJ. Dyson and T.A. King, Proc. R. Soc. London, Ser. A, 1964, 277, 270. AJ. Roberts, D.V. O'Connor and D. Phillips, Ann. N.Y. Acad. ScL, 1981,366,109. D. Phillips, AJ. Roberts and I. Soutar, Polymer, 1981, 22, 293. D. Phillips, AJ. Roberts and I. Soutar, J. Polym. ScL, Polym. Phys. Ed., 1982,20,411. D. Phillips, AJ. Roberts and I. Soutar, Polymer, 1981, 22,427. D. Phillips, AJ. Roberts and I. Soutar, J. Polym. ScL, Polym. Phys. Ed., 1980, 18, 2401. D.A. Holden, P.Y.K. Wang and J.E. Guillet, Macromolecules, 1981,14,405. F.C. DeSchryver, K. Demayer, M. Van der Anweraer and E. Quanten, Ann. N.Y. Acad. ScL, 1981, 109. AJ. Roberts, D. Phillips, F. Aboul-Rasoul and A. Ledwith, J. Chem. Soc, Faraday Trans. 7,1981,77,2725. K. Sienicki and G. Durocher, Macromolecules, 1991, 24,1102. C. David, M. Piens and G. Geuskens, Eur. Polym. J., 1972,8,1019. C David, M. Piens and G. Geuskens, Eur. Polym. J., 1972,8, 1291. CE. Hoyle, T.L. Nemzek, A. Mar and J.E. Guillet, Macromolecules, 1978,11, 429. G.E. Johnson, J. Chem. Phys., 1975,62,4697. J.C. Andre, F. Baros and M.A. Winnick, J. Phys. Chem., 1990, 94, 2942. T.C. Nemzek and W.R. Ware, J. Chem. Phys., 1975, 62,477. M.V. Smoluchowski, Z. Phys. Chem., 1917,92, 129.

[28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49]

F.C. Collins and GE. Kimball, J. Colloid ScL, 1949,4,425. D.L. Huber, Phys. Rev. B, 1979, 20, 2307. B. Movaghar, G.W. Sauer and D. Wurtz, J. Slat. Phys., 1982, 27, 473. B. Movaghar, J. Phys. C (Solid State), 1980,13,4915. E.W. Montroll, J. Math. Phys., 1969,10, 753. J. Klafter and R. Silbey, J. Chem. Phys., 1981,74, 3510. CR. Gochanour, H.C. Andersen and M.D. Fayer, J. Chem. Phys., 1970,70,4254. R.F. Loring, H.C. Andersen and M.D. Fayer, J. Chem. Phys., 1982,76, 2015. G.H. Fredrickson and H.C. Andersen, Macromolecules, 1984,17, 54. M. Griinewald, B. Pohlmann, B. Movaghar and D. Wurtz, Philos. Mag. B, 1984,49, 341. R. Richert, B. Ries and H. Bassler, Philos. Mag. B, 1984, 49, L25. A.D. Stein, K.A. Petersen and M.D. Fayer, J. Chem. Phys., 1990,92, 5622. W. Weixelbaumer, J. Burbaumer and H.F. Kaufmann, J. Chem. Phys., 1985,83,1980. K. Sienicki and M.A. Winnick, J. Chem. Phys., 1987,87, 2766. M.N. Berberan-Santos and J.M.G. Martinho, J. Chem. Phys., 1991,95,1817. J. Baumann and M.D. Fayer, J. Chem. Phys., 1986,85,4087. G.H. Frederickson and CW. Frank, Macromolecules, 1983,16, 572. W.C Tao and CW. Frank, J. Phys. Chem., 1989,93, 776. R. Gelles and CW. Frank, Macromolecules, 1982,15, 747. D. V. O'Connor and D. Phillips, Time-Correlated Single Photon Counting, Academic Press, London, 1984. R.L. Christensen, R.C Drake and D. Phillips, J. Phys. Chem., 1986,90, 5960. R.C Drake, Ph.D. Thesis, University of London, 1986.

Index Index terms

Links

A AB quartet

18

acrylonitrile-furan copolymers

27

adsorbtion

242

afine deformation

183

aggregation

355

alignment (Homeotropic, planar)

282

alkylcyanobiphenyl

282

alpha (shift) effect

339

9

56

alpha (greek) process

277

alpha helix

355

amorphous polymers

276

332

anisotropies

173

235

APT (attached proton test)

11

autocorrelation function

278

azobenzene groups

351

B Bernoullian statistics beta (shift) effect

21 9

beta (greek) process

277

biaxial orientation

176

blends

245

57

340

This page has been reformatted by Knovel to provide easier navigation.

391

392

Index terms

Links

C catalysts

33

C– –C(triple) stretch

214

CD Circular dichroism

350

chain transfer

32

charge-transfer complex participation

22

chiral macromolecules chemical shift chemical shift image cis double bonds

347 2 157

159

36

Cobalt-60 gamma irradiation

263

Cole-Cole plot

290

composites

159

conformation

55

conformational data

97

conformational transitions

352

correlation times

235

COSY

221

221

84

coupling constant cross polarization Robin

7

111

135

crosslinked systems

12

Cryogenic trapping

270

crystalline polymers

280

261

D deformation

203

degradation

253

263

11

73

DEPT Assignment technique

This page has been reformatted by Knovel to provide easier navigation.

393

Index terms

Links

desorption

165

diacetylene monomers

204

dichroic difference

187

dichroic ratio

180

dielectric constant/permittivity

258

dielectric relaxation modes

279

Dielectric Relaxation Spectroscopy (DRS)

275

dienes as monomers

287

25

diffusion

162

167

diglycidyl ether of bisphenol-A (DGEBA)

121

288

domain size

125

146

double bond dyada, triads dynamic dichroic

38 192

E elastomers

197

electroactive

282

electron spin resonance (esr)

231

electrooptical

282

enantiomer copolymerization

41

ethylene glycol dimethacrylate

254

ethylene-vinyl acetate copolymers excimer

253

88 374

F Fourier transform (NMR) Fourier transform vibration spectroscopy fractal

8 173

257

15

free radical

231

255

This page has been reformatted by Knovel to provide easier navigation.

315

394

Index terms fumarate-vinyl acetate copolymer furan-acrylonitrile copolymers

Links 245 27

G g value (esr) gamma gauche effect

235

255

57

64

97

gamma rays

263

gamma relaxation

280

gels

259

311

332

glass transition temperature

142

165

240

Goldman-Shen pulse sequence

126

H helix content

354

367

I imaging (NMR) INEPT assignment technique

151 72

inhomogeneities

151

interfacial

224

interferometer

177

IR

173

isotope enrichment (D)

257

30

K Karplus

111

Kerr Constant

280

Kevlar

204

Kohlrausch-Williams-Watts

277

207

This page has been reformatted by Knovel to provide easier navigation.

395

Index terms

Links

L lamellar morphology Lewis acid effect

125 29

light scattering

297

linear response theory

278

liquid crystalline polymers

145

282

loss (dielectric)

275

283

luminescence

369

M Magic-angle Spinning (MAS) NMR Markov statistics

92 144 359

meso dyads

18

metallacarbenes

35

methacrylate radical

260

methylmethacrylate

254

41

8

18

55

97

molecular anisotropy

173

molecular size

331

morphology

136

Motion (of polymer)

231

Motionally-narrowed

239

multidimensional NMR

135

N natural rubber

138

21

merocyanine

microstructure

119

161

198

This page has been reformatted by Knovel to provide easier navigation.

32

396

Index terms

Links

near lR

257

neutron scattering

325

nitroxide

232

NMR

7

117

135

160

281

27

103

151 NOESY NMR assignment

87

Norris-Tromsdorf region

257

nylon

128

O optical activity

347

orientation

173

P permittivity(dielectric)

275

phase separating mixtures

305

photophysics

369

pixel

165

poly(acrylonitrile)

19

poly(alpha amino acids)

351

poly(alpha methyl styrene)

265

poly(bisphenylurethane-2,4-hexadiyne-1,6-diol)

205

poly(butadiene)

27

poly(but-l-ene sulphone)

16

poly(isobutylene)

199

polycarbonate

167

poly(diacetylene) single crystal fibre

205

poly(dimethyl siloxane)

161

poly(2,6-dimethyl-l,4-phenylene oxide)

196

This page has been reformatted by Knovel to provide easier navigation.

21

397

Index terms polyester(branched) poly(ethyl cyanoacrylate) poly(2-ethylhexyl methacrylate) polyethylene

Links 9

12

15 248 9

181

184

210

212

281

polyethylene terephthalate)

145 277

182 281

189

poly(L-glutamic acid)

352

poly(2,4-hexadiyne-1,6-bis (p-toluenesulphonate))

205

poly(isoprene)

246

poly(L-lysine)

351

polymer dynamics

136

275

338

polymerization

253

poly(methacrylonitrile)

107

poly(methyl acrylate)

277

poly(methylmethacrylate)

7 165 259

10 246 260

107 254 268

poly(n-butyl isocyanate)

235

poly(norbornene)

35

43

poly(oxymethylene)

140

143

281

polypropylene

10 103

58 122

66

68

277

190 267

193 315

10

92

poly(propylene oxide) polystyrene polystyrene(syndiotactic) poly(styrene block butadiene block styrene) polysulphide

196 15

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246 373

398

Index terms

Links

poly(vinyl acetate)

243

277

poly(vinyl alochol)

104

371

poly(vinyl chloride)

105

130

poly(vinyl fluoride)

83

281

poly(vinylidene fluoride)

81

142

246

297

309

334

radical

231

255

Raman Spectroscopy

173

203

regio selectivity

18

38

40

resolution enhancement

12

Ring Opening Metathesis Polymerization (ROMP)

30

RIS (rotational isomeric state)

62

98

109

183

281 poly(vinyl methyl ether)

141

powder pattern spiess

137

prochiral face

35

Q quasi elastic scattering

R

Rotor-synchronized MAS NMR

144

Rouse modes

338

S SALS (small angle light scattering)

298

SANS (small angle neutron scattering)

330

semicrystalline polymers

298

semidilute

313

silica absorbent

242

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399

Index terms

Links

silicone polymer

282

simulation (esr spectrum)

266

solid polymer NMR

117

solution NMR

135

7

specular reflectance

177

spin density

157

spin label

231

spin probe

231

spin relaxation (proton)

125

spirobenzopyran

357

steroselectivity

35

stereospecific polymerization

32

strain

185

203

stress

185

203

styrene-MMA copolymers

84

substituent effects

56

surfaces

316

333

T1

119

125

T1rho(ρ)

125

T2

125

T

tacticity

15

Tactic sequence

98

tensile stress

222

thermoset (epoxy amine)

288

time-resolved measurements

184

two-dimensional IR

192

two-frequency-addressing

282

153

This page has been reformatted by Knovel to provide easier navigation.

153

400

Index terms

Links

U uniaxial orientation

174

urethane-diacetylene copolymers

219

UV light

351

V vinyl acetate copolymer vinyl chloride copolymers voxel

279 67 155

W WAAS

209

Wigner rotation matrix

286

WISE NMR

141

WLF (Williams Landel Ferry)

241

Y Young's modulus

206

Z Zeigler-Natta polymerization

31

This page has been reformatted by Knovel to provide easier navigation.