Thermal Behavior of Dispersed Systems

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THERMAL BEHAVIOR OF DISPERSED SYSTEMS

edited by Nissim Garti The Hebrew University of Jerusalem Jerusalem, Israel

Marcel Dekker, Inc.

New York • Basel

TM

Copyright © 2000 by Marcel Dekker, Inc. All Rights Reserved.

ISBN: 0-8247-0432-0 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright  2001 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microﬁlming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA

SURFACTANT SCIENCE SERIES

FOUNDING EDITOR

MARTIN J. SCHICK 1918–1998 SERIES EDITOR

ARTHUR T. HUBBARD Santa Barbara Science Project Santa Barbara, California

ADVISORY BOARD

DANIEL BLANKSCHTEIN Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts

ERIC W. KALER Department of Chemical Engineering University of Delaware Newark, Delaware

S. KARABORNI Shell International Petroleum Company Limited London, England

CLARENCE MILLER Department of Chemical Engineering Rice University Houston, Texas

LISA B. QUENCER The Dow Chemical Company Midland, Michigan

DON RUBINGH The Procter & Gamble Company Cincinnati, Ohio

JOHN F. SCAMEHORN Institute for Applied Surfactant Research University of Oklahoma Norman, Oklahoma

BEREND SMIT Shell International Oil Products B.V. Amsterdam, The Netherlands

P. SOMASUNDARAN Henry Krumb School of Mines Columbia University New York, New York

JOHN TEXTER Strider Research Corporation Rochester, New York

1. Nonionic Surfactants, edited by Martin J. Schick (see also Volumes 19, 23, and 60) 2. Solvent Properties of Surfactant Solutions, edited by Kozo Shinoda (see Volume 55) 3. Surfactant Biodegradation, R. D. Swisher (see Volume 18) 4. Cationic Surfactants, edited by Eric Jungermann (see also Volumes 34, 37, and 53) 5. Detergency: Theory and Test Methods (in three parts), edited by W. G. Cutler and R. C. Davis (see also Volume 20) 6. Emulsions and Emulsion Technology (in three parts), edited by Kenneth J. Lissant 7. Anionic Surfactants (in two parts), edited by Warner M. Linfield (see Volume 56) 8. Anionic Surfactants: Chemical Analysis, edited by John Cross 9. Stabilization of Colloidal Dispersions by Polymer Adsorption, Tatsuo Sato and Richard Ruch 10. Anionic Surfactants: Biochemistry, Toxicology, Dermatology, edited by Christian Gloxhuber (see Volume 43) 11. Anionic Surfactants: Physical Chemistry of Surfactant Action, edited by E. H. Lucassen-Reynders 12. Amphoteric Surfactants, edited by B. R. Bluestein and Clifford L. Hilton (see Volume 59) 13. Demulsification: Industrial Applications, Kenneth J. Lissant 14. Surfactants in Textile Processing, Arved Datyner 15. Electrical Phenomena at Interfaces: Fundamentals, Measurements, and Applications, edited by Ayao Kitahara and Akira Watanabe 16. Surfactants in Cosmetics, edited by Martin M. Rieger (see Volume 68) 17. Interfacial Phenomena: Equilibrium and Dynamic Effects, Clarence A. Miller and P. Neogi 18. Surfactant Biodegradation: Second Edition, Revised and Expanded, R. D. Swisher 19. Nonionic Surfactants: Chemical Analysis, edited by John Cross 20. Detergency: Theory and Technology, edited by W. Gale Cutler and Erik Kissa 21. Interfacial Phenomena in Apolar Media, edited by Hans-Friedrich Eicke and Geoffrey D. Parfitt 22. Surfactant Solutions: New Methods of Investigation, edited by Raoul Zana 23. Nonionic Surfactants: Physical Chemistry, edited by Martin J. Schick 24. Microemulsion Systems, edited by Henri L. Rosano and Marc Clausse 25. Biosurfactants and Biotechnology, edited by Naim Kosaric, W. L. Cairns, and Neil C. C. Gray 26. Surfactants in Emerging Technologies, edited by Milton J. Rosen 27. Reagents in Mineral Technology, edited by P. Somasundaran and Brij M. Moudgil 28. Surfactants in Chemical/Process Engineering, edited by Darsh T. Wasan, Martin E. Ginn, and Dinesh O. Shah 29. Thin Liquid Films, edited by I. B. Ivanov 30. Microemulsions and Related Systems: Formulation, Solvency, and Physical Properties, edited by Maurice Bourrel and Robert S. Schechter 31. Crystallization and Polymorphism of Fats and Fatty Acids, edited by Nissim Garti and Kiyotaka Sato

32. Interfacial Phenomena in Coal Technology, edited by Gregory D. Botsaris and Yuli M. Glazman 33. Surfactant-Based Separation Processes, edited by John F. Scamehorn and Jeffrey H. Harwell 34. Cationic Surfactants: Organic Chemistry, edited by James M. Richmond 35. Alkylene Oxides and Their Polymers, F. E. Bailey, Jr., and Joseph V. Koleske 36. Interfacial Phenomena in Petroleum Recovery, edited by Norman R. Morrow 37. Cationic Surfactants: Physical Chemistry, edited by Donn N. Rubingh and Paul M. Holland 38. Kinetics and Catalysis in Microheterogeneous Systems, edited by M. Grätzel and K. Kalyanasundaram 39. Interfacial Phenomena in Biological Systems, edited by Max Bender 40. Analysis of Surfactants, Thomas M. Schmitt (see Volume 96) 41. Light Scattering by Liquid Surfaces and Complementary Techniques, edited by Dominique Langevin 42. Polymeric Surfactants, Irja Piirma 43. Anionic Surfactants: Biochemistry, Toxicology, Dermatology. Second Edition, Revised and Expanded, edited by Christian Gloxhuber and Klaus Künstler 44. Organized Solutions: Surfactants in Science and Technology, edited by Stig E. Friberg and Björn Lindman 45. Defoaming: Theory and Industrial Applications, edited by P. R. Garrett 46. Mixed Surfactant Systems, edited by Keizo Ogino and Masahiko Abe 47. Coagulation and Flocculation: Theory and Applications, edited by Bohuslav Dobiáð 48. Biosurfactants: Production · Properties · Applications, edited by Naim Kosaric 49. Wettability, edited by John C. Berg 50. Fluorinated Surfactants: Synthesis · Properties · Applications, Erik Kissa 51. Surface and Colloid Chemistry in Advanced Ceramics Processing, edited by Robert J. Pugh and Lennart Bergström 52. Technological Applications of Dispersions, edited by Robert B. McKay 53. Cationic Surfactants: Analytical and Biological Evaluation, edited by John Cross and Edward J. Singer 54. Surfactants in Agrochemicals, Tharwat F. Tadros 55. Solubilization in Surfactant Aggregates, edited by Sherril D. Christian and John F. Scamehorn 56. Anionic Surfactants: Organic Chemistry, edited by Helmut W. Stache 57. Foams: Theory, Measurements, and Applications, edited by Robert K. Prud'homme and Saad A. Khan 58. The Preparation of Dispersions in Liquids, H. N. Stein 59. Amphoteric Surfactants: Second Edition, edited by Eric G. Lomax 60. Nonionic Surfactants: Polyoxyalkylene Block Copolymers, edited by Vaughn M. Nace 61. Emulsions and Emulsion Stability, edited by Johan Sjöblom 62. Vesicles, edited by Morton Rosoff 63. Applied Surface Thermodynamics, edited by A. W. Neumann and Jan K. Spelt 64. Surfactants in Solution, edited by Arun K. Chattopadhyay and K. L. Mittal 65. Detergents in the Environment, edited by Milan Johann Schwuger

66. Industrial Applications of Microemulsions, edited by Conxita Solans and Hironobu Kunieda 67. Liquid Detergents, edited by Kuo-Yann Lai 68. Surfactants in Cosmetics: Second Edition, Revised and Expanded, edited by Martin M. Rieger and Linda D. Rhein 69. Enzymes in Detergency, edited by Jan H. van Ee, Onno Misset, and Erik J. Baas 70. Structure-Performance Relationships in Surfactants, edited by Kunio Esumi and Minoru Ueno 71. Powdered Detergents, edited by Michael S. Showell 72. Nonionic Surfactants: Organic Chemistry, edited by Nico M. van Os 73. Anionic Surfactants: Analytical Chemistry, Second Edition, Revised and Expanded, edited by John Cross 74. Novel Surfactants: Preparation, Applications, and Biodegradability, edited by Krister Holmberg 75. Biopolymers at Interfaces, edited by Martin Malmsten 76. Electrical Phenomena at Interfaces: Fundamentals, Measurements, and Applications, Second Edition, Revised and Expanded, edited by Hiroyuki Ohshima and Kunio Furusawa 77. Polymer-Surfactant Systems, edited by Jan C. T. Kwak 78. Surfaces of Nanoparticles and Porous Materials, edited by James A. Schwarz and Cristian I. Contescu 79. Surface Chemistry and Electrochemistry of Membranes, edited by Torben Smith Sørensen 80. Interfacial Phenomena in Chromatography, edited by Emile Pefferkorn 81. Solid–Liquid Dispersions, Bohuslav Dobiáð, Xueping Qiu, and Wolfgang von Rybinski 82. Handbook of Detergents, editor in chief: Uri Zoller Part A: Properties, edited by Guy Broze 83. Modern Characterization Methods of Surfactant Systems, edited by Bernard P. Binks 84. Dispersions: Characterization, Testing, and Measurement, Erik Kissa 85. Interfacial Forces and Fields: Theory and Applications, edited by Jyh-Ping Hsu 86. Silicone Surfactants, edited by Randal M. Hill 87. Surface Characterization Methods: Principles, Techniques, and Applications, edited by Andrew J. Milling 88. Interfacial Dynamics, edited by Nikola Kallay 89. Computational Methods in Surface and Colloid Science, edited by Maùgorzata Borówko 90. Adsorption on Silica Surfaces, edited by Eugène Papirer 91. Nonionic Surfactants: Alkyl Polyglucosides, edited by Dieter Balzer and Harald Lüders 92. Fine Particles: Synthesis, Characterization, and Mechanisms of Growth, edited by Tadao Sugimoto 93. Thermal Behavior of Dispersed Systems, edited by Nissim Garti 94. Surface Characteristics of Fibers and Textiles, edited by Christopher M. Pastore and Paul Kiekens 95. Liquid Interfaces in Chemical, Biological, and Pharmaceutical Applications, edited by Alexander G. Volkov

96. Analysis of Surfactants: Second Edition, Revised and Expanded, Thomas M. Schmitt 97. Fluorinated Surfactants and Repellents: Second Edition, Revised and Expanded, Erik Kissa 98. Detergency of Specialty Surfactants, edited by Floyd E. Friedli 99. Physical Chemistry of Polyelectrolytes, edited by Tsetska Radeva 100. Reactions and Synthesis in Surfactant Systems, edited by John Texter 101. Protein-Based Surfactants: Synthesis, Physicochemical Properties, and Applications, edited by Ifendu A. Nnanna and Jiding Xia 102. Chemical Properties of Material Surfaces, Marek Kosmulski 103. Oxide Surfaces, edited by James A. Wingrave 104. Polymers in Particulate Systems: Properties and Applications, edited by Vincent A. Hackley, P. Somasundaran, and Jennifer A. Lewis 105. Colloid and Surface Properties of Clays and Related Minerals, Rossman F. Giese and Carel J. van Oss 106. Interfacial Electrokinetics and Electrophoresis, edited by Ángel V. Delgado 107. Adsorption: Theory, Modeling, and Analysis, edited by József Tóth 108. Interfacial Applications in Environmental Engineering, edited by Mark A. Keane 109. Adsorption and Aggregation of Surfactants in Solution, edited by K. L. Mittal and Dinesh O. Shah 110. Biopolymers at Interfaces: Second Edition, Revised and Expanded, edited by Martin Malmsten 111. Biomolecular Films: Design, Function, and Applications, edited by James F. Rusling 112. Structure–Performance Relationships in Surfactants: Second Edition, Revised and Expanded, edited by Kunio Esumi and Minoru Ueno

ADDITIONAL VOLUMES IN PREPARATION

Liquid Interfacial Systems: Oscillations and Instability, Rudolph V. Birikh, Vladimir A. Briskman, Manuel G. Velarde, and Jean-Claude Legros Novel Surfactants: Preparation, Applications, and Biodegradability: Second Edition, Revised and Expanded, edited by Krister Holmberg Colloidal Polymers: Preparation and Biomedical Applications, edited by Abdelhamid Elaissari

Preface

Many important everyday materials are known to be colloidal heterogeneous systems. Milk, margarine, ice cream, mayonnaise, cosmetic creams, hand lotions, blood, ink, paint, and other substances are heterogeneous systems that can ﬂow or become solid, and contain structural entities with at least one linear dimension in the size range of several nanometers to tens of microns. Colloidal systems consist of a dispersed phase of particles, droplets, and bubbles in a second continuous phase called the dispersion medium. Dispersed systems are said to be stable if, over a certain period of time, there is little detectable aggregation or settling of particles. In many colloidal systems, a stable thermodynamic state is reached only when all particles or droplets have become united in a single homogeneous lump of dispersed phase and, therefore, any apparent stability must be regarded as purely kinetic phenomenon. Dispersed systems are stabilized by a third component known to have amphiphilic properties and surface activity. The amphiphiles migrate to the interface and modify it to reduce the interfacial free energy and to minimize interactions between particles and droplets. It is obvious that any temperature change will affect the mobility of the amphiphiles from the continuous phase to the interface, and vice versa, and will affect the thermodynamic and geometric parameters of the interface. Therefore, the thermal behavior of dispersed systems is an essential parameter in studying structural and thermodynamic aspects. For generations, attempts have been made to heat and cool foams, emulsions, dispersions, and heterogeneous colloidal systems, and to learn about the stability of the systems through their thermal behavior. Differential scanning calorimetry (DSC) and differential thermo gravimetry (DTG) are classical instruments that iii

iv

Preface

through complex heating-cooling protocols provide important information on the behavior of the components of the dispersions. Dispersions (mostly emulsions and microemulsions) are used as microreactors or nanoreactors for important organic and enzymatic processes, and serve as reservoirs for the solubilization of materials. The behavior of the solubilized matter is also dramatically affected by thermal ﬂuctuations. Hydration or solvation, as well as other interactions of cosolvents, are also studied through thermal treatment. It is therefore important to bring to the reader’s attention the options and the scope, as well as the limitations, of the thermal behavior of dispersed systems. This book calls attention to some of the recent studies that have been carried out on heterogeneous colloidal (dispersed) systems. Chapter 1, by Turco Liveri (Italy), reviews calorimetric investigations on reversed micelles, in which the apolar molecules interact by dispersion forces that are always attracted independently of their relative orientation. The author describes the tendency of the apolar medium in reverse micelles to form a longrange, ordered molecular arrangement in condensed phases. The amphiphilic molecules, characterized by the coexistence of spatially separated polar and apolar moieties, work together to drive the intermolecular aggregation, giving rise to dimensionally limited supramolecular aggregates. From a thermodynamic point of view, self-aggregation of amphiphilic molecules in apolar solvents involves a favorable enthalpic term due to intermolecular bonding counteracted by an unfavorable entropic term as a result of partial loss of molecular translational and rotational degrees of freedom. V. Turco Liveri discusses structural aspects, the state of water and other solutes in reversed micelles, intermicellar interactions and percolation phenomena, solubilization of nonionic solutes, and the reversed micelles as nanoreactors. The second chapter, by D. Vollmer (Germany), brings a quantitative comparison of experimental data and theoretical predictions on thermodynamic and kinetic properties of microemulsions based on nonionic surfactants. Phase transitions between a lamellar and a droplet-phase microemulsion are discussed. The work is based on evaluation of the latent heat and the speciﬁc heat accompanying the transitions. The author focuses on the kinetics of phase separation when inducing emulsiﬁcation failure by constant heating. The chapter is a comprehensive, detailed study of all the aspects related to the phase separation phenomenon in microemulsions. In Chapter 3, Ezrahi et al. (Israel) discuss the use of subzero temperature behavior of water in microemulsions as an analytical tool to enable better understanding of the interfacial behavior of the surfactant. Microemulsions are cooled to subzero temperatures and the water in the internal reservoir freezes. In the heating cycle the thawing of the water is measured. The authors critically discuss the problems related to the use of this technique and the advantages derived from it.

Preface

v

Chapter 4, by Schulz et al. (Argentina and Mexico), describes the use of DSC techniques for studying binary and multicomponent systems containing surfactants. The authors explain how DSC helps to elucidate such properties as type of transition, phase boundaries, enthalpies of phase transition, and heat capacity of systems in heterogeneous states. Fouconnier et al. (France) introduce us in Chapter 5 to dispersed systems that are not stable thermodynamically, such as emulsions and double emulsions, and teach us how to carry out DSC measurements properly in order to obtain valuable information on the stability of the emulsions. Various physical and chemical phenomena that occur during cooling and heating have been pointed out. They may be associated with either the dispersed, the continuous, or the interfacial phase. A tentative description of some of these events is presented, and a correlation was made with the resulting properties of the emulsions themselves. Simple water-in-oil (W/O) or oil-in-water (O/W) emulsions, mixed emulsions, and multiple emulsions can be found during the fabrication process. Their storage and their use are considered. Senatra (Italy), who was a pioneer in the use of DSC as a technique to study interfacial phenomena, offers in Chapter 6 some interesting physical parameters and the essence of these observations. Chapter 7 is an interesting review by Kodama and Aoki (Japan) on the behavior of water in phospholipid bilayer systems. The authors distinguish between nonfreezable interlamellar water and freezable intralamellar and bulk water, and estimate the number of molecules of water in each category. They also examine the relationship between lipid phase transitions and ice-melting behavior in lipidwater systems. The behavior of water is also discussed in the gel phase of systems such as DPPC, DMPE, and DPPG. Part II concentrates on solid–liquid interfaces. Chapter 9, by Kira´ly (Hungary), attempts to clarify the adsorption of surfactants at solid/solution interfaces by calorimetric methods. The author addresses questions related to the composition and structure of the adsorption layer, the mechanism of the adsorption, the kinetics, the thermodynamics driving forces, the nature of the solid surface and of the surfactant (ionic, nonionic, HLB, CMC), experimental conditions, etc. He describes the calorimetric methods used, to elucidate the description of thermodynamic properties of surfactants at the boundary of solid–liquid interfaces. Isotherm power-compensation calorimetry is an essential method for such measurements. Isoperibolic heat-ﬂux calorimetry is described for the evaluation of adsorption kinetics, DSC is used for the evaluation of enthalpy measurements, and immersion microcalorimetry is recommended for the detection of enthalpic interaction between a bare surface and a solution. Batch sorption, titration sorption, and ﬂow sorption microcalorimetry are also discussed. Chapter 10, by De´ka´ny (Hungary), describes the microcalorimetric control of liquid sorption on hydrophilic/hydrophobic surfaces in nonaqueous dispersions.

vi

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The dispersed systems are mostly silicates. The author discusses interparticle interactions as a tool for evaluating the stability of dispersions. Parameters such as heat of immersion at solid–liquid interfaces and adsorption capacity are determined, and the mathematical treatment for determining the enthalpy isotherms is described. The heat of wetting in amorphous silica dispersion and on zeolites is discussed. Fu¨redi-Milhofer (Israel), in Chapter 11, provides a broad overview of the role of thermal analysis techniques in basic and applied studies of the formation and transformation of crystalline dispersions. Crystalline disperisons are formed by a succession of some of the following precipitation processes: nucleation, crystal growth, ﬂocculation, Ostwald ripening, and/or phase transformation. After a brief elaboration of the theories underlying these processes, a review is given of experimental studies on the formation and transformation of ionic precipitates from bulk electrolyte solutions. At relatively high supersaturations, compounds that include hydrophilic cations (such as Ca, Al, Fe, etc.) are likely to form highly hydrated amorphous precipitates via homogeneous nucleation and subsequent ﬂocculation. A number of important crystalline compounds, such as hydroxyapatite or zeolites, are formed by phase transformation via amorphous and/or gel-like precursor phases. Thermal analysis techniques yield information on the amount of incorporated water, and mechanism and strength of bonding, and pore sizes of such amorphous and poorly crystalline materials. In some cases they have been successfully used to detect the initiation of phase transformation, such as the formation of ordered subunits of a quasicrystalline zeolite phase within amorphous alumosilicate precursors. At low and medium supersaturations, hydrophilic cations form different crystal hydrates by heterogeneous nucleation and subsequent crystal growth and phase transformation. Dehydration curves give information on the modes of water incorporation resulting from different modes of crystallization. A useful application of thermal analysis is the analytical approach: by determining the mass loss due to dehydration, it was possible to quantitatively determine the proportion of different calcium oxalate hydrates in mixtures, which have been qualitatively analyzed by other techniques (X-ray powder diffraction, IR spectroscopy, etc.). The method yielded excellent results in studies of the kinetics of phase transformation and has been successfully used to demonstrate the potential of surfactant micelles to control the nature of the crystallizing phase. Chapter 11 also deals with crystallization in O/W emulsions and W/O microemulsions. Filipovic´-Vincekovic´ and Tomasˇic´ (Croatia) have contributed Chapter 12, ‘‘Solid-State Transitions of Surfactant Crystals,’’ which discusses the effect of surfactants on the crystallization of materials in aqueous and nonaqueous solutions. The chapter describes the crystalline structure of surfactant and its thermal

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vii

behavior, and the effects related to its crystallization. Single- and double-chain surfactants are reviewed, and the differences in their thermal behavior are elucidated. Chapter 13 is the only chapter that discusses thermal behavior of real complex systems. Raemy et al. (Switzerland and Israel) in ‘‘Thermal Behavior of Foods and Food Constituents,’’ reveal the complexity of studying such systems using different thermal calorimetric techniques. In conclusion, this book presents only a very small fraction of the options, scope, and limitations of using thermal behavior of dispersed systems as an analytical and physical tool for the evalution of phenomena occurring at the interface between the dispersed phase and the dispersion phase. It must be noted that much more work is required to enable better understanding of complex systems and real dispersions. These systems will be discussed in a separate book that will be devoted to complex dispersion systems that have been converted into commercial products. Nissim Garti

Contents

Preface iii Contributors xi Part I 1. Calorimetric Investigations of Solutions of Reversed Micelles 1 Vincenzo Turco Liveri 2. Thermodynamics and Phase-Separation Kinetics of Microemulsions 23 Doris Vollmer 3. Subzero Temperature Behavior of Water in Microemulsions 59 Shmaryahu Ezrahi, Abraham Aserin, Monzer Fanun, and Nissim Garti 4. DSC Analysis of Surfactant-Based Microstructures 121 Pablo C. Schulz, J. F. A. Soltero, and Jorge E. Puig 5. Effects of Cooling–Heating Cycles on Emulsions 183 B. Fouconnier, J. Avendano Gomez, K. Ballerat-Busserolles, and Daniele Clausse 6. Thermal Analysis of Self-Assembling Complex Liquids 203 Donatella Senatra 7. Water Behavior in Phospholipid Bilayer Systems 247 Michiko Kodama and Hiroyuki Aoki ix

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Contents

8. Heat Evolution of the Self-Assembly of Amphiphiles in Aqueous Solutions 295 Dov Lichtenberg, Ella Opatowski, and Michael M. Kozlov Part II 9. Calorimetric Methods for the Study of Adsorption of Surfactants at Solid/Solution Interfaces 335 Zolta´n Kira´ly 10. Microcalorimetric Control of Liquid Sorption on Hydrophilic/ Hydrophobic Surfaces in Nonaqueous Dispersions 357 Imre De´ka´ny 11. The Formation and Transformation of Crystalline Dispersions as Studied by Thermal Analysis 413 Helga Fu¨redi-Milhofer 12. Solid-State Transitions of Surfactant Crystals 451 Nada Filipovic´-Vincekovic´ and Vlasta Tomasˇic´ 13. Thermal Behavior of Foods and Food Constituents 477 Alois Raemy, Pierre Lambelet, and Nissim Garti Index 507

Contributors

Hiroyuki Aoki Department of Biochemistry, Okayama University of Science, Okayama, Japan Abraham Aserin Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel K. Ballerat-Busserolles UTC–De´partment Ge´nie Chimique, Laboratoire Ge´nie des Proce´de´s, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Proce´de´s Industriels, Compieg`ne, France Daniele Clausse UTC–De´partment Ge´nie Chimique, Laboratoire Ge´nie des Proce´de´s, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Proce´de´s Industriels, Compieg`ne, France Imre De´ka´ny Department of Colloid Chemistry, University of Szeged, Szeged, Hungary Shmaryahu Ezrahi Materials and Chemistry Department, The Ordnance Corps, Israel Defense Forces, Ramat Gan, Israel Monzer Fanun Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel Nada Filipovic´-Vincekovic´ Department of Physical Chemistry, Ruer Bosˇkovic´ Institute, Zagreb, Croatia xi

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Contributors

B. Fouconnier UTC–De´partment Ge´nie Chimique, Laboratoire Ge´nie des Proce´de´s, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Proce´de´s Industriels, Compieg`ne, France Helga Fu¨redi-Milhofer Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel Nissim Garti Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel J. Avendano Gomez UTC–De´partment Ge´nie Chimique, Laboratoire Ge´nie des Proce´de´s, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Proce´de´s Industriels, Compieg`ne, France Zolta´n Kira´ly Department of Colloid Chemistry, University of Szeged, Szeged, Hungary Michiko Kodama Department of Biochemistry, Okayama University of Science, Okayama, Japan Michael M. Kozlov Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel Pierre Lambelet

Nestle´ Research Center, Nestec Ltd., Lausanne, Switzerland

Dov Lichtenberg Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel Ella Opatowski Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel Jorge E. Puig Departamento de Ingenierı´a Quı´mica, Universidad de Guadalajara, Guadalajara, Mexico Alois Raemy Nestle´ Research Center, Nestec Ltd., Lausanne, Switzerland Pablo C. Schulz Departamento de Quı´mica e Ingenieria Quı´mica, Universidad Nacional del Sur, Bahı´a Blanca, Argentina Donatella Senatra Department of Physics—INFM Group, University of Florence, Florence, Italy

Contributors

xiii

J. F. A. Soltero Departamento de Ingenierı´a Quı´mica, Universidad de Guadalajara, Guadalajara, Mexico Vlasta Tomasˇic´ Department of Physical Chemistry, Ruer Bosˇkovic´ Institute, Zagreb, Croatia Vincenzo Turco Liveri lermo, Palermo, Italy

Department of Physical Chemistry, University of Pa-

Doris Vollmer Institute for Physical Chemistry, University of Mainz, Mainz, Germany

1 Calorimetric Investigations of Solutions of Reversed Micelles VINCENZO TURCO LIVERI Department of Physical Chemistry, University of Palermo, Palermo, Italy

I. Introduction II.

Reversed Micelles as Nanocontainers: The State of Water and Other Solutes Within Reversed Micelles

1 8

III. Intermicellar Interactions and Percolation

12

IV. Water-Containing Reversed Micelles as Nanosolvents: The Solubilization of Nonionic Solutes

13

V. Reversed Micelles as Nanoreactors

17

VI. Conclusion

19

References

20

I. INTRODUCTION Apolar molecules interact by means of dispersion forces, which are always attractive independently of their relative orientation, and for this reason they display little tendency to give a long-range ordered molecular arrangement in condensed phases. On the other hand, polar molecules interact also by means of dipole– dipole interactions, which are attractive or repulsive depending on the relative orientation of the molecules. It follows that these molecules display a more marked tendency to give a three-dimensionally unlimited ordered molecular arrangement. In the case of amphiphilic molecules, characterized by the coexistence of spatially separated apolar (alkyl chains) and polar moieties, both these parts 1

2

Turco Liveri

concur to drive the intermolecular aggregation giving rise to dimensionally limited supramolecular aggregates. In particular, when dissolved in apolar solvents, as a consequence of both dispersion and dipole–dipole interactions triggered by steric hindrance and thermal agitation, amphiphilic molecules self-assemble, forming a more or less wide spectrum of dynamical structures that differ in aggregation number, shape (linear, cyclic, three-dimensional), and lifetime [1]. Some examples of two-dimensional aggregates of ‘‘amphiphilic molecules’’ (obtained by combining rubber pipette bulbs and magnetic stir bars) oriented according to dipole–dipole interactions are shown in Fig. 1. From a thermodynamic point of view, self-aggregation of amphiphilic molecules in apolar solvents involves a favorable enthalpic term due to intermolecular bonding counteracted by an unfavorable entropic term due to a partial loss of molecular translational and rotational degrees of freedom. Using vapor pressure osmometry, for example, it has been found that the enthalpies of formation of molecular aggregates of dodecylammonium propionate in benzene and cyclohexane are ⫺83.4 kJ/mol and ⫺57.4 kJ/mol, whereas the entropy changes for the same processes are ⫺0.23 kJ/mol and ⫺0.14 kJ/mol, respectively [2]. It is generally agreed that the equilibrium concentrations of monomers and aggregates are well described by a multiple equilibrium model [3,4]. The relative populations of these aggregates are maintained in thermodynamic equilibrium by fast breaking and re-forming processes of labile intermolecular interactions and are controlled by some internal (nature and shape of the polar group and of the apolar molecular moiety of the amphiphile) and external (concentration of the amphiphile, temperature, etc.) parameters. Within a more or less restricted range of these parameters some amphiphilic molecules self-assemble in apolar solvents,

FIG. 1 Examples of linear and cyclic two-dimensional aggregates of ‘‘amphiphilic molecules’’ (obtained by combining rubber pipette bulbs and magnetic stir bars).

Solutions of Reversed Micelles

3

forming globular aggregates called reversed micelles, which are structurally characterized by an internal polar core constituted by opportunely arranged hydrophilic headgroups surrounded by the alkyl chains of the amphiphile (see Fig. 2) [5]. This kind of aggregation involves the formation of ‘‘supermolecules,’’ which appear from the outside as apolar objects dispersed in the apolar solvent. Many amphiphilic substances are able to form reversed micelles. Certainly, the most studied is sodium bis (2-ethylhexyl) sulfosuccinate (AOT) [6]. From this salt, other interesting surfactants able to form reversed micelles have been derived by simply changing the counterion [7]. Other frequently used surfactants are didodecyldimethylammonium bromide [8], benzyldimethylhexadecylammonium chloride, lecithin [9], tetraethylene glycol monododecyl ether (C 12 E 4) [10], decaglycerol dioleate [11], and dodecylpyridinium iodide [12]. With extensive aggregation, a number of translational and rotational degrees of freedom of surfactant molecules are converted into translational, rotational, and internal degrees of freedom of the entire aggregate. In the case of a reversed micelle, its dynamics are characterized by a wide variety of processes such as diffusion of a surfactant molecule within the aggregate, conformational dynamics of the polar and apolar molecular moieties, micellar shape ﬂuctuation, exchange of surfactant molecules between bulk solvent and micelle, structural collapse of the aggregate leading to its dissolution and vice versa, diffusion and rotation of the entire aggregate, and intermicellar collisions [13–16]. Dry reversed micelles ˚ , exchange of AOT have a mean aggregation number of 23 and a radius of 15 A ⫺6 monomers with the bulk in a time scale of 10 s, and dissolve completely in a time scale of 10 ⫺3 s [17,18].

FIG. 2 Micellar aggregate of ‘‘amphiphilic molecules.’’

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Water, aqueous solutions and many other strongly hydrophilic substances can be solubilized within the micellar core [19,20]. Water solubilization involves hydration of the surfactant headgroup accompanied by an increase in the headgroup area, a micellar swelling, a marked increase in the surfactant aggregation number, and, at constant surfactant concentration, a decrease in the number density of reversed micelles [21]. A representation of a spherical reverse micelle entrapping a polar solubilizate in the core is shown in Fig. 3. Moreover, in the case of ionic surfactants, the addition of water weakens the electrostatic interactions between the counterion and the surfactant ionic head, forming solvent-separated ion pairs. For electrostatic reasons, counterions and ionic heads together with molecules of water of hydration are conﬁned in a restricted interfacial shell. Nearly unperturbed water molecules (‘‘bulk’’ water) exist in the micellar core [22,23]. The size and shape evolution of reversed micelles as a function of the water and surfactant concentrations are system-speciﬁc. The micellar size is mainly controlled by the strong tendency of the surfactant to be located at the interface between water and apolar solvent, which involves an enormous value of the interfacial surface and micelles of nanometric size. Spherical micelles result from a minimization of the micellar surface-to-volume ratio, i.e., a minimization of water–surfactant interactions less favorable than water–water and/or surfactant– surfactant interactions, while rodlike micelles, characterized by a greater surfaceto-volume ratio, result from water–surfactant interactions more favorable than

FIG. 3 Micellar aggregate of ‘‘amphiphilic molecules’’ entrapping a ‘‘polar solubilizate.’’

Solutions of Reversed Micelles

5

water–water and/or surfactant–surfactant interactions. In the case of AOT, the radius (r) of nearly spherical and monodisperse reversed micelles increases linearly with the molar ratio R (R ⫽ [water]/[surfactant]; r (nm) ⫽ 1.5 ⫹ 0.175R) and is quite independent of the surfactant concentration [14,24]. With increasing R, the fraction of water molecules located in the core of spherical micelles (or the time fraction spent by each water molecule in the core) increases progressively as a consequence of the parallel increase in the micellar radius. In contrast, lecithin, being able to establish strong hydrogen bonds with water, forms very long rodlike water-containing reversed micelles [25,26]. Solubilization of water within the micellar core transforms reversed micelles from small and labile aggregates to more stable aggregates with a greater persistence in the size and shape of the entire aggregate (even if each molecular component is continuously exchanged with the surroundings), inﬂuences the intermicellar interactions, and widens the spectrum of their dynamics [27]. In addition to the dynamics of dry micelles, fast exchange of water molecules between the surface and the center of the hydrophilic core, micellar shape and charge (in the case of ionic surfactant) ﬂuctuations, breaking and re-forming of adhesive bonds between contacting micelles, and intermicellar exchange of material are generally considered. In the case of AOT, less than 1 in 1000 intermicellar collisions leads to micelle coalescence followed by separation and a material exchange process occurring in the microsecond to millisecond time scale [13,28]. The intermicellar exchange of material can also be assisted by the exocytotic–endocytotic mechanism, i.e., through the formation of minimicelles that encapsulate hydrophilic molecules in their interior and their subsequent coalescence with other micelles [15,21]. In spite of the closed structure of reversed micelles, some mechanisms have been suggested to account for their attractive interactions. In the case of watercontaining AOT reversed micelles, it has been suggested that a pivotal role in the intermicellar interactions is played by the surfactant dissociation, which leaves hydrated charged heads at the micellar surface and hydrated counterions in the aqueous core [29]. Then, the continuous jumping of AOT ⫺ anions (hopping mechanism) [30] among neighboring micelles forming oppositely charged micelles is responsible for the attractive intermicellar interactions leading to the formation of extended clusters of reversed micelles and for the conductometric behavior of water–AOT–hydrocarbon microemulsions [29,31]. Another mechanism, postulated to explain the conductometric behavior of these microemulsions, attributes it to the transfer of sodium counterions from one reversed micelle to another through water channels opened by intermicellar coalescence [32,33]. In the case of water-containing lecithin reversed micelles, an enhancement of hydrogen bonding induced by an increase in water and/or micellar concentration has been suggested to account for the huge increase in intermicellar interactions [21,34].

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Interesting properties are observed when the concentration of reversed micelles is increased, the temperature is changed, or suitable solutes are added. In some cases, in fact, a dramatic increase has been observed in some physicochemical properties such as viscosity, conductance, static permittivity, and sound absorption. Two main interpretive pictures have been proposed to rationalize this percolative behavior. One attributes percolation to the formation of a bicontinuous structure [35,36], and the other to the formation of very large transient aggregates of reversed micelles [30]. In this respect, most interesting is the observation that the percolation threshold is dependent on the physicochemical property. As an example, in Fig. 4 the trends of the viscosity and conductance of AOT– n-heptane solutions as a function of the volume fraction of AOT are reported. As can be seen in a range where a divergence of the viscosity is observed, the conductance does not display signiﬁcant variations. This implies that a deeper understanding of percolation requires a detailed description of the molecular processes involved and, in particular, that different molecular processes are responsible for charge and momentum transfer in these systems [37].

FIG. 4 Viscosity (䊐) and conductivity (■) of AOT–n-heptane solutions as a function of the surfactant volume fraction. (Data from Ref. 37.)

Solutions of Reversed Micelles

7

Temperature or water and surfactant concentrations can inﬂuence the intermicellar interactions and/or the micellar number density. Both effects could induce an extensive intermicellar connectivity due to intermicellar interactions or for topological reasons, creating a network able to enhance momentum and/or charge transfer in the system. By considering the viscosimetric behavior of water–AOT– n-heptane microemulsions at various values of R, it can be observed that at very low R values or at R ⬎ 10 these systems behave as suspensions of quite monodisperse hard sphere particles whereas at intermediate R values they interact strongly. This interesting conclusion can be drawn from Fig. 5, where the dependence of the relative viscosity (η/η 0) on the volume fraction (Φ) at various R values is compared with that of a suspension of hard silica spheres in cyclohexane [37,38]. This is consistent with the ﬁnding that, in the semidilute region, AOT reversed micelles form micellar clusters in the range 0 ⬍ R ⬍ 10 whereas they do not at R ⬎ 10 [39] and also that the globular structure of reversed micelles persists even at the higher volume fractions of the dispersed phase and bicontinuous structures never set in [40].

FIG. 5 Comparison of the relative viscosity of dispersions of silica hard spheres and water–AOT–n-heptane microemulsions. (䉱) Hard spheres; (䊊) R ⫽ 0; (䊉) R ⫽ 5; (䊐) R ⫽ 10; (■) R ⫽ 20; (䉭) R ⫽ 30; (䉬) R ⫽ 40. (Data from Refs. 37 and 38.)

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A number of investigations have been performed on solubilization of solutes within water-containing reversed micelles to probe micellar structure and dynamics, to deﬁne their preferential solubilization site, and to emphasize mutual modiﬁcations due to solute–micelle interactions. Electrolytes and strongly polar molecules are obviously solubilized in the micellar core. Adding electrolytes to water containing AOT reversed micelles has an effect that is opposite to that observed for direct micelles, i.e., decreases are observed in the micellar radius and intermicellar attractive interactions [41] owing to the stabilization of AOT ions at the water/surfactant interface. Polar solutes, increasing the micellar core matter, induce an increase in the micellar radius, while amphiphilic molecules, being preferentially solubilized at the water/surfactant interface and consequently increasing the interfacial surface, lead to a decrease in the micellar radius [42,43]. As a consequence of their size and speciﬁc interactions, hydrophilic macromolecules or solid nanoparticles cause strong changes in micellar size and dynamics, and their properties are strongly affected [4,44].

II.

REVERSED MICELLES AS NANOCONTAINERS: THE STATE OF WATER AND OTHER SOLUTES WITHIN REVERSED MICELLES

The study of the state of water within reversed micelles has received a lot of attention as it simulates the water conﬁned in biological membranes or tightly bonded to biopolymers, enzymes, and proteins. There has been some controversy over the number of types of water encapsulated within reversed micelles and the appropriate model to describe the distribution among them. In the case of AOT reversed micelles, three main states can be hypothesized: water hydrating the sodium counterion, water hydrating the surfactant anionic headgroup, and water in the core. Some contributions to the measured physicochemical property could arise from the small fraction of water dispersed monomerically in the bulk solvent. Taking into account the spatial distribution of water molecules within the reversed micelles and assuming a nearly constant ratio between the numbers of water molecules hydrating the headgroup and the counterion, only two types of water can be hypothesized, ‘‘interfacial’’ water interacting with surfactant headgroups and counterions and ‘‘bulk-like’’ water in the micellar core. These types of water exchange on the nanosecond time scale (a time scale greater than the infrared window) and can be considered in a continuous equilibrium or existing above a critical molar ratio R below which only interfacial water exists. Several authors have investigated the energetic state of water in reversed micelles by calorimetry [45–50]. To emphasize the information gained on this subject by use of calorimetry, the enthalpies of solution of water in AOT or in lecithin reversed micelles as a

Solutions of Reversed Micelles

9

function of the molar ratio R are reported in Fig. 6 [51,52]. These values, strongly different from the enthalpy of solution of water in apolar organic solvents (⫹33.1 kJ/mol) [53,54], immediately indicate that water is practically totally encapsulated in the micellar core. Incidentally, it must be pointed out that the heat effect arising from the very small fraction of water that dissolves monomerically in the organic solvent must be taken into account in order to avoid misinterpretations of the calorimetric data, especially at the lower R values [54]. The continuous variation of the enthalpy of solution of water for both systems is consistent with a continuous model of water partitioned between the micellar core and the interface of a reversed micelle, which swells with R. The small and positive values of enthalpies of solution of water in AOT reversed micelles indicate that the energetic state of the water is only slightly changed and that water solubilization (unfavorable from an enthalpic point of view) is mainly driven by a favorable change in entropy (the water state at the interface and its dispersion as nanodroplets could be prominent contributions) [48,51]. In contrast, the solubilization of water in lecithin is a relatively strong exothermic process. This has been taken as an indication that water interacts favorably

FIG. 6 Enthalpy of solution of water in AOT (■, left-hand scale) or lecithin (䉱, righthand scale) reversed micelles as a function of R. (Data from Refs. 51 and 52.)

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with the zwitterionic headgroup of lecithin, promoting the formation of strong intermolecular hydrogen bonds, which can account for the rodlike structure of lecithin reversed micelles (i.e., micelles with a surface-to-volume ratio greater than that of spherical micelles) [52,55]. Both thermodynamic and spectroscopic properties of ‘‘core’’ water in AOT reversed micelles are similar to those of pure water. This indicates that the penetration of counterions in the micellar core is negligible. From differential scanning calorimetric measurements a marked cooling–heating cycle hysteresis has been observed, showing that water encapsulated in AOT reversed micelles is only partially freezable and that the freezable fraction displays marked supercooling behavior as a consequence of the very small size of the micellar core. The nonfreezable fraction has been identiﬁed as the water hydrating the AOT ionic heads [56,57]. The state of water within AOT reversed micelles has also been probed indirectly through measurements of the speciﬁc heat of water–AOT–n-heptane microemulsions [54,58]. An analysis of these data made it possible to calculate the apparent speciﬁc heat (C AOT ) of AOT (see Fig. 7). The observed decrease of C AOT

FIG. 7 Apparent speciﬁc heat capacity of AOT (C AOT ) in the micellar phase as a function of R. (Data from Ref. 54.)

Solutions of Reversed Micelles

11

with R (i.e., by decreasing the AOT concentration in the micellar phase) was explained in terms of the breakdown of the water structure by the hydration of AOT ionic heads. Other strongly hydrophilic substances such as methanol, formamide, n-methylformamide, and ethylenediamine solubilized in dry AOT reversed micelles are able, like water, to create their own micellar core [20,59,60], whereas amphiphilic solubilizates such as 1-pentanol and cholesterol are partitioned between the micellar palisade layer and the bulk organic solvent. As an example of the evolution of the partitioning process of an amphiphilic solubilizate as its concentration increases, the molar enthalpy of solution of 1-pentanol in the AOT–n-heptane system is shown in Fig. 8 as a function of the alcohol molality at various AOT concentrations [61]. An analysis of these data showed that at inﬁnite dilution of the alcohol, following a Poisson distribution, 1-pentanol molecules distribute between AOT reversed micelles and the continuous organic phase, whereas at ﬁnite alcohol concentration, given the ability of alcohol to self-assemble in the apolar organic solvent, a coexistence between reversed micelles (solubilizing

FIG. 8 Enthalpy of solution of 1-pentanol in AOT–n-heptane solutions as a function of the alcohol molal concentration (m PentOH ) at various AOT concentrations. (■) [AOT] ⫽ 0 mol/kg; (䊉) [AOT] ⫽ 0.049 mol/kg; (䉱) [AOT] ⫽ 0.0986 mol/kg; (䉲) [AOT] ⫽ 0.196 mol/kg; (䉬) [AOT] ⫽ 0.292 mol/kg. (Data from Ref. 61.)

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1-pentanol) and alcoholic aggregates (incorporating AOT molecules) is realized. The observed humps have been qualitatively explained in terms of two opposite effects. The ﬁrst (predominant at low alcohol concentrations and responsible for the initial increase in ∆H ) was ascribed to the decrease in the binding constant with 1-pentanol concentration and attributed to rapid saturation of the binding sites of AOT reversed micelles or to alcohol-induced changes in the AOT reversed micelle structure. The second effect (predominant at high alcohol concentrations and responsible for the decrease in ∆H ) was attributed to the self-association of the alcohol molecules by intermolecular hydrogen bonds.

III. INTERMICELLAR INTERACTIONS AND PERCOLATION With a high degree of approximation, solutions of reversed micelles can be described as solutions of supramolecular objects that display more or less strong intermicellar interactions. By changing the concentration of these aggregates one can attain different physical conditions corresponding to various physical phenomena. In particular, above threshold values of the concentration of reversed micelles, a dramatic increase in static viscosity can be observed, leading to the formation of systems, called organogels, that are particularly interesting for industrial applications (biocatalysis, biomembrane mimetic systems, extraction processes, and preparation of nanoparticles) [62]. Using calorimetry, it has been observed that the enthalpy of dilution of water– AOT–n-heptane microemulsions and the apparent speciﬁc heat capacity of the micellar phase vary monotonically with the micellar concentration without any change in rate during the crossover of the percolation threshold [54]. The observed trends suggested that even at the highest values of the volume fraction of the dispersed matter (Φ), the microemulsions are made up of water-containing reversed micelles dispersed in the hydrocarbon and that the intermicellar interactions decrease as R increases, vanishing when R ⬎ 10. This hypothesis is in agreement with the observation that the percolation threshold of these microemulsions at R ⬎ 10 occurs at a Φ value of approximately 0.5, a value that corresponds to the packing fraction of a cubic array of contacting spheres. Moreover, it is consistent with the viscosimetric behavior of these microemulsions reported above. Whereas the dilution of solutions of AOT reversed micelles at R ⬎ 10 is an athermal process (clustering results from topological effects), the dilution of water–lecithin reversed micelles is a strongly endothermic process [52,54]. This has been attributed to a strong dependence of the micellar size upon the lecithin

Solutions of Reversed Micelles

13

reversed micelle concentration involving the breakage of many hydrogen bonds with dilution.

IV.

WATER-CONTAINING REVERSED MICELLES AS NANOSOLVENTS: THE SOLUBILIZATION OF NONIONIC SOLUTES

Solutions of water-containing reversed micelles are systems characterized by a multiplicity of domains: apolar bulk solvent, oriented alkyl chains of the surfactant, hydrated surfactant headgroup region at the water/surfactant interface, and ‘‘bulk’’ water in the micellar core. Many polar, apolar, and amphiphilic substances, which are preferentially solubilized in the micellar core, in the bulk organic solvent, and in the domain comprising the alkyl chains and the hydrated surfactant polar heads, henceforth referred to as the palisade layer, respectively, may be solubilized in these systems at the same time. Moreover, it is possible that (1) local concentrations of solubilizate are very different from the overall concentration, (2) molecules solubilized in the palisade layer are forced to assume a certain orientation, (3) solubilizates are forced to reside for long times in a very small compartment (compartmentalization, quantum size effects), (4) the structure and dynamics of the reversed micelle hosting the solubilizate as well as those of the solubilizate itself are modiﬁed (personalization). All these peculiarities have been exploited by using these systems as useful solvent and reaction media for technological applications. Also, some resemblance between these systems and biological environments has been the driving force to employ solutions of reversed micelles to model or to mimic biological processes or to realize pharmaceutical preparations [63]. Knowledge of the solubilization site in microemulsions and the interaction forces driving the partitioning of a solute between the different microregions is fundamental to the rationalization of many complex phenomena. Among the various techniques, calorimetry has been used to determine the complete set of thermodynamic parameters of the partitioning process and also to gain information on the solubilization site and on the mutual changes following the solubilization process [59,60]. The quantity experimentally determined is the thermal effect accompanying the mixing in the calorimetric cell of a solubilizate–organic solvent solution with a water–surfactant–organic solvent microemulsion at a given surfactant concentration ([S]). This thermal effect, corrected for the enthalpy of dilution of both solutions and referred to 1 mole of the solubilizate, corresponds to the enthalpy of transfer (∆H t) of the solubilizate from the organic to the micellar phase. In order to analyze the calorimetric data (∆H t, [S]), it is also necessary to develop

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a suitable model. Here I report brieﬂy on a simple one that has been proven to explain consistently the experimental data of nonionic solubilizates. Using a Nernstian approach to the partitioning of solubilizates among three different microdomains (organic continuum, micellar palisade layer, and micellar aqueous core), the following distribution constants may be deﬁned: Kp ⫽

mp mo

(1)

Kw ⫽

mw mo

(2)

where m p , m w , and m o are the equilibrium molal concentrations of the solubilizate in the palisade layer, aqueous core, and organic continuum, respectively. K p is the distribution constant of the solubilizate between the organic continuum and the micellar palisade layer, and K w is the distribution constant of the solubilizate between the organic continuum and the micellar aqueous core. Using Eqs. (1) and (2), it can be easily shown that the fraction of molecules bonded to the micelles, X b (X w to the micellar core and X p to the palisade layer), is given by Xb ⫽ Xw ⫹ Xp ⫽

K[S] 1 ⫹ K[S]

(3)

where K ⫽ KpPS ⫹ KwPwR

(4)

and P s and P w are the molecular weights of surfactant and water (expressed in kilograms), respectively. The last equation is important because from the dependence of K and R the solubilization site of the solubilizate can be deﬁned. Taking into account that ∆H t is related to the fractions of solubilizate molecules transferred to the aqueous core (X w) and to the micellar palisade layer (X p) by the equation ∆H t ⫽ X p ∆H°t,p ⫹ X w ∆H°t,w

(5)

where ∆H°t,p and ∆H°t,w are the enthalpies of transfer from the organic solvent to the palisade layer and to the aqueous core, respectively, and combining Eqs. (3)– (5), it can also be found that ∆H t ⫽

K ∆H°t [S] 1 ⫹ K[S]

(6)

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15

where ∆H°t is given by the equation ∆H°t ⫽

K p P s ∆H°t,p ⫹ K w P w ∆H°t,w KpPs ⫹ KwPwR

(7)

Then an analysis of the calorimetric data (∆H t , [S]) by Eq. (6) and using Eqs. (4) and (7) allow us to obtain the complete set of thermodynamic parameters for the transfer process. In order to show the information gained through calorimetric investigations on the partitioning of nonionic solubilizates, Table 1 lists the thermodynamic parameters for the transfer process of some amphiphilic solubilizates from the organic continuum to the micellar palisade layer or the micellar aqueous core. The standard free energies of transfer were obtained from the equations ∆G°t,p ⫽ ⫺RT ln K°p

(8)

and ∆G°t,w ⫽ ⫺RT ln K°w

(9)

where K°p and K°w are the K p and K w values converted to the molarity scale as suggested by Ben-Naim [64]. A perusal of the data reported in Table 1 shows that the distribution constants K w decrease with increases in the hydrophobic character of the solubilizate while the opposite is true for K p and that for the more hydrophilic solubilizates the preferential solubilization site changes as the water content of reversed micelles increases. It can also be observed that in terms of standard free energies the additivity rule holds for the transfer between microdomains. The enthalpies of transfer from the apolar solvent to the micelles are exothermic, and, in principle, changes in the micellar structure and/or preferential orientation of the solubilizate in the palisade layer also contribute to their values [59]. It can also be observed that the standard enthalpies of transfer from the organic continuum to the palisade layer are between ⫺26 and ⫺20 kJ/mol whereas the corresponding quantities for the transfer from the organic continuum to the aqueous core are in the range of ⫺45 to ⫺21 kJ/mol. This indicates that in the palisade layer the solubilizates are forced to be oriented such that only one polar group of a diamine interacts with a hydrophilic head of AOT, whereas this does not happen in the aqueous core, where both polar groups of the diamines can be hydrated [60]. In the case of Kryptoﬁx 221D, a cryptand able to complex the alkali metal cations [65], it has been observed that it is solubilized mainly in the palisade layer of the AOT reversed micelles, and from an analysis of the enthalpy of transfer of this solubilizate from the organic to the micellar phase it has been established that the driving force of the solubilization is the complexation of the sodium counterion. Moreover, the enthalpy values made it possible to show the

41 22 20 48 17 1.4 25

Methanol n-Propanol n-Pentanol Ethylenediamine N,N-Dimethylaminoethylamine N,N,N′,N′-Tetramethylenediamine Cholesterol

Source: Refs. 59 and 60.

Kp

Solubilizate 187 20 — 1990 319 17 —

Kw 21 24 24 25 22 20 26

⫺∆H°t,p (kJ/mol) 22 21 — 45 41 35 —

⫺∆H°t,w (kJ/mol)

10 9.0 8.7 11 8.3 2.1 9.2

⫺∆G°t,p (kJ/mol)

14 8.4 — 20 15 8.0 —

⫺∆G°t,w (kJ/mol)

TABLE 1 Thermodynamic Parameters for the Transfer of Some Nonionic Solubilizates from the Organic Continuum to the Micellar Palisade Layer or the Micellar Aqueous Core

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17

peculiar solvation state of sodium counterions and demonstrate that they are essentially located near the water/AOT interface [66].

V. REVERSED MICELLES AS NANOREACTORS The small size of water-containing reversed micelles together with their stability in form but not in constituent molecules (persistence of shape accompanied by fast material exchange dynamics) suggests the use of these systems as peculiar nanoreactors. It can be expected that reaction rates, reaction mechanisms, and equilibrium constants can be affected signiﬁcantly compared to the same processes occurring in bulk [67]. Preferential solubilization involves local concentrations different from the analytical values and catalytic effects. In addition, since reversed micelles share some fundamental features of biomembranes (dominance of interfacial effects, ordered arrangement of amphiphilic molecules), water-inoil microemulsions have also been proposed as advantageous reaction media for the investigation of biochemical reactions. A calorimetric investigation of the substitution reaction [Pd(bipy)(en)] 2⫹ ⫹ en → [Pd(en) 2] ⫹ bipy (where bipy ⫽ 2,2′-bipyridine and en ⫽ ethylenediamine) performed in water– AOT–n-heptane microemulsions demonstrated that with increases in R the reaction becomes less exothermic and its rate constant decreases, approaching the value observed in water. These features were rationalized in terms of the peculiar solvation state of reactants inside the AOT reversed micelles and/or the peculiar physicochemical properties of the micellar core [68]. Another ﬁeld recently opened is the use of water-in-oil (W/O) microemulsions as reaction media for the synthesis of solid nanoparticles. The interest in synthesizing nanoparticles in solutions of reversed micelles is due to their important technological applications as catalysts for redox reactions [69] or their use to model or mimic processes occurring in geological or biological environments [70]. Some calorimetric investigations have shown that the enthalpy of formation of metallic nanoparticles and the molar enthalpy of precipitation of inorganic salts become more negative with increasing R (i.e., increasing micellar radius) and level off at higher R values. This experimental evidence has been rationalized in terms of the formation of nanoparticles dimensionally controlled by the micellar radius [70–73]. Typical behavior is shown in Fig. 9, where the enthalpy of formation of AgCl nanoparticles in AOT reversed micelles is reported as a function of the molar ratio R at various salt concentrations. As can be seen, the enthalpies become more exothermic as R increases. The small ∆H values at lower R, corresponding to

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FIG. 9 Enthalpy of formation of AgCl nanoparticles in water–AOT–n-heptane microemulsions as a function of R at various concentrations (C ) of the reagent salts in the aqueous microphase. (■) C ⫽ 0.005 mol/kg; (䊉) C ⫽ 0.03 mol/kg; (䉱) C ⫽ 0.05 mol/ kg. (Data from Ref. 66.)

lower values of the micellar radii, indicate the formation of smaller microcrystals with higher surface-to-volume ratios and consequently in a higher energetic state. In the synthesis of ZnS nanoparticles in various W/O microemulsions, further effects have been revealed [74]. In Fig. 10 the molar enthalpy of precipitation of ZnS nanoparticles in some W/O microemulsions is reported as a function of R. The continuous line indicates the molar enthalpy for the same process performed in water. As can be seen, with increases in R the molar enthalpy value becomes more negative, and in the case of AOT it tends to level off at higher R values. Moreover, these molar enthalpies are always less negative than the corresponding value in water. This is consistent with an increase in the nanoparticle size with R. By comparing the enthalpies at the same R value it can be noted that these quantities are in the order DDAB ⬎ C 12 E 4 ⬎ lecithin ⬎ AOT. Moreover, since the enthalpies of precipitation of ZnS at the same nanoparticle radius were different for the various microemulsions, it was also concluded that some

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19

FIG. 10 Enthalpy of formation of ZnS nanoparticles in W/O microemulsions [(■) DDAB; (䊉) C 12 E 4; (䉱) AOT; (䉲) lecithin] as a function of R. The continuous line indicates the enthalpy of formation of bulk ZnS in water. (Data from Ref. 74.)

enthalpic contributions arise from interactions between nanoparticles and the water/surfactant interface.

VI.

CONCLUSION

In this chapter I have attempted to present a panoramic view of the contributions of calorimetry to the study of solutions of reversed micelles. In particular, it has been shown that it is possible with calorimetry to obtain information on the energetic state of water and that of other solubilizates within reversed micelles, the complete set of thermodynamic parameters for the solubilization process, and the preferential solubilization site as well as information on the intermicellar interactions and the energetic state of solid nanoparticles entrapped in the micellar core. All these data together with those obtained by other techniques help to better and better deﬁne the structural and dynamical picture of solutions of reversed micelles and to exploit their potential technological applications.

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Finally, it must be remarked that in spite of the importance of the information that can be gained by calorimetry, the numbers of calorimetric investigations on solutions of reversed micelles and relative to other experimental techniques are still very small.

ACKNOWLEDGMENTS Financial support from CNR, MURST 60%, and MURST 40% (coﬁn MURST 97 CFSIB) is gratefully acknowledged.

REFERENCES 1. N Muller. J Phys Chem 79:287–291 (1975). 2. FY Lo, BM Escott, EJ Fendler, ET Adams, RD Larsen, PW Smith. J Phys Chem 79:2609–2621 (1975). 3. JB Nagy. In: Solution Behavior of Surfactants, Vol. 2 (KL Mittal, EJ Fendler, eds.), Plenum Press, New York 1982, pp. 743–766. 4. PL Luisi, LJ Magid. CRC Crit Rev Biochem 20:409–474 (1986). 5. N Muller. J Colloid Interface Sci 63:383–393 (1978). 6. HF Eicke. Topics Curr Chem 87:85–145 (1980). 7. J Eastoe, TF Towey, BH Robinson, J Williams, RH Heenan. J Phys Chem 97:1459– 1463 (1993). 8. J Eastoe, RK Heenan. J Chem Soc Faraday Trans I 90:487–492 (1994). 9. R Scartazzini, PL Luisi. J Phys Chem 92:829–833 (1988). 10. A Merdas, M Gindre, R Ober, C Nicot, W Urbach, M Waks. J Phys Chem 100: 15180–15186 (1996). 11. AB Mandal, B Unni-Nair. J Chem Soc Faraday Trans I 87:133–136 (1991). 12. GR Seely, XC Ma, RA Nieman, D Gust. J Phys Chem 94:1581–1598 (1990). 13. PDI Fletcher, BH Robinson. Ber Bunsenges Phys Chem 85:863–867 (1981). 14. PDI Fletcher, AM Howe, BH Robinson. J Chem Soc Faraday Trans I 83:985–1006 (1987). 15. J Lang, A Jada, A Malliaris. J Phys Chem 92:1946–1953 (1988). 16. A D’Aprano, G D’Arrigo, M Goffredi, A Paparelli, V Turco Liveri. J Phys Chem 93:8367–8370 (1989). 17. M Wong, JK Thomas, T Nowak. J Am Chem Soc 99:4730–4736 (1977). 18. M Kotlarchyk, JS Huang, SH Chen. J Phys Chem 89:4382–4386 (1985). 19. PL Luisi, M Giomini, MP Pileni, BH Robinson. Biochim Biophys Acta 947:209– 246 (1988). 20. V Arcoleo, F Aliotta, M Goffredi, G La Manna, V Turco Liveri. Mater Sci Eng C5: 47–53 (1997). 21. V Turco Liveri. In: Current Topics in Solution Chemistry, Vol 2. (JE Desnoyers, F Franks, G Gritzner, LG Hepler, H Ohtaki eds.), Research Trends, Trivandrum, 1997, pp. 143–156. 22. P Linse. J Chem Phys 90:4992–5004 (1989).

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21

23. G Giammona, F Goffredi, V Turco Liveri, G Vassallo. J Colloid Interface Sci 154: 411–415 (1992). 24. R Day, BH Robinson, J Clarke, J Doherty. J Chem Soc Faraday Trans I 75:132– 139 (1979). 25. PL Luisi, R Scartazzini, G Hearing, P Schurtenberger. Colloid Polym Sci 268:356– 374 (1990). 26. G Cavallaro, G La Manna, V Turco Liveri, F Aliotta, ME Fontanella. J Colloid Interface Sci 176:281–285 (1995). 27. G D’Arrigo, A Paparelli, A D’Aprano, ID Donato, M Goffredi, V Turco Liveri. J Phys Chem 93:8367–8370 (1989). 28. J Clarke, J Nicholson, K Regan. J Chem Soc Faraday Trans I. 81:1173–1182 (1985). 29. V Arcoleo, M Goffredi, V Turco Liveri. J Solution Chem 24:1135–1142 (1995). 30. MW Kim, JS Huang. Phys Rev A 34:719–722 (1986). 31. H Mays. J Phys Chem B 101:10271–10280 (1997). 32. MA Van Dijk, G Casteleijn, JGH Joosten, Y Levine. J Chem Phys 85:626–631 (1986). 33. Y Feldman, N Kozlovich, I Nir, N Garti, V Archipov, Z Idiyatullin, Y Zuev, V Fedotov. J Phys Chem 100:3745–3748 (1996). 34. YA Shchipunov, EV Shumilina. Prog Colloid Polym Sci 106:228–231 (1997). 35. PG De Gennes, GJ Taupin. J Phys Chem 86:2294–2304 (1982). 36. M Borkovec, HF Eicke, H Hammerich, B Dasgupta. J Phys Chem 92:206–211 (1988). 37. A D’Aprano, G D’Arrigo, A Paparelli, M Goffredi, V Turco Liveri. J Phys Chem 97:3614–3618 (1993). 38. C G de Kruif, EMF van Iersal, A Vrij. J Chem Phys 83:4717–4725 (1985). 39. M Hirai, R Kawai-Hirai, S Yabuki, T Takizawa, T Hirai, K Kobayashi, Y Amemiya, M Oya. J Phys Chem 99:6652–6660 (1995). 40. SH Chen, JS Wang. Phys Rev Lett 55:1888–1891 (1985). 41. B Bedwel, E Gulari. J Colloid Interface Sci 102:88–100 (1984). 42. MP Pileni, T Zemb, C Petit. Chem Phys Lett 118:414–420 (1985). 43. PDI Fletcher, BH Robinson, J Tabony. J Chem Soc Faraday Trans I 82:2311–2321 (1986). 44. PL Luisi. Angew Chem 97:449–460 (1985). 45. J Rouviere, JM Couret, A Lindheimer, M Lindheimer, B Brun. J Chim Phys 76: 297–301 (1979). 46. M Nakamura, GL Bertrand, SE Friberg. J Colloid Interface Sci 91:516–524 (1983). 47. G Olofsson, J Kizling, P Stenius. J Colloid Interface Sci 111:213–222 (1986). 48. G Haandrikman, GJR Daane, FJM Kerkhof, NM van Os, LAM Rupert. J Phys Chem 96:9061–9068 (1992). 49. G Gu, W Wang, H Yan. J Colloid Interface Sci 167:87–93 (1994). 50. K Mukherjee, DC Mukherjee, SP Moulik. J Colloid Interface Sci 187:327–333 (1997). 51. A D’Aprano, A Lizzio, V Turco Liveri. J Phys Chem 91:4749–4751 (1987). 52. V Arcoleo, M Goffredi, G La Manna, F Aliotta, ME Fontanella. J Thermal Anal 50:823–830 (1997).

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53. R De Lisi, M Goffredi, V Turco Liveri. J Chem Soc Faraday Trans I 76:1660–1662 (1980). 54. F Goffredi, V Turco Liveri, G Vassallo. J Colloid Interface Sci 151:396–401 (1992). 55. YA Shchipunov, EV Shumilina. Mater Sci Eng C3:43–50 (1995). 56. C Boned, J Peyrelasse, M Moha-Ouchane. J Phys Chem 90:634–637 (1986). 57. H Hauser, G Haering, A Pande, PL Luisi. J Phys Chem 93:7869–7887 (1989). 58. JP Morel, N Morel-Desrosiers, C Lhermet. J Chim Phys 81:109–112 (1984). 59. A D’Aprano, ID Donato, F Pinio, V Turco Liveri. J Solution Chem 18:949–955 (1989). 60. G Pitarresi, C Sbriziolo, ML Turco Liveri, V Turco Liveri, J Solution Chem 22: 279–287 (1993). 61. A D’Aprano, A Lizzio, V Turco Liveri. J Phys Chem 92:1985–1987 (1988). 62. P Terech, RG Weiss. Chem Rev 97:3133–3159 (1997). 63. JH Fendler. Chem Rev 87:877–899 (1987). 64. A Ben-Naim. J Phys Chem 82:792–803 (1978). 65. JM Lehn, JP Sauvage. J Am Chem Soc 75:6700–6707 (1975). 66. A D’Aprano, ID Donato, F Pinio, V Turco Liveri. J Solution Chem 19:589–595 (1990). 67. JH Fendler. Membrane Mimetic Chemistry, Wiley, New York, 1982. 68. ML Turco Liveri, V Turco Liveri. J Colloid Interface Sci 176:101–104 (1995). 69. A Sobczynski, AJ Bard, A Campion, MA Fox, T Mallouk, SE Webber, JM White. J Phys Chem 91:3316–3320 (1987). 70. V Arcoleo, M Goffredi, V Turco Liveri. Thermochim Acta 233:187–197 (1994). 71. A D’Aprano, F Pinio, V Turco Liveri. J Solution Chem 20:301–306 (1991). 72. V Arcoleo, G Cavallaro, G La Manna, V Turco Liveri. Thermochim Acta 254:111– 119 (1995). 73. F Aliotta, V Arcoleo, S Buccoleri, G La Manna, V Turco Liveri. Thermochim Acta 265:15–23 (1995). 74. V Arcoleo, M Goffredi, V Turco Liveri. J Thermal Anal 51:125–133 (1998).

2 Thermodynamics and PhaseSeparation Kinetics of Microemulsions DORIS VOLLMER Institute for Physical Chemistry, University of Mainz, Mainz, Germany

I. Introduction II.

Phase Behavior of Microemulsions A. Microemulsions B. Phase diagrams C. Characteristic size of droplets D. Speciﬁc heat E. Free energy F. Latent heat G. Step in the speciﬁc heat

24 27 27 27 29 31 34 39 41

III. Phase Separation Kinetics A. Energy barrier B. Experimental observation of oscillations C. Mechanism of phase separation D. Temperature dependence of the droplet–droplet distance

43 43 45 47 48

IV. Conclusion

54

References

56

23

24

Vollmer

I. INTRODUCTION Mixtures containing surfactants and hydrophilic (for instance, water) and hydrophobic (for instance, alkanes) components show a fascinating thermodynamic and kinetic behavior. Gaining an understanding of this behavior poses a large variety of interesting physical and chemical challenges, which have been a focus of fundamental research in colloid science throughout recent decades. In addition to this interest from a statistical physics point of view, this research is also strongly stimulated by applications. Surfactants are ingredients of various products such as pharmaceuticals, lubricants, and cosmetics [1]. They are of importance for tertiary oil recovery and for emulsion polymerization. To improve production capacities, a better understanding of the varying forces of interaction between the surfactant molecules and the other ingredients in the course of production is desirable. In this review, we highlight recent insights into the driving forces of phase transitions and their kinetics in these mixtures that have been made possible by microcalorimetric studies. Binary and ternary mixtures of water, alkanes, and surfactants show a rich variety of phases [2–4]. At room temperature, they are typically organized on the scale of a few tens of nanometers, so that mesoscopic water and oil domains are separated by a surfactant monolayer. The domains can have various structures. Nearly monodisperse droplets or disordered cylindrical structures, lamellar arrangements of alternating water and oil layers, and spongelike structures have been observed. For several model systems, the approximate extent of these structures in the phase diagram is known [5–12]. There can be as many as ﬁve transitions between structures with vastly different mechanical properties in temperature intervals of only 10 K, and there are extended two-phase (2Φ) and three-phase (3Φ) regions, where these structures coexist with each other or with water- or oil-rich excess phases. Analysis of the underlying microstructures and understanding of the origin of the phase transitions between the structures have received a lot of attention (see Ref. 13 for a review). The improved experimental characterization of the phase behavior formed a basis for theoretical and computational modeling of phase diagrams [13–24]. In recent years the relevant parameters entering into the equilibrium free energies have been identiﬁed. However, their precise values, as well as their dependence on components, temperature, and composition, are still under debate [23,25–31]. Fascinating kinetics is observed when the systems are driven out of equilibrium. Typically, this is accomplished by mechanical treatment, by a sudden change of composition, or by a temperature jump. The most intensively studied mechanically induced transition is the formation of multilamellar vesicles (‘‘onions’’), which occur on shearing of a lamellar phase [32–36]. A sudden change of composition may lead to the formation of myelins [36–39]. Mechanical pinch-

Microemulsions

25

ing of a cylindrical vesicle might lead to a pearling instability, where the cylinder disintegrates into a row of equidistant droplets [40,41]. Temperature jump experiments have been performed to investigate the phase separation of bicontinuous, sponge, lamellar, or droplet phases into one or several coexisting phases of different morphologies [42–44]. Unlike the thermodynamics of surfactant mixtures, their kinetics is poorly understood. A main problem in modeling the kinetics is that, typically, temporal changes of the thermodynamic properties have to be combined with a complex hydrodynamics. In this chapter we argue that differential scanning microcalorimetry (DSC) is an outstanding method for investigating the thermodynamic and kinetic properties of surfactant mixtures [29,30,45–47], since it is highly sensitive to small changes in the surfactant monolayer. This is demonstrated for a three-component mixture of water, octane, and the nonionic surfactant C 12 E 5, i.e., CH 3 (CH 2) 11 (OCH 2 CH 2) 5 OH, where we focus on two structural transitions. This restraint allows us to compare quantitative predictions on the behavior of the mixtures with detailed experimental data. We investigate the thermodynamics of the temperature-induced phase transitions between a lamellar phase and a droplet phase and of the failure of water droplets to emulsify all water in a sample when the temperature is increasing (emulsiﬁcation failure) [48]. A schematic drawing of the varying microstructure for the phase sequence lamellar–droplet–2Φ is given in Fig. 1. The values for the latent heat of the transition between a lamellar and a droplet phase and for the height of a step in the speciﬁc heat at emulsiﬁcation failure are determined. Both are compared with predictions for the equilibrium free energies describing the mixtures. This permits identiﬁcation of the important contributions to the free energy. An application of DSC to study the kinetics of phase separation is demonstrated for the case of the phase separation of a droplet phase microemulsion. When heated across the emulsiﬁcation boundary the droplets tend to decrease in size (Fig. 1c). However, due to the small mutual solubility of the components this is hindered by the conservation of the area of the internal interface between water and oil and of the partial volumes of water, oil, and surfactant. As a consequence, the droplet size changes only when, with considerable overheating (or after exceedingly long times), large droplets are formed. They can be viewed as nuclei of the coexisting water-rich phase [43,49] that grow quickly by taking up excess water of small droplets and merging with larger ones (Fig. 1d). This leads to a fast decay of their number and average distance. Eventually, the distance between large droplets becomes so large that the diffusive transport of water from small to large droplets becomes inefﬁcient. Under constant heating, the small microemulsion droplets (Figs. 1d, 1e, or 1b) are overheated again until another wave of nucleation sets in (Fig. 1d). To emphasize this step-

26

Vollmer

FIG. 1 Schematic drawing of the temperature-dependent microstructure of a mixture of water, oil, and a nonionic surfactant. The temperature-induced phase sequence from lamellar to droplet phase microemulsion to two-phase microemulsion is shown. In the 2Φ region constant heating leads to a decrease in the average size of droplets in a stepwise manner. This is due to the process of repeated nucleation and growth, as indicated by the arrow below the schematically drawn test tubes. The mechanism is discussed in detail in Section III.

wise change in the droplet size, we term this phase separation ‘‘cascade nucleation’’ [50]. This chapter is organized as follows. In Section II we concentrate on a discussion of the thermodynamics of microemulsions. After a deﬁnition (Section II.A), special emphasis is put on a description of the temperature-dependent phase behavior (Section II.B) and typical length scales (Section II.C). In Section II.D we discuss the temperature-dependent speciﬁc heat of phase transitions. After a discussion of various contributions to the free energy (Section II.E), a quantitative comparison between experimentally determined values and theoretical estimates for the latent heat (Section II.F) and for the step in the speciﬁc heat accompanying emulsiﬁcation failure (Section II.G) is carried out. In Section III we discuss the kinetics of emulsiﬁcation failure. The parameter dependence of the energy barrier preventing phase separation is discussed in Section III.A. This is followed up by a discussion of oscillations in the speciﬁc heat that are induced by cascade nucleation (Section III.B). In Section III.C the mechanism of cascade nucleation is described, and in Section III.D we point out that a slight nonmonotonous dependence of the period of oscillation is due to the dependence of the diffusion length between small droplets on composition. Finally, in Section IV the main results are summarized.

Microemulsions

II.

27

PHASE BEHAVIOR OF MICROEMULSIONS

A. Microemulsions Water and oil are immiscible. A sample containing water and oil will phase separate into macroscopic water and oil domains, since the surface tension of the interface between water and oil tends to minimize the interfacial area. However, when surfactant molecules are added, the interfacial tension between the water and oil domains may decrease by several orders of magnitude [27,31,51–53]. These molecules have a water-soluble polar headgroup and an oil-soluble apolar tail, separating the water and oil domains by a liquid-like monolayer of ﬁxed average area per surfactant molecule [54]. In the case of very low interfacial tension, morphologies requiring a large interfacial area may be thermodynamically stable. Schulmann et al. [55] deﬁned microemulsions as mixtures of water, oil, and surfactant that are thermodynamically stable, isotropic, and of low viscosity. In the present review, we follow this convention and denote the system as an ‘‘amphiphilic mixture’’ when we wish to also include lamellar and other locally ordered structures of higher viscosity.

B. Phase Diagrams At present, amphiphilic mixtures containing surfactants of the type C i E j (alkylpolyglycol ether) are most completely characterized. Their phase behavior has been extensively studied by Kahlweit, Olsson, Strey, and coworkers, and detailed knowledge of the temperature- and composition-dependent morphology of such amphiphilic mixtures is available [2,11,22,23,31,53,54,56–58]. In view of this, the majority of theoretical work aiming at a comparison with experiments focuses on these mixtures.

1.

Gibbs Phase Triangle

Figure 2 schematically shows an isothermal cut through the Gibbs phase prism. Depending on composition, the mixture may be single-phase (1Φ), two-phase (2Φ), or three-phase (3Φ). 1Φ: In the single-phase region, the microemulsion solubilizes all water and oil. The mixture is macroscopically homogeneous. Its microstructure depends, however, on temperature and composition. Oil droplets in water, oil cylinders in water, bicontinuous and lamellar morphologies, water cylinders in oil, and water droplets in oil* have been observed.

* Oil and water droplets are also called swollen and reversed swollen micelles, respectively.

28

Vollmer

FIG. 2 Schematic drawing of the Gibbs phase triangle for a mixture of water, alkane, and nonionic surfactant (C i E j ). 1Φ, 2Φ, and 3Φ stand for a single-phase microemulsion, a microemulsion coexisting with a water- or oil-rich phase, and a microemulsion coexisting with a water-rich phase and an oil-rich phase.

2Φ: In the two-phase region, there is a microemulsion phase containing almost all amphiphile, which coexists with an oil-rich (2Φ, Winsor I [59]) or with a water-rich (2Φ, Winsor II [59]) phase [56]. 3Φ: If the mixture separates into three phases (Winsor III [59]), the amphiphile is mainly dissolved in the middle phase, which coexists with phases containing predominantly water and oil, respectively [56]. The extent of the 1Φ, 2Φ, and 3Φ regions in the Gibbs phase triangle depends on composition, on temperature, and on the choice of the components [2,13,53].

2.

Fish Cut

Nonionic surfactants of the type of C i E j show a strongly temperature-dependent phase behavior. In the present chapter we restrict ourselves to mixtures of water, octane (Merck, Darmstadt, Germany), and C 12 E 5 (Nikko Chemicals, Tokyo, Japan). These intensively studied mixtures show extended droplet phases [10,11,31,54,58,60]. Sample compositions are given by the volume fractions of water φ w, octane φ o, and surfactant φ s. Figure 3a shows a section through the phase prism as a function of temperature and surfactant concentration. The ratio φ w /φ o of the volume fractions of water and oil is ﬁxed. Because of its characteristic ﬁshlike shape, this section is called a ‘‘ﬁsh cut’’ [57]. The phase diagram is to a good approximation mirror symmetrical with respect to the phase inversion temperature T, where the value for T depends only on the choice of components and takes the value T ⫽ 305.6 K for

Microemulsions

29

the investigated mixtures. For T ⱕ T the surfactant monolayer is curved on the average toward oil, whereas for T ⱖ T it is curved toward water. For φs ⱕ 0.05 a three-phase region (3Φ) is formed close to T ⫽ T, whereas for higher surfactant concentrations the mixture becomes single-phase. For still higher surfactant concentrations a lamellar phase (lam), i.e., an alternation of water–surfactant–oil– surfactant layers is found (see Fig. 3a). The lamellar phase is birefringent and may be of high viscosity. It is bounded in the phase diagram by two clear microemulsion phases, enclosing oil (L 1) or water (L 2). The L 1 and L 2 phases are separated from the lamellar phase by a two-phase region whose width is not shown in Fig. 3. For φ w ⬍ φ o the microstructure in the L 2 region conforms to water droplets embedded in an oil matrix. Analogously, in the microemulsion channel L 1 oil droplets are formed for φ o ⬍ φ w. Even further from T, the single-phase microemulsion phase separates. The corresponding phase boundaries are called the water (for L 2 to 2Φ) and oil (for L 1 to 2Φ) emulsiﬁcation boundaries. For temperatures sufﬁciently above the water emulsiﬁcation boundary (i.e., well inside the 2Φ region), a water droplet microemulsion is in equilibrium with a water-rich phase. With increasing temperature the average size of the droplets decreases, leading to an increase in the volume fraction of the coexisting waterrich phase. A schematic drawing of a water droplet covered by a surfactant monolayer is given in Fig. 3b. The average radius of the hydrophilic part of the water droplet is given by R 1Φ, and l s denotes the average thickness of the monolayer. For simplicity, the hydrophilic headgroup [OCH 2 CH 2] j OH is drawn as a circle. The microstructure of the chain is similar to its hydrophobic counterpart H[CH 2] i .

C. Characteristic Size of Droplets For microemulsions containing various types of nonionic or ionic surfactants, the composition- and temperature-dependent size of microemulsion droplets was determined by highly sensitive scattering experiments [10,31,58]. These studies permit a determination of the average droplet size and of the effective thickness of the surfactant monolayer with relative errors of roughly 10%.

1.

The One-Phase Region

In the 1Φ region the droplet size is determined by composition. To a good approximation it does not depend on temperature. The average radius R 1Φ of the droplets is determined by the conservation of their enclosed volume, 4πNR 31Φ /3 ⫽ Vφ d, and of their surface area, 4πNR 21Φ ⫽ Vφ s /l s, from which one ﬁnds

R 1φ ⫽

冦

3l s φ d φs

where

φd ⯝ φw ⫹

φs 2

for water droplets

3l φ ⫺ s d φs

where

φd ⯝ φo ⫹

φs 2

for oil droplets

(1)

30

Vollmer

2F

(a)

(b)

Microemulsions

31

To distinguish water from oil droplets, we take water droplets to have a positive radius and oil droplets to have a negative radius. The enclosed volume φ d is the sum of the interior phase volume, i.e., water or oil, and the volume of the respective water- or oil-soluble part of the surfactant molecules. N denotes the number of droplets in a volume element V [11,31,58]. The effective thickness of the surfactant monolayer has been determined to be l s ⬇ 1.3 nm [54]. Depending on composition, the droplet radius is on the order of 2–20 nm, the total oil/water interfacial area is on the order of 100 m 2, and 10 16 –10 18 droplets are formed per cubic centimeter.

2.

The Two-Phase Region

In the 2Φ region only the surface area of the droplets is preserved; their volume can be adjusted so that the droplets take their optimum size R opt , i.e., a radius that locally minimizes the interfacial free energy. R opt depends only on temperature; it is independent of composition [23]. At the emulsiﬁcation boundary R opt ⫽ R 1Φ, whereas in the 2Φ region |R opt | ⬍ |R 1Φ |. For temperatures sufﬁciently below those corresponding to the micellar size and several degrees away from T, the optimum radius has been determined by small-angle neutron scattering (SANS) experiments to vary as [31] R opt (T) ⯝

1 a(T ⫺ T )

(2)

˚ ⫺1. where a ⫽ 1.2 ⫻ 10 ⫺3 K ⫺1A

D. Speciﬁc Heat The speciﬁc heat is measured by using a differential scanning microcalorimeter (VP-DSC, Microcal Inc.). This microcalorimeter measures the difference in the

FIG. 3 (a) Section through the phase prism for mixtures of water, octane, and C 12 E 5 for varying volume fractions of surfactant and nearly equal volume fractions of octane and water (φ o ⫽ 0.95φ w). The ﬁlled squares show experimentally determined values for the phase boundaries. L 1 and L 2 denote single-phase microemulsions, lam denotes a lamellar phase, 2Φ denotes a microemulsion phase in equilibrium with a water-rich (2Φ) or an oil-rich (2Φ) phase, and 3Φ denotes a microemulsion phase in equilibrium with a waterrich phase and an oil-rich phase. At sufﬁciently high temperatures, the microstructure close to and above the water emulsiﬁcation boundary corresponds to water droplets in oil, as indicated by the circles. The variation in the size of the circles shows the composition and temperature dependence of the droplet size in the 2Φ region. The increase in the volume fraction of the water-rich phase with increasing temperature is indicated by the size of the shaded area in the ‘‘test tubes.’’ (Data points taken from Ref. 31.) (b) Schematic drawing of a surfactant-covered water droplet.

32

Vollmer

speciﬁc heat between the sample and a suitably chosen reference system. By this means it provides a very accurate description of the variation of the speciﬁc heat C rel V (T) relative to a baseline set by the reference sample. A more detailed description of the application of this technique to microemulsions is given in Ref. 45.* Figure 4a shows the thermogram of a heating and cooling scan performed on a sample of equal volume fractions of water and oil (φ w ⫽ φ o ⫽ 0.40; φ s ⫽ 0.20). A heating rate of υ s ⬇ 5 K/h and a cooling rate of υ s ⬇ ⫺5 K/h were chosen. The solid line indicates the variation of the signal for the speciﬁc heat due to heating, while the dashed line shows the variation of C rel V (T) due to cooling. For convenience, the optically determined phase transition temperatures between single- and two-phase microemulsions are marked by arrows below the thermograms. Immediately after the start of the heating scan (solid line) at 294 K, i.e., slightly above the 2Φ → L 1 phase boundary, the signal for the speciﬁc heat shows a peak at T ⫽ 296.5 K. For T ⬍ 296.5 K the mixture is clear and gel-like, whereas in the L 1 region for T ⬎ 296.5 K the mixture remains clear and is of a lower viscosity. After going through a minimum, C rel V (T) increases sharply. It passes a very narrow peak, which is immediately followed by a large and relatively broad one. From a comparison with the phase diagram it can be concluded that the mixture is lamellar. The test probe appears slightly turbid and birefringent. According to the C rel V (T) signal, the mixture shows a single-phase lamellar region with a width of only 3 K, which is followed by another large peak (307–311 K). Comparison with the optically determined phase boundaries suggests that the latter is due to the phase transition of the lamellar phase into the L 2 channel. Before the signal has dropped toward the value it had in the lamellar phase, C rel V (T) increases again and starts to oscillate. The origin and parameter dependence of these oscillations is discussed in detail in Section III. The cooling scan (dashed line) starts in the L 2 channel. Both, the L 2 → lam and the lam → L 1 phase boundaries give rise to a peak in the speciﬁc heat. Due to hysteresis, the peaks are shifted toward slightly lower temperatures compared to the boundaries observed during the heating scan. A broad peak in the L 1 channel is visible. We attributed this peak to a structural transition accompanying an appearance of local ordering in the L1 region. Passing the L 1 → 2Φ phase boundary leads to a small peak in C rel v (T). Within the range 288 K ⬍ T ⬍ 293 K the signal for the speciﬁc heat is nearly constant; it increases only at T ⱗ 285 K, where another large peak is visible. From optical investigations it is expected that the peak at T ⫽ 293.5 K is due to the entrance into the 2Φ region. However, the mixture is metastable. Close to T ⫽ 293.5 K the mixture remains clear, and

* The difference between the MC2-MicroCal described in Ref. 45 and the VP-DSC is that the latter has a cell volume of 0.519 cm 3 and better baseline reproducibility.

(a)

(b) FIG. 4 A heating scan (solid line) and a cooling scan (dashed line) for the speciﬁc heat relative to a reference mixture containing appropriate amounts of water and oil. The vertical bars indicate the optically determined phase boundaries for the compositions. The numbers above the bars denote the optically determined phase transition temperatures. (a) φ s ⫽ 0.2, φ w ⫽ φ o ⫽ 0.4; (b) φ s ⫽ 0.2, φ w ⫽ 0.15, and φ o ⫽ 0.65. The inset in (b) shows the low temperature region on an enlarged scale.

34

Vollmer

it is several hours before a macroscopic phase separation is observed. Below T ⱗ 285 K the mixture immediately becomes turbid.* Finally, we point out that the width of a peak gives a measure for the width of the two-phase region separating the two single-phase regions. It has been checked that the width does not depend on scan speed. The area under a peak corresponds to the heat absorbed during a phase transition; i.e., in ﬁrst-order phase transitions it is a measure of the latent heat of the transition. As required by thermodynamics, all transitions are endothermic for up scans and exothermic for down scans. A more detailed discussion of the structure of the thermograms and the peak shape is given in Ref. 30. For equal-volume fractions of oil and water, the peaks related to the transition from a lamellar into an L 1 or L 2 phase, respectively, are broad and look similar. Note, however, that the transition lam → L 1 gives rise to two peaks that are very close to each other. The differences between the high and low temperature regions become even more apparent upon entry into the 2Φ or 2Φ region. This is interesting to note, since the phase diagram (see, e.g., Fig. 3a) gives the impression that the microstructure and the thermodynamic properties do not change when T is replaced by 2T ⫺ T and water and oil are simultaneously interchanged. Therefore, the C 12 E 5 –water–octane system is called a symmetrical microemulsion [31]. The inﬂuence on the thermograms of changing the water-to-oil ratio is demonstrated in Fig. 4b, where C rel V (T) is shown for a sample with φ w ⫽ 0.15, φ o ⫽ 0.65, and φ s ⫽ 0.2. For both the heating (solid line) and cooling (dashed line) scans, a heating rate of | υ s | ⬇ 6 K/h is used. In comparison to Fig. 4a, the spectrum looks strongly asymmetrical. In contrast, the transition lam → L 2 gives rise to a narrow large peak, whereas the transition lam → L 1 is accompanied by a small peak at T ⬇ 292 K. A second small peak is visible when the 2Φ region is entered. Also, in the L 1 channel, C rel V (T) does not remain constant, but the signal shape suggests that in the L 1 channel the microstructure changes with temperature (inset in Fig. 4b). On the other hand, C rel V (T) is nearly constant in the L 2 channel, and, again, passing the water emulsiﬁcation boundary leads to a step in the speciﬁc heat.

E. Free Energy To describe the phase behavior, contributions to the free energy arising from the bending of the interfacial monolayer, F b; from undulations of the lamellae, F u ; and from the entropy of mixing of water and oil domains, F mix , are discussed in

* Similar behavior was observed by Olsson and coworkers [42], who investigated the turbidity after quenching the mixture into the 2Φ region.

Microemulsions

35

the literature for mixtures of water, alkane, and surfactant [14–17,19,21–24]. Since in the present review we deal solely with nonionic surfactants, electrostatic contributions to the free energy need not be considered. The surfactant ﬁlm is treated as an incompressible, tensionless two-dimensional ﬂuid. In addition, it is assumed that all surfactant molecules are located at the interface and that water and octane are immiscible. Both assumptions hold to within a few percent for this model system, and the corrections can be incorporated into the theory when the deviations become more signiﬁcant. The free energy per unit area arising from the bending of the interfacial monolayer was introduced by Helfrich [61] and applied to amphiphilic mixtures by various authors [15,19,23,30];

冤

κ 1 1 ⫹ ⫺ 2c o Fb ⫽ 2 R1 R2

冥 ⫹ κ R 1R 2

1

(3) 2

Here, R 1 and R 2 denote the local radii of curvature [30]. The bending modulus κ, the Gaussian modulus κ, and the spontaneous curvature* c 0 (T) are empirical material constants; κ and κ describe the elastic energy needed to curve the interface away from its preferred curvature. According to Refs. 22 and 29, they take the values κ ⫽ 0.8k B T and κ ⫽ ⫺0.4 k B T. For monodisperse spheres of radius R, the local radii of curvature identically fulﬁll R 1⫺1 ⫽ R 2⫺1 ⫽ R ⫺1. In that case, the bending free energy per unit volume becomes Fs ⫽

冢冣冢

φ s 2κ ls R2

[1 ⫺ Rc o (T)] 2 ⫹

κ 2κ

冣

(4)

where R ⫽ R 1Φ in the single-phase region and R ⫽ R opt in the 2Φ region and ⫺1 c 0 (T) ⫽ R opt (1 ⫹ κ/2κ) [63]. The factor φ s /l s R 2 corresponds to the interfacial area per unit volume. For a ﬂat lamellar phase one has R 1⫺1 ⫽ R 2⫺1 ⫽ 0, yielding φ F lam ⫽ 2κ s c o (T) 2 ls

(5)

It will be assumed that the linear dependence of c 0 (T) on temperature, c 0 (T) ⫽ ⫺1 R opt (1 ⫹ κ/2κ), still holds. Equations (4) and (5) do not account for ﬂuctuations

* The relationship between the spontaneous curvature and the optimum radius is still under debate. The relationship used here is a good approximation for the investigated mixture if (1) the microstructure conforms to droplets and (2) the droplets are sufﬁciently larger than micelles.

36

Vollmer

of the interface. Undulations of the lamellae are expected to give important contributions to the free energy of lamellar structures [17,20]. To account for this, Helfrich’s result [62] for the free energy of undulating lamellar liquid crystals has been generalized heuristically [17]: F u ⫽ (k B T ) 2

冢冣冢

χ φ 3s κ 4l 3s

冣冢

1 1 ⫹ 2 2 φo φw

冣

1 φo ⫹ φw

(6)

Following Ref. 17 we choose χ ⫽ 0.05. The free energy is positive and represents the entropic repulsions between ﬂuctuating sheets that cannot cross. Additional contributions to the free energy result from equivalent possibilities to realize surfaces with a given structure in space. In particular, there are many different possibilities to distribute a given set of droplets in space, giving rise to a free energy of mixing [17],

冮

F mix ⫽ ⫺ S dT

F mix ⫽

冦

(7)

k B T φ 3s [φ d log φ d ⫹ (1 ⫺ φ d) log(1 ⫺ φ d)] 6 3 l 3s φ 3d (1 ⫺ φ d) 3

1Φ channel

k B T φ 3s {φ d (T ) log φ d (T ) ⫹ [1 ⫺ φ d (T )] log [1 ⫺ φ d (T )]} 6 3 l 3s φ d (T ) 3 [1 ⫺ φ d (T )] 3

2Φ channel

(8)

In the 1Φ region, F u and F mix depend only on temperature owing to the factor k B T. After crossing the emulsiﬁcation boundary, the volume fraction of droplets φ d becomes temperature-dependent, φ d (T) ⬅ φ (opt) ⫽ d

φs φs R opt (T) ⫽ 3l s 3l s a(T ⫺ T)

(9)

leading to a second temperature-dependent term in F mix . In that case Fmix ≠ ⫺TS. Figure 5a shows a survey of the temperature dependence of the bending free energies per unit volume according to Eqs. (4) and (5) for the case φs ⫽ 0.2 and φ w ⫽ φ o ⫽ 0.4. The indices o and w on the symbol for the free energies distinguish between morphologies, where the average curvature of the monolayer is toward oil and water, respectively. F oopt and F wopt denote the free energy for an oil and water droplet phase microemulsion, respectively, where the droplets take their optimum radius. The dashed lines visualize the evolution of the free energies for a lamellar structure F lam and those of oil F os and water droplets F ws. The solid line

Microemulsions

37

shows the temperature evolution of the thermodynamic free energy. By deﬁnition, it follows the lowermost of these curves, provided the constraints of conservation of the respective partial volumes can be fulﬁlled. It has different branches crossing over between morphologies. The free energy follows F opt except for a temperature window around T, where there is too little water or oil to let the droplets assume their optimum size. Consequently, the temperature of the intersection between every two such energies can serve as an estimate for the phase transition temperature. The resulting calculated phase diagrams agree within a few degrees with experiment [22].* In Fig. 5b, the inﬂuence of F u and F mix on the previously discussed energies is shown. The composition of the sample is kept the same. Fu leads to a signiﬁcant increase in the free energy of the lamellar phase. The entropy of mixing F mix opt leads to a comparatively smaller decrease in free energy. Close to T ⫽ T, F mix (T) is not deﬁned. After all, the optimum size of the droplets diverges in such a manner that the constraints due to the conservation laws can no longer be fulﬁlled. [This is underlined by the divergence of φ d (T) ⫽ φ s /[3l s a(T ⫺ T)], although, clearly, φ d (T ) may never exceed 1.] Note that the entropy of mixing does not affect the position of the emulsiﬁcation boundary, since R 1Φ ⫽ R opt at that boundary. In contrast, both F mix and F u decrease the range of stability of a lamellar morphology, so the phase boundary between the droplets and the lamellar phase moves closer toward T. The inﬂuence of the water-to-oil ratio on the temperature dependence of the free energies is demonstrated in Fig. 5c, where the bending free energies F s, F lam , and F opt are shown for φ s ⫽ 0.2, φ w ⫽ 0.15, and φ o ⫽ 0.65. Note that F opt and F lam remain the same since their values are affected only by φ s; they do not depend on φ w and φ o . In contrast, this change in composition strongly changes the free energies for the droplet structures; F os depends on φ o, and F ws depends on φ w. In comparison with Fig. 5a, the slope of F ws (T) has increased around T, and its minimum is shifted toward lower energies. This implies that the intersection of F ws (T) and F lam (T) and that of F ws (T) and F wopt (T) are shifted toward higher temperatures. In contrast, the slope of F os (T ) decreases close to T, and its minimum increases. Note that for this composition and temperature interval, F os (T ) does not correctly describe the morphology, since it has been shown to be cylindrical or bicontinuous for T ⬍ T [54]. Surprisingly, although an incorrect morphology is considered, the temperatures of the intersections of the free energies deviate from the experimentally determined ones (see Fig. 4b) by only a few degrees [22].

* Taking the intersection of the free energies as the position of the phase transition does not account, however, for the width of the 2Φ region, which can be calculated by evaluating the components’ chemical potentials in the respective coexisting phases (cf. Refs. 17,21,20).

38

Vollmer

FIG. 5 Survey of different contributions to the free energy. (a) The bending free energy for nonﬂuctuating interfaces of oil droplets (F os, F oopt), water droplets (F ws, F wopt), and a lamellar morphology (Flam). (b) Free energies when undulations of lamellae F u and the entropy of mixing Fmix are included. For these parts the composition is φ w ⫽ φ o ⫽ 0.4 and φ s ⫽ 0.2. (c) Inﬂuence of composition on the temperature-dependent bending free energy; φ w ⫽ 0.15, φ o ⫽ 0.65, and φ s ⫽ 0.2.

Microemulsions

39

(c)

F.

Latent Heat

The experimentally determined values for the heat absorbed during a transition, ∆Q exp, can be compared directly to theoretical estimates ∆Q th. The value for the latent heat of a ﬁrst-order phase transition can be calculated from the free energy, yielding ∆Q th ⫽

冮

T⫹

T⫺

冢

冮

dT C υ (T) ⫽ ⫺

⫽ ⫺ T⫹

∂F (T) ∂T

冷

T⫹

T⫺

⫺ T⫺ T⫹

dT T ∂F (T) ∂T

∂ 2 F (T) ∂T 2

冷冣 ⫹ F (T ) ⫺ F (T ) ⫹

⫺

(10)

T⫺

⬅ ⫺F′(T ⫹) ⫹ F′(T ⫺) ⫹ F(T ⫹) ⫺ F(T ⫺) where the last equation was obtained by partial integration and we deﬁned F′(T) ⬅ T ∂F(T)/∂T. Note that this expression for ∆Q th contains only the values for the free energy and its ﬁrst derivative with respect to temperature, evaluated at the borders T ⫺ and T ⫹ of the coexistence region. Figure 6 gives a survey of the contributions to the latent heat due to the temperature derivatives F′ ⬅ ⫺TS(T ) of the free energies F opt, F s, F lam , and F mix . The

40

Vollmer

FIG. 6 Dependence of the heat ⫺TS ⫽ T ∂F/∂T ⬅ F′ on temperature for φ s ⫽ 0.2 and φ w ⫽ φ o ⫽ 0.4.

composition is again (cf. Figs. 5a and 5b) φ s ⫽ 0.2 and φ w ⫽ φ o ⫽ 0.4. The heat o w quantities F′s o, F′sw, F′lam, F′mix , and F′mix show a linear temperature dependence. o w F′s , F′s , and F′lam have slopes of a comparable magnitude. However, they are shifted relative to each other. The slope of F′opt is of comparable magnitude but has the opposite sign. F′mix almost vanishes in the single-phase region and in the 2Φ region. F′u is not shown, since it almost vanishes in the relevant parameter range, too. All heat curves depend explicitly on surfactant concentration. In addition, the slopes of F′s o and F′sw depend on the water-to-oil ratio. The contribution of the difference F(T ⫹) ⫺ F(T ⫺) of the free energies to the latent heat [see Eq. (10)] can in general be neglected, since it is much smaller than the difference F′(T ⫹) ⫺ F′(T ⫺) (note the vastly different scales of the y axes of Figs. 5 and 6). Using Eq. (10) and the experimentally determined values of T ⫹ and T ⫺, the values for the latent heat of a phase transition can be read off from Fig. 6 by taking the difference of the respective values belonging to T ⫹ and T ⫺.

1.

Lamellar to L 2 Transition

We now evaluate the values for the latent heat for the transition of a lamellar phase into a microemulsion phase of water droplets. According to Eq. (10), the latent heat is given by

Microemulsions

冢

∆Q th ⬇ ⫺ T ⫹

41

冷

冷

∂F ws (T) ∂F (T) ⫹ T ⫹ mix T⫹ ∂T T ⫹ ∂T

⫺ T⫺

(11)

冷冣

冷

∂F lam (T) ∂F (T) ⫺ T⫺ u T⫺ ∂T ∂T T ⫺

where we have already dropped the contribution F ws (T ⫹) ⫹ F mix (T ⫹) ⫺ F lam (T ⫺) ⫺ F u (T ⫺) to ∆Q th. Moreover, for narrow and large peaks, the value for the latent heat is dominated by the temperature derivative of the bending free energy evaluated at T ⫹ ⬇ T ⫺ ⬇ T peak , where T peak corresponds to the temperature of the maximum of the corresponding peak in C rel V (T ) (see Fig. 6). Inserting Eqs. (4) and (5) into Eq. (11) yields [29,30] ∆Q th ⫽

冢冣冢

4aκT peak φ2s 3l 2s φd

1⫹

κ 2κ

冣

(12)

Figure 7 shows experimental data (squares) and the corresponding theoretical predictions (solid line) for the values of the latent heat for the lam → L 2 transition for varying surfactant concentrations and a ﬁxed ratio of water and octane, φ o /φ w ⫽ 5.67. We ﬁnd close agreement between the theoretical curve and the experimental results, both in absolute magnitude and in the dependence on the surfactant volume fraction. The errors for the calculated values for the latent heat depend strongly on the width-to-height ratio of the peak [30]. For the samples studied the peaks are comparatively narrow, leading to errors for ∆Q th on the order of 10% when Eq. (12) is applied rather than Eq. (11).

G. Step in the Speciﬁc Heat According to Fig. 4, there is a step in the speciﬁc heat C rel V when the emulsiﬁcation boundary is passed. In Fig. 8, the height ∆C step V of the step in the speciﬁc heat is plotted for different sample compositions. The different data points for a single surfactant concentration denote repeated measurements at different heating rates between 8 and 50 K/h. In evaluating the height of the step, it should be kept in mind that the values for ∆C rel V may depend on υ s . Within experimental accuracy no scan speed dependence is observed for ∆C step V when the measurement is started in the L 2 channel and the L 2 channel is entered during the cooling and stirring of a mixture that was previously in a 2Φ region or when it is started in the L 1 channel and the L 1 channel is entered during the heating and stirring of a mixture that was previously in the 2Φ region. The thermodynamic value for the height of the step, i.e., ∆C step th , can be calculated from the free energies via Eq. (4):* * In principle, the entropy of mixing [cf. Eq. (8)] will also contribute to the step. It has been checked that in general this contribution is much smaller than the one resulting from the bending free energy [47]. Therefore, we neglect it in the following.

42

Vollmer

FIG. 7 The latent heat ∆Q per cubic centimeter of sample volume for the transition lam → L 2 is plotted as a function of φ s at a ﬁxed ratio φ o /φ w ⫽ 5.67. The squares are obtained from the calorimetric spectra, and the solid line is the prediction of Eq. (12) for the heat changes obtained from the interfacial model [29]. The inset shows the location of the sample compositions in the Gibbs phase triangle.

冤∂ F∂T(R ) 冷 4κT φ a κ 1⫹ ⫽ 冢 l 2κ冣 2

∆C step th ⫽ ⫺T e

s

opt

2

e

s

2Φ,T⫽T e

⫺

∂ 2 F s (R 1Φ) ∂T 2

冷

1Φ,T⫽T e

冥

(13)

2

s

The predicted value increases linearly with surfactant concentration. It is in remarkably good agreement with the experimental data shown in Fig. 8. We stress that the good agreement between calculated and calorimetrically determined data is found without ﬁtting parameters. This underlines the dominant role that the bending free energy, Eq. (3), plays in the description of the equilibrium behavior of the mixtures. Entropic contributions determine the width of the coexistence regions between different morphologies [13,20]. However, for a ﬁrst prediction of the topology of the phase diagram, the positions of phase boundaries, and connected anomalies in the speciﬁc heat, they are of minor importance.

Microemulsions

43

FIG. 8 Dependence of the height of the step in the speciﬁc heat ∆C Vstep on surfactant concentration φ s . The squares correspond to φ o /φ w ⫽ 5.67, and the crosses to φ o /φ w ⫽ 0.35 [47]. To a good approximation the height of the step depends linearly on φ s , as predicted by the theory (solid line).

III. PHASE SEPARATION KINETICS To explore the origin of the oscillations in the signal for the speciﬁc heat (see e.g., Fig. 4a) we ﬁrst discuss the parameter dependence of the energy barrier preventing the formation of smaller droplets coexisting with a water-rich phase. This oscillating phase separation involves a complex collective nucleation process, which will be identiﬁed as the origin of the stepwise phase separation.

A. Energy Barrier The formation and growth of a nucleus, i.e., of a droplet having a radius larger than the optimum radius, is energetically hindered by the unfavorable bending energy of that droplet. On the other hand, because of volume and surface conservation, large droplets must be formed to allow the majority of small droplets to attain their optimum size. The height of the energy barrier the microemulsion droplets have to pass in order to be able to form a single large droplet is the maximum value of the difference ∆F s between the bending free energy F s (N, R)

44

Vollmer

of the supersaturated state of N monodisperse droplets of radius R (cf. Fig. 1c) and that of the state F s (N′, R′) ⫹ F s (1, ρ) (see Fig. 1d), where N′ droplets of radius R′ (R ⬎ R′ ⲏ R opt) coexist with a single large droplet of radius ρ [49]: ∆F s ⫽ F s (N′, R′) ⫹ F s (1, ρ) ⫺ F s (N, R)

(14)

As soon as ∆F s ⬍ 0, it is energetically favorable to form N′ droplets of radius R′ and a single big droplet of radius ρ. For a system with initially 1000 monodisperse droplets, Fig. 9 shows the dependence of ∆F s on the reduced size of the large droplet, (ρ ⫺ R 1Φ)/ρ, at different degrees of overheating, τ ⬅ R 1Φ /R opt ⬀ (T ⫺ T ). The monodisperse state corresponds to (ρ ⫺ R 1Φ)/ρ ⫽ 0, whereas (ρ ⫺ R 1Φ)/ ρ → 1 for ρ ⬎⬎ R 1Φ. Thermodynamically stable monodisperse systems are characterized by values for τ less than 1, while τ ⬎ 1 corresponds to the two-phase system. For a system with a ﬁnite number of particles N, the phase transition can occur only at τ ⬎ 1, and it only requires the production of a ﬁnite size excess

FIG. 9 Dependence of the energy difference ∆F s separating a system of monodisperse droplets (radius R 1Φ) from a phase-separated state of smaller droplets coexisting with a single large droplet of radius ρ. The initial number of droplets is ﬁxed at N ⫽ 1000. The different curves correspond to different degrees of overheating, τ. (Dashed line: τ ⫽ 1.1; solid line: τ ⫽ 1.15; dotted line: τ ⫽ 1.22.)

Microemulsions

45

droplet. For small values of τ (τ ⫽ 1.1, dashed line), the energy difference ∆F s always increases as the reduced size of the large droplet increases. The monodisperse system is still stable, showing that more than 1000 droplets are needed to form a phase-separated state. As the overheating increases, a second minimum shows up. For τ ⬇ 1.15, the energy difference can become negative for the ﬁrst time (solid line). In this case, the mixture has to pass an energy barrier ∆F max s the order of 10 k B T to reach phase separation, and the excess droplet takes on a reduced size larger than (ρ ⫺ R 1Φ)/ρ ⬇ 0.75, i.e., ρ ⬇ 4R 1Φ. Its volume exceeds that of the microemulsion droplets by more than a factor of 50. For even greater rapidly decreases, becoming only a few k B T for τ ⫽ 1.22, overheating, ∆F max s where it becomes negative for (ρ ⫺ R 1Φ)/ρ ⬇ 0.55, i.e., for ρ ⬇ 2R 1Φ (dotted line). The height of the energy barrier depends only slightly on the number of droplets. However, due to the conservation of volume and total interfacial area, a minimal number of droplets are required to build a sufﬁciently large droplet for ∆F s to become negative (Fig. 9). Energy barriers of a few k B T require values for R 1Φ /R opt ⬇ 1.2 in accordance with experimental observations [46]. In this case, a few hundred droplets participate in nucleating a large droplet. Consequently, the nucleation of large water droplets is a strongly collective process.

B. Experimental Observation of Oscillations In the last paragraph we observed that the conservation of volume and interfacial area is essential for the occurrence of the energy barrier. In contrast to classical nucleation processes [65,66], it is energetically unfavorable for a single large droplet to be formed and to grow. Large droplets form only in order to decrease the free energy of the whole system. This novel feature can modify the phase separation kinetics signiﬁcantly. This comes to light when the system is driven into the 2Φ region by constant heating. Constant heating may lead to periodic clouding and clearing of the mixture [46,49,64]. The repeated appearance of clouding is due to strong threshold behavior in the formation of aggregates (i.e., water-rich domains) larger than the wavelength of light, which is reﬂected in an oscillating variation of the turbidity [46,64]. Two to four periods of clouding can be discerned optically for most compositions and heating rates. More detailed information about the kinetics of this phase separation can be achieved from microcalorimetric measurements [46]. In contrast to optical measurements, which are sensitive to large particles in the system, the DSC signal is affected by all droplets. After all, it measures changes in the average curvature of the interface (see Section II.E and Ref. 29). In particular, it is therefore governed by the vast majority of small droplets. As a consequence, the values for the speciﬁc heat contain less noise. They even show an oscillating signal when

46

Vollmer

nothing can be discerned any longer in the optical data. Up to 20 oscillations can clearly be dissolved. Due to their favorable signal-to-noise ratio, the microcalorimetric data allow us to quantitatively investigate the oscillations. Figure 10 shows the temperature-dependent variation of the microcalorimetric signal for the speciﬁc heat C rel V (T ) for different heating rates υ s . All thermograms show about 15 oscillations. From the scan speed dependence it is clear that the thermograms do not resemble the equilibrium values for the speciﬁc heat. Rather, they reﬂect aspects of the phase separation kinetics. To stress this nonequilibrium nature of the data we denote them as ‘‘apparent speciﬁc heat.’’ In agreement with expectations from thermodynamics, the onset of the oscillations shifts to higher values for increasing surfactant concentration. The time lag ∆T between two succeeding maxima (cf. inset of Fig. 10) increases with increasing υ s. In Refs. 46 and 50 it is shown that ∆T ⬃ υ 1/2 s .

FIG. 10 Temperature-dependent variation of the apparent speciﬁc heat C Vrel (T ) while entering the 2Φ region by constant heating for φ s ⫽ 0.1 and φ w ⫽ 0.33 and different heating rates. Top to bottom: υ s ⫽ 4 K/h, solid line; υ s ⫽ 14 K/h, dotted line; υ s ⫽ 27 K/h, crosses. The respective baselines are chosen in such a way that thermograms do not cross. The inset shows the deﬁnition of the height of a peak ∆C v and of the period of oscillation ∆T.

Microemulsions

47

The time lag ∆T between the peaks of C rel V changes nonmonotonously with the number of oscillations, i.e., with the temperature. This dependence is most evident when the signal for the apparent speciﬁc heat also shows a pronounced superimposed structure. An explanation of the dependence of ∆T on the number of oscillations will give a hint about a relevant process to understand the kinetics of this phase separation.

C. Mechanism of Phase Separation We now further discuss Fig. 1, in order to clarify the origin of cascade nucleation in more detail (also see Refs. 49 and 50). To this end, we observe that for a small degree of supersaturation (Fig. 1c, τ ⱗ 1.15), nucleation is strongly suppressed for energetic and kinetic reasons, while it becomes fast for larger values of τ, leading locally to a structure such as the one shown in Fig. 1d. Typically, a large droplet is nucleated from a few thousand small ones. Nevertheless, in a very short time, a macroscopic number of nuclei (ⲏ10 12) appear in the sample (note that there are 10 16 –10 18 droplets per cubic centimeter). They are homogeneously distributed with typical distances of less than a few hundred nanometers between them, so they induce rapid relaxation of the size distribution of droplets to a state close to equilibrium. At the same time, the nuclei grow in size and merge into water-rich domains, whose mutual distance soon exceeds 10–100 µm. By that time, a typical neighborhood of a water-rich domain contains a few thousand small droplets. It looks very much like those sketched in Fig. 1b. Due to the large distance between the water-rich domains and typical neighborhoods of small droplets, water transport—no matter whether by molecular diffusion of water through the oil or by diffusion and collisions of droplets—from small droplets of a to the water-rich domains is negligible on the time scales ∆T/υ s ⬃ υ ⫺1/2 s single oscillation. Consequently, the droplets cannot change in size upon heating, leading again to supersaturation (Fig. 1c) and eventually to nucleation (Fig. 1d), but now for droplets with a slightly different radius and density. This possibility for repeated bursts of nucleation is hinted at in Fig. 1 by the arrow pointing back from parts (d) and (e) to part (b). The stepwise decrease in the droplet size is hence due to an alternation between long periods of slow heating and a comparatively rapid relaxation after nucleation arises in the system. As a consequence, cascade nucleation involves at least two, typically quite different, time scales t 1 and t 2: The time scale t 1 ⬃ (a R opt υ s) ⫺1 characterizes the change in the optimum radius of droplets due to heating. The time scale t 2 ⬃ γ ⫺1 is set by the inverse of the decay rate γ of the number of big droplets in the system due to coalescence. When the Stokes–Einstein law is applied, t 2 depends on the distance between large droplets D big and on their diffusion velocity Ᏸ diff like t 2⫺1 ⬃ γ ⬃ Ᏸ diff /D 2big.

48

Vollmer

For a theoretical discussion of this picture from a more general point of view, we refer to Ref. 50. Here, we remark only that the bottom line of the arguments presented in that paper is that the time ∆T/υ s between subsequent bursts of nucleation scales as the geometric mean of the time scales t 1 and t 2. This leads to

冢冣 υs ∆T

2

⫽

1 Ᏸ ⬃ a R opt υ s diff t1 t2 D 2big

(15)

Moreover, the distance D big between large droplets can be related to the composition of the microemulsion by equating D 3big with the volume occupied by N small droplets in the region of the sample containing only a single large droplet, D 3big ⫽

4π R 3opt N 3 φ d(opt)

(16)

Combining Eqs. (15) and (16) leads to the prediction ∆T 2 ⬃

R

φ

opt (opt) 2/3 d

υs

(17)

when one assumes that Ᏸ diff and N can be considered constant. For the ﬁrst oscillations after crossing the emulsiﬁcation boundary the radius of droplets is still very close to its value in the single-phase region, R opt ⬇ R 1Φ. In this situation, the prediction of Eq. (17) agrees remarkably well with experimental data, as demonstrated in Fig. 11. When ∆T is plotted against (υ s R 1Φ φ ⫺2/3 ) 1/2 on a log-log scale, the data for a variety of compositions and scan d speeds converge to a single line with a slope of 0.5, as predicted by Eq. (17).

D. Temperature Dependence of the Droplet–Droplet Distance In Fig. 11, the dependence of ∆T on (υ s R 1Φ φ ⫺2/3 ) 1/2 is shown only for the respecd tive ﬁrst oscillations. This is the most accurate test of the theoretical prediction, because there are only small errors in the composition, which is still very close to the one in the 1Φ region. On the other hand, it leaves the question open as to how to explain the evolution of ∆T with the number of oscillations. As shown in Fig. 10, the speciﬁc heat may show a pronounced superimposed structure. To shed light on this behavior, one has to keep track of the temperature dependence of the volume fraction and radius of the microemulsion droplets. According to Eq. (2), the radius of the droplets decreases with increasing temperature. Accompanying the decrease of R opt (T), the volume fraction of droplets decreases also. To a good approximation, the small droplets account for all the interface in the sample, φ s V ⫽ 4πN R 2opt l s, and they occupy the volume φ d(opt) V ⫽ 4πN R 3opt /3.

Microemulsions

49

FIG. 11 Dependence of the period of the ﬁrst oscillation log(∆T ) on log(υ s R 1Φφ ⫺2/3 ). d The symbols show the results of microcalorimetric measurements on nine different compositions and typically three different heating rates per sample. The straight line is a ﬁt through the data points with a slope of 0.5. Sample compositions: (䉮) φd ⫽ 0.096, R ⫽ 5.8 nm; (⫹) φ d ⫽ 0.094, R ⫽ 16 nm; (䉭) φ d ⫽ 0.19, R ⫽ 5.8 nm; (䊉) φ d ⫽ 0.19, R ⫽ 6.8 nm; (䉫) φ d ⫽ 0.19, R ⫽ 15 nm; (䉭) φ d ⫽ 0.38, R ⫽ 6.0 nm; (■) φ d ⫽ 0.37, R ⫽ 8.2 nm; (䊐) φ d ⫽ 0.38, R ⫽ 11 nm; (⫻) φ d ⫽ 0.38, R ⫽ 15 nm.

In the 2Φ region φ (opt) depends on the temperature and on surfactant concentrad tion, φ (opt) ⫽ φ s /[3l s a(T ⫺ T )] according to Eq. (9). Figure 12 shows the variation d in the period of ∆T for different heating rates and two surfactant concentrations. However, now ∆T is plotted as a function of the scaling variable υ s R opt φ (opt)⫺2/3 . d The open triangles correspond to φ s ⫽ 0.1 and the ﬁlled squares to φ s ⫽ 0.05. The heating rate increases from the left (v s ⬇ 1 K/h) to the right (v s ⬇ 31 K/ h). The data points still follow the scaling of ∆T with (υ s R opt φ (opt)⫺2/3 ) 1/2. However, d in all cases one clearly discerns a superimposed nonmonotonous behavior of ∆T; . In view of it ﬁrst increases and then decreases under increasing υ s R opt φ (opt)⫺2/3 d this observation, we conclude that the nonmonotonous dependence of the oscillation amplitude may be caused by a variation of the period of the oscillations due to an adiabatic change of composition. For larger ∆T also the amplitude of the oscillations increases, since the system is driven further into the metastable region and hence more heat is released when nucleation sets in.

50

Vollmer

FIG. 12 Log-log representation of the dependence of ∆T on υ s R optφ d(opt)⫺2/3. (䉮) φ s ⫽ 0.1; (■) φ s ⫽ 0.05. The scan speed increases from left to right; (䉮) υ s ⫽ 1.2, 4, 13, and 27 K/h; (■) υ s ⫽ 1.4, 4, 15, and 31 K/h.

To understand this additional temperature dependence of ∆T, the implications of volume and surface conservation for the number of droplets and the average droplet–droplet distance D d–d have to be considered. In contract to the volume fraction of droplets, their number density n increases with increasing temperature, n⬅

N φs a2 φs ⫽ ⫽ (T ⫺ T ) 2 2 V 4πl s R opt 4πl s

(18)

The average droplet–droplet distance in the 2Φ region can be estimated by assuming a locally close-packed arrangement of droplets [67]: D d–d ⯝

冢冣冢

1 16π √2 3

1/3

冣

2/3 R opt (T) R opt ⬃ 1/3 ⬃ φ ⫺1/3 (T ⫺ T ) ⫺2/3 s (opt) 1/3 φd φs

(19)

where Eqs. (9) and (2) have been used to express φ d(opt) in terms of the conserved quantity φ s and in terms of the droplet radius R opt. D d–d decreases with increasing

Microemulsions

51

temperature and surfactant concentration. For the collision frequency, however, not the average droplet–droplet distance but the diffusion length D 2 between the interfaces of neighboring droplets is relevant. Its square root is given by D ⬅ D d–d (T) ⫺ 2R opt (T) ⫺ l s ⯝ 2(l s R )

2 1/3 opt

冤冢冣冢冣冥⫺l 1 2π √2 φ s

1/3

R opt ⫺ ls

1/3

s

(20)

i.e., it comprises the difference of two different power laws in T ⫺ T. As a consequence, D 2 always shows a maximum. The changes in R opt, n, and D d–d with increasing temperature are schematically shown in Fig. 13. (The relationship of the droplet sizes is chosen to reﬂect the situations at the beginning and end of a typical experiment.) In Fig. 13a, a droplet conﬁguration is given as it might exist close to the emulsiﬁcation boundary. The droplets take their optimum radius R 1Φ ⬇ R opt (T 1); D(T 1) denotes the average distance between the respective surfaces of neighboring droplets. In Fig. 13b, at T ⫽ T 2, the mixture is deep in the 2Φ region. The size of the droplets has decreased toward R opt (T 2), and the average droplet–droplet distance has decreased toward D d–d (T 2). Due to conservation of the total interfacial area and of the volume fraction of all components, the number of droplets has increased but their total surface area is preserved. The excess water, which is no longer dissolved in the smaller droplets, has been expelled into a water-rich phase formed at the bottom of the test tube. In Fig. 14, the temperature dependence of ∆T (left axis, squares) is compared to the temperature dependence of D (T ) 2 (right axis, solid line). Similar to ∆T, for small values of (T ⫺ T ⫽ T ⫺ 305.6 K ), the distance D(T) increases with

FIG. 13 Sketch of the radius of the droplets R, the average droplet-droplet distance D d–d and the average distance between droplet boundaries D for (a) a mixture at a temperature close to the emulsiﬁcation boundary T ⫽ T 1, and (b) deep in the 2Φ-region at T ⫽ T 2.

52

Vollmer

FIG. 14 The variation of ∆T and diffusion length D 2 with temperature for φ s ⫽ 0.1 and υ s ⫽ 4 K/h.

increasing temperature, then it passes a maximum at T ⫽ T max , and eventually it decreases with increasing temperature. The nonmonotonous temperature dependence of D(T) 2 arises from a crossover: Close to T, D 2 increases due to the fast decrease of R opt with increasing temperature, until at sufﬁciently high temperatures the diffusion length D 2 is dominated by the decrease in D d–d , which is caused by an increase in the number of droplets with increasing temperature. Similar to the volume fraction of droplets in the microemulsion phase [cf. Eq. (18)], D 2 depends solely on temperature and on surfactant concentration. On the other hand, the emulsiﬁcation temperature [solving R 1Φ ⫽ R opt (T) for T ] depends on the overall volume fraction of water φ w in the sample. For sufﬁciently small φ w and ﬁxed φ s, the emulsiﬁcation temperature is to the right of the maximum, leading to a monotonously decreasing behavior of ∆T with increasing temperature (as noted in Ref. 46), while for sufﬁciently high φ w, ∆T can go through a maximum as shown in Figs. 12 and 14. To verify that the temperature-dependent change in the average distance droplet has to diffuse before it can collide with another droplet is the dominant process determining the nonmonotoneous behavior of ∆T, the data for ∆T shown in Fig.

Microemulsions

53

FIG. 15 Dependence of ∆T D ⫺2 υ ⫺1/2 on the number of oscillations N for φ s ⫽ 0.1 and s φ w ⫽ 0.33. The data points correspond to four different scan speeds. (䊐) υ s ⫽ 1.2 K/h; (䉭)υ s ⫽ 4 K/h; (*) υ s ⫽ 13 K/h; (䉫) υ s ⫽ 27 K/h.

12 were replotted. Since the presented argument does not depend on υ s, the observed square root dependence of ∆T on √υ s should remain valid [46]. Figure 15 shows the evolution of ∆TD ⫺2 υ ⫺1/2 with the number of oscillations N, i.e., s with temperature. The different symbols denote different heating rates, while the composition of the mixture is kept constant (φ s ⫽ 0.1 and φ w ⫽ 0.33). Within the margin of error, the data for ∆TD ⫺2 υ ⫺1/2 no longer depend on N, s in contrast to the pronounced maxima for ∆T shown in Fig. 12. The slight deas the heating rate increases may be due to different concencrease in ∆TD ⫺2 υ ⫺1/2 s trations of oil and surfactant in the water-rich phase. This additional change in composition (besides the expulsion of water) is more pronounced for high heating rates, because in that case the water-rich phase has less time to relax to a state close to equilibrium. This leads to more signiﬁcant changes in the composition of the microemulsion phase. In any case, however, the very weak dependence of ∆TD ⫺2 υ ⫺1/2 on N strongly suggests that the observed nonmonotonous variation s of ∆T with temperature is due to the change in the average distance between droplet boundaries. This dependence of ∆T on the diffusion length supports our earlier assumption that the water transport from small to big droplets is via diffu-

54

Vollmer

sion and mass exchange during collisions of the nanometer-sized microemulsion droplets.

IV.

CONCLUSION

We have surveyed recent experimental and theoretical developments of a thermal characterization of phase transitions and the kinetics of the emulsiﬁcation failure in water–oil–surfactant mixtures. As a model surfactant, we chose the nonionic surfactant C 12 E 5. Microcalorimetric measurements are demonstrated to be an efﬁcient method to determine phase transitions, the width of the accompanying coexistence regions, and the kinetics of the phase separation. This method traces changes in the average curvature of the surfactant monolayer with a very high sensitivity [29]. Its value as a method that is complementary to more traditional approaches such as optical inspection and scattering techniques is highlighted by three ﬁndings. 1. Mixtures of water, octane, and C 12 E 5 are commonly considered as typical symmetrical surfactant mixtures, since under optical inspection the phase behavior is almost unchanged when the volume fractions of water and oil are exchanged and the temperature is varied from T to 2T ⫺ T. Surprisingly, however, for equal volume fractions of water and oil, the thermograms (cf. Fig. 4) are not at all mirror symmetrical under this change of temperature, suggesting that the symmetry does not necessarily hold on the microscopic level. Furthermore, under these conditions, the peaks are especially broad. Although the mixtures appear to be singlephase close to the microemulsion channels L 1 and L 2 , the higher level of the baseline close to the water emulsiﬁcation boundary (cf. Fig. 4a) strongly suggests that almost always, microstructures of different morphologies coexist on a microscopic scale. This should be kept in mind when setting up other experiments and calculating polydispersities. 2. Microcalorimetry yields a direct measure of the latent heat ∆Q of ﬁrstorder phase transitions in the mixtures. Comparing the experimental data with the predictions of various models allows us to identify relevant contributions to the free energy describing the mixture. Quantitative predictions can most easily be performed for a large ratio of peak height to-width. In that case, the theoretical estimate for the latent heat is dominated by the bending free energy. Up to the factor T, it is to a very good approximation the difference between the slopes of the free energy functionals (in mean-ﬁeld approximation) for the respective structures at their point of intersection. In addition, the latter gives a good estimate of the phase transition temperature. No ﬂuctuations of the interface need to be considered for this. For a small peak height-to-width ratio, the extent of the twophase region has to be taken into account in calculating the latent heat (also cf. Ref. 30). We stress that the good agreement between experiments and predictions

Microemulsions

55

was obtained without ﬁtting any parameters. It requires only a knowledge of the bending rigidities of the surfactant monolayer at the interface between the water and oil microdomains and of its spontaneous curvature. These material constants have been tabulated for many amphiphilic mixtures (e.g., in Ref. 27). Alternatively [29,47], they can be determined by ﬁtting the results of a few independent temperature scans. 3. Crossing the emulsiﬁcation boundary by means of constant heating leads to an oscillating signal for the speciﬁc heat. An alternation between a slow increase in supersaturation due to heating and a fast relaxation at strong supersaturation appears to be the origin of this dynamic instability of the phase separation. The delay of relaxation is caused by an efﬁcient energy barrier, which the droplets have to pass in order to collectively decrease their average radius at the expense of a large droplet taking up the excess water. The height of the energy barrier can be estimated from the bending free energy of the interface. It decreases strongly with increasing degree of overheating. The time lag ∆T between bursts of nucleation depends, like √υ s, on the heating rate υ s. This dependence not only holds for a vast range of compositions but also remains valid throughout the entire phase separation process. An additional variation of ∆T with the number of oscillations is found to be properly described by the temperature-dependent change in the average distance between the surfaces of neighboring droplets, which strongly inﬂuences the transport of water from small to large droplets. This distance varies nonmonotonously with temperature due to the interplay of a temperature-induced decrease in the droplet size and increase in the number of droplets. The success of this modeling shows that the bending free energy may also serve as a starting point to describe the local equilibrium of surfactant mixtures driven far outside equilibrium. In conclusion, we point out that the presented measurements strongly suggest that (1) the temperature dependence of the preferred curvature of the surfactant monolayer, (2) the conservation of the total interfacial area, and (3) the conservation of the partial volumes of water and oil are the dominant parameters needed to understand temperature-dependent phase transitions in the considered mixtures. We expect that these are also the crucial parameters needed to describe the equilibrium properties and kinetics in other amphiphilic mixtures.

ACKNOWLEDGMENTS It is a pleasure to thank M. Schmidt for support in performing this work and R. Strey and J. Vollmer for fruitful and pleasant collaborations. Stimulating discussions with B. Du¨nweg, U. Olsson, M. Kahlweit, and M. E. Cates are gratefully acknowledged. This work has been supported by the Deutsche Forschungsgemeinschaft.

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REFERENCES 1. K Hill, W von Rybinski, G Stoll. Alkyl Polyglycosides, VCH; Weinheim, 1997. 2. M Kahlweit, R Strey, G Busse. Phys Rev E 47:4197 (1993). 3. R Strey, R Schoma¨ker, D Roux, F Nallet, U Olsson. J Chem Soc Faraday Trans 86: 2253 (1990). 4. S-H Chen, S-L Chang, R Strey. J Chem Phys 93:1907 (1990). 5. W Jahn, R Strey. J Phys Chem 92:2294 (1988). 6. M Kotlarchyk, SH Chen, JS Huang, MW Kim. Phys Rev Lett 53:941 (1984). 7. GJM Koper, WFC Sager, J Smeets, D Bedeaux. J Phys Chem 99:13291 (1995). 8. G Porte, J Marignan, P Bassereau, R May. J Phys France 49:511 (1988). 9. F Nallet, D Roux, J Prost. Phys Rev Lett 62:276 (1989). 10. U Olsson, P Schurtenberger. Langmuir 9:3389 (1993). 11. S Clark, PDI Fletcher, X Ye. Langmuir 6:1301 (1990). 12. EW Kaler, KE Bennett, HT Davis, LE Scriven. J Chem Phys 79:5673. EW Kaler, HT Davis, LE Scriven. J Chem Phys 79:5685 (1983). 13. G Gompper, M Schick. In: Phase Transitions and Critical Phenomena, Vol. 16 (C Domb, JL Lebowitz, eds.), Academic Press, London, pp. 1–175. 14. PG De Gennes, C Taupin. J Phys Chem 86:2294 (1982). 15. SA Safran, LA Turkevich, P Pincus. J Phys Lett 43:2903 (1984). 16. B Widom. J Chem Phys 81:1030 (1984). 17. D Andelman, ME Cates, D Roux, SA Safran. J Chem Phys 87:7229 (1987). 18. DH Anderson, H Wennerstro¨m, U Olsson. J Phys Chem 93:4243 (1989). 19. ME Cates, D Andelman, SA Safran, D Roux. Langmuir 4:802 (1988). 20. J Daicic, U Olsson, H Wennerstro¨m. Langmuir 11:2451 (1995). 21. U Schwarz, K Swamy, G Gompper. Europhys Lett 36:117 (1996). 22. D Vollmer, J Vollmer, R Strey. Phys Rev E 54:3028 (1996). 23. U Olsson, H Wennerstro¨m. Adv Colloid Interface Sci 49:113 (1994). 24. P Pieruschka, U Olsson. Langmuir 12:3364 (1996). 25. D Roux, N Nallet, E Freyssingeas, G Porte, P Bassereau, M Skouri, J Marignan. Europhys Lett 17:575 (1992). 26. CR Saﬁnya, EB Sirota, D Roux, GS Smith. Phys Rev Lett 62:1134 (1989). 27. T Sottmann, R Strey. J Chem Phys 106:8605 (1997). 28. F Sicoli, D Langevin, LT Lee. J Chem Phys 99:4759 (1993). 29. D Vollmer, R Strey. Europhys Lett 32:693 (1995). 30. D Vollmer, J Vollmer, R Strey, H-G Schmidt, G Wolf. J Thermal Anal 51:9 (1998). 31. R Strey. Colloid Polym Sci 272:1005 (1994). 32. J Arrault, C Grand, W Poon, M Cates. Europhys Lett 38:625 (1997). 33. O Diat, D Roux, F Nallet. J Phys II 3:1427 (1993). 34. O Diat, D Roux, F Nallet. Phys Rev E 59:3296 (1995). 35. M Bergmeier, H Hoffmann, C Thunig. J Phys Chem B 101:5767 (1997). 36. M Buchanan, J Arrault, ME Cates. Langmuir 14:7371 (1998). 37. K Mishima, K Yoshiyama. Biochim Biophys Acta 904:149 (1987). 38. I Sakurai, T Suzuki, S Sakurai. Biochim Biophys Acta 985:101 (1989). 39. CA Miller, KH Raney. Colloid Surfact A 74:169 (1993). 40. R Bar-Ziv, E Moses. Phys Rev Lett 73:1392 (1994).

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52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67.

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RE Goldstein, P Nelson, T Powers, U Seifert. J Phys II France 6:767 (1996). J Morris, U Olsson, H Wennerstro¨m. Langmuir 13:606 (1997). H Wennerstro¨m, J Morris, U Olsson. Langmuir 13:6972 (1997). A Kabalnov, J Weers. Langmuir 12:1931 (1996). D Vollmer, P Ganz. J Chem Phys 103:4697 (1995). D Vollmer, R Strey, J Vollmer. J Chem Phys 107:3619 (1997). D Vollmer, J Vollmer. Physica A 249:307 (1998). SA Safran, LA Turkevich. Phys Rev Lett 50:1930 (1983). J Vollmer, D Vollmer, R Strey. J Chem Phys 107:3627 (1997). J Vollmer, D Vollmer. Faraday Disc 112:51 (1999). D Langevin, J Meunier. In: Micelles, Membranes, Microemulsions, and Monolayers (WM Gelbart, A Ben-Shaul, D Roux, eds.) Springer-Verlag, Berlin, 1994, pp. 485– 519. K Bonkhoff, A Hirtz, GH Findenegg. Physica A 172:174 (1991). M Kahlweit, R Strey, G Busse. J Phys Chem 94:3881 (1990). R Strey, O Glatter, K-V Schubert, EW Kaler. J Chem Phys 105:1175 (1996). JH Schulmann, W Stoeckenius, LM Prince. J Phys Chem 53:1677 (1959). M Kahlweit, R Strey. Angew Chem Int Ed 24:654 (1985). M Kahlweit, R Strey, P Firman. J Phys Chem 90:671 (1986). H Bagger-Jo¨rgensen, U Olsson, K Mortensen. Langmuir 13:1413 (1997). PA Winsor. Trans Faraday Soc 44:376 (1948). M Gradzielski, D Langevin, T Sottmann, R Strey. J Chem Phys 106:8232 (1997). W Helfrich. Z Naturforsch C 28:693 (1973). W Helfrich. Z Naturforsch C 33a:305 (1978). SA Safran. Phys Rev A 43:2903 (1991). D Vollmer, J Vollmer, R Strey. Europhys Lett 39:245 (1997). K Binder. Rep Prog Phys 50:783 (1987). JL Gunton, M San Miguel, PS Sahni. In: Phase Transitions and Critical Phenomena, Vol. 8. (C Domb, JL Lebowitz, eds.), Academic Press, New York, pp. 1–175. NW Ashcroft, ND Mermin. Solid State Physics, Holt-Saunders, Philadelphia, 1976.

3 Subzero Temperature Behavior of Water in Microemulsions SHMARYAHU EZRAHI Materials and Chemistry Department, The Ordnance Corps, Israel Defense Forces, Ramat Gan, Israel ABRAHAM ASERIN, MONZER FANUN, and NISSIM GARTI Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

I. Introduction II.

The Behavior of Water Near Surfaces

60 60

III. State of Water

61

IV.

63

Methodology

V. Information Obtained via the Exothermic Scanning Mode A. Structural transitions B. Percolation transitions VI.

VII.

67 67 69

Information Obtained via the Endothermic Scanning Mode A. Ethoxylated alcohols B. Ethoxylated siloxanes C. Sucrose esters D. Phosphatidylcholine

76 76 77 77 80

Results and Discussion A. Variation of water peak temperatures with water content B. Full hydration of the surfactant C. Free water D. Nonfreezable water E. Evaluation of the thickness of the bound water layer F. Alcohol interaction with other constituents

80 80 83 87 89 93 94

59

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G. Exothermic peaks H. The problem of phase separation

98 107

VIII. Conclusion

113

References

114

I. INTRODUCTION The purpose of this review is to examine several methodological aspects concerning the use of subzero temperature differential scanning calorimetry (hereafter designated as SZT-DSC), for the study of surfactant–water interactions and to highlight some recent results related to (mostly) nonionic microemulsions. In contrast to the common view that there need not be any a priori relation between properties of hydration measured at low temperatures and those measured at room temperature [1], we shall try to show that if the water–surfactant interaction is deﬁned in terms of a perturbation to the freezing (or melting) of water at about 0°C, then the thermal behavior of microemulsions at ambient temperature is directly related to that at subzero temperatures. It should be stressed that SZT-DSC allows us only a dim glance into the microstructure of microemulsions and an even dimmer glance into its details. Yet the combination of SZT-DSC data and the results of spectroscopic measurements may deepen our understanding of these problems, as will be shown in this review. The review is organized as follows. First we deﬁne several states of water in terms of their thermal behavior. Then we compare the exothermic and endothermic modes of SZT-DSC and discuss how to evaluate the relative amounts of free and bound water in a microemulsion sample. After some information obtained via the exothermic scanning mode is demonstrated, we concentrate on the endothermic scanning mode. We analyze the distribution of free and bound water as a function of (total) water content in microemulsion systems. This is followed by a discussion of nonfreezable water and evaluation of the thickness of the bound water layer. The interaction of alcohol with other components of microemulsion systems and the signiﬁcance of exothermic peaks are also highlighted. Special emphasis is put on the often ignored problem of phase separation during the cooling and freezing of microemulsion samples. Finally, the role of SZT-DSC in the investigation of microemulsions is summarized.

II.

THE BEHAVIOR OF WATER NEAR SURFACES

It is widely known that liquid water departs considerably from its average bulk behavior due to the presence of adjacent interfaces, be they organic, such as biomembranes and proteins, or inorganic, such as clays and ion exchangers [2,3].

Subzero Behavior of Water in Microemulsions

61

The investigation of the interaction between water and such interfaces is relevant to the study of such problems as the behavior of water in living organisms [4,5] and sludge dewatering [6]. Moreover, water enclosed in very small volumes plays a dominant role as the medium that controls structure and behavior near biological membranes, for example, and microemulsions may well serve as model systems for the study of water in conﬁned spaces [2,7,8].

III. STATE OF WATER When describing the state of water in relation to any surface, several distinguishably different types of water, ranging from the most tightly bound (nonfreezable) to free, bulk-like water, may be considered. Besides the general distinction between ‘‘free’’ and ‘‘bound’’ water, more detailed classiﬁcations have been suggested. Senatra et al. [9], for example, have used a differentiation based on the difference in melting (freezing) points: 1. ‘‘Free’’ water melts at 0°C. 2. ‘‘Interphasal’’ (or ‘‘interfacial’’ [8]) water melts at about ⫺10°C. 3. ‘‘Bound’’ water melts at temperatures lower than ⫺10°C. The distinction between ‘‘interphasal’’ and ‘‘bound’’ water is based on empirical observations pertinent to speciﬁc surfactant-based systems (including some of our model systems, as is shown later on). The melting temperatures of these types of water vary as a function of composition. Two examples will sufﬁce to show our point. Thus, altering the (total) water content may shift the melting point of interphasal water between ⫺15°C and ⫺5°C in some cases. In other cases the shift is only 2–3 degrees. Also, the transition from quaternary systems (containing water, alcohol, oil, and surfactant) to binary systems (containing water and surfactant) shifts the melting point of interphasal water to higher (less negative) temperatures, as is demonstrated later in relation to our model system A (see Section VI.A). The melting temperature, ⫺10°C, is just an arbitrary (and not always sharp) limit between various grades of water–surfactant interactions. Moreover, it should also be emphasized that the attribute ‘‘bound’’ does not refer to covalent binding but rather to dipole–dipole interactions (in nonionic systems) and dipole– ion interactions (in ionic systems). Thus, the degree of order and mobility and the strength of the binding in water–surfactant interactions are lower than might be inferred from the somewhat misleading term ‘‘bound’’ water [10]. Thermograms depicting these three types of water are shown in Fig. 1 for the system dodecane–potassium oleate–water–hexanol [11]. Schulz [8] classiﬁed water in microstructured systems in a more descriptive way:

62

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FIG. 1 Typical DSC thermograms of K-oleate–hexanol–dodecane–water microemulsion samples. Surfactant/oil ⫽ 0.2 g/mL; alcohol/oil ⫽ 0.4 ml/mL; water/(water ⫹ oil) ⫽ 0.222–0.4 g/g. Curve a, W/O microemulsion sample; curve b, D 2O/oil microemulsion sample. Endothermic peaks due to the fusion of D 2O (277 K), ‘‘free’’ water (273 K), dodecane and ‘‘interphasal’’ water (263 K), ‘‘bound’’ water (233 K), and hexanol (220 K) were identiﬁed. (From Ref. 11.)

1. 2. 3. 4.

Free water Interstitial water, which remains unfrozen at temperatures well below the normal freezing point Surface water—physically and/or chemically adsorbed water Internal water—chemically bound water

The nature of water–substrate interactions and the extent to which water is bound have been investigated using spectroscopic methods such as nuclear magnetic resonance (NMR) [2,12–14], infrared (IR) spectroscopy [15–21], electron spin resonance (ESR) [12], and calorimetric methods, which may be divided into ambient [21–25] and low-temperature [11,12,26,27] measurements. In aqueous solutions of several globular proteins, the degrees of hydration calculated from calorimetric and NMR measurements of frozen samples agree well [28]. In the case of tropocollagen, for instance, hydration numbers of 2.4 and 2.7 mol water per residue were evaluated by using calorimetric and NMR techniques, respectively [29].

Subzero Behavior of Water in Microemulsions

63

Analysis of low-temperature thermal events such as freezing and supercooling is important for understanding the behavior of water in microporous materials, gels, biological tissues, foods, and other microstructured ﬂuids at subzero temperatures [8].

IV.

METHODOLOGY

Low-temperature behavior of surfactant-based systems may conveniently be investigated by utilizing SZT-DSC. Such measurements are usually performed in either the exothermic (i.e., controlled cooling of samples) or endothermic (i.e., controlled heating of previously frozen samples) scanning mode. A characteristic feature of the exothermic mode is the supercooling (or undercooling) phenomenon. Under equilibrium conditions, water freezes at 0°C and ice is the stable phase at subzero temperatures. Usually, in the absence of ice crystallites, water will remain liquid below 0°C. The degree of this supercooling depends on factors such as the volume of water, its purity, and the cooling rate. Once frozen, this unstable, supercooled liquid state cannot be regained directly by heating; the ice must ﬁrst be melted at 0°C [30]. Actually, the melting of ice in a polycrystalline sample begins at subzero temperatures. The freezing point depression of water between ice crystals is due to the occurrence of hydration forces in thin ﬁlms of water. These forces cause the chemical potential and freezing point of water to decrease with decreasing ﬁlm thickness. Thus, the onset of ice melting (as determined by the beginning of the deviation of the endotherm from the baseline) occurs at about ⫺50°C [30]. In a similar way, the separation of ice from the aqueous solution is based on the generation of crystal nuclei, which are capable of growing into macroscopic crystals. Nucleation is a stochastic process caused by random density ﬂuctuations owing to Brownian diffusion of molecules and leading to the formation of a transient embryonic crystallite that has a sufﬁciently long lifetime for further condensation of molecules to occur. The nucleation probability at any subzero temperature is inversely proportional to the volume of the water droplets [31]. The almost inevitable presence of particulate matter leads to ice formation via a heterogeneous nucleation mechanism at a temperature that depends on the catalytic efﬁciency of the catalyst particle, its radius of curvature, and its degree of wetting by ice and water. For example, in suspensions of dipalmitoylphosphatidylcholine (hereafter designated as DPPC) vesicles, the formation of ice by such a mechanism occurs ﬁrst in the extraliposomal space at about ⫺20 to ⫺25°C. The remaining supercooled water will diffuse through the phospholipid bilayers to the ice-containing regions or will form ice between the bilayers via a homogeneous nucleation mechanism at about ⫺45 to ⫺50°C. The slower the cooling rate, the smaller the amount of water that will freeze after homogenous nucleation [30].

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In both modes, the calorimeter measures and records the heat ﬂow rate (dH/ dt) of the samples as a function of temperature T, while the samples undergo the aforementioned thermal events (in accordance with the respective scanning mode). The instrument also determines the total heat transferred in the observed thermal processes. The enthalpy changes associated with thermal transitions are evaluated by integrating the area of each pertinent peak [10]. DSC peaks obtained in the exothermic mode are sharper than those of the endothermic mode. This was ascribed to the effect that the substrate had on the melting process, while ice nucleation has preserved its autonomy [32]. Moreover, the overlapping of close peaks, which may occur in the endothermic mode, is not usually observed in the exothermic mode [8] (albeit peak overlap is still problematic in aqueous solutions of polyethylene glycols of sufﬁciently high molecular weights [33]). Cooling curves were utilized by de Vringer et al. [34]. However, the experimental determination of the enthalpy of fusion is difﬁcult, even if the effect of supercooling is allowed for [33]. On the other hand, it has been argued [35] that the exothermic scanning mode may be used to obtain microstructural information about microemulsions. In our opinion, such information should be treated with caution and be fully corroborated by independent techniques. Even then, we must often settle for something less than a detailed microstructural picture of microemulsions. The endothermic scanning mode is more frequently used to circumvent possible complications from supercooling. In the following, we show some of the results obtained in the endothermic mode for several types of (mostly) nonionic microemulsions. We followed the method used by Senatra et al. [2,9,11,36–39] in which the endothermic scanning mode was applied and the peaks representing various states of water were identiﬁed and analyzed. The simple but elegant way by which Senatra and coworkers solved the problem of identifying interphasal water in dodecane-containing systems should be noted. Both interphasal water and dodecane melt at about ⫺10°C, thus leading to overlapping of their fusion peaks. However, the existence of interphasal water may be clearly shown by taking the following into consideration [10]: 1.

The heat of fusion, measured at ⫺10°C, is higher than that required for the known amount of dodecane in the system. By subtracting the enthalpy change due to the dodecane, the contribution of the interphasal water is readily calculated by the equation [10] WI ⫽

∆H I (exp) ⫺ ∆H D f D ⫻ 100 ∆H I

(1)

where W I is the interphasal water concentration (in weight percent); ∆H I (exp) is the measured enthalpy change for the ⫺10°C peak, which includes contributions of interphasal water and dodecane; ∆H D is the heat of fusion

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of pure dodecane (191.6 J/g); f D is the dodecane weight fraction; and ∆H I is the heat of fusion of interphasal water. This enthalpy depends on the polymorphic form of ice that is assumed by the interphasal water at its freezing points. Some authors neglect the polymorphism of ice and use the crystallization enthalpy of water without introducing an appreciable error [40]. We followed Senatra et al. [26] and used the corrected enthalpy: ∆H I ⫽ 312.28 J/g. In some systems, part of the oil may be trapped between the alkyl chains of the surfactant. For example, in the system water–AOT (dioctyl sulfosuccinate)–isooctane, only about 50% of the oil contributed to the melting peak [41]. In such a case, an appropriate correction should obviously be applied. 2. The endothermic peak at ⫺10°C remained in the absence of dodecane or when hexadecane was substituted for dodecane [10,26,35,37,38,42] (see Fig. 2). 3. Analysis of samples in which D 2O was used instead of water, with all other components and compositions being the same, showed a typical shift of the D 2O-relevant endothermic peaks toward higher temperatures [2,10,11,35,36,39,41–47] (see Fig. 1). In a similar way, the concentration of free water is calculated, using the equation [8,10] WF ⫽

∆H F (exp) ⫻ 100 ∆H°F

(2)

where W F is the free water concentration (in weight percent), ∆H F (exp) is the measured enthalpy change for the 0°C peak, and ∆H°F is the heat of fusion of pure water, measured at the same experimental conditions. The heat of fusion of freezable water is slightly lower than that of pure water (about 334 J/g). We measured ∆H°F ⫽ 323.72 J/g [10,45]. A similar value (321 J/g) was extrapolated from data derived for the water–polyoxyethylene 1550 system during the heating stage of the DSC cycle [34]. Antonsen and Hoffmann [33] measured ∆H°F ⫽ 307 J/g. For our model system A (a quaternary microemulsion; see below) we obtained [45] ∆H°F ⫽ 308 J/g by a similar extrapolation procedure, in good agreement with our measured ∆H°F ⬃ 324 J/g for pure water [10,45]. Even lower values of ∆H°F were obtained in binary water–polymer systems by extrapolating ∆H I (exp) vs. polymer weight fraction (w 1) plots to w 1 ⫽ 0. Thus, for aqueous solutions of methoxypoly(ethylene glycol) 750 and polyoxyethylene 440, the extrapolated enthalpy of melting for pure water was 280 and 246 J/g, respectively [33]. For a polyoxyethylene 1550–water system investigated in the exothermic mode, the extrapolated ∆H°F was 289 J/g [34]. These rather low values were ascribed to overlapping between peaks of free and interfacial water. The same phenomenon occurs in biopolymers, and it was attributed to the presence of small amounts of solutes in the water [48].

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FIG. 2 Differential scanning calorimetric endotherms of the system K-oleate ⫹ hexanol 3: 5 (w/w)–hexadecane (samples a, b, c) or dodecane (sample d)–water. In all samples, the surfactant/oil weight ratio is 0.68 and the water concentration C was expressed as the weight ratio of added water to total sample. C a ⫽ 0.071, C b ⫽ 0.108, C c ⫽ 0.290, C d ⫽ 0.275; dT/dt ⫽ 4 K/min. ∆H x , ∆H b , (∆H w) 263, ∆H d , ∆H w, and ∆H h are the enthalpies of fusion for hexanol, bound water, interphasal water, dodecane, free water, and hexadecane, respectively. Note that the dodecane peak at 263 K superimposes on the peak of interphasal water shown for sample b. (From Ref. 38.)

Neglecting [34] the heat of mixing may also contribute to the decrease in ∆H°F : The area under the endothermic peak about 0°C represents the heat consumed in the melting of ice not to pure water but rather to water in a mixed phase. This contribution is, however, rather small [49]. For example, in 10% polyoxyethylene–90% water solutions, the correction is only 5 J/g [34]; for 50 wt% water–50 wt% polyoxyethylene, this correction is about 6 J/g [34]. When the decrease in the melting point of pure water is signiﬁcant, the following correction should be applied [50]:

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∆H F ⫽ ∆H°F ⫹ (C P,W ⫺ C P,I)(T f ⫺ 273.16)

(3)

where T f is the fusion temperature and C P,W ⫺ C P,I is the difference between the respective speciﬁc heats of liquid water and ice, which is usually taken as 2.3 J/(g ⋅ K) [34]. The original designation of the enthalpic terms was changed in order to adjust it to that of Eqs. (1) and (2). The correction for supercooling (including melting point depression) leads to ∆H°F ⫽ 325 J/g, using the exothermic mode for polyoxyethylene 1550–water systems [34]. Another prediction of the enthalpy of the ice–water transition in bulk is based on its lowering by about 1% per 1°C depression. With the addition of surface effects the apparent enthalpy may be lowered to about 200 J/g. Thus, the enthalpy of ‘‘ice’’ melting inside the aqueous spacing between bilayers of DPPC was evaluated as about 173 J/g [32]. An additional method for the determination of the bound water fraction is to use the equation [51] φ⫽1⫺

∆H m f ∆H w

(4)

where φ is the fraction of nonfreezing (bound) water, f is the weight fraction of water present in the sample, ∆H m is the measured enthalpy change, and ∆H w is the heat of fusion of pure water at 0°C (∆H°F in our notation). According to de Vringer et al. [34], the method based on Eq. (4) is very sensitive to small errors in the measured enthalpy changes or in the estimated water fractions for samples with a high water content.

V. INFORMATION OBTAINED VIA THE EXOTHERMIC SCANNING MODE In spite of the aforementioned complications, several studies have used the exothermic scanning mode to obtain more insight into the structure of microemulsions and to identify percolation processes in model systems.

A. Structural Transitions Senatra et al. [35] studied the system H 2O–hexadecane or dodecane–K-oleate– hexanol [with mass ratios K-oleate: hexanol ⫽ 0.6 and (K-oleate ⫹ hexanol): oil ⫽ 0.4]. They argued that the exothermic scanning mode may provide some information about the structural modiﬁcations occurring in the system as a function of water content. Typical thermograms recorded in the exothermic mode are shown in Fig. 3. The compositions of all the microemulsions tested lie along the dilution line PP′ (see Fig. 4).

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FIG. 3 DSC-exo recordings of the water in hexadecane microemulsion samples with increasing water content C (expressed as the weight ratio of added water to total sample). Concentrations: C a ⫽ 0.069, C b ⫽ 0.087, C c ⫽ 0.105, C d ⫽ 0.138, C e ⫽ 0.169, C f ⫽ 0.25; dT/dt ⫽ 2 K/min. The designation iso.T refers to a 10 min isothermal period that followed the dynamic part of the thermogram. ∆H h , ∆H w, ∆H b , and ∆H x are enthalpy changes relating to hexadecane, water, bound water, and hexanol, respectively. (From Ref. 35.)

The variation of water freezing temperature T wfz with (total) water content C is considered to provide structural information (see Fig. 5). The plateaus in Fig. 5 are thought to indicate microstructural transitions as summarized in Table 1. A basic question that might be raised here concerns whether objective criteria for establishing this quite detailed picture can be ascertained. We can seldom reach this level of description with regard to microstructure of surfactant-based systems when we rely on only calorimetric data. The salient features of such

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FIG. 4 Pseudoternary phase diagram of the water in hexadecane system. All measurements were performed in microemulsion samples whose compositions lie on the experimental path PP′. According to Clausse [52], line Γ 1 deﬁnes compositions at which all the available surfactant molecules are engaged in shells of W/O micelles possessing a core of ‘‘free’’ water. Line Γ 2 deﬁnes compositions at which the system forms nonspherical micelles or, more likely, micellar clusters resulting from the aggregation of spherical micelles that tend to ‘‘ﬂocculate’’ so as to offer the optimum surface-to-volume ratio. Dots on the PP′ line correspond to the composition of the samples at the intersection points between the PP′ line and the W/O microemulsion monophasic domain (dots 1 and 5) as well as between the PP′ line and the curves designated by Γ 1 and Γ 2. LC designates a liquid crystalline phase region. (From Ref. 35.)

structural transitions as those described in Table 1 should obviously be substantiated by more direct evidence. However, since the initial concentration of the surfactant on the dilution line PP′ is relatively high (weight fraction of 0.6 ⫻ 0.4 ⫽ 0.24), spectroscopic methods would fail to give accurate details. As an alternative (albeit similar) interpretation we would suggest that a plateau in a T wfz vs. C plot means that the strength of the water–surfactant interaction is approximately the same within the respective concentration subinterval. The difference between the plateaus just reﬂects the difference between various grades of such interactions, which may not be directly related to deﬁnite microstructures.

B. Percolation Transitions It is known [53–63] that percolation processes are revealed at certain volume fractions of droplets or at speciﬁc temperatures (designated here as T P). Senatra

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FIG. 5 Water freezing temperature T wfz versus increasing water concentration C for the water in hexadecane system. Values taken from DSC recordings performed at 2 K/min. The ﬁrst experimental point reported corresponds to the very ﬁrst exotherm observed at C b ⫽ 0.087. (From Ref. 35.)

et al. [41] showed that the thermal behavior of ‘‘percolative microemulsions’’ could be readily characterized. The ﬁrst-order exotherms associated with the freezing of the dispersed phase did not show a sharp, well-shaped peak but rather a distribution of thermal events that were not always well separated (Figs. 6–8). They interpreted these typical thermograms by assuming that the nonuniform water clusters (or pools) formed at temperatures close to T p freeze at different temperatures when the system undergoes the exothermic scanning procedure. The smaller the water cluster, the lower its freezing temperature. T p was identiﬁed using three methods [41]: 1.

2. 3.

Electrical conductivity measurements as a function of temperature. It is known that at a certain temperature (or volume fraction of droplets) the electrical conductivity increases sharply by several orders of magnitude [56–58]. Heat capacity measurements as a function of temperature [59]. DSC recording (dH/dt vs. dT ). T p is revealed as a peak in the plot.

≠0 ≠0 ≠0

0.122–0.198 0.198–0.273 0.273–0.355

(∆H w) 263

Interphasal water b

∆H h ⫽ ∆H°h ∆H h ⯝ ∆H°h ∆H h ⬍⬍ ∆H°h

∆H h ⫽ ∆H°h ∆H h ⫽ ∆H°h

Hexadecane c — Small ∆H w contribution 1st plateau 2nd plateau 3rd plateau

Enthalpy contribution 1st ∆H w exotherm ∆H w ≠ 0 ∆H w ≠ 0 ∆H w ≠ 0

(∆H w) fz

b

242 249 252

— 234

T wfz

DSC-EXO study d

(Total) water concentration (ⱕ)intervals within which typical thermal events occur. (∆H w) 263 ⫽ enthalpy change of interphasal water. (This type of water melts at 263 K). c ∆H°h ⫽ enthalpy change of pure hexadecane. d (∆H w) fz ⫽ enthalpy change of water at freezing. Source: Ref. 35.

a

— —

Free water

DSC-ENDO study

冧冧

From monodisperse W/O droplets to the appearance of larger droplets: prolate elipsoids (onset of bicontinuous structure?)

From hydrated soap aggregates to the onset of W/O microemulsions

Type of structure

Thermal Characteristics of W/O Microemulsions in the System Water–Hexadecane–K-Oleate–Hexanol

0.03–0.105 0.105–0.122

∆C a

TABLE 1

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FIG. 6 Top: DSC-exo thermogram of the system D 2O–sodium dioctylsulfosuccinate, hereafter designated as Na(AOT)–decane [volume fraction (water ⫹ surfactant)/total ⫽ 0.35; molar ratio of water to surfactant ⫽ 40.7]. The 4 K difference in the D 2O melting temperature with respect to that of H 2O helps to distinguish between the freezing contributions of water and decane (which, due to supercooling, freeze at about the same temperature) and shows the spreading of the exothermic peaks due to the freezing of the dispersed phase. Bottom: The corresponding endo spectrum compared with DSC recording of the system water–Na(AOT)–decane [volume fraction (water ⫹ surfactant)/ total ⫽ 0.35; water/surfactant molar ratio ⫽ 40.8]. The 10 min isothermal period that followed or preceded the dynamic part of the thermogram is also shown. (From Ref. 41.)

The use of SZT-DSC in relation to percolation transitions (which obviously occur at ambient temperatures) requires close scrutiny. The detection of T p is very sensitive to experimental conditions such as the type of surfactant, heating rate, and thermal history [41]. Thus, Senatra et al. could not detect the percolation transition a second time immediately after it had occurred (Fig. 9), implying that

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FIG. 7 DSC-exo (top) and endo (bottom) of two samples of the system water– Na(AOT)–isooctane [volume fraction (water ⫹ surfactant)/total ⫽ 0.31; water/surfactant molar ratio ⫽ 37]. The isooctane freezes at 145 K and thus does not inﬂuence the thermal behavior of the water phase. Curve 1, T 0 (the temperature at which the samples were kept isothermally at the very beginning of the DSC analysis) ⫽ 313 K; curve 2, T 0 ⫽ 300 K. The small exotherm in the melting curve is due to recrystallization. (From Ref. 41.)

liquid samples ﬁrst frozen and then thawed maintain the memory of their thermal history. Relying on these data to answer the question of how the microemulsion structure is altered due to freezing is not a simple matter. ‘‘Percolation’’ is a term frequently used to describe microemulsions as having a bicontinuous structure. However, ‘‘bicontinuity’’ describes a situation with dynamic equilibrium structure that results from a particular spontaneous curvature of the surfactant ﬁlms, with a minor contribution of the volume fraction of the speciﬁc solvent. Thus, at the same composition, different systems may have either water droplets, oil droplets, or a bicontinuous structure. ‘‘Percolation’’, on the other hand, describes

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FIG. 8 DSC-exo thermograms of the system water–Ca(AOT) 2 –decane. Microemulsions of this system do not percolate. Curve 1, T 0 ⫽ 308 K; curve 2, T 0 ⫽ 298 K; curve 3, T 0 ⫽ 283 K. (From Ref. 41.)

a process conceived as a temporary opening of extended pathways between droplets [64]. The difference between these two concepts was highlighted by using DSC measurements. Vollmer et al. [59] demonstrated that T p does not coincide with the temperature of formation of a single-phase bicontinuous structure, T b . In fact, T p may be several degrees below T b. All this may prima facie be considered not to be connected with SZT-DSC. Yet the very fact that a percolative transition was observed after the microemulsion sample had been frozen (and thawed) in the ﬁrst thermal cycle and the characteristic thermograms (Figs. 6 and 7) clearly show that the freezing process did not cause the microemulsion to separate into just oil and water bulk phases. This conclusion is further supported by the observation that microemulsion samples that had been quenched in liquid

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FIG. 9 (a) DSC recordings of the percolative transition in water–Na(AOT)–decane microemulsions. (1) T 0 (temperature of the isothermal stage at the very beginning of the DSC analysis) ⫽ 303 K, sample mass 18.250 mg; (2) T 0 ⫽ 278 K, mass 13.413 mg; (3) T 0 ⫽ 302 K, mass 10.259 mg. (b) Top: Onset analysis of the transition of curve 3 of part (a). Bottom: Curve 1, an oscillating trend obtained by measuring a second time the higher order phase transition with or without again following the temperature scanning procedure used for the detection of T p . Curve 2, an example of failure recorded on a sample of water–Na (AOT)–decane microemulsion [volume fraction of (water ⫹ surfactant)/total ⫽ 0.35; water/surfactant molar ratio ⫽ 40.8]. If a scan speed of 4 K/min is applied during the scanning procedure used for the determination of T p, the percolative transition escapes detection. (From Ref. 41.)

nitrogen did not phase separate. After several cycles of freezing and thawing, once melted, the samples that were marble white in their frozen state appeared newly isotropic and transparent. Only microemulsions with compositions close to the transition line between the one-phase and two-phase domains were unstable and phase separated [35]. The inability to detect T p in the consecutive thermal cycles may be connected with the presumed mechanism underlying the percolation transition. For example, Vollmer et al. [59] suggested that at room temperature surfactant molecules in the contact area of two droplets may be excited to ﬂip. This entropy-driven mechanism might fail if the heating rate in the thermal cycles were too fast for the water and surfactant molecules to reorganize themselves. More work is certainly needed to clarify this point. An additional underlying cause for this behavior may be the distillation of some free water from the aqueous system onto the lid of the sample pan and its subsequent freezing in the cooling stage of the DSC cycle. This amount of evaporated water (or part of it)

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might not participate in the dynamic processes that lead to percolation if the preceding isothermal step, 20 K below T p [41] is too short (only 10 min) [41]. Condensation and subsequent freezing of water on the DSC pan lid were also suggested as an explanation for the appearance of an ice-melting peak at about 0°C during the warming of frozen solutions of polyvinylpyrrolidone and hydroxyethyl starch [65] and in DPPC–water dispersions [30]. In our opinion, this evaporating water is free in the sense that it has virtually no interaction with the surfactant (or polymer) molecules. Such water molecules would melt at about 0°C even if they are not involved in the evaporation and condensation processes. Therefore, the relative distributions of free and bound water do not change. Our argument may prima facie seem to be hardly tenable, since it was found that the endothermic peak at about 0°C did not appear when the samples were covered by oil [30,66]. Yet a three-component [surfactant (or polymer)–water–oil] system does not necessarily have the same structure as the binary [surfactant (or polymer)– water] one. The addition of oil may restrict the mobility of both evaporating and nonevaporating ‘‘free’’ water molecules. The melting peak of ‘‘less free’’ water (for example, in a core of a W/O microemulsion before the inversion to an O/W microemulsion) shifts to lower (more negative) temperatures [10,45]. In such a case, it may merge into the broad endothermic peak of ‘‘bound’’ water. The general problem of phase separation, due to freeze–thaw cycles, is further discussed in the following section VII.H.

VI.

INFORMATION OBTAINED VIA THE ENDOTHERMIC SCANNING MODE

The endothermic scanning mode is more frequently used than the exothermic mode in SZT-DSC measurements. We exemplify the information that can be obtained from such a technique by reviewing some recent results related to several model systems based on various types of nonionic (and zwitterionic) surfactants that we studied with SZT-DSC.

A. Ethoxylated Alcohols System A. Water–pentanol ⫹ dodecane 1:1 (by weight)–octaethylene glycol mono n-dodecyl ether) [hereafter designated as C 12 (EO) 8]. This system was investigated along the water dilution line for which the surfactant/alcohol/ oil weight ratio is 2: 1:1. Henceforth, this dilution line is marked as W5 (see Fig. 10). System B. Water–butanol ⫹ dodecane 1:1 (by weight)–polyoxyethylene [10] oleyl alcohol [hereafter designated as C 18 :1 (EO) 10 or Brij 97]. This system was investigated along the water dilution line for which the surfactant/alcohol/

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FIG. 10 Phase diagram for the system dodecane ⫹ pentanol 1: 1 (by weight)–C 12 (EO) 8 – water at 27°C. The dashed line represents the water dilution line W5 along which the dodecane/pentanol/C 12 (EO) 8 weight ratio is 1: 1: 2. LC designates the liquid crystalline phase region. (From Ref. 67.)

oil weight ratio is 4: 3:3. Henceforth, this dilution line will be marked as XB4 (see Fig. 11).

B. Ethoxylated Siloxanes Another group of model systems was based on polymethylhydrogen siloxanes (PHMS) grafted with polyoxyethylene (POE). As a representative of this group we used the surfactant known by its commercial name Silwet L-7607 (molecular weight 1000; EO content 75 wt%). System C. Water–Silwet L-7607–dodecanol. This system was investigated along two water dilution lines for which the oil (dodecanol)/surfactant weight ratios are 1: 1 and 7: 3, respectively [46] (see Fig. 12).

C. Sucrose Esters Sucrose esters have two attractive properties: biocompatibility and temperature insensitivity [68–77]. We are investigating microemulsions based on sucrose esters in order to use them as microreactors for enzymatic and chemical reactions [42,78,79]. SZT-DSC has been applied to model microemulsion systems based on sucrose monostearate (HLB 15, also designated as S-1570). System D. Water–butanol ⫹ dodecane 1: 1 (by weight)–S-1570. The thermal behavior of this system was studied along two dilution lines for which the surfactant/alcohol/oil weight ratios were 0.94: 1:1 and 1.5: 1:1, respectively.

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FIG. 11 Phase diagram for the system dodecane ⫹ butanol 1: 1 (w/w)–Brij 97–water at 27°C. Along the XB4 water dilution line, the Brij 97/butanol/dodecane weight ratio is 4: 3: 3. LC designates the liquid crystalline phase region. (From Ref. 67.)

The respective initial concentrations of S-1570 on these dilution lines are about 32 wt% and 43 wt% (see Fig. 13). System E. Water–butanol ⫹ hexadecane 1:1 (by weight)–S-1570. This system was studied along the water dilution line 43 for which the surfactant/alcohol/ oil weight ratio is again 0.94 :1: 1 (see Fig. 14).

FIG. 12 Phase diagram for the system dodecanol–water–Silwet L-7607. Along the water dilution lines 1 and 2 the dodecanol/Silwet L-7607 weight ratios are 1: 1 and 3: 7, respectively. (From Refs. 46 and 47.)

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FIG. 13 Phase diagram for the system dodecane–butanol–S-1570–water. No attempt was made to further identify the liquid crystals (not shown) or any other phase within the two-phase area. The dashed lines represent the water dilution lines along which the dodecane/butanol/S-1570 weight ratios are kept constant at 1: 1: 0.94 (dilution line 32) and 1: 1: 1.5 (dilution line 43), respectively. (From Ref. 42.)

FIG. 14 Partial phase diagram for the system hexadecane–butanol–S-1570–water. The dashed line represents the water dilution line 43 along which the hexadecane/butanol/ S-1570 weight ratio is 1:1: 0.94. (From Ref. 42.)

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D. Phosphatidylcholine The zwitterionic surfactant phosphatidylcholine (PC) was used for the study of enzymatic hydrolysis reactions in microemulsions [80–82]. The oil used in all the investigated systems was tricaprylin (TC). System F. Tricaprylin ⫹ butanol (60 wt% in varying weight ratios)–PC (25 wt%)–water (15 wt%). System G. Tricaprylin ⫹ alcohol (60 wt%, molar ratio of 1:5, respectively)– PC (25 wt%)–water (15 wt%).

VII. RESULTS AND DISCUSSION In this section we describe some parameters relevant to water behavior at subambient temperatures that were evaluated by using SZT-DSC.

A. Variation of Water Peak Temperatures with Water Content The variation of the temperatures of the midpoints of the peaks related to water (bound, interphasal, and free) as a function of water content followed the same pattern: a gradual increase of the temperature to a less negative value and then a more or less constant temperature. Such behavior was observed for systems A [10], B [45], D [42], and E [42]; for the binary system water–C 12 (EO) 8 [45]; and for aqueous solutions of polymers (here as a function of the sorbed water content) such as poly(4-hydroxystyrene) [40] and mucopolysaccharides [83]. For example, system A has an endothermic peak at about ⫺10°C, which is ascribed to the melting of interphasal water (and dodecane). In fact, it begins at about ⫺12°C, increases in height with increasing water content, and levels off at about ⫺10°C, when (total) water content approaches 30 wt%. For the binary system water ⫹ C 12 (EO) 8, interphasal water melts between ⫺3 and ⫺4°C [45,84]. The case of system E is rather unusual. Increasing its (total) water content from 8 to 16 wt% gradually leads to the merging (or more precisely, superposition) of the melting peaks of the interfacial and free water at ⫺3 ⫾ 1°C (see Figs. 15a and 15b). A similar superposition of water melting peaks was observed for the xanthan– water system [85]. In contrast to system E, in the corresponding system D (where the hexadecane was replaced by dodecane) these melting peaks remain separate even at much higher concentrations [42] (see Figs. 15c and 15d). Two other related differences between systems D and E should be mentioned:

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FIG. 15a Thermograms for system E microemulsion samples with varying amounts of water along dilution line 43. Heating rate 5°C/min. (From Ref. 42.)

1. The maximum water solubilization is 80 wt% in system E and only 40 wt% in system D. 2. The ﬁrst observation of free water is at 14 wt% of (total) water in system D and at 16 wt% (i.e., the concentration at which the water melting peaks merge) in system E [42]. A similar difference in the appearance of free water was shown for the system AOT–isooctane or dodecane–water [27]. Thus, in the case of dodecane, all the water except for the last 6.5 water molecules freezes when the AOT reversed micelles are cooled down to ⫺50°C. The same applies to the isooctane microemulsion, where all the water except for the last 4.5 water molecules freezes when the AOT reversed micelles are cooled down to ⫺50°C. It was suggested that this effect is due to diminished penetration of the longer dodecane within the hydrophobic chains of AOT molecules [27]. On a molecular level, this phenomenon may be interpreted in terms of the Hou and Shah mechanism [86–88].

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FIG. 15b Melting temperatures of the interfacial water as a function of water content for system E along dilution line 43. (From Ref. 42.)

The reduced penetration of the oil into the alkyl chains of the surfactant (and the consurfactant) in the palisade layers of ternary (or quaternary) microemulsions tends to cause the interface to become less curved, thereby favoring the growth of the natural (or spontaneous) radius of curvature, R°, and the formation of larger W/O microemulsion droplets [89] as well as increasing the accessibility of the binding sites on the surfactant molecules. The merging of the water melting peaks in system E is yet to be investigated, but it may be associated with the presence of more butanol molecules at the interface relative to system D [42]. The amount of alcohol present at the interface of microemulsion systems increases with the chain length of the oil. Thus, we evaluated [45] the molar ratio of alcohol to surfactant, N A /N S, for the system water–C 12 (EO) 8 ⫹ hexanol (1:1)–oil, using an equation derived by Kunieda et al. [90] for the determination of the surfactant/alcohol weight ratio at the interface (for systems present on the border between Winsor III and Winsor IV). For heptane, N A /N S ⫽ 1.8; for decane, N A /N S ⫽ 2.4; and for hexadecane, N A /N S ⫽ 3.3. The role of alcohol in surfactant-based systems is discussed later in this review. Here it is sufﬁcient to say that alcohol molecules present at the interface of such a system may weaken the association between the surfactant and the outer interfacial water layers, although for the complete detachment of these

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FIG. 15c Thermograms for system D microemulsion samples with varying amounts of water along dilution line 43. Heating rate 5°C/min. (From Ref. 42.)

layers—thus transforming them to free water—a critical alcohol concentration is needed [45]. Another possible explanation that may help in understanding this phenomenon of merging melting peaks is that signiﬁcant microstructural changes must have occurred in view of the intensive water solubilization in system E.

B. Full Hydration of the Surfactant In system A the surfactant becomes saturated with water at N W/EO ⫽ 3, where N W/EO is the number of (interphasal) water molecules per ethylene oxide (EO) group of the surfactant. For this water/surfactant molar ratio, (total) water content is again about 30 wt%. A similar value was determined for the system water/dodecanol ⫹ polydimethylsiloxane 1:4 (by weight) [46,47]. The hydration of EO groups in surfac-

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FIG. 15d Melting temperatures of the free water as a function of water content for system D along dilution line 43. (From Ref. 42.)

tants and polymers has been amply investigated. Yet when values of N W/EO obtained in different systems by different techniques are compared, two points should be considered: 1. 2.

N W/EO depends signiﬁcantly on the method of measurement [91]. The value of N W/EO may be altered owing to factors such as temperature or qualitative and quantitative composition of the system.

Thus, for C 12 (EO) 8, N W/EO values lower than 5 but closer to 2–3 were measured by 17 O relaxation NMR [92], values between 2.6 and 3.3 by sedimentation [93], about 6 by micellar self-diffusion, between 3 and 4 by self-diffusion of water [91], and between 8 and 9 by self-diffusion of water, according to a cell model [94]. SZT-DSC was used for the determination of N W/EO in binary systems. For 70–90 wt% water–30–10 wt% C 12 (EO) 8, N W/EO ⫽ 4.3–3.7 [84]. For water– C 16 (EO) 20 and water–C 12 (EO) 23, N W/EO ⫽ 3.07 [16,44]. Much more attention has been paid to aqueous solutions of polyoxyethylene. For example, values of N W/EO ⫽ 2.3–3.8 (depending on molecular weight) were measured by SZT-DSC [33]; N W/EO ⫽ 2.8 [51]; N W/EO ⫽ 3 in crossed gels (even at 100°C) [95]; and N W/EO ⫽ 2–3 (depending on molecular weight) [96]. Similar values have generally been obtained also by other techniques: N W/EO ⫽ 3 by ESR

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and NMR; between 2 and 6 by the relaxation rate of 17 O and 2 H; between 5 and 6 by dielectric measurements; N W/EO ⫽ 6 by SANS; N W/EO ⫽ 2 by NMR and IR; and N W/EO ⫽ 2.9 by molecular simulation [97–100]. To summarize, for polyoxyethylene, N W/EO values ranging between 0.9 and 6 have been determined by using various techniques [97]. The close agreement between system A and the binary systems water–C 16 (EO) 20 and water–C 12 (EO) 23 may, prima facie, lead to the conclusion that the water–surfactant interaction is independent of the length of the hydrophilic headgroup of the ethoxylated surfactant and that the presence of pentanol (and dodecane) does not affect the interaction between water and the EO groups of nonionic surfactants. The picture, however, is not so simple, because long headgroups form coils in which water molecules may become trapped. These molecules do not interact directly with polar atoms of the headgroup, but nonetheless they form part of kinetic unit in the water–surfactant system, thereby increasing N W/EO [44]. Even for the relatively short surfactant C 12 (EO) 8 we ﬁnd that N W/EO for the binary system water– C 12 (EO) 8 is nearly twice that for the quaternary system (model system A). This observation was interpreted as being the result of the hexagonal liquid crystalline structure of the binary system: A considerable part of the interphasal water is trapped within the voids of the mesophase cylinders without being bound to a speciﬁc site on the surfactant headgroup. It should be emphasized that all interfacial (including the trapped) water manifests itself as a distinct endothermic peak at about ⫺3°C. Therefore, from the viewpoint of the intensity of the water– surfactant interaction, these two types of water states (trapped and directly bound to surfactant headgroups) should be treated as though there were no sharp distinction between them in the binary water–C 12 (EO) 8 system. The amount of water thus assigned to each EO group is on average larger than in the case of the quaternary system, leading to N W/EO ⬃ 5.7 [45]. Similar considerations apply to other water binding sites. For example, protein hydration is based on various types of sites: ionic, polar (EOH, ENH, ⬎CO), and apolar (hydrophobic hydration). The perturbation of water by the protein decays as a function of distance, and the decay function depends on the particular hydration site on the polypeptide chain [28]. Franks [28] even thinks that the expression of hydration numbers as the water/organic residue molar (or weight) ratio is ‘‘likely to be meaningless,’’ because some water is trapped randomly within the freeze-concentrated amorphous solid rather than being associated with speciﬁc polar sites. In our opinion, the crucial question is whether this trapped water manifests itself as a distinct melting peak during the heating stage of the DSC cycle (see below). The case of zwitterionic surfactants (such as in binary water–PC systems) is instructive. The ‘‘hydration shells’’ around the PC headgroups are reported to include between 1 [101,102] and 25 [103] moles of water per mole of lipid, utilizing various methods such as the isolation of mono- [102] and dihydrate of DPPC [104,105]; adsorption isotherms [106–109] and water distribution data

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for two-phase systems [110]; a radiotracer technique using gel ﬁltration [111]; hydrodynamic methods using viscosity [112,113] and ultracentrifugation [114] measurements; X-ray diffraction [102,115–118]; calorimetry [30,32,119–121] with different cooling protocols giving different results; and NMR spectroscopy [101,109,122–132]. This wide range of results extends from tightly bound [‘‘inner shell’’ or ‘‘nonfreezable’’ water (see below)] to weakly bound water intercalated between phospholipid bilayers. The motional characteristics of this ‘‘trapped’’ water approach those of free water. There is also a rapid exchange (⬎10 4 s ⫺1) between trapped and bound water molecules [133]. The different results may reﬂect different phospholipids (synthetic and natural phosphatidylcholines) or different binding sites (phosphate [101,127,132,133] or trimethylammonium [132,133]; for example, using 2 H NMR relaxation and intensity measurements, it was argued that ﬁve to six water molecules reside near the (CH 3) 3 N group and only one or two water molecules are associated with the PO 4 group [132]; and different structures (which may have different cross sections for the headgroups and alkyl chains of the lipids and different degrees of tilt [117] such as anhydrous crystals, small spherical micelles in organic solvents, lamellar liquid crystals, and vesicles [133]. For instance, Nagle and Wiener [118] inferred from various diffraction data that 8.6, 13.6, and 23 water molecules are bound per DPPC molecule in the C (crystal, L c), G (gel, L β′), and F (ﬂuid, L α) phases, respectively. Another problem is the experimentally difﬁcult detection of the onset of phase separation between water and phospholipid units [119]. Yet remarkable agreement was achieved between the various hydration numbers. Based on the different rotational correlation times, it was found that the innermost hydration shell of PC consists of one tightly bound molecule. The main hydration shell consists of 11–12 water molecules per lipid [133]. This is the minimal number of water molecules needed to construct a hydrogen-bonded hydration shell around the phosphorylcholine headgroup according to space-ﬁlling molecular models [123]. This hydration number was derived from the results of X-ray diffraction [115], proton NMR [123,124], and 2 H NMR [122,125,130] data and measurements of the diffusion coefﬁcients of 3 H-labeled water [132]. From DSC measurements [102,120,122] a range of 11–15 mol water per mole of lipid is obtained. Hydrodynamic techniques give about 25 mol water/mol lipid as the total hydration, but this hydration number reduces to 12–16 when allowance is made for the water in the core of the lipid aggregate. The water in excess of 24 mol water/mol lipid is free, being outside the phospholipid bilayers and exchanging only slowly (⬍10 2 s ⫺1) with the water (trapped and bound) incorporated within the hydrated bilayers. A ratio of 12 mol water/mol PC was also obtained for the quaternary system F by plotting the free water content as a function of tricaprylin (TC) content in the organic phase of the microemulsion sample and extrapolating it to 100% TC (no butanol) as seen in Fig. 16.

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FIG. 16 Variation of free water content as a function of tricaprylin (TC) content in the organic phase of a microemulsion sample containing TC⫹butanol (60 wt% in varying weight ratios), PC (25 wt%), and water (15 wt%).

By subtracting this amount from the ﬁxed water content, the amount of water bound to PC alone is readily evaluated [82].

C. Free Water Free water is usually detected by DSC at higher water/surfactant ratios, i.e., when the surfactant is virtually fully hydrated. Such a behavior was observed for the system AOT–dodecane or isooctane–water [27], for system B [45], for the system PC–TC–butanol–water [82], for model systems D and E [42], and for the related system water–butanol ⫹ medium chain triglycerides (MCT) ⫹ sucrose monostearate (SMS) ⫽ 1: 1:1 (by weight) [79] also using SZT-DSC. In the last case, free water is detected at higher (total) water content when the butanol/ MCT/SMS weight ratio is 3:1:1 and at lower (total) water content when SMS is replaced by glycerol esters, which have far fewer hydroxyl groups available for binding water [79]. However, free water is sometimes formed while the surfactant is still not fully hydrated. The apparent plateau in the plot of interphasal

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water content versus (total) water concentration for system A (Fig. 6 in Ref. 10) is a demonstration of this phenomenon [45], which will be treated in more detail elsewhere. The same concurrent formation of free and bound water was shown for the gel phase of the DPPC–water system. A deconvolution analysis of the ice melting peak in the relevant DSC thermograms has indicated that in a ‘‘pre-region’’ for which the water/lipid molar ratio N w is in the range 8 ⬍ N w ⬍ 15, free water is formed together with freezable (i.e., bound) interlamellar water [134]. DPPC becomes fully hydrated at N w ⫽ 15. At this stage, there are ﬁve nonfreezable interlamellar water molecules, ﬁve freezable interlamellar water molecules, and ﬁve free water molecules per lipid [134]. In the sugar ester-based model systems D and E, the binding sites of the surfactant are seven hydroxyl groups, three β etheric oxygen atoms, and one ester group. At saturation, 11–13 water molecules are bound to each surfactant molecule. Assuming that these three types of binding sites are equivalent as far as the formation of hydrogen bonds with water is concerned, the ‘‘bound’’ water/sucrose ester binding oxygen atom molar ratio is approximately 1 [42]. Recently, the same behavior was demonstrated for the system water (NaCl 8%) ⫹ decane 1:1–butanol–N-octylribonamide (C 5 N 8), by using 1 H chemical shift and relaxation time data. At saturation, the molar ratio of ‘‘bound’’ water to OH groups is again about 1 [135]. This is somewhat surprising, as usually the water solubilization behavior revealed by spectroscopic techniques is entirely different. Thus, NMR [14] (Fig. 17), time domain dielectric spectroscopy (TDS) [136], ESR [137], and Fourier transform infrared (FTIR) [15] measurements indicate that upon the addition of even a small amount of water, an equilibrium between free and bound water is established. This apparent discrepancy is readily understood because the spectroscopic techniques sense the water molecules most near the surfactant. On the other hand, DSC ‘‘regards’’ the binding of water molecules (which is conceived of as a restriction imposed on their mobility) in terms of interference with their freezing at 0°C [14]. The formation of a reservoir of free water in systems A and B is accompanied by signiﬁcant microstructural changes [67,138–141]. The water reservoirs (cores) swell until an inversion from a W/O to an O/W microemulsion occurs at 55– 60 wt% and 60–65 wt% of (total) water for systems A and B, respectively [67]. This conclusion, which was corroborated using electrical conductivity [140], DSC [10], and NMR [14] data for system A and electrical conductivity, DSC, and viscosity data [67] for system B, is at variance with a postulated inversion at 20–30 wt% water for system B, as was suggested (incorrectly in our opinion) by Usacheva et al. [142]. Another type of subzero temperature behavior of water was demonstrated for systems based on oligomeric ethoxylated siloxanes (system C [46,47] and the

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FIG. 17 Fraction of bound water (α) as a function of the water/surfactant molar ratio (W o) for system A, along the water dilution line W5. (䊊) DSC data [45]; (䊉) NMR data [14]. (Results based on chemical shift measurements were taken from Fig. 7 in Ref. 14 and reduced to scale. The decrease of α with the increase of W o is slower when α is evaluated from T 1 relaxation time data; see Table 2 in Ref. 14.)

system [143] water–copolymer Ketjenlube 522 ⫹ dimethylaminoethanol (3 :1), respectively, (by weight)–toluene along the water dilution line for which the (surfactant ⫹ cosurfactant)/oil weight ratio is 4:1). These systems, because of geometrical restrictions of the amphiphiles and the nature of their curvature, which prevents inversion, cannot further solubilize water in the surfactant aggregate’s core and phase separation results. A similar phenomenon was observed for systems based on the siloxane surfactant L77-OH [144] and on C 12 (EO) 5 [145,146].

D. Nonfreezable Water Surfactant–water association may lead to the formation of ‘‘nonfreezable water,’’ which can obviously be detected by SZT-DSC only in an indirect manner. This term is often deﬁned too loosely. Sometimes, any water that does not freeze at about 0°C is considered to be nonfreezable, thus obscuring the important distinction between the various types of bound water. A more plausible way to make this distinction is to choose an arbitrary, very low temperature, say ⫺100°C, as

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a threshold value. The existence of nonfreezable water in an aqueous system maintained above this temperature may be indicated in two ways: (1) by the absence of water-related DSC peaks or (2) by a signiﬁcant difference between the total water content of the system and the amounts of free and bound water evaluated from their respective peaks. Two cases may be discerned concerning the inability of DSC to directly detect nonfreezable water: 1.

2.

There are water molecules that interact so strongly with the surfactant headgroups that they cannot undergo a water–ice transition (i.e., they never freeze). Sometimes this strong interaction is due to the formation of a deﬁnite, stable hydrate. There are water molecules that might, in fact, crystallize (and melt), but these processes are not revealed by calorimetric techniques. The underlying reason is that such changes in the state of water would be observed at very low temperatures and with very weak enthalpy of transition, leading to such a poor calorimetric signal that it could not be detected [119].

The virtually ultimate limit to freezing is set by the glass transition. As the system is cooled to low temperatures, the water transforms from a ﬂuid whose viscosity rises to very high values via a viscoelastic ‘‘rubber’’ to a brittle solid (‘‘glass’’). ‘‘Glass’’ is, in fact, a very viscous supercooled liquid with a ﬂow rate of 1–10 µm/yr. At this stage, freezing has become so slow that it can no longer be detected on a measurable time scale [31]. In some cases, both NMR and DSC techniques have been used to determine the amount of nonfreezable water. For example, pulsed NMR relaxation data for the hydrated copolymer poly(N-vinyl-2-pyrrolidone/methyl methacrylate) allow one to estimate the relative fractions of three distinguishably different types of water [147]: (1) tightly bound (type B) at speciﬁc polymer sites, such as carbonyl groups; (2) more loosely bound (type A) that is more moderately inﬂuenced by the polymer matrix, for example, multilayer water and water in interstices; and, in samples with water content in excess of about 76 wt%, (3) bulk-like water that freezes at the vicinity of 273 K. Both type A and type B, which have nearly the same energy, are nonfreezable in the accepted sense of the term but undergo glasslike transitions at 170–200 K. NMR is sensitive to both type A and type B, whereas DSC is sensitive only to type A and correspondingly predicts a lower estimate for the amount of nonfreezable water [147]. The amount of nonfreezable water (deﬁned relative to a very low temperature, e.g., ⫺100°C) may be determined by plotting the total melting enthalpy of water per unit weight of sample versus the sample composition and extrapolating to zero enthalpy [8], i.e., the nonfreezable water content is equated with the maximum amount of water for which no enthalpic peak has been detected [147]. We used a material balance method for this determination. During the investigation

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of systems A and B by SZT-DSC [10,45], we determined, among other things, the amounts of bound (‘‘interphasal’’) and free water for all the compositions studied. Using the equation W NF ⫽ W T ⫺ (W B ⫹ W F)

(5)

where W NF, W T, W B , and W F are the weights of nonfreezable, total, bound, and free water, respectively, per sample, the amount of nonfreezable water is readily calculated. In the case of water–polymer systems, W T was determined gravimetrically, and the amount of freezable water was computed from the peak area by using the heat of fusion for bulk water, ∆H°F ⫽ 333.2 J/g. This method was considered to be ‘‘clearly incorrect’’ [147]. In our opinion, even if this high value of ∆H°F were used, an indication for the absence of nonfreezable water might be achieved when W T ⬃ W B ⫹ W F. More accurate estimations of W NF can be obtained by using our Eqs. (1) and (2). Another indication of the presence of nonfreezable water is the appearance of bound water fusion peaks only after the total water content has reached a threshold value. This phenomenon was observed for several aqueous polymer solutions [40,85,148–150]. It should, however, be noted that for high water content microemulsions, as the surfactant is already saturated, all added water, either before the inversion to O/W microemulsions or after it, is free. The bound water fraction α ⫽ W B /W T then becomes smaller and smaller, and the error in determining W B from the area under its corresponding DSC peak is rather high. The difference W T ⫺ (W F ⫹ W B), which according to Eq. (5) would be equal to W NF, may in such cases just reﬂect a higher experimental error. Thus, the existence of nonfreezable water cannot be inferred from Eq. (5). Yet for water-rich microemulsions (especially after inversion), the formation of nonfreezable water is hardly conceivable. Schulz [8] suggests two mechanisms for the formation of nonfreezable water: 1. Water may exist in very small clusters centered on hydrophilic groups or ions. These clusters may be too small to form nuclei for ice formation. In some cases, water may be too viscous and vitriﬁcation occurs instead of crystallization, since diffusion becomes rate-limiting rather than nucleation [8]. 2. The hydrogen bond network typical of structured water is disrupted by energetically favored ion–water interactions. The presence of nonfreezable water was demonstrated, e.g., in binary ionic surfactant–water systems with surfactants such as AOT [151], sodium dioctylphosphinate [152], didodecyldimethylammonium bromide [44,45], and dioctadecyldimethylammonium bromide [44]. In the binary water–PC system the values for tightly bound water and the ‘‘inner hydration shells’’ show a much larger spreading (relative to those for

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ordinary and loosely bound water; see above) depending on the physical techniques used. The values vary between 1 and 6 mol water/mol lipid [133]. However, there is no sharp border between nonfreezable and bound water. Bronshteyn and Steponkus [30] argue that overestimates of the unfrozen water content of DPPC liposomes are obtained owing to an erroneous determination of the baseline of DSC thermograms and to the dependence of the amount of water that freezes during cooling on the thermal history of the sample. Using an iterative procedure for a correct estimation of the baseline in the DSC thermograms and a three-step protocol of temperature change, they obtained hydration numbers of 4.7 and 5.6 mol water/mol DPPC for suspensions containing 30–70 and 16.2 ⫾ 0.2 wt% water, respectively. Gru¨nert et al. [153] used dielectric spectroscopy, X-ray diffraction methods, and DSC runs to show that DPPC–water mixtures with more than seven H 2 O molecules per molecule of lipid undergo a phase transition at subzero temperatures. Below the transition temperature, only seven H 2 O molecules per lipid remain between the bilayers and seem to be nonfreezable, at least down to ⫺40°C. The amount of bound water that exceeds these seven H 2 O molecules per lipid is thought to be squeezed out of the interbilayer regions together with the free water, which exists in samples with concentrations ⱖ15 H 2 O molecules/lipid [153]. However, the number of nonfreezable water molecules was only inferred from ˚ (typical of water– the jump of the interlamellar repeat distance from about 75 A DPPC mixtures with ⱖ15 mol water/mol lipid and of temperatures ⱖ0°C) to ˚ (typical of DPPC–water mixtures with fewer than seven H 2O moleabout 58 A cules per molecule of lipid and of temperatures lower than 0°C). On the other hand, the enlarged inset of thermogram 1a in Ref. 153 clearly shows an endothermic peak below 0°C of bound water superimposed almost completely on the free water melting peak at about 0°C. Due to the supercooling effect (which is not mentioned explicitly in Ref. 153), this bound water peak may be identical with the unexplained peak IV that appeared at about ⫺40°C during the cooling DSC run of the same sample (Fig. 1b in Ref. 153). If all bound water (except for seven H 2 O molecules per lipid molecule) were squeezed out of the interbilayer regions (as was assumed by Gru¨nert et al.), then no bound water peak could be detected by DSC measurements. It is more plausible that the seven H 2 O molecules per lipid constitute ‘‘real’’ nonfreezable water (which is not detected by DSC) and freezable interlamellar water (to which the above-mentioned melting peak below 0°C may be ascribed). This number is to be compared with the ﬁve nonfreezable water molecules per molecule of lipid plus ﬁve freezable interlamellar water molecules per molecule of lipid that were evaluated by Kodama and Aoki [134] for the gel phase of the ˚ (⫽ 65 ⫺ 58) DPPC–water system, using a deconvolution analysis. The ⬃7 A decrease in the interbilayer distance is then due to the loss of ﬁve molecules of

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free water per molecule of lipid that are present in the preregion 8 ⬍ N W ⬍ 15 [134] (see above). The behavior of ethoxylated alcohols depends on the length of their hydrophilic headgroup. Although there is no clear evidence for nonfreezable water in systems A [10,45] and B [45], nonfreezable water has unequivocally been observed in related systems such as the binary systems C 12 (EO) 23 (Brij 35)–water [44,45] and C 16 (EO) 20 (Brij 58)–water [44]. It is assumed [154] that some water is trapped in the helicoidal structure adopted by long polyoxyethylene hydrophilic chains. The space available for the trapped water is very restricted. Thus, the water–surfactant interaction may be strong enough to prevent the water from freezing. The short headgroups of C 12 (EO) 8 (system A) and C 18: 1 (EO) 10 (system B) do not form such coils [155] (system B can form only one coil at most; see below), and thus no nonfreezable water is expected [10]. The same considerations apply to model systems D and E [42].

E. Evaluation of the Thickness of the Bound Water Layer The thickness of the bound water layer in surfactant-based systems may be evaluated by several methods. In this review we focus on one that was originally derived from the interaction of interfacial water with solid surfaces. Gilpin [156] suggested the power law δµ w ⫽ al 0⫺α

(6)

where δµ w is the chemical potential of interfacial water; l 0 is the distance from the water/substrate interface (i.e., the thickness of the water layer adhered to the substrate); and a and α are adjustable parameters (α is usually taken as 2). Thus, δµ w and the freezing point depression ∆T of interfacial water decrease with l 0 [156]. On the basis of this power law and thermodynamic considerations the following equation was derived for planar bilayers [121]:

冢冣

∆T min l ⫽ 2 α⫹1 0 ∆T max L

α

(7)

where ∆T min is the highest melting point of ice (the position of the endothermic peak of free water), ∆T max is the maximum depression of the freezing point of water in the presence of the bilayers (the position of the endothermic peak of interphasal water), and L is (for microemulsion systems, which have such a bilayered microstructure) the thickness of the (total) water layers, alternating with surfactant (together with oil and alcohol) layers [10,45]. For system A, a local lamellar structure was directly imaged for the ﬁrst time by cryo-transmission

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electron microscopy (cryo-TEM) [138] along the water dilution line W5 (between about 20 and 60 wt% water). The existence of this structure was corroborated by data obtained from several techniques, including small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS), NMR, and electrical conductiv˚ ity [45,138,140,141]. L was evaluated from SAXS data, leading to l 0 ⬃3–6 A for 30–50 wt% of (total) water [10]. Other methods gave (for system A) about ˚ ; i.e., two monolayers of interphasal water are closely associated with the 5A surfactant. For the reversed micellar system of AOT–isooctane or cyclohexane– ˚ [157]. water, the bound water layer thickness lies between 3 and 5 A ˚ A thickness of about 5 A was evaluated for water freezing at ⫺10°C in cells of organic tissues [158]. The thickness of water layers freezing at temperatures ˚ [159]. between ⫺6°C and ⫺10°C on mineral surfaces lies in the range of 5–8 A ˚ A thickness of 4.5–6 A per two layers of bound water was determined for proteins [48] and clays [160]. Similarly, the thickness of the interfacial water layer in cylindrical pores was estimated to be 0.54 ⫾ 0.10 nm [161,162]. This determined thickness of the bound water layer is speciﬁcally related to the freezing of water. Thicker layers have been evaluated by deﬁning other characteristic properties of bound water and using various experimental techniques. For example, a thickness close to 10 nm (36 water molecules) has been suggested as the distance over which the cooperativity of hydrogen bonding extends [163].

F.

Alcohol Interaction with Other Constituents

It was demonstrated for system A that although pentanol enhances water solubilization and is present at the interface, its interaction with water or surfactant is not revealed by SZT-DSC. This point has been investigated in the same way as the water–surfactant interaction [10]. We determined the concentrations of pentanol from the measured enthalpy change associated with the pentanol peak and the enthalpy change associated with pure pentanol. The derived concentrations were compared with the actual concentrations determined gravimetrically (see Table 2) [45]. These results suggest that no evidence for interaction of pentanol with water or surfactant can be found in SZT-DSC measurements [10]. Two arguments may be suggested to explain this behavior [45]: 1.

The amount of alcohol that is present at the interface is rather small. Thus, for system A, the interfacial molar ratio of pentanol to C 12 (EO) 8 is 2 at most [140]. Pentanol has only one hydroxyl group (residing, in contrast to the hydrophobic alkyl chain of the alcohol, at the hydrophilic side of the inter˚ 3 [164], while the much bulkier (moface), whose molecular volume is 17 A ˚ 3 [165]) headgroup has eight or nine binding sites. lecular volume ⬃508 A The surfactant has then a higher probability of interacting with water.

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TABLE 2 Pentanol Concentration in Microemulsions of System A Along the Dilution Line W5 Total water concentration (wt%) 2.9 10.0 20.1 22.9 25.0 35.3 45.0 47.9 51.9 58.0 79.9

Pentanol concentration (wt%) Determined gravimetrically

Evaluated from SZT-DSC data

24.2 22.5 20.2 19.4 18.7 16.0 13.7 13.1 12.0 10.5 5.1

22.8 23.8 19.1 20.9 18.4 14.8 13.6 12.8 11.9 10.3 4.5

2. When water competes with alcohol for the binding sites of the surfactant, the alcohol is rejected from the solvation shell. This type of behavior was demonstrated for several systems [135,166]. TDS measurements indicate a possible migration of alcohol from the interface to the oil phase as a preliminary step before the inversion (to O/W microemulsions) in systems A and B [136]. It can then be suggested that alcohol affects water solubilization via indirect mechanisms. Alcohol adsorbs at the interface and makes it more ﬂexible. In addition, alcohol molecules may function as spacers for the surfactant molecules, thus making more room for the formation of the water core typical of swollen micelles and microemulsions. Alcohol may also affect the distribution of (total) water between the free and bound states. It was shown [45], for example, that the swelling of a ﬁxed amount of 1: 1 (by weight) water–C 12(EO) 8 mixture with increasing amounts of 1:1 (w/w) solution of pentanol ⫹ dodecane led to the formation of free water above a threshold concentration of the alcohol (Fig. 18). It should be stressed that in this case the relative amount of (total) water was constantly decreased upon the addition of pentanol (and dodecane). Nevertheless, when the pentanol concentration reached a certain value, some of the (bound) water became free. This phenomenon may be interpreted by assuming that the pentanol molecules residing at the interface distort the three-dimensional tetrahe-

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FIG. 18 Variation of interphasal and free water content as a function of pentanol content along a swelling line on which pentanol ⫹ dodecane 1: 1 (w/w) solution is added in increasing amounts to a ﬁxed amount of 1: 1 (w/w) water–C 12(EO) 8 mixture. (䊊) Free water; (䊉) interphasal water. (From Ref. 45.)

dral network of water about the surfactant headgroups, thereby tearing the outer water layers [45]. The same phenomenon was observed in system G. The alcohols used were ethanol, butanol, and hexanol, and free water content increased in that order [82]. In contrast, it was found, for sucrose ester–based microemulsions, that at the same total water content the formation of free water will be inhibited as a function of alcohol hydrophilicity (i.e., the effect will be inversely proportional to the alcohol chain length) and concentration [79]. This is understandable in view of the increased solubility of shorter alcohols in water. Alcohol also strengthens the interaction of the surfactant with water molecules adjacent to it. This is revealed by the shift of the endothermic peak (ascribed to interphasal water) toward more negative temperatures upon the addition of alcohol. We showed this behavior for system A (peak at about ⫺10°C) compared with that of the binary system water–C 12 (EO) 8, which has an endothermic peak at ⫺3 to ⫺4°C (see above). It was found that the effect of alcohol becomes more pronounced as the alcohol chain shortens. This phenomenon was observed for bound (and interphasal) water endothermic peaks in systems A and B [45] and in systems D and E [42]. However, the melting temperature of bound water in these systems levels off at a

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certain alcohol chain length. In system A, for example, this plateau is formed at ⫺10°C, beginning with butanol [45]. We assume that melting temperatures on the plateau characterize systems in which the alcohol operates via its adsorption at the interface. On the other hand, the variation of the melting points (before the plateau) as a function of alcohol chain length is typical of water-soluble alcohols. These alcohols may affect water binding via cyclic intermediates like that suggested by Bastogne et al. [135]. The variation of the melting temperature of bound water depends on the relative roles of both surfactant and alcohol in determining water binding. For example, C 18: 1 (EO) 10 (Brij 97) is a commercial product that has headgroups of varying lengths. Water may then be trapped in the voids formed between these nonuniform headgroups. Using NMR [167], the same effect was shown for commercial Triton X-100. In addition, the 10 EO groups may form one coil [155], within which water may be caged. It was argued that a stable trihydrate (melting at ⫺10°C) is formed in a water–polyethylene oxide system, where the molecular weight of the polymer is ⱖ440 [i.e., at least 10 monomers, having the same length as the headgroup of C 18 :1 (EO) 10] [168]. Even if we assume that Brij 97 is not able to form such a deﬁnite structure in the four-component system B, the surfactant still has one more way of stabilizing the system that is not applicable to polyethylene oxide. C 18: 1 (EO) 10 has a long hydrophobic chain [relative to C 12 (EO) 8, for example], which is better dissolved in oil and thus helps to stabilize the quaternary system. It may also be suggested that the unsaturated alkyl chain of Brij 97 can induce a more favorable arrangement of its headgroup, leading to more hydration of the surfactant. A similar phenomenon was observed in a system based on polyoxyethylene (20) sorbitan. The measured molar ratio of bound water to EO group, N W/EO, was 4.42 when the hydrophobic residue was monolaurate, increasing to N W/EO ⫽ 6.07 for monostearate and to N W/EO ⫽ 8.84 for monooleate [169]. That is for surfactants having the same headgroup, the degree of hydration is determined by the hydrophobic residue, being higher for the unsaturated alkyl chain of oleyl alcohol as in Brij 97 [45]. Indeed, the variations of the melting temperature of bound water as a function of alcohol chain length is much less prominent in system B (based on Brij 97) than in system A, where C 12 (EO) 8 plays only a minor role in determining water binding [45]. In contrast to water-insoluble alcohols (like pentanol in system A), the melting peaks of water-soluble alcohols in quaternary systems (like butanol in system B) do not coincide with those of the corresponding pure alcohols. The same behavior was observed in system F [82]. Even in a 2.5 wt% water–butanol solution, the melting peak of butanol disappears, presumably because water molecules break the alcohol chain–like structure [82]. Increasing the TC/butanol weight ratio in system F leads to the formation of more free water at the same ﬁxed (total) water content [82]. This phenomenon, which deserves further study, may be assigned to factors such as diminished water solubilization in the continuous phase or a

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migration of butanol from the interface. Such a migration may weaken water– surfactant interactions that are mediated by water-soluble alcohols (see above). Comparing the systems 30 wt% PC/(TC ⫹ butanol) ⫽ 1:9 (w/w)–water and 20 wt% PC/(TC ⫹ butanol) ⫽ 3:1 (w/w)–water, we found that in both systems the free water content increased as a function of (total) water added but was higher by 3–5 wt% in the alcohol (and surfactant)-poor system [82]. These results are readily explained just by the higher proportion of bound water (i.e., leaving less free water) in the surfactant-rich system. Simple calculations have shown that the alcohol contribution in this case was rather small, even though the difference in butanol content between the two systems is 2700% [82]. We have shown (Fig. 18) that adding pentanol (and dodecane) to ﬁxed amounts of 1:1 (w/w) water–C 12 (EO) 8 mixtures leads to the formation of free water above a threshold concentration of pentanol. In these PC-based systems, the amount of water is constantly increased and, moreover, butanol is considerably dissolved in TC. Thus, the alcohol can hardly reach the threshold concentration presumably needed for the tearing off of outer water layers and for the formation of free water. Surfactants behave virtually the same as water-soluble alcohols. Thus, pure C 12 (EO) 8 melts at ⫹29.5°C, but its melting point shifts to 18°C or 13°C [45], and this melting peak is reduced or even disappears when the system contains water, as a result of their interaction [10]. The effect of water is also manifested at ambient temperatures. For example, the melting temperatures of both the alkyl chains and the polar headgroups of monosodium n-decanephosphonate and disodium n-decanephosphonate decrease in the presence of water, the effect being inversely proportional to water content [170]. Similar behavior is observed for transitions such as solid to liquid crystal or gel to liquid crystal occurring in binary systems of water and surfactants such as dioctadecyldimethylammonium bromide [171] and didodecyldimethylammonium bromide [16,44]. It is thought that the introduction of water weakens the ionic layer and disrupts the crystalline structure of the surfactant, thereby leading to reduced melting points [170,171].

G. Exothermic Peaks The a priori surprising appearance of exothermic peaks during the heating of previously ‘‘frozen’’ samples was ﬁrst reported by Luyet et al. [172] for aqueous solutions of glycerol, ethylene glycol, and polyvinylpyrrolidone (PVP). Similar peaks were observed in the ternary systems H 2O–NaCl–glycerol and H 2O– NaCl–dimethyl sulfoxide (DMSO) [173]. This phenomenon was also reported in binary systems of water and synthetic polymers such as polyethylene oxide [33,34,96,174,175], PVP [174,175], and poly(vinyl methyl ether) [174,175]. Such exothermic peaks also occurred in cross-linked hydrogels of dextran [176], hydrogels of poly (2-hydroxyethyl methacrylate) [147,177,178], concentrated aga-

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rose gels [179], hydrogels of xanthan [85], hydrogels of guar and of polyacrylamide ⫹ a cross-linker (e.g., chromic nitrate) [180], gelatin, and urea-(but not SDS-) denatured globular proteins in water [174,175], The position and size of the exothermic peaks depend on structural and chemical factors such as the nature of the polymer, its structure and degree of cross-linking, the size of pores available for water within the cross-linked network of the polymers, water content, and the presence of additives (such as silver iodide crystals, which inhibit supercooling) [174,175]. The exothermic peaks are also affected by thermal factors such as the cooling and subsequent heating rates and the number of freeze–thaw cycles. We observed such exothermic peaks in some microemulsion systems based on ethoxylated polymethylsiloxanes (Silwets) [46,47], ethoxylated alcohols [e.g., C 18: 1(EO) 10 (Brij 97), but not C 12(EO) 8!] [45], and sucrose esters [42]. For example, exothermic peaks were observed in system C (surfactant/oil ⫽ 3:7, by weight) with 10–20 wt% water (Fig. 19).

FIG. 19 Thermal behavior of microemulsions prepared with dodecanol and Silwet L7607 at surfactant/oil weight ratio of 3:7 and in the presence of 10, 20, and 30 wt% solubilized water (heating rate 3°C/min). (From Refs. 46 and 47.)

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Comparing sucrose esters with the same headgroup but different hydrophobic tails has led us to the notable observation that in the system dodecane ⫹ butanol ⫹ sucrose ester (1: 1:1.5, w/w)–water, only with the most hydrophilic surfactant, sucrose laurate (L-1695), is an exothermic peak observed (Fig. 20). In the sucrose laurate–based system, the exothermic peak disappears as water content approaches 30 wt% (Fig. 21). When an exothermic peak appears, heat is given off during the warming period, in apparent contradiction to the Le Chatelier principle [175]. Luyet et al. [172] explained this phenomenon on the basis of a devitriﬁcation process, contending that a prior rapid cooling converts normal liquid water to amorphous ice and that it is the transformation of this vitreous ice into normal ice I during rewarming that gives rise to the heat-releasing exothermic peaks [172,175]. This explanation was refuted by Zhang and Ling [174,175], who stressed (along with other evidence) the fact that polymer–water systems cooled to ⫺70°C remain viscous liquids and not solid vitreous ice. They offered the explanation that in the presence of certain polymers of suitable concentration, the bulk of water does not exist as normal liquid water but rather in the state of polarized multilayers (which, in fact, we may envisage as ‘‘bound’’ or ‘‘interfacial’’ water).

FIG. 20 Thermal behavior of microemulsions prepared with sucrose ester ⫹ dodecane ⫹ butanol (1.5: 1: 1, by weight) in the presence of 16 wt% solubilized water (heating rate 5°C/min). L-1695 ⫽ sucrose laurate; M-1695 ⫽ sucrose myristate; P-1670 ⫽ sucrose palmitate; S-1570 ⫽ sucrose stearate. (From Ref. 42.)

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FIG. 21 Thermal behavior of microemulsions prepared with L-1695 ⫹ dodecane ⫹ butanol (1.5 : 1:1, by weight) in the presence of various amounts of added water (heating rate 5°C/min). The thermogram for 16 wt% water is identical to that of L-1695 in Fig. 18. (From Ref. 42.)

The restricted motion of water molecules in this state forms a substantial energy barrier that impedes the transformation of this water into ice I. Two ways may be suggested to overcome this energy barrier: increasing temperature and lengthening the time of exposure to the low temperatures of the cooling stage in the endothermic mode of SZT-DSC. This interpretation may help us to understand the thermal behavior of system B along the dilution line XB4 (Figs. 22a and 22b). The crystallization of a commercial surfactant like Brij 97 on cooling is hindered by the presence of entrapped water (and, in quaternary system B, of dissolved butanol too) within the voids formed between the unequal headgroups and by the nonuniformity of the chains of the surfactant itself. Heating the system leads to the release of surfactant molecules. The subsequent glass transition is sometimes reﬂected as a broad step in the thermogram (not seen in Fig. 22). Such a step was observed between ⫺80°C and ⫺70°C in the polyethylene oxide–water system [96]. Additional heating accelerates the rearrangement of surfactant molecules into a regular crystalline structure, thereby giving rise to the heat-releasing exothermic peak at ⫺75°C in system B (Fig. 22a) and at about 60°C in the binary Brij 97–

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(a)

(b) FIG. 22 Thermograms for a system B microemulsion sample lying on the dilution line XB4. (a) Composition (in wt%): dodecane, 22.4; butanol, 22.4; Brij 97, 30.0; water, 25.2. Heating rate 3°C/min. (b) Composition (in wt%): dodecane, 18.0; butanol, 18.0; Brij 97, 24.0; water, 40.0. Heating rate 3°C/min. (From Ref. 45.)

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water system. The water concentration in both systems is about the same, but the surfactant concentration in the binary system is nearly 2.5 times as high as in the quaternary system. These exothermic peaks did not shift to lower temperatures when the water was replaced by D 2O [45]. For comparison, an exothermic peak at ⫺53°C in the polyethylene oxide–water system was ascribed to eutectic polyethylene oxide [181]. It may be assumed that the exothermic peak in system B and in its binary counterpart is due rather to the crystallization of the surfactant headgroups. A difference between the melting points of the polar headgroups and alkyl chains of the same surfactant was observed at ambient temperature in a hydrous surfactant such as C 18(EO) 7 [182] and sodium dioctylphosphinate [152] and in hydrated surfactants such as monosodium n-decanephosphonate and disodium n-decanephosphonate [170]. The difference between our quaternary and binary systems is attributed to the presence of butanol in system B. Alcohol molecules participate in retarding the crystallization of, presumably, surfactant headgroups, thus leading to a lower temperature exothermic peak in the quaternary system. Further heating induces more motional freedom (both translational and rotational) for the surfactant and water molecules. These molecules reorient themselves in unison, leading to the crystallization of a hydrate that may have a deﬁnite structure. In system B and in the Brij 97–water system, the corresponding exothermic peaks were observed at about ⫺46°C, and in both cases the peaks were shifted to less negative temperatures when D 2O was substituted for the water [45]. Such a water-related exothermic peak was observed between ⫺50°C and ⫺40°C in many systems. For example, in system C microemulsions (based on polymethylsiloxanes), this exothermic peak was observed at ⫺45°C (Fig. 19). In sucrose ester–based microemulsion systems, it was observed only for sucrose laurate (the most hydrophilic surfactant investigated in this study [42]), and it shifted from ⫺35°C to ⫺42°C as water content increased from 10 wt% to 22 wt% (Figs. 20 and 21). In a polyethylene oxide–water system (where the polymer crystallizes at ⫺53°C), the water-related exothermic peak was observed at ⫺44°C [181]. In other reports it was observed between ⫺44°C and ⫺38°C [174], at ⫺50°C [33], at ⫺41°C [183], and between ⫺40°C and ⫺50°C [34]. In a xanthan–water system, this exothermic peak was observed between ⫺40°C and ⫺50°C [85]; in water–chromium nitrate (cross-linker)–guar systems, it was observed at ⫺35 ⫾ 5°C [180]; in hydrogels of poly(2-hydroxyethyl methacrylate) [177] at ⫺40°C; and in water–sodium cellulose sulfate systems at ⫺43°C [150]. Obviously, the peak temperature and size depend on many experimental variables, and crystallization temperatures were also observed outside the range of ⫺50°C to ⫺40°C. Further heating should melt the hydrate. The endothermic peak at ⫺25°C in system B (Fig. 22a), which is the direct continuation of the exothermic peak at ⫺46°C, may be interpreted in this manner. The temperature range

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between ⫺46°C and ⫺25°C indicates the strength of surfactant–water interaction in the system, because if ordinary ice were formed at ⫺46°C, just a slight warming would sufﬁce to melt it. A signiﬁcant temperature difference between related exothermic and endothermic peaks was also observed in a 55 wt% C 12 (EO) 23 (Brij 35)–water binary system sample (Fig. 23). There is a 50° difference between the water-related exothermic peak at ⫺59.4°C and the endothermic peak at ⫺9.5°C. It seems that the relatively long headgroups of Brij 35 inhibit water crystallization more than the shorter headgroups of Brij 97 [45]. This suggestion may be further supported by the observation of some nonfreezable water in Brij 35–water systems [16,44,45]. The same phenomenon also occurs in polymer–water systems. For example, in a polyethylene oxide–water system, crystallization was observed at ⫺44°C, with melting occurring between ⫺30°C and ⫺22°C [181], or crystallization at ⫺41°C, with melting at ⫺8°C [183]. A more complicated behavior is exhibited in Fig. 24. In Fig. 24 it may be seen that one water-related exothermic peak is split into two peaks at ⫺72°C and ⫺68.2°C. Splitting of exothermic peaks was also observed in some compositions of water–nonionic polyacrylamide–ammonium nitrate (cross-linker) [180] and in the recrystallization of amorphous cellulose at

FIG. 23 Thermogram for a 55 wt% C 12 (EO) 23 (Brij 35)–45 wt% water system sample. Heating rate 3°C/min. Note the broad step (ascribed to the glass transition of the surfactant) near the exothermic peak. (From Ref. 45.)

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FIG. 24 Thermogram for a Brij 35-based quaternary system sample. Composition (in wt%): Brij 35, 34.9; water, 35.1; dodecane, 15.2; pentanol, 15.0. Heating rate 3°C/min. (From Ref. 45.)

elevated temperatures [184]. These two peaks may be ascribed to the interaction of water with different headgroups of the commercial surfactant Brij 35. The temperatures of both exothermic peaks are lower (more negative) than that observed in the absence of pentanol (Fig. 23). It seems that pentanol molecules adsorbed at the interface retard the reorganization of both Brij 35 and water. In Fig. 24 small water-related exothermic peak is observed at ⫺28.7°C. This peak may represent the crystallization of an additional amount of freezable water that melts at ⫺13.8°C just after it has crystallized [45]. Another distinction between the exothermic peaks at ⫺75°C and ⫺46°C in system B is revealed upon the addition of water. The temperature of the surfactant-related peak increases (i.e., it becomes less negative) while the temperature of the water-related peak decreases (i.e., it shifts to more negative values). A possible interpretation is that as more water interacts with the surfactant, the reorientation of surfactant molecules (as a preliminary stage before crystallization) will be more restricted so that higher temperatures will be needed. On the other hand, at higher water content, more water molecules will be available for the formation of a hydrate by interacting with surfactant molecules. Less energy will then be required, and accordingly the hydrate will crystallize at a lower temperature [45].

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The exothermic peaks vanish upon the formation of free water (compare Figs. 22a and 22b). The same phenomenon was observed for Brij 35-based systems (Fig. 25). At such a relatively high water content, there are no exothermic peaks. The endothermic peaks at ⫺10.4°C and ⫺3.0°C were ascribed to interphasal and free water, respectively [45]. It is easily understood that at high water content some water molecules have such freedom of motion that they are more eligible for freezing (crystallization) in the initial cooling run of the SZT-DSC cycle, giving rise, therefore, to melting peaks of free and interphasal water in the subsequent heating stage [45]. In a similar way, the exothermic peak in hydrogels of dextran disappears (or becomes very small) when the pores of the cross-linking network are large [176]. In system C [Silwet L-7607/dodecanol ⫽ 3:7 (w/w)], the exothermic peaks observed at 10 and 20 wt% water disappear at 30 wt% (Fig. 19). These exothermic peaks are also absent from the 50% water–Silwet L-7607 binary system [47]. Another way to dispose of (or diminish) exothermic peaks is to cool the system slowly in the initial state of the SZT-DSC cycle. For example, a system B microemulsion sample containing (in wt%) 30.8 Brij 97, 23.2 butanol, 23.1 dodecane, and 22.9 water was cooled to ⫺120°C at a rate of 100°C/min and then heated back to ambient temperature at a rate of 3°C/min. Two exothermic peaks were observed, at ⫺73°C and at ⫺40°C, in addition to the usual endothermic peaks at ⫺25°C and ⫺11°C. Another sample of the same composition was cooled to

FIG. 25 Thermogram for a Brij 35-based binary system sample. Composition (in wt%): Brij 35, 35.0; water, 65.0. Heating rate 3°C/min. (From Ref. 45.)

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⫺120°C but this time at a rate of 5°C/min. As the sample was heated back to ambient temperature at the rate of 3°C/min, the exothermic peaks disappeared altogether [45]. However, in some polymer–water systems, the appearance of exothermic peaks does not depend on rapid cooling. For instance, a 250-fold slowdown of the cooling rate did not alter the exothermic peaks of a 50% poly(vinyl methyl ether) aqueous solution [175]. In such a case, the favored way (besides heating) to achieve the transformation from the ‘‘chilled multilayer state’’ [175] to the (ordinary) ice I state is to lengthen the time of exposure to the minimal (most negative) temperature of the SZT-DSC cycle. This prolonged exposure enables all the water molecules to cross the energy barrier and to gear themselves (albeit slowly) toward the more stable state of ice I [175] and, in many systems, toward various types of ‘‘bound’’ water, which have deﬁnite freezing (and melting) temperatures.

H. The Problem of Phase Separation The usefulness of SZT-DSC hinges on the solution of the problem of extrapolating low-temperature data to ambient temperature. It is surprising, therefore, that this question rarely merits a short discussion, let alone a detailed analysis, in relevant papers and reviews. The main argument against the use of SZT-DSC in the investigation of microemulsions is that the cooling and freezing of an equilibrated microemulsion system might lead to phase separation as has been observed in numerous cases [185– 187]. Obviously, such a frozen phase-separated mixture of water, surfactant, and oil (and, in many cases, cosurfactant) cannot be deﬁned as a microemulsion even though the same composition would unequivocally be regarded as a microemulsion at room temperature. Yet this is not always the case. The degree and rate of phase separation is a function of several factors such as the microemulsion stability, the water-to-surfactant ratio, and the cooling temperature. Thus, depending on the kinetics (which are expected to vary from system to system), the DSC experiment may be probing—at one extreme—a frozen high temperature structure or—at the other extreme—an intensive phase separation, or perhaps some intermediate situation. Cooling a microemulsion may also cause a phase transformation. Thus, the reversed micelles in the AOT–isooctane–water system are spherical at 20°C but become rodlike at ⫺15°C and below [187]. Another instance is related to system A microemulsions, which, upon cooling, have been transformed to lamellar (L α) and hexagonal (H I ) liquid crystalline phases as was conﬁrmed by using smallangle X-ray scattering (SAXS) data (Figs. 26a, 26b). It is seen that whereas at room temperature only a single scattering peak is observed, cooling the sample to 4.5°C leads to the appearance of two scattering peaks separated by a distance typical of lamellar phases [45,140]. In a similar

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FIG. 26 Variation of scattering intensity I(q) as a function of the scattering vector q for a system A microemulsion sample having the composition (in wt%) C 12 (EO) 8, 45; pentanol, 15; dodecane, 15; water, 25. (a) 23°C; (b) 4.5°C. (From Ref. 45.)

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case, a microemulsion sample containing 48 wt% C 12(EO) 8, 10 wt% pentanol, 10 wt% dodecane, and 32 wt% water was cooled to ⫺14°C and transformed to a hexagonal (H I ) liquid crystalline phase. The surfactant surface areas thereby calculated ﬁt well into the pattern set by the other samples (of the same quaternary system), which are liquid crystals at room temperature [45,140]. Our efforts are therefore aimed at demonstrating that though phase separations and transformations are frequently observed upon cooling of microemulsion systems, as far as surfactant–water interactions are concerned SZT-DSC measurements give reliable results. Our arguments are based on three proofs: 1. Analysis of DSC endotherms utilizing the ability of the DSC instrument to distinguish between free and bound water 2. Similarity in the thermal behavior of binary and multicomponent systems 3. The effect of different oils on the thermal behavior of otherwise identical systems The ﬁrst proof is the most conclusive. When the water content of a microemulsion system is gradually increased, it is usually observed that the surfactant interacts with the added water, and only after it becomes fully (or almost fully) hydrated is free water formed and detected as a melting peak (providing the endothermic mode is used) at about 0°C (see above). It is not possible that free water is formed but not revealed by this peak. In most cases, no peak of free water is seen before the saturation of the surfactant. If the phase separation that evidently occurs during cooling can lead to the detachment of water molecules that are already bound to the surfactant headgroups, and thereby to the inevitable formation of free water, then this speciﬁc water should be detected by SZT-DSC in two ways: (1) the appearance of a freezing (melting) peak of free water, as we have shown, and (2) the vanishing of (or signiﬁcant decrease in) the bound (or interfacial) water peak. Moreover, we may also safely rule out the opposite possibility—that free water that has been formed during the equilibration of the microemulsion sample at room temperature would rather interact with surfactant molecules at subzero temperature during the cooling stage of a DSC experiment and become bound water. The very fact that before the saturation of the surfactant no peak of free water is seen while the peak of bound water steadily increases clearly shows that free water is not formed by breaking off the surfactant–(bound) water interaction but rather by the addition of water to a fully (or almost fully) hydrated surfactant. This free water is inevitably formed at room temperature (during the preparation and equilibration of the microemulsion samples) before the beginning of SZTDSC measurements. The phase separation should then be conceived, in our opinion, as a segregation of some (or all) of the pure (free) components (water, oil, or alcohol) of the microemulsion. Our argument implies that the distribution of bound and free water in a microemulsion system does not depend on the degree

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of phase separation [10,45]. More light may be shed on this understanding of SZT-DSC data by examining the interaction of water with individual surfactants (and, for that matter, with other organic compounds having hydrophilic groups— polymers, proteins, etc.). We ﬁrst exemplify our ideas using system A. In this system, the DSC results demonstrate that no free water is detected below about 30 wt% of the total water [10], whereas in the binary counterpart [water–C 12 (EO) 8 mixtures] no free water is detected below about 60 wt% of the total water (!) [44]. The same water content at surfactant saturation was observed in the water–C 16 (EO) 20 system [44]. In the binary system water–C 12 (EO) 8, interphasal water indeed melts at about ⫺3°C, but when free water forms it melts at about ⫺1°C [45]. It may then be concluded that the freeze–thaw process imposed on the interphasal water clearly does not cause water segregation. At higher water concentrations, free water begins to appear. The interphasal water concentration (relative to the constant total weight of the microemulsion) is not altered. Yet its fraction in total water content constantly decreases as more and more free water is formed. Thus, a gradual decrease of its peak (at ⫺10°C) is expected and observed [10,45]. The amount of total water (revealed as free water) equals, more or less, that of added water plus the ﬁxed amount of interphasal water at saturation, for each microemulsion sample. It is most probable that free water at subzero temperature maintains the form of ice lumps within what is called (when the sample is kept at room temperature) a ‘‘microemulsion core,’’ or as an outer ice shell after the inversion to an O/W microemulsion. The thermal behavior of system A is then quite clear: Free water is not formed by breaking off the surfactant–(bound) water interaction but rather by the addition of water to a fully hydrated surfactant. The problem of phase transformation is more complex. We have already shown that system A microemulsions transform to liquid crystalline phases upon cooling. Such a transformation could, in principle, lead to a change in the bound and free water distribution in the system. In our opinion, the onus of proof that, in such a case, bound water is torn away from the surfactant and transforms into free water rests with the claimant. Indeed, in the case of the DPPC–water system, Gru¨nert et al. [153] argued— relying on X-ray diffraction data—that bound water is squeezed out of the interbilayer regions. We, on the other hand, have tried to show that the expulsion of only free water is sufﬁcient to interpret their data (see above). In the case of system A, no such attempt was made. Since no free water melting peak is detected below 30 wt% of total water, the only discussible argument might be that water, which is presumably free in the microemulsion at ambient temperature (before the surfactant has become saturated), interacts with the hydrophilic headgroups during the phase transformation. This argument is refuted by using room temperature electrical conductivity data, which show a sharp increase beginning at about 30 wt% water [45,140]. Moreover, at about 55–60

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wt% water, system A is inverted from a W/O to an O/W microemulsion, as has been conﬁrmed with room temperature NMR [14] and electrical conductivity [140] data as well as SZT-DSC measurements [10]. The same agreement between ambient temperature methods such as electrical conductivity and viscosity [67] and SZT-DSC [45,67] was also observed for system B (see above). We may then safely conclude that although system A undergoes a phase transformation at low temperatures, its free and bound water distribution is not changed. It is thus obvious that ‘‘suspected’’ systems should be individually analyzed according to these principles in order to interpret their SZT-DSC data. Another piece of evidence showing that bound water is not separated by cooling is based on the similarity between binary (water ⫹ surfactant) and multicomponent (surfactant ⫹ water ⫹ oil, with the possible presence of a cosurfactant) systems in thermal behavior. For example, the data derived from an isotropic three-component micellar dispersion of the AOT–isooctane–water system [12] (which was cooled to ⫺40°C and thus phase separated) were in good agreement with the DSC results obtained from aqueous AOT dispersions containing no organic solvents and forming lamellar (smectic) phases. Both kinds of dispersions gave a consistent set of data from which it can be concluded that about six water molecules are bound per AOT molecule. This water was unfreezable in AOT reversed micelles (presumably due to supercooling that took place in the submicroscopic droplets of AOT reversed micelles) but froze in the lamellar phase (with peaks at ⫺7°C and ⫺11°C) [12]. This behavior may alternatively reﬂect the weakness of surfactant–water interactions in binary systems relative to the same interactions in multicomponent systems, as we have shown for system A (see above). Similar behavior of related binary and quaternary systems was shown for phosphatidylcholine (PC). In contrast to the AOT-based system, where NMR data indicated 13 bound water molecules per AOT molecule, compared with only six as revealed by DSC measurements [12], several experimental techniques (including 2 H NMR and DSC; see above) show that, on average, about 12 molecules of water per PC molecule are bound in binary PC–water systems [133]. The same ratio was determined for the quaternary model system F [82] (see above). It should be noted that the evidence based on the similar behavior of binary and multicomponent systems is only signiﬁcant after the fact. This is because, as we have seen, there need not, a priori, be any relationship between the hydration properties of the compared systems. For instance, N W/EO for the binary C 12 (EO) 8 –water system is almost twice that of the quaternary model system A [45]. We explained this behavior on the basis of the different structures of the systems, which were ﬁxed during the preparation and equilibration of the samples at room temperature. The third proof is related to the effect of different oils on the thermal behavior of a microemulsion system as revealed by SZT-DSC. Oil may be indirectly involved in surfactant–water interactions. Thus, in the system AOT–dodecane–

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water, all the water, except for the last 6.5 water molecules, freezes when the AOT reversed micelles are cooled to ⫺50°C. The same applies to the AOT– isooctane–water system, where all the water, except for the last 4.5 water molecules, freezes when the AOT reversed micelles are cooled to ⫺50°C. It was suggested that this effect is due to the diminished penetration of the longer dodecane within the hydrophobic chains of AOT molecules [27]. Obviously, the degree of penetration is determined at room temperature, when the oil molecules have great freedom of motion and are not in their frozen state. This phenomenon may be interpreted in terms of the Hou and Shah mechanism [86–88] (see Section VII.A). This behavior was conﬁrmed at room temperature, e.g., for the system C 18 :1 (EO) 10 (Brij 97) or C 18(EO) 10 (Brij 76)–butanol ⫹ oil 1: 1 (by weight)–water [89]. Water solubilization goes through a maximum in such cases because of the opposite effect of the critical radius R c , which limits the increase of the droplet size due to interdroplet attractive interactions. As shorter chain oils penetrate more easily, water solubilization controlled by R c will increase with the decreasing length of the oil molecule. The reasoning underlying this proof is eventually based, as a little reﬂection will show, on our argument that the interaction between the microemulsion components will preferentially occur at ambient temperature. An interaction that is not possible at room temperature will not occur at subzero temperature either. As for oil, prima facie objection to what we argued may be made. In the case of a signiﬁcant difference between the melting points of the alcohol and the oil, it may happen that at some temperature during the heating stage of the SZT-DSC cycle, the water, alcohol, and surfactant (or at least its polar headgroups) will be in a liquid state encapsulated within a core crusted over with solid oil. Such an aggregate is obviously different from an ordinary microemulsion, so a totally different distribution of water states might be expected for the capsule and the microemulsion. Nevertheless, we again contend that the distribution of the water states, even in such an encapsulated system, was determined at room temperature before the DSC experiments were conducted. Let us ﬁrst take a hypothetical case, where excess liquid alcohol is contained in the capsule together with water and surfactant. If the alcohol could interact in any way with water or surfactant at subzero temperature, it would have undergone the same interaction, faster, at room temperature. The reason for this is that usually the oil is not directly involved in interactions with the polar headgroups of the surfactant, and even less with water. (The relatively rare case of system C, in which the oil itself interacts with surfactant or water, is analyzed in the following.) Obviously, the alcohol cannot cause a saturated surfactant to bind more water, nor can it detach (free) water from a partially hydrated surfactant. Thus, in a microemulsion sample containing 18.6 wt% hexadecane, 18.6 wt% pentanol, 37.2 wt% C 12(EO) 8, and 25.6 wt% water, only two melting peaks were observed: one at ⫺10.4°C for interphasal water and one at ⫹15.3°C for hexadecane. This

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oil is, of course, still frozen at 0°C. C 12(EO) 8 is almost fully hydrated at this (total) water concentration; nonetheless, free water is not detected yet [10,45]. The case of system F also supports our argument. The oil (TC) is still frozen at 0°C, but the distribution of bound (to surfactant and alcohol) and free water is such that the amount of water bound to PC agrees with that determined for the corresponding water–PC binary system by both 2 H NMR and DSC. As was evidenced by the shift in its melting point and by the decrease in its enthalpy of fusion, the oil (dodecanol) in system C participates, to some extent, in the structure of the aggregated system and, unlike many other oils in W/O microemulsions, does not behave as a free, continuous-phase oil. The penetration of the OH groups of the oil into the water phase facilitates the formation of structures capable of solubilizing signiﬁcantly more water [46,47]. One may ask how this behavior is to be reconciled with the fact that dodecanol melts at ⫹24°C so that it is still frozen in the temperature range within which bound water melts. If water and oil molecules compete for available binding sites on the surfactant, then the immobilization of dodecanol might lead to enhanced water–surfactant interactions that should be reﬂected in higher N W/EO values. Since such arguments have been raised in relation to system C, we shall treat them in more detail. First, it should be emphasized that there can be no free water at ambient temperature available for additional binding to the surfactant after the thawing of all components, except for the oil. If the dodecanol–Silwet L-7607 interaction is the favored one at room temperature and it prevents the water from replacing the alcohol, then why does the same water at subzero temperatures ‘‘prefer’’ to reject the dodecanol (and ‘‘succeed’’) instead of crystallizing as stable ordinary ice? The observation of the reduced enthalpy of fusion of dodecanol and the shift of its melting point to lower temperature implies that this oil (alcohol) participates in some kind of interaction with the surfactant, or rather with water. Should such an interaction occur, the bound water would not be torn off from the surfactant, as no free water melting peak is observed. The same consideration applies to the oil. If all dodecanol is free of any interaction, then it should melt only at its usual melting temperature, with unreduced enthalpy of fusion. So, the frozen dodecanol (which melts only at ⫹24°C) is that part of the oil which is not involved in any interaction.

VIII.

CONCLUSION

In this chapter we surveyed the use of SZT-DSC in recent investigations of microemulsions. Two factors combine to militate against the more frequent use of this technique in microemulsion research. First, a great deal of careful work is required to obtain insight into the nature of interactions between microemulsion components and, especially, into the role of water in such interactions. Second,

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subzero data must be extrapolated in order to predict microemulsion behavior at ambient temperature. This problem takes on added poignancy with the welldocumented observation that microemulsions can phase separate at low temperatures. Before recalling the ways that have allowed us to validate the conclusions reached by way of the SZT-DSC data, it is worthwhile to stress that the data derived from SZT-DSC refer to concept such as bound and free water that have operational deﬁnitions based on the low temperature behavior of water. For example, water in which the thermodynamic properties have been sufﬁciently modiﬁed that it remains unfrozen at subzero temperature may be called bound water [10]. Sometimes it is difﬁcult to conﬁrm data, such as the amount of bound water in a microemulsion sample, by using independent techniques that operate at ambient temperature. However, as was shown in this review, a close agreement of such techniques and SZT-DSC was obtained, for instance, regarding the evaluation of the water concentration range within which an inversion (from W/O to O/W microemulsions) occurs. We maintain that a central key to justifying the use of SZT-DSC data lies in recognizing that the interactions between the components of microemulsion samples are ﬁxed during the preparation and equilibration of the microemulsions before application of the freeze–thaw cycle. The distribution of the various water states is not altered, and thus useful information about the microemulsion system can be safely obtained. Moreover, this conclusion is, in our opinion, virtually inevitable in light of the operational deﬁnitions of bound and free water. The surfactant–water interaction is manifested by the interference with the melting of frozen water at 0°C. SZT-DSC shows only the degree of this interference. Thus, the freedom of ‘‘free’’ water molecules assumed to form at room temperature is revealed only at subzero temperatures. When we say that a certain amount of water is free at room temperature, we only mean that after being frozen this water will melt at about 0°C. Had we used another experimental technique to determine the distribution of the various water states, the same water might be considered as bound.

ACKNOWLEDGMENTS We thank Dr. I. Tiunova for her careful experimental work pertinent to many microemulsion systems described in this review and Dr. G. Berkovic for critical reading of the manuscript and helpful discussions.

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181. B Bogdanov, M Mihailov. J Macromol Sci Phys B 26:59 (1987). 182. JA Bouwstra, DA van Hal, HEJ Hoﬂand, HE Junginger. Colloids Surf A 123–124: 71 (1997). 183. NB Graham, M Zulﬁker, NE Nwachuku, A Rashid. Polymer 30:528 (1989). 184. M Kimura, T Hatakeyama, J Nakano. J Appl Polym Sci 18:3069 (1974). 185. PL Luisi, LJ Magid. CRC Crit Rev Biochem 20:409 (1986). 186. M Zulauf, H-F Eicke. J Phys Chem 83:480 (1979). 187. P-O Quist, B Halle. J Chem Soc Faraday Trans I 84:1033 (1988).

4 DSC Analysis of Surfactant-Based Microstructures PABLO C. SCHULZ Departamento de Quı´mica e Ingenieria Quı´mica, Universidad Nacional del Sur, Bahı´a Blanca, Argentina J. F. A. SOLTERO and JORGE E. PUIG Departamento de Ingenierı´a Quı´mica, Universidad de Guadalajara, Guadalajara, Mexico

I. Introduction II.

Experimental and Theoretical Remarks

122 123

III. Heat Capacity and Other Thermodynamic Properties

124

IV.

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The Phase Diagram

V. Thermal Transitions Detected in Phase Studies A. Melting B. Liquid crystal transitions C. Vaporization D. Decomposition E. Vesicles and liposomes VI.

VII.

Micellization of Block Copolymer Surfactants A. Effect of other surfactants on block copolymer micellization

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Emulsions

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VIII. The State of Water in Surfactant-Based Systems IX.

132 132 141 142 143 143

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Lowering of the Melting Point

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References

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I. INTRODUCTION Differential scanning calorimetry (DSC) is widely used for studying binary and multicomponent systems containing surfactants. Transition temperatures and enthalpies are often determined and used to draw the limits of existence of the different phases of surfactant-based systems [1–6]. The state of the surfactant molecules in these phases is studied by means of thermal analysis [7,8]. DSC is also a useful technique to obtain information about the phase diagrams of surfactant-based systems and the various microstructures formed in these systems. The properties that can be obtained from DSC for binary systems are the following [6]: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Type of phase transition (isothermal or nonisothermal, transformation of one phase into another or a three-phase process) Temperatures of invariant transitions, initial and ﬁnal temperatures for univariant phase transitions Phase boundaries, extent of heterogeneous regions, coordinates of invariant points for a complete phase diagram consistent with the phase rule Enthalpies of phase transitions; Tamman triangles and enthalpies of threephase processes Speciﬁc heats of systems in homogeneous states Heat capacity of systems in heterogeneous states Heat capacity jumps taking place when the number of phases present in the system changes Three-dimensional diagrams of the dependence of the system heat capacity on temperature and composition Differential entropy and enthalpy of dissolution of one phase in another

In particular, the enthalpies of invariant processes (melting of pure substances, eutectic and peritectic points, extreme phase transition temperature, etc.) can be measured with great precision. Calorimetric methods are isoplethal, that is, they follow a line on a phase diagram (binary or ternary) along which the composition remains constant as temperature is varied. Differential scanning calorimetry is widely used to obtain phase information. Many phase diagrams are inferred from calorimetric data jointly with some other techniques. Calorimetry has been used extensively for physical studies of polar lipids and provides invaluable information about the numerical values of the thermodynamic variables [9]. A sample cannot be viewed during calorimetric studies, but in combination with observations in hot stage microscopy (with common and/or polarized light) the nature of phase transitions and their temperature can be determined.

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There are some limitations to the use of DSC in phase studies in addition of its inability to identify phases [5]. They are that (1) there are difﬁculties in locating very steep phase boundaries in heterogeneous systems from DSC data alone because heat capacity depends strongly on the slope of phase boundaries and so the heat capacity jumps are small [10] and (2) the determination of phase boundaries in systems with slow nucleation rate, interfacial transport problems, or inherently slow phase changes may not be possible [11]. This is why it is hard to discover a liquid miscibility gap by DSC measurements.

II.

EXPERIMENTAL AND THEORETICAL REMARKS

Pans for volatile samples must be used to run DSC thermograms of surfactant– water systems and of systems containing other volatile solvents. Samples must be weighed before and after DSC runs, and results of samples that lost weight must be discarded. To facilitate mixing and homogenization and to obtain reproducible thermograms, the samples are often heated and cooled before the actual measurements are taken [12]. However, if the temperature of a ﬂuid liquid phase is reached during this procedure, it is not recommended that the equilibrium state be attained by this method because high-temperature phases at phase transitions are highentropy phases. The rate of phase equilibration is in general fast during the heating stage but comparatively slow during the cooling stage. Reheating a cooled sample (that may have partially reached equilibrium) will therefore rapidly destroy any low-entropy phase (such as crystals) that may have started to form. State equilibrium may exist at the end of the heating stage, but it may not at the end of the cooling stage. The attainment of equilibrium from the disordered state during cooling must therefore start anew during each cooling stage. For example, for the determination of the Krafft boundary, either a new sample must be used in each scan or conditions must be maintained such that equilibrium is attained after cooling below the phase boundary temperature [13]. Changing the temperature of a mixture often dictates that not only heat transport but also mass transport must occur to maintain the state equilibrium. Heat ﬂow is relatively fast, but mass transport may be much slower. Whether or not sufﬁcient time is allowed for the mass transport equilibration to occur is determined by the scanning rate, and during most calorimetric studies the scanning rates are too fast for reaching mass transport equilibrium. In the SDS–water system, even a scanning rate of 0.2°C/min was too fast to maintain equilibrium, and a qualitative distortion in the form of the thermograms occurred at this scanning rate. Only when the scanning rate was less than 0.08°C/min was the true phase boundary peak detected. With sufﬁciently low scanning rates (0.1°C/min), narrow, sharp well-deﬁned peaks form in invariant phase processes, i.e., in isothermal transitions. In fact,

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the peak width tends to zero as the scanning rate goes to zero. Wider peaks appear in univariant (nonisothermal) processes; nonzero values of the transition temperature intervals are observed as the scanning rate goes to zero [14]. The theoretical forms of thermograms for a variety of situations that take into account the dynamics of heat ﬂow have been suggested by Kessis [15] and by Wunderlich [16] and have also been incorporated into the analysis of thermograms by Grabielle-Madelmont and Perron [17]. A particularly important aspect of these theories is that a phase transition that is strictly isothermal (that is, a transition that spans a zero temperature range) inevitably yields a peak that spans a ﬁnite temperature range. A theory of heat transfer inside water-in-oil (W/O) emulsions in DSC experiments and during crystallization of undercooled droplets developed by Dumas et al. [18] shows that, despite the small cell size, important temperature gradients appear that explain the shape of the thermograms upon cooling. Their model indicates that the undercooling is well characterized by the beginning of the peak and not by the peak minimum as suggested earlier [19]. A model of heat transfer inside emulsions near the melting temperature of the crystallized droplets demonstrated signiﬁcant temperature gradients, in contrast to the classical assumption of uniform melting temperature. The melting kinetics of the droplets depends on their location [20]. The evaluation of thermodynamic properties (enthalpy, entropy, and free energy) by DSC was discussed by Richardson [21]. He found that isothermal enthalpy changes are readily obtained by simple extrapolation even though the apparent location of a thermal event is much inﬂuenced by rate effects. The corresponding entropies are always ﬂawed by departures from reversibility, and data must be corrected by forcing them to obey the condition of ∆G ⫽ 0 at a ﬁrst-order transition. Free energy curves may then be used to deﬁne the relative stabilities of the different structures. The DSC-measured phase transition enthalpies are often complex functions of the true phase transition enthalpy and the heat capacity difference between the coexisting phase [21]. Thermodynamic properties may also be obtained from conventional DSC heat capacity measurements [22,23] without the need of time-consuming extrapolations to zero heating rate [21].

III. HEAT CAPACITY AND OTHER THERMODYNAMIC PROPERTIES In general, the enthalpy and temperature of thermal transitions are directly determined from DSC thermograms. However, other thermodynamic properties, such as heat capacity, can also be obtained from these experiments.

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Differential scanning calorimetry is a simple and rapid method for measuring heat capacities of small samples over a wide temperature range. It is applicable to any liquid and solid materials in a variety of forms (powders, ﬁlms, granules, etc.) [24]. The raw data produced by DSC are the difference in the amount of heat transferred to a sample relative to a reference, q, as a function of temperature. The heat capacity is then equal to dq/dT. Differential scanning calorimetry studies of aqueous surfactant mixtures are typically measured in closed hollow containers or pans where the expansion of condensed phases causes only a minimal increase in pressure under these circumstances. Changes in pressure in surfactant–water systems resulting from the increase in water vapor pressure are typically small (a few atmospheres at most). In these cases, the measured heat capacities can be precisely deﬁned as heat capacities at saturated vapor pressure [25], but usually they are numerically similar to those that would be obtained during constant pressure measurements [26] and so they are commonly taken as the latter. A DSC determination of heat capacity (c p) is based on the comparison of signals in the scanning mode from the sample (subscript s) and a calibrant (subscript c) of known heat capacity, c c . The calibrant must not be mistaken for the reference, which is usually an empty (inert) cell. Determinations of c p are based on changes of signal in sequential runs with empty (subscript e) and loaded cells. The sample heat capacity is given by [24] cs ⫽

冢冣

SS s ⫺ SS e m c c c SS ⫺ SS e ⫽ s SS c ⫺ SS e m s Km s

(1)

where m x is the additional mass of sample (x ⫽ s) or calibrant (x ⫽ c) and SS x is the scanning signal of sample (x ⫽ s), calibrant (x ⫽ c), and empty (x ⫽ e). ‘‘Empty’’ refers to conditions with empty pans in both sample and reference cells. Quantities SS x ⫺ SS e in Eq. (1) are dynamic signals, which depend on sample mass, heat capacity, and heating or cooling rate. Equation (1) holds only when the pans used in all determinations are of the same mass and material. Ideally, the same pan should be used throughout any set of measurements. However, this is not possible after crimping or sealing or for strongly adhering samples, and here pans of matched masses must be used. Aluminum pans are easily matched, but this can be difﬁcult when only a few custom-made pans are available. In this case, an additional run must be made with the empty pan removed from the sample cell so that the ‘‘empty contribution’’ is reduced by Km e c e, and then Eq. (1) becomes cs ⫽

冢冣

SS s ⫺ SS e ⫹ (SS e ⫺ SS*es ) (1 ⫺ m es /m e) m c c c SS c ⫺ SS e ⫹ (SS e ⫺ SS ec) (1 ⫺ m es /m e) m s

(2)

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where m ex is the mass of the removed pan (containing the calibrant or the sample) and SS*ex is the corresponding scanning signal. Another condition for obtaining reproducible results is that identical surface conditions should be maintained in successive runs. This condition is obtained by carefully attending to the position of the platinum lid of the pan holder. It is also important that the pan and its contents present a reproducible environment to the cell. This means that lidded pans should always be used. More experimental details can be found elsewhere [24]. For converting c p to c v data, a Nernst–Lindemann type of equation can be used, since compressibility and expansivity data are usually not available [27]. This equation has the form c p ⫺ c v ⫽ 3RA 0 c p T/T m°

(3)

where R is the ideal gas constant, T°m is the melting point and A 0 (⫽ 3.18 ⫻ 10 ⫺3 kmol/J) is a universal parameter [27]. The average deviation in using this equation is about 3%. Finite jumps in heat capacity have been detected at the transition from heterogeneous (isotropic liquid ⫹ crystals) regions to one-phase isotropic regions [11,28]. This jump appears when a two-component system undergoes a transition from a one-phase state (phase a) to a two-phase state (phases a ⫹ b) [6]: ∆c p (a → a ⫹ b) ⫽ c(1 ⫹ b,m a → 1) ⫺ c a

(4)

which is linked to differential entropy and enthalpy effects of dissolution of phase a in phase b as follows: ∆c p (a → a ⫹ b) ⫽

TS b/a (dx b /dT) p H b/a (dx b /dT) p ⫽ xa ⫺ xb xa ⫺ xb

(5)

where x a and x b are the molar compositions of the phases coexisting at a given temperature and (dxb /dt) P is the slope of the phase b boundary at this temperature. S b/a is the variation of the entropy of the two-phase system at the isothermic– isobaric dissolution of 1 mol of phase a in an inﬁnite amount of phase b, and H b/a ⫽ TS b/a is the differential enthalpy effect in the same process of dissolution. The values of S b/a and H b/a characterize the phase transition b → a (at constant temperature). The phase transition entropy, ∆S b/a , and enthalpy, ∆H b/a , characterize thermodynamically the b → a transition. At an invariant point (i.e., a eutectic transition), the transformation occurs at constant T and x, so ∆S eutectic ⫽ ∆H eutectic / T ⫽ S eutectic and ∆H eutectic ⫽ H eutectic. A two-phase system consisting of phases b and c has a eutectic point (composition x eutectic) in which the temperatures of the transformation b → a and that of

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c → a are equal and minima. The entropy of the eutectic transformation follows the relations ∆S b/a ⫽ m b S eutectic(a/b) ⫹ m c S eutectic(a/c)

(6)

and m b S eutectic(a/b)

冢

冣

dx a,a ⫹ c dT

⫹ m c S eutectic(a/c) p

冢

冣

dx a,a ⫹ b dT

⫽0

(7)

p

where m b and m c are the masses of phases b and c at the eutectic point, which can be found with the lever rule and (dx a, a ⫹ x /dT) p is the value of the slope at the eutectic point of the phase boundary between phase a and the heterogeneous region a ⫹ x, a. Equations (6) and (7) allow the calculation of S eutectic(a/b) and S eutectic(a/c) from the entropy of the eutectic process. Values of the differential entropy of dissolution of lyomesophases in isotropic liquids are very small. For instance, in the dimethyldecylphosphine oxide

FIG. 1 Temperature dependence of the heat capacity (joules per gram of mixture) of the dimethyldecylphosphine oxide–water system with surfactant mole fraction 0.315 at two different heating rates: (䊊) 1 K/min; (䉭) 0.5 K/min. (From Ref. 6.)

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(C 10 PO)–water system, these effects are two orders of magnitude smaller than those of dissolution of crystals in liquids [6]. In other systems the difference may be up to three orders of magnitude [2]. Mu¨ller and Borchard [29] studied the correlation between DSC curves and isobaric state diagrams. From enthalpy and mass conservation considerations, they derived some universal formulas that permit the calculation of the speciﬁc heat capacity as a function of temperature during the melting of a binary sample and provide a generalized description of any other continuous phase transition in a binary mixture, such as evaporation, sublimation, fusion, and mixing–demixing phenomena. These authors found that, due to a ﬁnite thermal conductivity and a limited heat ﬂow within the sample to be melted, the resulting melting peaks of pure compounds or eutectic points turn out to be not inﬁnitely sharp; instead, time delays are observed, which lead to a peak broadening (‘‘smearing’’). They concluded that the correlation between the heat ﬂow registered during a DSC scan and the speciﬁc heat capacity plotted against temperature holds only when the present heating rate and the total mass of the sample vanish whereas its thermal conductivity approaches inﬁnity; otherwise, the distortion of the resulting DSC melting peak with respect to time would become noticeable. The model also reproduces heat capacity–temperature curves by superimposing several Gaussian curves.

FIG. 2 The heat capacity jump of the dimethyldecylphosphine oxide–water system versus concentration at a constant temperature (C p in J/g mixture) of 316 K. (From Ref. 6.)

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Heat capacity data at two heating rates measured by DSC for the C 10 PO– water system are shown in Fig. 1 [6]. Crystals (C) ⫹ laminar mesophase (L)– and L–isotropic (I ) phase transitions take place at the concentration studied. cp values of the isotropic liquid phase are more reproducible than those of the twophase system because DSC is a dynamic method and there is some dependence of the heat capacity jumps on the scanning rate. If the inﬂuence of the scanning rate is unacceptably large, the values of ∆cp can be obtained by extrapolating to zero scanning rate. The heat capacity of a two-phase system is strongly dependent on temperature, whereas that of a single-phase system is very small. A ﬁnite heat capacity jump at a transition from a two-phase state to a homogeneous state has been clearly observed [30,31]. When a mixture is an isotropic liquid over the entire concentration range, there are no abrupt changes in the plot of c p vs. x. The order of magnitude of ∆c p differs in the transitions between crystals and mesophase and between mesophase and isotropic liquid (Fig. 2) [6]. The heat

FIG. 3 (a) Phase diagram of the dimethyldecylphosphine oxide–water system. C, crystals; Lam, lamellar mesophase; I, isotropic liquid. (b) Heat capacity jumps vs. concentration for the transition from the liquid to a two-phase state. Curve 1, Along the BE phase boundary in (a), I → I ⫹ Lam transition; curve 2, along EA, I → I ⫹ C transition. Arrows indicate values exceeding the scale (theoretical C p → ∞). (c) Transitions from the lamellar mesophase to the two-state phase. Curve 1, Along the BD phase boundary, Lam → Lam ⫹ I transition; curve 2, along the DF phase boundary, Lam → Lam ⫹ C transition. (From Ref. 6.)

FIG. 3

Continued

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capacity jump is measured between the peak summit and the peak baseline when the single-phase system appears. In certain intervals ∆c p is a continuous function of the composition x (Fig. 3) [6]. This implies that ∆c p can be obtained by interpolation at any concentration within this interval, which helps in plotting the concentration dependence of the heat capacity of the system at various temperatures and the three-dimensional diagram of c p (x, T ). Heat capacity jumps taking place when the number of phases in the system changes are very sensitive to the kind of process, the nature of phases participating in the transition, temperature, and concentration. According to thermodynamic considerations [32], heat capacity jumps in a binary system tend to inﬁnity as x → 1, that is, at the pure component edges of the phase diagram, and when a point of the extremum of a transition temperature is approached; at the eutectic point, ∆c p is discontinuous because of the intersection of two different liquidus

FIG. 4 Concentration dependence of the heat capacity jumps in the dimethyldodecylphosphine oxide–water system at the transitions lamellar mesophase ⫹ isotropic liquid → isotropic liquid (curves 1 and 2) and crystal ⫹ isotropic liquid → isotropic liquid (curve 3). (From Ref. 2.)

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curves (Fig. 4). An example of C p measurements in a surfactant system is reported in Ref. 2, and one of heat capacity of water in poly(methyl methacrylate) hydrogel membranes is reported in the work of Ishikiriyama and Todoki [33]. A detailed analysis of the entropy data on extensive examples using the empirical fusion rules was given by Xenopoluos et al. [34]. The three types of disordering that have been studied by these rules are positional [35], orientational [36], and conformational [37–39], which have typical entropy changes of 7–14, 20– 50, and 7–12 J/(mol ⋅ K), respectively [34]. Positional and orientational motions are independent of molecular size, whereas conformational motion is proportional to the number of ﬂexible bonds in the molecule.

IV.

THE PHASE DIAGRAM

Differential scanning calorimetry provides numerical thermodynamic data and is frequently the main technique used to determine phase diagrams [40,46–57]. Some surfactant systems studied by DSC analysis in the literature are soap–water [41–43], dipalmitoylphosphatidyl choline–water [17,44], sodium dodecylsulfate–water [13], C 10 PO–water [1,2,6], perﬂuorosurfactants–water [45], and dioctadecyldimethylammonium bromide–water [46].

V. THERMAL TRANSITIONS DETECTED IN PHASE STUDIES A. Melting Melting is generally observed as a rather sharp peak in calorimetry. The area under the melting peak is a direct measure of the heat of fusion of the material. However, the sharpness of the melting peak can be inﬂuenced by factors such as purity and crystalline defects. The presence of impurities broadens the peak and lowers the temperature at which the phase transition begins. Moreover, the melting temperature is less deﬁned as the concentration of impurities increases (Fig. 5). Melting is not always a simple, one-step event. Frequently, multiple melting peaks are observed in surfactant-based systems. These multiple peaks may arise for a variety of reasons. The gel–liquid crystal transition in surfactant-based systems is the result of the cooperative melting of the hydrocarbon chains [58]. The melted state in a surfactant-based system is less disordered than that of liquid hydrocarbons due to the anchoring of one end of the molecule to the microstructure surface via its polar headgroup. This transition can be sharp in pure synthetic phospholipids and surfactants, but it is broad and ill-deﬁned in natural phospholipids and surfactants, which are usually mixtures with a variety of hydrocarbon chain lengths. The transition temperature, T c, depends on the nature of the polar headgroup and the

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FIG. 5 Effect of impurities on the DSC melting peak shape of benzoic acid.

length, branching, and unsaturation of the hydrocarbon tails. Increasing saturation increases the transition temperature. Trans isomers of unsaturated compounds have higher transition temperatures than cis isomers. Surfactants with longer chain lengths have higher T c values than shorter ones [40]. Chain ramiﬁcation reduces T c more effectively at the middle than at the end of the chain, mainly because it induces a ‘‘kink,’’ which is essential for this transition. Ramiﬁcations near the headgroup are relatively immobilized, whereas carbon atoms near the terminal end are quite mobile [59]. In some cases, melting of the alkyl chains is the only thermal transition in anhydrous surfactants. Anhydrous alkyl ether surfactants show only the melting peak of the alkyl chain by DSC. In surfactants with three oxyethylene groups, no additional peaks appear, but the heptaoxyethylene alkyl ether surfactants display an additional broad peak at about 3°C below the tail melting peak (Fig. 6) [60]. This pretransition peak may correspond to the melting of the polyoxyethylene chain. The texture of anhydrous sodium dioctylphosphinate changes at 56°C because of the melting of the crystal hydrocarbon network. This transition is reversible, but another one at 77°C is irreversible and corresponds to the decomposition of the polar network without melting [55].

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FIG. 6 DSC thermograms of nonhydrated nonionic surfactants. (a) C 18 EO 3; (b) C 18 EO 7. (From Ref. 60.)

Many pure surfactants exhibit a very complex melting process. Many of them go through several crystalline and/or liquid crystalline phases before they form an isotropic liquid phase. As an example, crystals of n-decanephosphonic acid undergo melting of the hydrocarbon chain network at 44°C (∆H ⫽ 98 J/g) while retaining the external crystalline shape; however, the microscopical texture changes from that of transparent crystals to that of an opaque, waxy solid. The resulting structure was named ‘‘waxy solid.’’ The hydrogen-bonded polar network undergoes small changes, but it remains ‘‘solid’’ as corroborated by Fourier transform infrared (FT-IR) studies [54]. At 53°C, the polar network melts, but this transition is related to the transformation from a static hydrogen-bonded polar network to a dynamic one, giving a cubic liquid crystal. The low ∆H (21 J/g) associated with this transition implies minor structural changes. In addition, at 89°C, this liquid crystal melts to yield an isotropic liquid, and there is a large reduction in the number of hydrogen bonds, which is reﬂected in the larger ∆H (59 J/g) [54]. Generally, materials that melt on heating crystallize on cooling, as evidenced by a sharp exotherm on DSC thermograms. Since all materials supercool, the crystallization rate may be faster than the melting rate. Consequently, the crystallization exotherm may be larger than the melting endotherm. However, when complete crystallization has occurred, the energy is the same. The difﬁculty in

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crystallization studies is that a number of materials do not crystallize completely or even partially on cooling. Surfactant–water systems may melt from hydrated crystals and freeze as a gel whose structure is different from that of the original crystals. Surfactants that have been recrystallized from solution often do not crystallize from the melt, or they form a different crystalline structure. Fast cooling of surfactant–water systems can produce a metastable structure whose crystallization is very slow (days, weeks, or even months) due to the slow molecular diffusion. Both water-related and surfactant-related phase transformations exhibit supercooling phenomena. The hydrocarbon chain melting in surfactant-based systems may give rise to the formation of liquid crystals or molecular or micellar solutions, depending on concentration. The addition of water to surfactant decreases T c and the enthalpy associated with the transition. This is probably due to a reduction in the cohesion of the polar headgroup network. The effect is especially strong in transitions from solid to solid plus liquid crystals. In pure dioctadecyldimethylammonium bromide (DODAB), the polar layer melts at 86.5°C with a ∆H of 130 J/g. The transition temperature decreases as water content increases and disappears at about 75% DODAB. At this point, the gel–liquid crystal transition happens at a temperature that is independent of water content [46]. In a similar fashion, the hydrocarbon tails of didodecyldimethylammonium bromide (DDAB) melt at about 61°C in the absence of water, with a ∆H of 83.3 J/g sample or 61 J/g hydrocarbon tails, whereas those of n-dodecane melt at ⫺9.6°C with a ∆H of 214.8 J/g. The smaller melting enthalpy of the DDAB hydrocarbon tails is the result of the higher melting temperature of the surfactant hydrocarbon tails, in agreement with Kirchhoff ’s law. The higher melting temperature of the hydrocarbon tails is caused by the additional cohesion provided by the polar groups in the DDAB crystal. In fact, DDAB crystals melt to yield an isotropic phase at 76.5°C with a ∆H of 17 J/g [61]. Upon addition of water, the transition due to the ‘‘melting’’ of the polar network shifts to lower temperatures, becomes broader, and vanishes when bulk-like water is detected. At this concentration, the solid changes into solid–liquid crystal. The transition of the hydrocarbon tails also becomes broader and shifts to lower temperatures upon addition of water because the cohesion of the ionic layers becomes weaker. The gel-toliquid crystal transition becomes invariant (about 15°C) once the bulk-like water peak is detected [62]. Schulz et al. [46,61] reported that the melting peak of the hydrocarbon chains in DDAB–water is really the superposition of two peaks over the whole concentration range where it appears. Sometimes a shoulder is detected, but in other cases two very close peaks are observed by DSC. This is particularly noticeable in cooling scans. These results suggest that melting transitions of the hydrocarbon chains of DDAB are not entirely equivalent. Two superimposed (and sometimes split) peaks were seen in the two lamellar phases (L 1 and L 2) that form DDAB

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and water. The transition temperature increases and the peak broadens as the concentration of DDAB rises, and it disappears when bulk-like water is detected by DSC. Similar results were observed in mesophases prepared with other double-tailed cationic surfactants, such as dioctadecyldimethylammonium bromide (DODAB) [62,63]. On the assumption that each peak corresponds to the melting of one of the chains, one melts at 60°C with an enthalpy of 31 J/g DDAB (which corresponds to 77 J per gram of chain) whereas the other melts at 69°C with an enthalpy of 19 J/g DDAB (which corresponds to 47 J/g chain) [61]. The melting temperature and enthalpy of octadecane are 28.2°C and 241 J/g, respectively [64]. The melting points of the surfactant chains are higher than that of n-dodecane because of the additional cohesion given by the ionic layer of the crystal. The decrease in melting enthalpy in both chains of DODAB is due to the increase in melting temperature, as expected from Kirchhoffs law. The melting of the ﬁrst chain reduces the cohesion of the second one, so it melts with a lower enthalpy. Upon addition of water, the ionic layer of DODAB crystals loses cohesion, and as a consequence the melting point of the chains is lowered. In monosodium n-decanephosphonate–water and disodium n-decanephosphonate–water, the main transitions are the melting of the hydrocarbon network followed by the melting of the polar headgroups. The temperatures at which both transitions occur, as well as their enthalpies, increase as the water content in the system decreases [65]. The hydrocarbon chain melting transition is facilitated by factors that reduce the polar headgroup network cohesion. The addition of water to cetyltrimethylammonium tosylate produces a peak at 23°C, which is related to the melting of CTAT crystals (embedded in saturated aqueous solution below 23°C) to produce a liquid crystalline phase (in highly concentrated CTAT systems) or micellar solutions (in dilute systems). The peak is broad, probably due to the existence of a biphase transition zone. No melting peak related to the polar network was detected, probably because of the relatively weak cohesive forces in this particular polar network. The second peak detected in concentrated water–surfactant samples was due to the hexagonal mesophase–isotropic liquid transition [53]. The lower concentration limit of existence of some phases may be found by plotting the enthalpy per gram of sample against concentration and extrapolating to zero enthalpy. In n-decanephosphonic acid–water and n-dodecanephosphonic acid–water systems, the lower limit of existence of the waxy solid was determined by plotting the enthalpy associated with the hydrated crystals–waxy solid transition, and that of the low-temperature lamellar mesophase (L α) by plotting the enthalpy associated with the waxy solid–L α transition [54].

1.

Melting of Blends

In multicomponent systems or in some surfactants that are not pure (i.e., natural compounds), some of the phases that form may be blends. When two materials

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are physically mixed, they may retain their individual thermal behavior. In some cases the thermograms of blends and mixtures may be used for identiﬁcation purposes or the blend ratio can be determined from them. However, some surfactants can form solid solutions, and in general they are mutually soluble in liquid microstructures such as liquid crystals and micelles (exceptions are hydrocarbon– and ﬂuorocarbon–surfactant mixtures). Mixtures of amphiphiles with different chain lengths melt over a wider temperature range than pure amphiphiles [66]. The T c and the shape of the transition depend on the composition, and asymmetrical transitions may occur with compositions other than the equimolar one. Ideal mixing occurs when the difference between hydrocarbon chain lengths of the amphiphiles is only two carbon atoms [66,67], giving asymmetrical transitions intermediate between the two components. Mixtures of components differing by four carbon atoms give systems that depart signiﬁcantly from ideality [66]. Some experiments suggest that immiscibility occurs in the gel phase [68,69]. Mixtures of amphiphiles differing by six carbon atoms result in systems so far moved from ideality that monotectic behavior is observed [66]. When interdigitated palisades form, as occurs in bilayers containing phospholipids or two-tailed surfactants that have one hydrocarbon chain approximately twice as long as the other, there is a single, highly cooperative phase transition over a wide temperature range, indicating the existence of a single type of gel phase below T c. The longer chains in one monolayer penetrate into the opposite monolayer palisade, end to end with the opposite shorter chains [70]. Because this situation is required to meet structural conditions, the inclusion of cholesterol in these bilayers affects the transition much more than in noninterdigitated bilayers [71]. The transition temperature decreases with increasing cholesterol content [71] at a rate of about ⫺0.24°C per mole percent of cholesterol. This is greater than in the equivalent symmetrical phosphatidylcholine–cholesterol mixtures. The inclusion of cholesterol disturbs the crystalline structure of the gel phase, and the phospholipid chains are more mobile than in its absence. This prevents the crystallization of the hydrocarbon chains into the rigid crystalline gel phase. In the more ﬂuid liquid crystalline phase, the rigid cholesterol molecules restrict the movement of the hydrocarbon chains. In consequence, the addition of cholesterol to lipid bilayers or lamellar mesophases gradually diminishes the gel–liquid crystal transition temperature and the enthalpy and broadens the DSC transition peak [72,73]. No transition can be detected by DSC at 50% cholesterol [73,74] (curve f of Fig. 7), which is the maximum concentration of cholesterol that can be incorporated before phase separation. However, laser Raman spectroscopic studies show that a noncooperative transition occurs over a very wide temperature range [75]. Because of the gradual thermal decomposition of some surfactants on succes-

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FIG. 7 DSC curves for dispersions of dipalmitoylphosphatidylcholine in water containing different proportions of cholesterol. (a) 0 mol%; (b) 5 mol%; (c) 12.5 mol%; (d) 20 mol%; (e) 32 mol%, (f ) 50 mol%. (From Ref. 72.)

sive DSC runs, the thermograms change. Cetyltrimethylammonium methacrylate (CTAM) undergoes Hoffmann elimination at relatively low temperatures. The ﬁrst DSC run (presumably) depicts the pure CTAM thermogram. Successive runs show the gradual decomposition and formation of CTAM–hexadecene–trimethylammonium methacrylate mixtures of increasing complexity. At the eighth run, the thermal behavior of the system resembles that of a mechanical mixture of pure CTAT and a CTAT solution in hexadecene, plus trimethylammonium methacrylate [76]. The thermal behavior of a molecular complex is different from those of pure components. Molecular complexes of alkyltrimethylammonuim bromide surfac-

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tants and additives such as diphenylamine, naphthylamine, indole, and acridine were studied by Hirata and Iimura [77]. The additives show a single peak upon melting. In surfactants they also showed a sharp single peak that corresponds to a transition from the gel phase to a smectic liquid crystalline phase. In a repeated run, the endothermic peak often shifts by 2–3°C or changes into multiple peaks. Sometimes the peak disappears. These results may imply a thermal instability at higher temperatures or monotropicity between two phases of low and high temperatures. Such thermal behaviors have also been observed in surfactant– phenol systems. The very high temperature transition of pure surfactants was remarkably depressed after complexation with certain additives. The sharpness of the complex endotherms implied that the specimens used for the thermal test were pure and constituted a single species [78].

2.

The Krafft Temperature and the Gel–Micellar Solution Transition

In surfactant systems the stable hydrated crystals have a structure different from that of the metastable gel phase. Thus, the melting characteristics of the two structures will be different. Kaneshina [79] found two transitions in the dodecylammonium bromide–water system. The ﬁrst was at 32.3°C [∆H ⫽ 49.7 kJ/mol, ∆S ⫽ 163 J/(mol ⋅ K)], which is the Krafft temperature and corresponds to the transition from the stable coagel phase (hydrated crystals) to the micellar solution. The other transition was detected at 24.3°C [∆H ⫽ 41.4 kJ/mol; ∆S ⫽ 139 J/ (mol ⋅ K)] in supercooled samples, which corresponds to the transition from the metastable gel phase to the micellar solution. The entropy changes associated with the transitions were calculated from ∆S ⫽ ∆H/T, where T is the transition temperature. The values of ∆S reﬂect the less organized structure of the gel phase compared to the coagel one, inasmuch as the ﬁnal state is the same (i.e., the micellar solution).

3.

Crystal Polymorphism

Some surfactants show crystal polymorphism. Transitions between different crystalline structures are observed as sharp endothermic peaks on DSC thermograms. Frequently, crystal–crystal transitions are not reproducible because impurities or thermal treatment can promote the formation of metastable states. Visual observations are recommended to distinguish crystal–crystal transitions from melting.

4.

Eutectic Melting

Eutectic melting is encountered in binary mixtures that form a simple eutectic phase [80]. At the eutectic temperature, it is known from the phase rule [81] that all of the minor component along with a sufﬁcient amount of the major component melt to form a mixture with the eutectic composition. Consequently, a sharp

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endothermic peak is observed on DSC thermograms at the invariant eutectic temperature. Also, as the temperature is increased, the major component continues to melt until the eutectic melting point is reached. Thus, the sharp eutectic peak is followed by a broad melting peak of the major component. A typical thermogram is shown in Fig. 8. The closer the sample composition is to the eutectic composition, the greater will be the amount of melting at the eutectic point. The eutectic temperature is invariant. Furthermore, by studying the eutectic heat of fusion as a function of composition, it is possible to determine the eutectic composition, limits of solid solubility, and unknown compositions [80]. To correctly interpret calorimetric thermograms determined at concentrations greater than that of the liquid phase at the Krafft eutectic point, it is important to recognize that eutectic discontinuities are introduced at the lower temperature limit of each phase as a consequence of the existence of several liquid crystalline states. Each of these discontinuities is encountered along isopleths that pass through them, so at very high compositions all these eutectics are encountered. As the composition is reduced, those that lie at high temperatures are not encountered, so the number of eutectics becomes smaller as the concentration is reduced [27]. The latent heats at the various eutectic points may, in principle, be revealed along the isoplethal path by calorimetric studies, but often they are not detected because the scanning rate is too fast. In the sodium dodecyl sulfate (SDS)–water system, for example, a scanning rate of 0.2°C/min failed to reveal all of the existing isothermal discontinuities. Only at scanning rates of 0.08°C/min was it

FIG. 8 Thermogram of a mixture of triphenylmethane and stilbene (0.931 mol fraction of stilbene), showing the eutectic peak.

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possible to obtain this information [13]. Similar observations have been made in calorimetric studies of polar lipid–water systems [17].

B. Liquid Crystal Transitions Transitions between liquid crystals are frequent in surfactant-based systems. The order in liquid crystals requires a small amount of thermal energy (generally about 2 J/g) to break down. This absorption of thermal energy is observed as a small endothermic peak by DSC. Additional information (i.e., optical observations with a polarizing microscope) is needed to distinguish the crystal–mesophase, mesophase–mesophase, and mesophase–isotropic liquid transitions from normal melting. Liquid crystalline behavior is usually reversible and can be distinguished from normal crystallization because of the small degree of associated supercooling behavior [82]. The heat effects that are observed by DSC as one passes into liquid–liquid miscibility gaps are relatively small. Measurable effects have been observed along isopleths, which span the concentrated part of the gap, but the gap may be calorimetrically undetectable along more dilute isopleths [26]. It is intriguing that the same pattern is found within liquid crystal regions [10]. The numerical values of the observed heat effects along more concentrated isopleths are greater than those observed along more dilute isopleths in both instances. The temperature range of the mesophase stability is maximum at the compositions corresponding to the invariant points [14]. In hydrated decanephosphonic acid (DPA) systems, all the transitions detected in pure DPA became weaker and broader because the crystalline structure of the pure amphiphile is disrupted. With increasing water content, other transitions appear [65]. The main transition is the melting of the hydrocarbon network, giving a waxy solid, which in turn melts to produce a lamellar liquid crystal. This liquid crystal changes in texture at higher temperatures of about 50°C. The hightemperature lamellar mesophase melts into an isotropic liquid at about 85°C. The melting of the hydrogen-bonded headgroup network is affected by the presence of water, which interacts with the phosphonic acid groups via hydrogen bonding. The transitions between different liquid crystals and between liquid crystal and isotropic liquid are low-energy transitions, reﬂecting changes in degree of order instead of drastic changes in structure [54]. Faure et al. [83] found a melting point at 253°C due to the transition from inverted hexagonal phase to isotropic liquid, followed by a degradation at 275°C in Areosol OT (sodium bis-2-ethylhexyl sulfosuccinate). Samples with water showed the transition from lamellar mesophase to isotropic liquid with weak reversible peaks (∆H ⬇ 1–5 J/g) within a very narrow temperature range. The hysteresis was low (max. 3°C). This transition occurs via a narrow biphase region. However, transitions in a wide biphase

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region occur with wide peaks but with low enthalpies at the composition of 85 wt%.

1.

Crystalline Hydrates

With some exceptions, such as phosphine oxides [84] and alkanephosphonic acids [54,61,62], practically all surfactants form crystalline hydrates. Crystalline hydrates invariably decompose upon heating to a certain temperature. Two modes of decomposition are known: congruent decomposition, during which another (usually liquid) phase of the same composition forms, and incongruent decomposition, during which two phases of differing composition result. The crystalline hydrates formed by C 12 E 6 decompose congruently [85]. Most surfactant crystalline hydrates decompose incongruently via the peritectic phase reaction. The ﬂuid phase formed during peritectic reactions of surfactant crystalline hydrates is always a liquid crystal. When a mixture of coexisting liquid crystal and crystalline hydrate is heated to the peritectic temperature of the crystalline hydrate, the hydrate is replaced at this temperature (at equilibrium) by another crystal of lower hydration. Because of this discontinuity of state in the crystal phase, a cusp exists in the boundary of the liquid or liquid crystal region at peritectic temperatures [26].

2.

Hydrogen Bonding

The effect of hydrogen bonding on the formation and stability of microstructures can be studied by DSC. Kato et al. [86] found that hydrogen bonding between nonmesogenic compounds produces liquid crystals and that increasing hydrogen bonding raises the liquid crystal-isotropic transition temperature. Liu et al. [87] measured the gel–liquid crystal transition temperature of a series of synthetic phospholipids and found that it rose as the intermolecular hydrogen bonding between lipid headgroups increased and that T c also increased as the headgroup electrostatic repulsion and hydration decreased. Differences in molecular packing associated with chain–backbone junctional groups also affect T c. For instance, T c was consistently higher in ether-linked compounds than in ester-linked or amidelinked compounds with equivalent N-terminal headgroups.

C. Vaporization Vaporization is observed as an endothermic peak with a shape that depends on the vaporization rate. This rate is inﬂuenced by the surface area and container opening through which the vapor is lost. Since vapor is easily removed from open pans, it is possible for the sample to vaporize completely before its normal boiling point is reached. In surfactant–water systems, water vaporization must be avoided by using DSC pans for volatile samples. Samples must be weighed before and after runs, and those that lost weight must be discarded.

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D. Decomposition Decomposition is generally observed as a broad exothermic peak. However, variations in experimental conditions can alter the nature of the decomposition. In any case, the decomposition is easily determined by visually inspecting the sample after analysis. Repetition of DSC runs in a sample that has decomposed gives different thermograms than those obtained before the decomposition temperature was reached. In the case of anhydrous sodium dioctylphosphinate, the hydrocarbon melting peak at 56°C was not detected in a second run after the decomposition temperature (77°C) had been reached [55].

E. Vesicles and Liposomes Because of their biological importance, vesicles and liposomes have been extensively studied by DSC. They can be made from synthetic surfactants or biological phospholipids. The latter, on heating, do not undergo a simple melting process, i.e., they do not change directly from a solid to a liquid state, but, depending on the amount of water present, they go through one or more intermediate liquid crystalline forms. In general, vesicles exhibit a phase transition behavior that is very different from that observed with multilamellar (liposomes or lamellar mesophase) preparations [90–93]. Suurkuusk et al. [92] found that unsonicated (multilamellar liposome) and sonicated (vesicle) samples of dimyristoylphosphatidylcholine exhibit different heat capacity maxima (Fig. 9) [94]. This difference implies a change in the organization of the phospholipids upon sonication. ESR and NMR spectroscopy showed that the small radius of curvature of the vesicles leads to less efﬁcient packing and to greater freedom of motion of the hydrocarbon chains. The phase diagram of reversed vesicles was studied by DSC by Kunieda et al. [95]. Multilamellar aqueous dispersions of phospholipids are characterized by highly cooperative reversible thermal phase transitions, which have been determined to be transitions in the lipid hydrocarbon chains from an all-trans conﬁguration in an ordered gel state at low temperatures to a more disordered ﬂuid state at high temperatures. In synthetic phospholipids, the transformation temperature depends on the nature of the polar headgroup and the length and degree of unsaturation of the fatty acyl chains [96]. In general, the introduction of double bonds reduces the transition temperature, and in saturated phospholipids an increase in the number of carbon atoms results in an increase in the transition temperature [66,96,97]. Trabelsi et al. [98] measured the chain melting of vesicle-forming trisubstituted perﬂuoroalkylated thiourea surfactants at a concentration of 10 wt% in water. The C 6 F 13 and C 8 F 17 chains melted at 51.7°C (∆H ⫽ 2.23 kJ/mol), which is in the expected range for perﬂuorocarbon surfactant bilayers.

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FIG. 9 DSC thermograms of unsonicated multilamellar and sonicated vesicle suspensions prepared from dimyristoylphosphatidylcholine 0.1% w/v. (From Ref. 94.)

Multilamellar dispersions of homogeneous phosphatidylcholines exhibit two reversible phase transitions. The major chain-melting transition is a sharp symmetrical ﬁrst-order endothermic transition in the DSC thermogram. For a series of saturated phospholipids, the enthalpy of the main transition is a linear function of the transition temperature (Fig. 10) [94], and the extrapolation to zero enthalpy suggests that saturated phosphatidylcholines with hydrocarbon chains shorter than 12 carbon atoms cannot form stable bilayers.

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FIG. 10 Enthalpies for the main transitions of phosphatidylcholines with acyl groups containing 12, 14, 16, 18, and 22 carbon atoms plotted versus the transition temperature. (From Ref. 94.)

In lipids having the same number of carbon atoms in the acyl chains, the nature of the polar headgroup is also important. As an example, phosphatidylethanolamines exhibit only a single asymmetrical transition [66,99]; also, it has been reported that changing the polar headgroup may shift the gel–mesophase transition by 20–25°C. This difference may be due to differences in crowding in the different headgroups. More compact headgroup layers stabilize the crystal structure, which arises the gel–mesophase transition temperature. Fully hydrated long-chain phosphatidylcholines exist in the condensed crystalline subgel state (L c), in which the hydrocarbon chains are in the fully extended all-trans conformation and the polar headgroups are relatively immobilized [100– 102]. On heating, this subgel undergoes a transition (subtransition) to the L Β state, in which the mobility of the polar headgroups increases and there is increased water penetration into the interfacial region of the bilayers [101–103]. This additional broader transition of lower enthalpy (pretransition) occurs 5–10°C below the main transition—the temperature difference between them decreases with increasing chain length (Fig. 11) [94]. Subtransitions may be classiﬁed into two

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FIG. 11 DSC thermograms showing the phase transitions of (a) didodecylphosphatidylcholine, (b) dimyristoylphosphatidylcholine, (c) dimyristoylphosphatidylethanolamine, and (d) distearoylphosphatidylcholine. (From Ref. 94.)

groups. Type I are ‘‘solid–solid’’ and are found in dipalmitoylphosphatidylglycerol [104] and saturated phosphatidylcholines with C 16 –C 18 chains [105,106]; here, changes between the subgel and gel phases are observed, which are characterized by a very small change in rotameric disorder. Type II subtransitions involve more important changes in rotameric and melting disorder by transformation from the subgel to the liquid crystalline state. Subtransitions are inﬂuenced by headgroup interactions because the addition of small amounts of cholesterol or the opposite stereoisomer prevents the subtransition [107]. Subtransitions have been found in various phosphatidylethanolamines [105,108] but not in equimolecular mixtures of phosphatidylcholines, even though the individual constituents showed subtransitions [106]. In some cases the pretransition is related to the rotation of the polar headgroups of the phospholipid molecules or to the cooperative movement of the rigid hydrocarbon chains prior to melting [97]. In other cases, it is due to structural changes in the lamellar lattice [109]. Several researchers concluded that the pretransition is associated with conformational rearrangements and rotation of the headgroup

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portion of the lipid molecule [67,99,110,111], while others suggest that it is related to the packing of the acyl chains [112–114]. In some cases, the gel phase may be different from that commonly found in surfactant systems, and the change in the nature of the gel may be detected by DSC. Sommerdijk et al. [115] used a synthetic phospholipid that shows that bilayer structures pile up at high amphiphile concentrations (20–80 wt%), whereas small platelets were observed at low concentrations (0.1–1 wt%) by electron microscopy. Figure 12 shows the DSC thermograms at different concentrations [115]. The highly concentrated samples showed an endothermic peak at 45°C (∆H ⫽ 30 J/g), indicating the gel–liquid crystalline phase transition [116]. Lowering the concentration gives rise to a second phase transition at 38°C. This one becomes the main transition when the concentration is about 50 wt%. Further

FIG. 12 DSC thermograms of dispersions of a synthetic chiral phospholipid at different amphiphile concentrations: (a) 99%, (b) 95%, (c) 50%, (d) 10%, and (e) 1% (w/w). (From Ref. 115.)

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dilution causes the endothermal peaks to shift to lower temperatures, which is common in phospholipids [117]. At about 1 wt%, a single-phase transition is again observed at 20°C (∆H ⫽ 88 J/g). This peak belongs to the phase transition from gel to platelets.

1.

Mixed Vesicles and Liposomes

In contrast to pure lipids, which exhibit sharp, highly cooperative phase transitions extending over a few tenths of a degree, mixtures of lipids containing different hydrocarbon chains melt over a much wider temperature range. Moss and Jiang [118] studied liposomes of mixed surfactants by DSC, revealing domain formation or lipid sorting within the liposomes. Liposomes of the pure components melted at very different temperatures (30°C and 56°C). Mixed vesicles melt at temperatures near but lower than that of the main component, and the peaks are broader than those of the pure components. The transition temperature approaches that of the main pure component, and the peak becomes sharper with increasing concentration of that component. The transition enthalpies change as a function of the lipid composition. Morigaki et al. [119] used DSC to study mixtures of chiral fatty acid vesicles. Pure vesicles of the R and S isomers have similar gel–mesophase transition temperatures, T c, but their mixtures showed a remarkable dependence of T c on composition (Fig. 13), with a maximum value at the equimolar (racemic) mixture and two minimum temperatures at the R isomer mole fractions of 0.2 and 0.8 in the mixture. These temperatures correspond to the two eutectic mixtures of enantiomeric and racemic crystals, and the shape of the (pseudo) binary phase diagram indicates that the crystal of the racemate is a racemic compound, as in the case of the bulk compound. This difference enabled the authors to qualitatively follow the kinetics of surfactant exchange between the R and the S isomer vesicles, following the disappearance of the 9.5°C peak and the rise of the 15°C peak at the time (Fig. 14) when equimolar solutions of the R and S isomers were mixed. The transformation of a mixture of the R and S vesicles into homogeneous racemic ones was attained in less than 30 min. Jaeger et al. [120] found differences between DSC behavior of vesicles of enantiomers and racemate, but not as signiﬁcant as those found by Morigaki et al. [119]. They found similar T c values but different ∆H values for the pure enantiomers. The racemic compounds had the same T c . Then the behavior found by Morigaki et al. is not a general one. Chiral discrimination has been found in a number of DSC studies of phospholipid bilayers [120–126].

2.

Interaction with Additives

Thermal analysis of the interaction between drugs and phospholipid bilayers has been used to investigate the action of drug molecules on biological membranes [127–131], especially their effect on the gel–mesophase transition. The inﬂuence

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FIG. 13 Dependence of the phase transition temperature (T c) of the vesicles on the composition of (R)- and (S)-2-methyldodecanoic acid. Total concentration of acid was 100 mM, and half of the carboxyl groups were ionized. (From Ref. 119.)

depends on the location of guest molecules in the packing of the hydrocarbon palisade. The mobility of the chains and the probability of the gauche conformations needed for ﬂuid structures increase along the chain away from the headgroup. Up to the ninth carbon atom, there is considerable segmental packing, such that the highly cooperative nature of the main phase transition is regulated by the interaction of the ﬁrst 10 CEC bonds. The additives may be located at the ﬁrst eight carbon atoms near the polar headgroups, at the surface of the aggregates, or at the deep interior of the structures of aggregation. Moreover, some additives may interact with the polar headgroups. Some additives that interact with polar headgroups are polyvalent ions of opposite charge, which can modify the phase transition proﬁle. As an example, Gd 3⫹, Eu 3⫹, Pr 3⫹, Ca 2⫹, and Mg 2⫹ ions modify the phase transitions of dipalmitoylphosphatidylcholine. The addition of these cations reduces the original transition peak and the appearance of a new peak at higher temperatures [130]. At very high counterion concentrations, the parent peak is completely removed. The

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FIG. 14 Changes in the DSC thermograms upon mixing equal amounts of (R)- and (S)2-methyldodecanoic acid vesicles. Concentration was 100 mM. (a, b, c) (R)-2-Methyldodecanoic acid vesicles (a) before mixing, (b) 3 min after mixing, and (c) 30 min after mixing. (d) 2-Methyldodecanoic acid racemic vesicles after several days equilibration. (From Ref. 119.)

addition of multivalent oppositely charged electrolytes can have a signiﬁcant effect on the packing of surfactant molecules in the aggregates due to rearrangements of the headgroup distribution in the polar layer [132]. This change produces a modiﬁed phase that has the same enthalpy of transition and the same size cooperative unit as the unmodiﬁed phase [130]. The change of monovalent counterions usually does not affect the transition behavior [130]. The half-height width (HHW) of the transition peak is used as a measure of the interactions between solubilized compounds and the phospholipid bilayers [130,133]. This is one of the few available methods for determining the amount of hydrophobic material incorporated into the liposomes. Fildes and Oliver [131] used this criterion to maximize the incorporation of hydrocortisone-21-palmitate in dipalmitoylphosphatidylcholine liposomes. The temperature of the main phase transition was considered independent of steroid content, although the HHW increased to a maximum of 9 at 13.2% before diminishing, indicating the maximum

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level of drug incorporation, i.e., bilayer saturation. This method has also been employed by other authors [134,135]. Raudino et al. [136] proposed a DSC method based on the van’t Hoff model of the depression of the freezing temperature to investigate slow kinetics involving lipid vesicles or liposomes and drug complexes. The melting temperature of vesicles is affected by drug solubilization according to ∆T c (X) ⫽ ⫺ RT c2 (1 ⫺ K)X/∆H

(8)

where ∆T c (X) is the melting temperature depression, T c is the transition temperature in the absence of solute, ∆H is the associated enthaply, R is the gas constant, and K is the partition coefﬁcient of the additive between the gel and the liquid crystalline phases (generally K ⬍⬍ 1 in lipid systems). Equation (8) is valid for a small solute mole fraction X, and it was proved to be valid for several classes of chemical compounds in lipid membranes [137–139] and placed on a theoretical basis by some authors [140,141]. Both T c and ∆H strongly depend on the length and unsaturation of the hydrocarbon chain [142]. The dependence of ∆T c on X may not be linear at high values of X, depending on the solute and the lipid, so a calibration curve must be made. When the concentration of an additive within a lipid bilayer undergoes a slow time variation, the depression of the melting point can be used to monitor kinetic processes such as the uptake of molecules from the aqueous phase or transfer of surface-bound additives from liposomes to other carriers. Here ‘‘slow’’ means that the kinetic phenomenon takes place over a shorter period of time than the time required to perform the thermal analysis. Several researchers investigated by DSC the interactions of additives with vesicles and liposomes. Genz et al. [143] worked on dipalmitoylphosphatidylcholine (DPPC) vesicles with and without the linear polypeptide gramicidin A (GA). DSC peaks showed that at least two types of lipids coexisted in DPPC–GA vesicles in the concentration range 0.02 ⱕ x GA ⱕ 0.04. Measurements performed at 0.36°C/min demonstrated a phase temperature transition T c in DPPC vesicles that was shifted slightly to lower values by the incorporation of GA. A broadening of the calorimetric peaks and a reduction of the transition enthalpy was reported for DPPC-PP (Lys 2-Gly-Leu 24-Lys 2-Ala-amide) multilamellar structures when the PP content is increased [144]. It is known that small unilamellar vesicles show broader DSC transition peaks than multilamellar structures (Fig. 15). For the DPPC–GA system, the transition enthalpy also decreased with increasing GA concentration. In the calorimetric peaks for this system (Fig. 15), a shoulder appears at a GA/DPPC ratio of about 1/60. This indicates the existence of a second, lower melting, lipid phase. The DSC peaks for higher GA concentrations may even be the superposition of three different components. Hasegawa et al. [146] studied suspensions of mixtures of phosphatidylcholine and a fatty acid. Upon

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FIG. 15 DSC thermograms of dipalmitoylphosphatidylcholine containing different amounts of gramicidin A, as a function of the gramicidin/phospholipid ratio. (From Ref. 145.)

increasing the proportion of the fatty acid, the melting peak of the phospholipid liposomes remained as a single peak, although the melting temperature increased. However, at a certain concentration, the phospholipid became saturated with the fatty acid, and although the melting temperature of the mixture remained constant a second endotherm appeared due to the free fatty acid. Thus, in some cases DSC may serve to determine the composition of mixed liposomes. Fujiwara et al. [147] used DSC to follow the interactions between multilamellar vesicles of dipalmitoylphosphatidylcholine (1.4 mM) and polyacrylic acid as a function of pH. The thermograms showed the gradual disappearance of a small pretransition peak at 35°C and of the main transition peak (sharp) at 41°C, with the simultaneous appearance of a broad peak at 44°C as the pH was lowered from 7.6 to 3.8. At the latter pH value, only the 44°C peak was seen (Fig. 16). The peak at 41°C corresponds to pure vesicles, whereas the one at 44°C is due to the vesicles interacting with polyacrylic acid. The sum of the enthalpies of these peaks remained constant. Hence, the gel to liquid crystal transition tempera-

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FIG. 16 DSC thermograms and the corresponding parameters of dipalmitoylphosphatidylcholine liposome phase transition in the presence of polyacrylic acid (1: 1 w/w) at various pH values. (From Ref. 147.)

ture was increased by the interaction with the polyelectrolyte at low pH value. At the same time, the transition cooperativity was reduced. The pretransition peak is associated with long-axis rotation of the phosphatidylcholine molecules [148,149]. Results were interpreted as having been caused by modiﬁcation of the headgroup hydrogen bonding by the polyelectrolyte, affecting the headgroup conformation and the alkyl chain packing.

VI.

MICELLIZATION OF BLOCK COPOLYMER SURFACTANTS

The critical micellization temperature (CMT) and the cloud point (CP) of poly (ethylene oxide)-block-poly(propylene oxide)-block-poly(ethylene oxide) amphi-

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philic copolymers have been studied by DSC and have allowed the estimation of the enthalpy of micellization ∆H mic [150]. Alexandridis and Holzwarth [151] determined both the CMT and the phase separation (CP) of aqueous solutions of poly(ethylene oxide)-block-poly(propylene oxide)-block-poly(ethylene oxide) amphiphilic copolymer (Pluronic L64) in the presence of various salts. Both the CMT and the CP were endothermic (Fig. 17). The pronounced endothermic peak is indicative of micelle formation by block copolymers [150–155], which is typical for a ﬁrst-order phase transition, at concentration-dependent characteristic temperatures [150], while the smaller peak at higher temperatures corresponds to the phase separation (CP). The onset of the thermal transition due to micellization corresponds to the copolymer CMT [150]. Other authors [156,157] also found that micellization is an endothermic process (Fig. 18), and since micelles were stable at higher temperatures the micellization is also characterized by a positive entropy change, in the range of 100– 300 kJ per mole of propylene oxide. This may be due to the melting of structured water during micellization [158]. Measurements on different systems have shown that the total heat ﬂow is related to the amount of propylene oxide in the solution. The peak is associated with the change of the polypropylene blocks from the aqueous surroundings into the lipophilic micellar state and hence can be identiﬁed as the heat of micelle formation. The peaks yield rather high enthalpy values and are broad, extending over more than 10°C. This is probably because copolymers are not pure compounds

FIG. 17 DSC curves for 1% and 10% Pluronic L64 aqueous solutions. The main endothermic peak corresponds to micellization; the smaller one at higher temperatures, to the cloud point. (From Ref. 151.)

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FIG. 18 DSC thermogram of 10% triblock copolymer EO 28 PO 48 EO 28 in water showing the micellization phenomenon. (From Ref. 157.)

but have a broad molar mass distribution [154]. The enthalpy change is not the standard enthalpy change but depends on the real states of the copolymer molecules before and after micellization. The micellization enthalpy was much greater than the CP enthalpy, demonstrating the dominance of the poly(propylene oxide)–water interactions. The strongly endothermic enthalpy indicates that the micellization is an entropydriven process, since micellization is a spontaneous phenomenon. Although cooperative, the micellization process was rather long and spanned a temperature range of 10–20°C due to the temperature dependence of the amount of unimers in equilibrium with the micelles (as temperature increases, more copolymer molecules associate into micelles) [159,160] as well as to the size polydispersity inherent in copolymers. The CMT shifted to lower temperatures as the polymer concentration increased, but its width was not affected much. The CP increased with polymer concentration. The aggregation and phase separation of mixtures of small copolymers (oligomers) in aqueous solution was studied by Chowdhry et al. [161] by deconvolution of the DSC peaks, using a mass action thermodynamic model of aggregation [162]. DSC has also been used to evaluate the surfactant monomer concentration in equilibrium with micelles and its temperature dependence for triblock copolymers [160].

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The output of scanning calorimetry is a data set of power (heat ﬂow in joules per second) versus temperature. This may be readily converted to molar heat capacity using the equation c p ⫽ P/sn

(9)

where P is the power (J/s), s is the scanning rate (K/s), and n is the number of moles of sample. The heat capacity of a triblock copolymer surfactant–water system under thermal micellization can be represented by [163] c p ⫽ ∆H

dα ⫹ αc p,m (T) ⫹ (1 ⫺ α)c p,s (T) dT

(10)

where ∆H is the enthalpy change for the micellization process, a ⫽ n micelle /n total is the degree of micellization, n x is the number of moles in situation x, and c p,m and c p,s are the heat capacities of products (micellized surfactant) and reactants (single surfactant molecules), respectively, ∆H is taken as independent of temperature, which is strictly true if c p,m ⫽ c p,s . If the difference between heat capacities is small and/or the temperature range over which the transition occurs is narrow, only a small error arises from this assumption. Selection and subtraction of an appropriate baseline for the scanning calorimetric output allow the last two terms in Eq. (10) to be eliminated. Thus, by integration of the simpliﬁed expression the extent of micellization at any temperature can be evaluated as α ⫽ Q(T )/∆H

(11)

Here ∆H is the enthalpy absorbed that brings about a total conversion and is obtained by integration of the DSC output, and Q(T) is obtained by partial integration from the start of the endothermic transition to a temperature T. The fraction of nonmicellized monomer in equilibrium with micelles can be obtained from the deﬁnition of α and the mass balance of surfactant: n total ⫽ n monomer ⫹ n micelle

(12)

A. Effect of Other Surfactants on Block Copolymer Micellization With the addition of SDS to solutions of block copolymers, the CMT peak becomes smaller as the SDS proportion is increased, and ﬁnally disappears [164]. Simultaneously, the peak shifts slightly to lower temperatures. The amount of SDS associated with one copolymer molecule that is enough to suppress micelle formation was found by extrapolation to zero enthalpy change associated with micellization. Hecht and Hoffmann [164] found that 5–11 SDS molecules bind

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FIG. 19 Micellization enthalpy of poloxamer EO 97 PO 69 EO 97 from DSC as a function of added SDS concentration. (䊐) 1 wt% poloxamer in H 2 O; (䊉) 3 wt% poloxamer in D 2 O; (䉮) 5 wt% poloxamer in H 2 O. (From Ref. 166.)

to one EO 97 PO 69 EO 97 molecule (Fig. 19). The amount of bound SDS increases somehow with increasing copolymer concentration. The interaction of this copolymer with CTAB was indistinguishable from that with SDS. However, the adsorption of the cationic surfactant started at higher concentration and was higher than that of SDS [165]. Zwitterionic surfactants bind much more weakly to block copolymers, and much higher surfactant concentrations are required to suppress the micelle formation in this case. Hecht et al. [166] found that the surfactants bind cooperatively on the block copolymer molecules, and then the hydrophobic block changes to hydrophilic. At very low SDS concentrations, the micellization peak of the copolymer was not inﬂuenced; hence, no binding occurred, or this binding of SDS to the poloxamer was reversible. From the plot of the micellization enthalpy versus SDS concentration, it is possible to determine the concentration at which SDS starts to adsorb on the poloxamer as the intersection of two straight lines (Fig. 19 [166]). From the difference between this concentration and that at which ∆H mic becomes zero, the amount of bound SDS can be estimated.

VII. EMULSIONS Differential scanning calorimetry is a useful technique to determine the proportion of free and emulsiﬁed water. The overfreezing behavior of emulsiﬁed water

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is very different from that of free water. Signiﬁcant information can be obtained in the study of multiple emulsions in which water can coexist in both states. Microemulsiﬁed water freezes at a lower temperature than free water, and the difference is greater the smaller the drop size. Thus, DSC may give an indication of the size distribution of water droplets. Both freezing temperature and enthalpy may be affected by the presence of solids, which may act as nucleation centers. The thermograms of some emulsiﬁed systems depend on the heating and cooling rates. However, Senatra et al. [167] measured the effect of heating and cooling rates on the thermograms of microemulsions and found no differences in the thermograms recorded (Fig. 20). Other DSC studies on microemulsions were made by Chittofrati et al. [168] and Senatra and Zhou [169], which detected the transition between microemulsions and lyotropic mesophases.

FIG. 20 Temperature dependence of the DSC thermograms of water–hexadecane with mass fraction of water 0.25. From curves a–d, the temperature rates were 1, 2, 4, and 8°C/min. All measurements were made on the same sample. (From Ref. 167.)

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159

THE STATE OF WATER IN SURFACTANTBASED SYSTEMS

One of the principal components of surfactant-based systems is water, which is often neglected, and sometimes only the melting point of this component in the system is reported. The behavior of water is sensitive to the presence of adjacent interfaces of different types, such as biomembranes, proteins, and inorganic compounds [170]. Properties of water molecules depart considerably from their average bulk values when there are solutes or interfaces in the neighborhood. Water in very small volumes plays a dominant role as the medium that controls structure, function, dynamics, and thermodynamics near biological membranes or in other conﬁned regions of space [171]. Several types of water have been detected in surfactant-based microstructures such as microemulsions and liquid crystalline phases [83,169,172–177]. Water in microstructured systems may be roughly classiﬁed into four categories: free water, interstitial water, surface or interfacial water (physically and/or chemically adsorbed), and internal water (chemically bound water). The state of interstitial water may be similar to that of bulk free water. A reduction in the free energy would make the water remain unfrozen at a temperature well below the normal freezing point. These ‘‘types of water’’ have different enthalpies of melting and melting temperatures as well as anomalously low supercooling temperatures [173]. Supercooling and freezing of water in nonbulk states are important for understanding the behavior of water in microporous materials, gels, biological tissues, foods, and other microstructured ﬂuids at subzero temperatures. Besides, water exists in various states with different properties in living beings. Much pertinent information about phase structures in surfactant-based systems and interactions among polar (ionic and nonionic) species and water may be obtained by studying the state of water in microstructured systems. Knowledge of the properties of water at interfaces of organized assemblies, at the microscopic level, is a prerequisite for understanding the effects of these species on chemical reactivity and equilibria. Interfacial water is involved in, among other things, solvation of reactants and transition states, solvation of surfactant headgroups and counterions, and protons [178]. Sludge dewatering is one of the most difﬁcult problems in wastewater treatment, and knowledge of the state of water in different sludges is of industrial and economic importance [179]. There are still questions about, for instance, the degree and extension of the perturbations made by surfaces, their inﬂuence on diffusion and other physical properties, their effects on chemical reactions such as acid–base equilibria, and phenomena taking place in biological microsystems [180]. These questions are of great interest because of the fundamental role that interfacial water plays in many physical, geophysical, chemical, biological, and industrial processes.

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In some cases, water transitions may be misinterpreted as other types of transitions. This has been the case for the transition at ⬃0°C in the system Aerosol OT (AOT)–water, which was interpreted as the gel–liquid crystal transition. Using D 2 O instead of water shifted the transitions to 4°C, which demonstrated that these peaks are due to water melting [62,181]. AOT does not form a gel phase up to ⫺150°C. Another way to identify the melting transition of water is to plot the enthalpy per gram of sample versus composition, giving a value of 319.6 J/ g at 100% water, which corresponds to the melting enthalpy of pure water. In various surfactant-based systems containing water, part of the water does not freeze. Different methods give almost the same value for the amount of this nonfreezing water [182]. This amount may be determined by extrapolating to zero enthalpy a plot of the total melting enthalpy of water per unit weight of sample against sample composition. Nonfreezing water has a very small vapor pressure [61]. Hence this type of water has been interpreted as water bound to solutes in a ﬁrst hydration shell, based on the close proximity of determined amounts with hydration numbers of ions measured at room temperature [63,183]. However, this interpretation is not necessarily the only one possible [183]. In some cases, water may not be free because of two different constraints: It may exist in very small clusters centered on hydrophilic groups or ions, clusters too small to form a nucleus for ice formation. In some cases, stretched water may not freeze because of its extreme viscosity at low temperatures, which yields vitriﬁed water instead of ice crystals since diffusion rather than nucleation becomes the rate-limiting step [184–186]. In some biological microstructures, nonfreezing water is in a metastable viscous state [187]. Stretched water has an increased local partial molar volume owing to interaction with surfaces. The postulation that nonfreezing water forms a hydration layer in ionic surfactant microstructures was based on the coincidence of the hydration numbers of ions and polar headgroups determined by different methods. The extent of hydrogen bonding in water is modiﬁed by the presence of ions (see Ref. 188 and references therein). Neutron scattering measurements have shown that one hydrogen bond is lost for every direct association of a water molecule with an ion that disrupts the structure by means of energetically favorable ion–water interactions [188]. Hydration water molecules are very close to the ion surface. As an example, the maximum distance between protons of water molecules at opposite sides of the hydrated Cl ⫺ and Li ⫹ ions is 0.7 nm, and that between neighboring protons on a hydrated ion is only 0.31 nm [188]. Hydration number is a function of concentration and type of ion. Lithium ions have a coordination number that decreases from about 6 at concentrations of about 4 M to 3 at 10 M [188]. In contrast, Cl ⫺ ions possess at most six water molecules in the ﬁrst hydration shell over a wide range of concentrations and a much weaker hydration structure [189]. In Aerosol OT (AOT)–water systems, there are about six molecules of nonfreezable water per molecule of AOT [63]. The hydration number of the Na ⫹

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ion is about 5 ⫾ 1, so the hydration number of the sulfosuccinate group must be 1 ⫾ 1, similar to that of phosphate groups of phospholipids (⬃1,5) [190]. The melting enthalpy of water becomes zero at 90 wt% surfactant in the sodium dioctylphosphinate (SDOP)–water system, which corresponds to two hydration water molecules [55]. In the didodecyldimethylammonium bromide (DDAB)– water system, the melting enthalpy of water per gram of sample vanishes at 93 wt% surfactant, which yields about two water molecules per molecule of surfactant [191]; this value corresponds to the ﬁrst hydration layer of the bromide ion (⬃2). This means that the dimethylammonium group has a negligible primary hydration capacity. The dioctadecyldimethylammonium bromide (DODAB)–water system shows similar results. In n-alkanephosphonic acid–water systems, the global enthalpy of water melting per gram of sample vanished at 100 wt% surfactant, regardless of the chain length of the n-alkanephosphonic acid, indicating that there is no hydration water [54]. However, in monosodium n-alkanephosphonate–water systems, there are four water molecules per surfactant molecule, which coincides with the water of crystallization [192]. In some biological gels, such as bovine corneas, up to 30% of the water does not freeze [193,194], according to DSC analysis. Castoro et al. [193] and Aktas et al. [194] classiﬁed the water in samples into two categories, free and bound water, based on a temperature of ⫺40°C. This is the reference temperature, accepted by numerous researchers [195–200], where the water content that achieves complete freezing is termed free water and the remaining unfrozen water is termed bound water. The disappearance of the melting enthalpy of water coincides with phase changes, e.g., in the AOT–water system, where a transition occurs from the lamellar to the inverse hexagonal phase [201–203]. The vapor pressure of water falls only when water of hydration exists in the system. When the system is sufﬁciently diluted, ‘‘free’’ or ‘‘bulk’’ water is present in it. Free water is assumed to have physicochemical properties not much different from those of pure water. Its presence is detected by the melting peak at about 0°C (with a slight dependence on water content). Its melting enthalpy is similar to that of pure water (320 J/g water). Free water heat capacities are nearly the same as those of ice below the melting point and are very close to those of water above the melting point [183]. The concentration at which free water disappears can be determined by extrapolation to zero enthalpy per gram of sample. For the AOT–water system, free water vanishes at 60% (w/w) surfactant [61]. Free water has the same vapor pressure as pure water (23.8 mmHg at 25°C in the AOT–water system) [61]. In the sodium dioctylphosphinate (SDOP)–water system, free water exists up to 60 wt% SDOP [55]. In some systems the melting point of free water is between ⫺1 and ⫺2°C, which suggests that this water is not entirely free or pure [177,192]. It must also be remembered that in concentrated ionic surfactant microstructures, free water is a very concentrated ionic solution, which reduces the activity of water and its melting point.

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Garti et al. [177] computed the amount of free water in inverse microemulsions using the equation Wf ⫽

∆H f (exp) ⫻ 100 ∆H 0f

(13)

where W f is the weight percent of free water, ∆H f(exp) is the measured enthalpy change for the 0°C peak, and ∆H 0f is the heat of fusion of pure water measured at the same experimental conditions. The enthalpy change associated with the melting of free water in the poly(ethylene glycol) (PEG)–water system is smaller than the enthalpy of free water, as is true of most aqueous solutions [204,205]. The amount of free water per polymer repetitive unit, Φ, is calculated with the formula [206,207]. Φ⫽

冢

冣冢冣

∆H f 1 w2 ⫺ w1 Hw

Mp Mw

(14)

where w 1 and w 2 are the weight fractions of polymer and water respectively, ∆H f is the heat of fusion from heating experiments, and ∆H w is that of pure water at the transition temperature. M p and M w are the molecular weights of a polymer repetitive unit and water, respectively. When the depression of the melting point of free water is signiﬁcant, the enthalpy of fusion of water must be corrected according to the equation ∆H w ⫽ ∆H°w ⫹ (c p,w ⫺ c p,i)(T f ⫺ 273.16)

(15)

where ∆H °w is the melting enthalpy of pure water at 0°C, T f is the melting temperature, and c p,w and c p,i are the speciﬁc heats of liquid water and ice, respectively [202]. The quantity c p,w ⫺ c p,i can be taken as 2.3 J/(g ⋅ K) [207,208]. A further correction for the heat of mixing is not needed because it is much smaller than the heat of fusion [207,209]. The plot of the dependence of the heat of fusion of free water on surfactant concentration should give a straight line if the amount of bound water is independent of concentration. The intercept must be ∆H°w. However, this value could be slightly different than that of pure water (334 J/g) [204]. Values of 280 and 246 J/g have been reported [204,207]. De Vringer et al. [207] attribute these low values to the overlap between peaks of free and interfacial water in the heating thermogram. ∆H f should be zero when all the water present is bound. At constant PEG concentration, the melting point of free water is smaller than the melting point of ice when the PEG molecular weight is low and rises toward the melting point of ice as the molecular weight increases. This can be attributed to the colligative effect, since at low molecular weights there is a signiﬁcantly higher number density of polymer molecules than at higher molecular weights. The magnitude of the freezing point depression is much greater than that pre-

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dicted by ideal solution behavior, due to the highly nonideal character of PEG solutions [209,210]. Bulk-like water can be supercooled to temperatures around ⫺16 to ⫺23°C. However, water in thin ﬁlms or in emulsiﬁed microdroplets can be supercooled to temperatures as low as ⫺40°C [211–213]. In surfactant systems, free water is in enough large domains to supercool at ⫺16 to ⫺22°C [54,61,211]. In several systems, ‘‘interfacial’’ water, which is associated with the hydrophilic surfaces (polar groups and counterions) of surfactant microstructures, is present. This kind of water is also called ‘‘bound water,’’ ‘‘hydration shell,’’ ‘‘hydration water,’’ ‘‘solvent shell’’ [182], or ‘‘vicinal water’’ [171]. This water can be operationally deﬁned as water detected by a certain technique as it had been inﬂuenced by the surface of the substrate in contact with the water [177]. The presence of the microstructure surface may alter the thermodynamic properties (such as melting point, melting enthalpy and entropy, and heat capacity) and the spectroscopic properties (such as IR absorption frequencies and band shapes) of water [61,214]. The chemical potential of bound water is different from that of bulk water [216]. Properties of bound water (viscosity, density, freezing point, etc.) adsorbed on different surfaces of adsorbents differ from those of bulk water [216–223]. In bulk water, very distinct structures exist, e.g., tetrahedral icelike structures. Near the solid surface, owing to interactions of surface centers, the number of such structures increases as a result of adsorbate–adsorbent interactions. In the literature [224–231] there are various schemes of linear and cyclic structures that are formed by water molecules bonded to solid surfaces as well as calculations of the interaction energy corresponding to one water molecule. Vicinal water shows very interesting structural transitions near temperatures of 15, 30, and 45°C [232–234], showing maxima in viscosity, disjoining pressure, and entropy [235–237]. Studies on the heat capacity of vicinal water and heavy water in the pores of silica gel and porous glasses have been reported, giving values 25% greater than that of bulk water [238–241]. The glass transitions of supercooled aqueous solutions and organic liquids were examined by DSC [242,243]. Some papers [244,245] present DSC studies of the glass transition of water in hydrogels that reﬂect the interactions of water with polysaccharide. Freezing bound water forms metastable ice upon slow cooling and amorphous ice upon quenching. Other DSC results showed cyclical changes in heat ﬂow that were associated with changes in the properties of water due to changes in temperature, particularly of a tetrahedral icelike structure found in bulk and vicinal water [246]. The existence of boundary layers of water possessing modiﬁed properties was indicated by several different experiments (see Ref. 247 and references therein). In many ways, bound water is the most interesting type of water related to surfactant-based microstructures. Differences in the structure of interfacial water

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(relative to that of bulk water) have large effects on micellar catalysis by changing both the activation enthalpy and entropy [245]. The properties of water at the interfaces between surfactant microstructures and solution affects the absorption spectra of solubilizates, which are used to enhance analytical methods [249]. Almost all water in the inner part of cells is close to a membrane, which is an amphiphile aggregate. This means that almost all reactions in living beings occur in an interfacial water medium. Up to three different kinds of interfacial water may be detected in some systems. These kinds of water may be detected as small melting peaks (Fig. 21). In the AOT–water system, two kinds of interfacial water may be detected whose melting points are ⫺5°C and ⫺9°C [61]. These peaks were not detected by DSC in pure water at any sensitivity. When the melting enthalpy of water per gram of surfactant is plotted versus concentration, it remains constant, which is strong

FIG. 21 DSC thermograms of AOT–water liquid crystalline samples as a function of AOT concentration, showing the peaks of (1) free water and (2, 3) interfacial water. (From Ref. 61.)

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evidence of its association with surfactant. The vapor pressure of water drops abruptly when no free water is present [61]. The lack of quantitative data characterizing the structural changes of adsorbed water is mainly due to experimental difﬁculties. Such experimental conditions as sensitivity of the calorimeter, heating rate, purity of water, and position of the sample pan in the measuring cell should be selected very carefully and precisely. Besides, because of the anomalous properties of water molecules (small dimensions and little asymmetry) and their speciﬁc structure and great ability to undergo structural changes, the structural transitions shown by water are of low energy and sudden but occur throughout the entire volume. Various methods for measuring bound water content have been proposed (see Lee and Lee [179], and references therein). A considerable amount of work on the properties of interfacial water of organized assemblies has been done with probes or reactions whose rates are sensitive to the microenvironment [250–252]. These methods often involve hydrophobic solutes whose (average) solubilization site in the micellar pseudophase is still a matter of discussion, and which may perturb the aggregate structure [253,254]. This is not the case in thermal analysis. The amount of interfacial water has been evaluated as the difference between the concentration at which the enthalpy of melting of total water vanishes and the concentration of free water. In some cases the melting peak of one kind of water may be superimposed on that of another component of the system, such as dodecane in an inverse microemulsion [177]. In this situation, the amount of interfacial water is estimated as [177] W1 ⫽

∆H 1 (exp) ⫺ ∆H D f D ⫻ 100 ∆H 1

(16)

where W I is the interfacial water content in weight percent; ∆H I (exp) is the measured enthalpy for the transition, which includes the contribution of the dodecane; ∆H D is the heat of fusion of pure dodecane (191.6 J/g); f D is the dodecane weight fraction; and ∆H I is the melting heat of interfacial water. This enthalpy depends on which of the polymorphic forms of ice is assumed by the interfacial water. Some authors used the crystallization enthalpy of water without introducing an appreciable error [255], whereas others used a corrected value (312.38 J/g) [177,256]. The overlapping of close peaks on heating may be avoided by using cooling thermograms. On this basis, de Vringer et al. [207] used cooling curves to calculate bound water. However, it is difﬁcult to get reliable values for ∆H f, even when corrections are made for supercooling [204]. In the same experiment with polyoxyethylene glycol of different molecular weights, Antonsen and Hoffman [204] found between 3 and 3.8 bound water molecules per oxyethylene group by heating and between 2.3 and 2.8 by cooling. The two methods gave the same results with polymer of low molecular weight.

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LOWERING OF THE MELTING POINT

The lowering of the melting point is related to the size and shape of the water domains [177,257,258]. For water in cylindrical pores of radius a, the reduction in melting temperature, ∆T (°C), is ∆T ⬃ ⫺52/a. The following modiﬁed Kelvin equation was also proposed [215]: ∆T (K) ⫽

49.5 ⫾ 2.0 a ⫺ 0.349 ⫾ 0.036 (nm)

(17)

However, only a fraction [(a ⫺ 0.55 ⫾ 0.04 nm)/a] 2 of the water within the cylindrical pores of radius a freezes out at this temperature. For pores of radius close to 0.55 nm, the fraction of water that freezes out within the pore is very small. The remaining part of the water undergoes a phase transition at a lower temperature, within the range ⫺73 to ⫺66°C. This latter phase transition is not a normal thermodynamic bulk water transition, in the sense that no hysteresis is observed. The thickness of an unfrozen water layer on a mineral surface, d u , is related to the fusion temperature via the equation ∆T ⬇ ⫺50/d u . For planar bilayers, the following equation holds [55]:

冢冣

∆T min l ⫽ 2α ⫹ 1 0 ∆T max L

α

(18)

where L is the total layer thickness, l 0 is the thickness of the interfacial water, α is an adjustable parameter (usually taken as 2), ∆T min is the highest melting point of ice (the position of the endothermic peak of free water), and ∆T max is the maximum depression of the freezing point of water in the presence of the bilayers (i.e., that of interfacial water). Equation (18) gives a value of 0.5 nm as the thickness of the interfacial water in polyoxyethylene chains [177]. In samples with no free water, interfacial water freezes at about ⫺40°C [61]. Lee and Lee [179] found a thermodynamic dependence between the lowering of the freezing point of bound water and the binding strength between water molecules and the surface of microstructures in sludges and the colligative effects of solutes in the aqueous phase:

冢

∆T ⫽ R xB ⫹

EB Tf0

冣冢冣 T 2f0 ∆H f

(19)

where x B is the mole fraction of solutes in the interaggregates solution, R the ideal gas constant, E B the speciﬁc energy of interaction of water with surfaces, T f 0 the standard fusion temperature of water (273.16 K) and ∆H f the fusion en-

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thalpy of water. This equation leads to estimating the value of E B as 25–37 kJ/ kg sludge for ∆T ⫽ ⫺20 to ⫺30 K, a value much larger than the one usually supposed (1 kJ/kg) [251]. When an AOT–water sample containing interfacial and free water was cooled from room temperature, a single peak appeared at ⬃ ⫺16°C due to supercooling of bulk-like water. However, when the sample was heated to ⫺1°C or ⫺6°C to melt only bound water, the free water remained frozen and the interfacial water froze without supercooling, because the two kinds of interfacial water could not remain supercooled in contact with frozen water. The melting of the two kinds of interfacial water was followed by 1 H NMR. One of them melted between ⫺11 and ⫺8°C, and the other between ⫺3 and ⫺1°C [61]. In some lyotropic liquid crystals, the fusion temperature of interfacial water remained almost constant with concentration [61,260], but in some cases, as in inverse microemulsions [177], there is a dependence of the fusion temperature on water content: from about ⫺12.3°C at very low water content to a plateau at about ⫺9.5°C when free water appeared. In microemulsions, the dependence of the amount of interfacial water on total water content shows the changes in phase structure. The amount increases up to the concentration at which free water begins to appear, then forms a plateau in a concentration range in which all added water behaves as free water, and then the amount of interfacial water diminishes when the inverted (W/O) microemulsion changes to a normal (O/W) one [177]. Senatra et al. [261] found three kinds of water in inverse microemulsions: free, interfacial, and bound, according to their melting temperatures of 0°C, ⫺10°C, and ⫺40°C, respectively. The enthalpy of melting was 333.42 J/g, 321.38 J/g, and 313.54 J/g, respectively. In AOT–water systems, the disappearance of interfacial water peaks at 80 wt% AOT is accompanied by a change in liquid crystalline structure; the lamellar mesophase is replaced by an inverse hexagonal mesophase [201–203]. The presence of different types of water in the AOT–water system at room temperature was corroborated by FT-IR spectroscopy. By deconvolution analysis of the OH stretching region (3700–3100 cm⫺1) [61], three peaks appeared, at 3290 cm ⫺1 (free water), 3490 cm ⫺1 (interfacial water), and 3690 cm ⫺1 (matrix isolated trapped water) [262–264]. The amounts of these three kinds of water changed with concentration when the structure of the liquid crystalline phases changed. The amount of bulk-like water is very small above 80 wt% AOT, but below this concentration it increases rapidly, and at about 55 wt% AOT there is more free water than interfacial water. Interfacial water dominated at intermediate (60 wt% AOT ) to high concentrations, in agreement with DSC measurements [61]. The maximum value of trapped water was at 80 wt% AOT, where the melting enthalpy of water became zero. In the sodium dioctylphosphinate (SDOP)–water system, the enthalpy of the interfacial water vanished at 90 wt% SDOP, whereas

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that of free water became zero at 60%. This means that 9.6 water molecules per surfactant molecule are bound in some way to the polar heads and counterions [55]. In the sodium 4-(1-heptylnonyl)benzenesulphonate (SHBS)–water system, three kinds of interfacial water, whose melting points were ⫺50, ⫺40, and ⫺31°C, plus free water melting at 0°C were detected by DSC [260]. Incidentally, the hydrocarbon domains of this system ‘‘melt’’ at ⫺70°C, so the gel structure coexists with ﬂuid hydrocarbon chains and solid water. Unfortunately, the amounts and the limits of the domain of existence of these different kinds of water were not investigated in the paper. No interfacial water was detected in didodecyldimethylammonium bromide– water systems [191]. In alkanephosphonic acid–water systems, interfacial water freezes at ⫺20°C, with an average freezing enthalpy of 47.2 J/g surfactant. However, when heated, only one melting peak is detected. This indicates that this type of water was associated with the acid headgroups when liquid, but this association does not exist when the system is a solid phase [54]. FT-IR spectra demonstrate that there are no interactions among phosphonate headgroups and water in frozen samples. In systems with Brij surfactants (polyoxyethylene-based nonionic surfactants), the the melting peak of free water appears when there are three water molecules per oxygen atom in the polyethylene oxide chain. The same value was found by Garti et al. [177] in inverse microemulsions with octaethylene glycol mono-ndodecyl ether [C 12 (OE) 8]. The melting enthalpy of interfacial water vanished at 1.40 water molecules per oxygen atom [61,62], which gives an average of 4.47 water molecules bound to the polyoxyethylene chain per oxygen atom, in good agreement with the value of 5.05 found by Tokiwa and Ohki [265]. Antonsen and Hoffman [204] found that the amount of bound water varies between 2.3 and 3.8 molecules per oxyethylene group. Tilcock and Fisher [266] found between 1.8 and 2.7 by determining the polymer concentration at which the peak of free water disappears. Earlier results gave values of between two and three water molecules bound per oxygen atom in the polyoxyethylene chains [206,207,266–271]. A gradual increase in this range was reported to accompany an increase in molecular weight. However, Elias [272] reported values ranging from 8.23 to 10.06, depending on the chain length, which suggest that those water molecules in excess of ﬁve that are strongly bound to the oxygen atoms may be trapped in the helicoidal structure of the hydrophilic chain of the surfactant ethers [273] and may be participating in the kinetic entity without being part of the true hydration of the surfactant molecules. Garti et al. [177] did not ﬁnd nonfreezing water in relation to C 12 (OE) 8 and concluded that its existence may be related to the helicoidal structure adopted by the large polyoxyethylene chains, where the trapped water may be in a very restricted space, giving an interaction between water and oxygen atoms strong enough to prevent water from freezing.

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In poly(ethylene glycol) (PEG)–water systems, an exothermic peak was found at about ⫺50°C on heating, which is associated with changes in ice structure [276]. Two endothermic peaks, one at about ⫺14°C and the other at 0°C, were also observed. The latter was caused by the melting of ice, whereas the lower temperature peak was interpreted as having been caused by the melting of a polymer hydrate containing approximately two water molecules per polymer repetitive unit [26,204,206]. Antonsen and Hoffman [204] found that between the two water fusion peaks the system was composed of ice and a concentrated polymer solution. The melting point of interfacial water (which is about 50% of the polymer hydrate) [267] increased rapidly with polymer molecular weight before leveling off at approximately ⫺10°C, at a molecular weight of 1200 (about 26 oxyethylene units). The melting point of interfacial water was not detected at polymer molecular weights lower than 400 (eight oxyethylene units) at temperatures as low as ⫺80°C. This behavior is related to the helicoidal structure adopted by large polyoxyethylene chains, in which loosely bound water molecules can be more easily shared between adjacent segments of a single chain. The PEG hydrate generally solidiﬁes slowly [207]. Thus, during cooling only one exotherm is observed, corresponding to the freezing of free water. Lee and Lee [179] measured free and bound water in natural and artiﬁcial sludges by DSC. They found that there was about 6–7 kg of bound water per kilogram of dry solid mass. After a freezing and thawing treatment, the bound water content had been reduced by approximately 50%. Staszczuk [223] determined phase and structural transitions of vicinal water on protein surfaces by DSC. He observed cyclical changes in heat ﬂow in samples of water adsorbed on the surface of bovine serum albumin, during cooling and heating runs. These cyclical changes reﬂect structural transitions occurring in the water adsorbed on the surface at subambient and elevated temperatures. This is connected with cyclical changes (decay and reproduction) of icelike structures existing in the adsorbed layers. Figure 22 [223] shows a structural transition of water adsorbed on pure bovine serum albumin, on cooling in the temperature range from ⫺1 to 0°C. Peak corresponds to the water structure and peak B to the freezing of adsorbed water. Figure 23 [223] shows structural transitions of water adsorbed on silica gel covered with bovine serum albumin on heating, depicting the ‘‘melting’’ of the water structure (peak A) and the ‘‘freezing’’ of the adsorbed water. The shapes of the curves are analogous to those of DSC curves obtained during the investigations of phase transitions occurring in organic substances [242], pure water and silica gel, alumina oxides, active carbon, and zeolites containing adsorbed water ﬁlms [246]. These changes reﬂect the transitions in the icelike structure of adsorbed water. In these ﬁlms, water is enriched in tetrahedral icelike structures with respect to that in bulk water (40% vs. 10% in bulk water). These spontaneous transitions occurred in the water structure in irregular temperature ranges during cooling and heating of samples. The observed phenomenon is a

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FIG. 22 Structural transitions of water adsorbed on pure bovine serum albumin during sample cooling. Peak A, ‘‘melting’’ of the water structure; peak B, ‘‘freezing’’ of the adsorbed water. (From Ref. 243.)

FIG. 23 Structural transitions of water adsorbed on silica gel covered with bovine serum albumin during sample heating. Peak A; ‘‘melting’’ of the water structure; peak B, ‘‘freezing’’ of the adsorbed water. (From Ref. 243.)

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sudden decomposition of the icelike structures of water (creation of a metastable system) followed by the reconstruction of these structures. Depending on the temperature and direction of the experimental process, the number of reconstructed icelike structures increases (in the cooling process) or decreases (in the heating process). In the cooling process, the number of these structures increases as long as the temperature of transformation of water to ice is not attained. During the heating process, the gradual decomposition of increasingly larger numbers of icelike structures takes place and proceeds until the end of evaporation of water from the solid surface. The structure of the boundary layers of water depends on the nature of the surface. Near a hydrophilic surface this structure must be essentially different from that on a hydrophobic substrate because of the absence of hydrogen bonds between water and the surface in the latter case. When the surface is chemically and physically inert, the inability of the water molecules to extend their hydrogen bond structure into such a surface could have the same effect as heating. If the surface interacts with water, the inability of those molecules forcibly oriented near the surface to maintain normal hydrogen bonding with their neighbors creates the same type of perturbation [172]. Neutron-scattering experiments demonstrated that the electrostriction effects are small in the secondary hydration shell of ions and beyond [275]. This conclusion probably holds for the hydration layer on the hydrophilic surfaces of surfactant microstructures. Several estimates were made of the thickness of the interfacial layer. Derjaguin and Churaev [247] estimated the thickness of the boundary layers of water with peculiar structure to be close to 10 nm. This thickness diminishes with increasing temperature and reduces to a monolayer at 65–70°C [276]. The distance of 10 nm (36 water molecules) has been proposed on the basis of several experiments [277–279] as the distance over which the cooperativity of hydrogen bonding extends [185]. Some experiments indicate that the upper limit is between 3 and 5 nm [280–286], where the differences in properties between bound and bulk water are signiﬁcant. As discussed above, the thickness of the boundary water was estimated to be 0.54 ⫾ 0.10 nm in cylindrical pores [287]. In micellized sodium soaps, the distance between the carboxylate carbon and the nearest water proton is around 0.3–0.4 nm [288], which means that the lower limit of the thickness of the interfacial layer is about one water molecule. Interfacial water exists in biopolymers in two states: stretched water, which has expanded and thus increased its local partial molar volume, and compacted water, whose local partial molar volume has decreased. Compacted water is in the closest proximity to the surface. These changes in density are accompanied by changes in water–water hydrogen bond strength and therefore by changes in all physical and chemical properties of the liquid. Some results showed that hydrophobic headgroups (phenyl or n-butyl) en-

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TABLE 1 Degree of Structure of Interfacial Water Due to Surfactant Headgroups Headgroup N ⫹ (C 4 H 9) 3 Br ⫺ COO ⫺ Na ⫹ N ⫹ (CH 3) 2 (C 6 H 6)Br ⫺ N ⫹ (CH 3) 3 Cl ⫺ N ⫹ (CH 3) 3 Br ⫺ SO 4⫺ Na ⫹ N ⫹ (CH 3) 2 (CH 2) 3ESO 4⫺ N ⫹ (C 2 H 4 OH) 3 Cl ⫺ EO(C 2 H 4 O) 9.5EH

Fractionation factor ϕ M 1.14 1.08 1.06 1.06 1.06 1.06 1.02 ⬃1 0.95

Source: Ref. 178.

hance the structure of interfacial water. The main factors are electrostriction by the charged interface and hydrophobic hydration of the bulk group. The fractionation factors ϕ M measured by NMR spectroscopy give information about the structure of interfacial water. If ϕ M ⬎ 1, interfacial water is more structured than bulk water. Interactions that decrease surface charge density decrease ϕ M because of the lower electrostriction by the charged interface. The interaction between the headgroup and counterion affects the structure of interfacial water. Some examples of decreasing degree of structure of interfacial water measured by ϕ M are given in Table 1. Based on these data, it may be concluded that ionic and zwitterionic headgroups generally increase the degree of structure of interfacial water. Some groups do not change the structure of water, e.g., tri(2-hydroxyethyl), and with polyoxyethylene groups interfacial water is less structured than bulk water. The water of hydration of the nonionic surfactant Triton X-100 is less structured than bulk water [289–291]. The same conclusion was reached about the hydration layer of nonionic and zwitterionic micelles by NMR spectroscopic measurements [292].

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5 Effects of Cooling–Heating Cycles on Emulsions B. FOUCONNIER, J. AVENDANO GOMEZ, K. BALLERATBUSSEROLLES, and DANIELE CLAUSSE UTC–De´partment Ge´nie Chimique, Laboratoire Ge´nie des Proce´de´s, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochi´mie de Proce´de´s Industriels, Compieg`ne, France

I. Introduction II.

Liquid–Solid Transitions

183 184

III. Differential Scanning Calorimetry Technique

187

IV. Experimental Results

194

V. Conclusion

201

References

201

I. INTRODUCTION An emulsion is conventionally deﬁned as a heterogeneous system, made by dispersing one liquid in another, that forms globules in a continuous phase. Additives referred to as surfactants are added to the system to increase the stability of the emulsion. The surfactant molecules are adsorbed onto the surface of the droplets and consequently modify the interfacial properties as shown in other chapters of this book. During cooling and heating, various physical and chemical phenomena have been observed. They may concern either the disperse, continuous, or interfacial phases. The aim of this chapter is to give a tentative description of some of these events and make a correlation with the resulting properties of the emulsions themselves. Simple water-in-oil (W/O) or oil-in-water (O/W) emulsions, mixed emulsions, and multiple emulsions that can be found during the fabrication pro183

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FIG. 1

Scheme of a W/O/W multiple emulsion.

cesses and their storage and use are considered in this chapter. W/O or O/W emulsions consist of water or oil droplets dispersed within oil or water, respectively. By mixed emulsions we mean emulsions that are obtained by gently mixing two different emulsions, avoiding coalescence. The dispersed phase in a mixed emulsion is a population of droplets of different compositions. Special attention has been recently devoted to these emulsions by various research groups [1–4] in order to understand and to predict composition ripening. Multiple emulsions are generally obtained by a two-step process [5,6]. First a simple W/O or O/W emulsion is made, and then it is dispersed within an aqueous phase or an oil phase to obtain a multiple W/O/W or O/W/O emulsion. Figure 1 is a schematic representation of such an emulsion. These emulsions resemble liquid membrane systems [7,8] and are considered either as substance reservoirs [9–12] or as liquid–liquid separation systems [8,13]. During the cooling-and-heating cycles of the emulsions previously described, the more obvious physical phenomena that may occur are liquid–solid transitions. Solid–solid transitions have also been observed for organic materials dispersed in emulsions and are described elsewhere [14]. Section II is devoted to the analysis of liquid–solid transitions and what can be deduced from them when emulsions are concerned. In Section III the technique used to analyze these transitions is described. Section IV is devoted to a description of results obtained from experiments performed on emulsions previously described.

II.

LIQUID–SOLID TRANSITIONS

Liquid–solid transitions may concern either the dispersed or continuous phase of an emulsion. Nevertheless, whichever phase is concerned, the ﬁrst step in the

Effects of Cooling–Heating Cycles

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transition is the formation of a germ, or nucleus. For instance, in the case of water dispersed in a W/O emulsion or continuous water in an O/W emulsion, the transition from liquid water to ice requires the formation of at least one ice nucleus. Afterward, the total ice formation in the two kinds of emulsions will be drastically different. With regard to O/W emulsions, all the volume of the aqueous phase crystallizes as a result of a single germ. In contrast, a single aqueous droplet dispersed into a nonpolar phase crystallizes separately, leaving the other aqueous droplets in the liquid state. Before we study the way in which the continuous and dispersed phases solidify, we consider the conditions of formation of one germ. The formation of the germ is the result of local density [15,16], which can be enhanced by speciﬁc materials playing the role of nucleating agents, the structure of which is close to that of the germ. With or without nucleating agents, both germ size ranges in the colloidal domain and capillary effects have to be taken into account. From thermodynamic considerations, the energy formation, ∆Φ, can be expressed as ∆Φ ⫽

4 πR 2 γ 3

(1)

where γ is the interfacial energy of the germ/surrounding interface and R is the radius of the germ in metastable equilibrium with the surrounding medium. The radius R is temperature-dependent according to the relation ln

冢冣

2γV i Tm ⫽ T RL m

(2)

where T m is the melting temperature reached at time t m, V i is the ice molecular volume, and L m is the molar melting enthalpy. According to Eqs. (1) and (2), ∆Φ decreases if T and R decrease. Aspects of kinetics also have to be taken into account through the nucleation rate J, the number of germs formed per unit time per unit volume. J is expressed as

冢冣

J ⫽ K exp ⫺

∆Φ kT

(3)

K is a parameter characteristic of the medium in which the germs are supposed to appear. The schematic curve showing the change of J versus T is given in Fig. 2. J is generally found to be zero near T m and to increase dramatically when the temperature is decreased signiﬁcantly. Referring to the droplets dispersed in an emulsion, it is possible to predict the temperature of solidiﬁcation. Let us assume that all the droplets have the same volume V and that a single germ is enough to attain total solidiﬁcation of the

186

FIG. 2

Fouconnier et al.

Changes in the nucleation rate J versus temperature.

droplet in which the germ is born. As soon as the solid–liquid equilibrium temperature T m (0°C for water) is exceeded, some germs may be formed inside the droplets. Very few droplets are expected to solidify near T m, as the nucleation rate is nearly zero and the energy of formation of the germ is the highest (∞) at T, as shown earlier. Let us suppose that the number of solid droplets at time t is N. The number dN of droplets that will solidify during further cooling within the time interval dt can be related to the number of germs formed during this time: dN ⫽ JV(N 0 ⫺ N t )dt

(4)

according to the deﬁnition of J and the assumption made. N 0 represents the total number of droplets. From Eq. (4), it is possible to deduce the proportion dN/N 0 of droplets that are going to be solid during time dt:

冢

冣

N dN ⫽ JV 1 ⫺ t dt N0 N0

(5)

Assuming a regular cooling, the rate T˙ being given by the equation dT T˙ ⫽ ⫺ dt

(6)

Effects of Cooling–Heating Cycles

187

FIG. 3 Nucleation rate versus temperature.

it is possible to express dN/N 0 versus temperature T as

冢

冣

JV N dN ⫽⫺ 1 ⫺ t dT N0 T˙ N0

(7)

As shown before, J increases exponentially from a value approaching zero when T is close to the melting temperature (T m ⫽ 0°C for water) to very high values when T is far from T m. As the quantity (1 ⫺ N t /N 0 ) decreases from 1 (all the droplets are liquid) to 0 (all the droplets are solid), dN/N 0 is expected to go through a maximum as depicted in Fig. 3. During heating, the melting behavior is completely different from the freezing behavior because it does not require the formation of a germ. Moreover, there is no delay, and ice globules will be found to melt at 0°C. As solidiﬁcation of the droplets will release energy and melting will adsorb energy, differential scanning calorimetry (DSC) of emulsions has been proposed as a means to detect the solidiﬁcation or melting of the droplets within them. Some general details about this technique that are needed for the analysis of the thermograms are given in the next section.

III. DIFFERENTIAL SCANNING CALORIMETRY TECHNIQUE Differential scanning calorimetry allows measurement of the heat exchanged between a sample (S) and a reference (R). The solidiﬁcation and melting of phases induce the release and absorption of energy, respectively, and consequently are

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FIG. 4 Scheme of Perkin-Elmer DSC 2 apparatus. T S, sample cell temperature; T R, reference cell temperature; T P, temperature imposed to the plates; C S, heat capacity of the sample cell; C R, heat capacity of the reference cell; R, R′, heating resistances.

detected through the appearance of peaks. The peak areas are proportional to the energies involved, as is shown subsequently. Figure 4 is a schematic representation of a Perkin-Elmer DSC 2 differential scanning calorimeter, whose principles are given by Gray [17]. The calorimeter head is constituted of two identical plates in continuous contact with a cold source and heaters that supply the required energy to impose the programmed temperature T p to the plates. The heaters run independently, and an electronic system compensates for temperatures between the plates. If melting is supposed to occur in the sample cell, energy is absorbed by the sample. That absorption induces a temperature difference between the two cells that is compensated for by the heaters. The power exchange dq/dt expressed as the equation dq T P ⫺ T S T P ⫺ T R ⫽ ⫺ dt R R′

(8)

is measured and is represented by a thermal signal recording. The same argument is applicable for an exothermic phenomenon due to solidiﬁcation. The relation between dh/dt (the heat released or absorbed per unit time during emulsion solidiﬁcation or melting) and dq/dt is given by the equation dq dT dh d 2q ⫽ ⫺ ⫹ (C S ⫺ C R ) P ⫺ RC S 2 dt dt dt dt

(9)

This equation is obtained from the energy conservation equations T ⫺ TS dT dh ⫽ CS S ⫺ P dt dt R

(10)

Effects of Cooling–Heating Cycles

189

and 0 ⫽ CR

dT R T P ⫺ T R ⫺ dt R′

(11)

for the sample and the reference, respectively. When no thermal phenomenon occurs, dh/dt ⫽ 0, and the solution to Eq. (9) is: dq dT ⫽ (C S ⫺ C R ) P ⫹ Ae ⫺t/RCS dt dt

(12)

When t ⬎⬎ RC S (3–4 s), dT dq ⫽ (C S ⫺ C R ) P dt dt

(13)

C S depends on the composition of the emulsion and on the speciﬁc heat of all the different phases constituting the system. Equation (13) represents the baseline, a line parallel to the zero signal of the calorimeter. C S is considered to be almost constant when no thermal phenomenon occurs. If C S varies during the melting or solidiﬁcation transition, the baselines before and after the transformation are shifted apart. This baseline drift induces a difﬁculty in the interpretation and is analyzed later in the chapter. In the general equation, Eq. (9), dh/dt is the sum of three terms. The ﬁrst term, ⫺dq/dt, represents the power recorded by the calorimeter. The second is the difference between the baseline and the zero level of the signal due to the difference between the speciﬁc heats of the sample and the reference. The third term is the slope of the recorded curve multiplied by the time constant RC S. Temperatures are not obtained directly by DSC. The problem is to determine the sample emulsion temperature T S knowing the temperature T P of the oven. The combination of the energy conservation equations (10) and (11) with the expression of heat ﬂow, Eq. (8), gives the equation T S ⫽ T P ⫺ RC S

dQ dT P ⫺R dt dt

(14)

where dQ dq dT ⫽ ⫺ (C S ⫺ C R ) P dt dt dt dq/dt represents the signal deviation from the baseline during the transition. RC S (dT P /dt) is a term of inertia for the sample cell, which is almost constant during the cooling or heating.

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R(dQ/dt) depends on the thermal phenomenon amplitude and remains equal to zero when dh/dt ⫽ 0 and t ⬎ 3–4 s. It is therefore possible to calibrate the calorimeter to determine temperature T S by studying pure compounds with well-known melting temperatures. Knowing those physical considerations, we can now analyze the thermograms obtained for a pure compound during the melting and solidiﬁcation processes. Those results can then be extended to emulsion systems. For a pure compound the shape of the melting signal can theoretically be determined from the expression dh/dt by considering two points: 1.

When the sample reaches the melting temperature T m, the temperature of the sample, T S, remains equal to T m throughout the melting process. Therefore, dT S /dt ⫽ 0 and

冢冣

dT dq dT P t ⫽ ⫹ (C S ⫺ C R ) P dt dt R dt 2.

(15)

After the melting, dh/dt ⫽ 0, and

冤冢冣

冥

dq dT dT dT P t ⫽ (CS ⫺ CR) P ⫹ ⫺ (C S ⫺ C R ) P e⫺t/RCS dt dt dt R dt

(16)

The observed peak (Fig. 5) is composed of an initial linear part where the slope is

FIG. 5

Shape of thermogram of a pure compound melting.

Effects of Cooling–Heating Cycles

191

given by (1/R)(dT P /dt) followed by an exponential return to the baseline through Ae ⫺t/RCS ⫹ B. The melting temperature is determined by the intersection of the baseline with the tangent to the (1/R)(dT P /dt) slope. The signal recorded can be analyzed if one knows the relationship existing between dh/dt and dq/dt [Eq. (9)]. The area A of the signal is deﬁned by the integral A⫽

冮

t2

t1

冢

冣

dT dq ⫺ (C S ⫺ C R ) P dt dt dt

(17)

where t 1 is the time at which the transition begins and t 2 the time it ends. From Eq. (9) Eq. (17) can be expressed as A⫽

冮

t2

A⫽

冮

t2

t1

t1

冤

⫺

⫺

冥

dh d 2q ⫺ RC S 2 dt dt dt

dh dt ⫺ RC S dt

冮

t2

t1

(18)

d 2q dt dt 2

(19)

or A ⫽ ⫺∆H ⫺ RC S

冤冢dqdt冣 ⫺ 冢dqdt冣冥 t2

(20)

t1

I If melting or solidiﬁcation transitions are supposed to occur with no speciﬁc heat variation, the term I is equal to zero because

冢冣冢冣 dq dt

⫽

t2

dq dt

t1

⫽ (C S ⫺ C R )

dT P dt

Thus, the area of signal delimited by the extension of the baseline gives the energy released or absorbed during the transition. When there is a signiﬁcant difference between the solid and liquid values for liquid C S [for example, with water, C ice ⫽ 4.18 J/(g ⋅ K)], S ⫽ 2.09 J/(g ⋅ K) and C S the signal has to be delimited as shown in Fig. 5. It has not been yet mentioned that the dispersed solid droplets melt at the same temperature. The determinations of thermal signal shape and area are similar to those for bulk systems if the continuous medium does not show high thermal resistance. To reach those conditions, the heating rate has to be less than 2 K/ min and the mass sample sufﬁciently small. To study emulsions quantitatively, it is necessary to know precisely the total mass of dispersed liquid, m L . The

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integration of the melting peak allows us to determine the amount of liquid if its latent heat of fusion L m is known and is expressed as Eq. (21). This method is often used to estimate the amount of dispersed water contained in W/O emulsions [18]. mL ⫽

∆H A ⫽ Lm Lm

(21)

Let us now study solidiﬁcation. Generally, crystallization of a pure compound is an instantaneous phenomenon that occurs at a temperature lower than T m depending on the volume according to relation (4). The thermogram shape has been calculated [14] by writing the equation dh ⫽ ∆H c δ(t ⫺ t c ) dt

(22)

where ∆H c represents the total quantity of heat released during transition and δ(t ⫺ t c ) is the Dirac function. At t ⱕ t c, dh ⫽0 dt

and

dq dT ⫽ (C S ⫺ C R ) P dt dt

(23)

and

dq ∆H c ⫺t/RCS dT ⫽ (C S ⫺ C R ) P ⫺ e dt dt RC S

(24)

At t ⱖ t c, dh ⫽0 dt

The crystallization occurs at t ⫽ t c or T c, and the signal is composed of a line perpendicular to the baseline followed by an exponential return to the baseline (Fig. 6). The energy released is directly determined from the area delimited by a straight line between the baselines before and after the transition. The transition temperature is given by the intersection of the vertical segment and the baseline. In the case of a rather big sample and a rather high cooling rate (T˙ ⬎ 5 K/min) crystallization is not instantaneous. The important release of heat during the transformation induces the solidiﬁcation of some parts of the sample at higher temperature. Thus, the enthalpies of solidiﬁcation measured are overestimated. Bulk water represents the most unfavorable case: Its latent heat of crystallization varies strongly with temperature. In the case of monodispersed systems, dh/dt can be stated, supposing that the heat of solidiﬁcation varies only a little with temperature during the transformation [19], as dN dh 4 3 ⫽ πr ρL C dt 3 dt

(25)

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193

FIG. 6 Shape of thermogram of a pure compound solidifying.

with L C ⫽ ∆H C /m L ⋅ ρ is the mass per unit volume of the droplets, r the radius of a droplet, and dN/dt the number of droplets crystallizing per unit time. Thus, knowing dh/dt, we can deduce dN/dt or dN/dT. The relationship between dh/dt and the recorded value dq/dt is not straightforward, and therefore it is not so easy to get dh/dt from the thermogram. Nevertheless, according to the analysis done in Section II, it can be expected that the shape of the thermogram will show a peak. The apex of the peak is very close to the point of maximum freezing events. It has been checked that the slower the cooling rate, the closer the apex temperature is to the maximum deduced from Eq. (7). This temperature has been referred to as the most probable temperature of freezing of the dispersed droplets. A safe way to determine the freezing rate of the droplets versus time or temperature is to proceed as follows. First the sample is cooled until time t i or temperature T i and then immediately heated to the melting point. The melting area A i is proportional to the quantity of liquid crystallized. From Eq. (14), the sample temperature is known at time t i. Thus, the plot of curve A i /A as function of the temperature T Ai provides at any time or temperature the proportion of liquid solidiﬁed at T Ai . A is the total dispersed liquid melting. Ai 1 ⫽ A n

冮

ti

0

⫺

dN ⫽ f(t i) ⫽ ϕ(T Si ) dt

(26)

From integral curve (26), it is possible to plot the differential curve and obtain dN/dt as a function of T Ai or t i. Therefore, the signal for the crystallization is

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represented by a Gaussian distribution, and the probable melting temperature is given by the apex of the peak, which means that 50% of the sample is crystallized [20,21]. This method is applicable owing to the low thermal inertia of the calorimeter and the stability of the emulsion. Nevertheless, when the cooling programmed temperature is reached at time t i the sample continues to crystallize. To avoid this perturbation, the sample is rapidly heated to temperature T Si and then melted more slowly. Techniques such as microscopy or the use of a Coulter counter are common techniques to study O/W emulsion stability, but they are applicable only to dilute systems. DSC represents a suitable technique to characterize a W/O emulsion without disturbing the system. Characterization of a water-in-crude oil emulsion has been studied in the laboratory. The degree of undercooling and the probable temperature obtained from a cooling thermogram allows the determination of the distribution size of dispersed droplets. By knowing the latent heat of solidiﬁcation, it is also possible to determine the number of droplets crystallized at temperature T*.

IV.

EXPERIMENTAL RESULTS

The thermodynamic and physical concepts explained above can help in solving phase transition problems as well as mass transfer or composition ripening in different kinds of emulsions. Figures 7–14 are illustrations of the results obtained with different kinds of emulsions submitted to regular cooling and heating in a Perkin-Elmer DSC 2. Figure 7 presents thermograms of the solidiﬁcation of water and the melting of ice in a simple W/O emulsion (emulsion 1) made of vaselin oil and lanolin (lipophilic emulsiﬁer) as the continuous phase and deionized water as the dispersed phase. Figure 8 shows the cooling and the heating thermograms of another W/O emulsion (emulsion 2) constituted of Exxol D80 and Berol 26 (nonionic surfactant) as the oil-continuous phase and a dispersed aqueous solution of 5% (w/w) sodium chloride. For both cooling thermograms, the signals observed are related to the crystallization of the dispersed droplets at temperature T* that is given by the apex of the Gaussian peak as discussed in Section II. At this apex temperature, 50% of the droplets have been crystallized by breakdown of undercooling. In Figs. 7 and 8 the baselines before and after the crystallization are shifted apart due to the difference between the speciﬁc heats of the supercooled liquid and the crystallized droplets. Generally in W/O emulsions the size distribution of pure water droplets varies between 1 and 5 µm, and they crystallize at about ⫺40°C as

Effects of Cooling–Heating Cycles

195

FIG. 7 Solidiﬁcation and melting of dispersed water in a simple W/O emulsion of vaselin oil and lanolin as the continuous phase.

FIG. 8 Solidiﬁcation and melting of dispersed saline aqueous solution in a simple W/O emulsion made of Exxol D80 and Berol as the continuous oil phase.

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shown in Fig. 7. The presence of solute in the water delays the solidiﬁcation of dispersed droplets. This delay in solidiﬁcation varies with the concentration of salt as shown in Ref. 3. In Fig. 8, the solidiﬁcation of the dispersed droplets is delayed and occurs at ⫺48°C. The presence of solute is indicated by the thermogram because the solid–liquid equilibrium temperature, T SL, is changed. For pure ice, the fusion occurs at about 0°C as shown in Fig. 7 and the shape of thermogram is similar to the theoretical shape for a pure compound during melting. Nevertheless, the melting temperature is slightly displaced, probably due to the presence of the surfactant added to stabilize the emulsion. The temperature is determined by the intersection of the baseline and the tangent to the point of greatest slope. In Fig. 8 the melting of aqueous salted frozen droplets begins at the eutectic temperature T e (ﬁrst peak at ⫺21°C) and continues until ice–solution equilibrium is reached (following the second peak at T SL ⫽ ⫺7°C). In this case, the shape of the thermogram is divided into four parts [22]: For T S ⬍ T e at t ⬍ t 0, the heat ﬂow shape follows Eq. (13). For T S ⫽ T e at t 0 ⬍ t ⬍ t 1, the shape is a straight line. This is the case of a pure compound melting at constant temperature T e. For T e ⱕ T S ⬍ T SL at t 1 ⬍ t ⬍ t 2, there is equilibrium between the solid and liquid phases. T SL is the temperature at which the progressive melting ends and is expressed using Eq. (14) as T SL ⫽

dT P dT dq (t 2 ⫺ t 0 ) ⫹ R(C S ⫺ C R ) P ⫹ T e ⫺ R (t 2 ) dt dt dt

(27)

The equilibrium temperature is given by the intersection of the baseline and the tangent to the point of greatest slope during the progressive melting. This tangent is a straight line parallel to the tangent plotted to determine the eutectic temperature. For T S ⬎ T SL at t ⬎ t 2, the sample is entirely liquid, and the shape of the thermogram is represented by an exponential return to the baseline, following Eq. (16). Calorimetry is able to distinguish dispersed water from bulk water. Water crystallization is volume-dependent; the probable temperature of bulk water solidiﬁcation is around ⫺14°C for cm 3 or mm 3 volume [22]. W/O system destabilization can be detected during cooling by using the solidiﬁcation temperature. If W/O emulsions break, water behaves as bulk water. Figure 9 presents a cooling thermogram of an emulsion made of the same chemicals as emulsion 2, whose dispersed droplets do not contain sodium chloride. The cooling is performed just after the emulsion preparation and shows that the system is unstable because the water solidiﬁcation appears at ⫺17°C. The solidiﬁcation is instantaneous, and

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FIG. 9 Solidiﬁcation and melting of dispersed deionized water in a simple W/O emulsion made of Exxol D80 and Berol as the continuous oil phase.

the curve shape is given by Eqs. (23) and (24). It can be concluded that salt acts as a stabilizer for this system. Figure 10 presents the cooling and heating thermograms of a W/O/W multiple emulsion. The internal phase is constituted of water dispersed in vaselin oil stabilized by lanolin as lipophilic emulsiﬁer. This primary emulsion is then dispersed in water stabilized by sodium lauryl sulfate as hydrophilic surfactant. The droplets dispersed in the oil drops crystallize at ⫺42°C, and the external water phase solidiﬁes at ⫺17°C. There is no measurable delay in the melting of the solidiﬁed droplets. Hence, all droplets of both aqueous phases melt at the same temperature, around 0°C. The shape of the thermogram is similar to that of the melting of a pure compound mentioned in Section II. Another interesting phenomenon that can be studied by calorimetry is socalled composition ripening. In that case, an O/W emulsion can be formed in which the dispersed medium is characterized by droplets of two different oils in a common aqueous solvent. The mixed solution is prepared by blending two different O/W simple emulsions of well-known compositions. An instability is then created in the emulsion, due to the difference in the nature of the drops. The oils will tend to diffuse through the water medium from one drop to another, ﬁnally forming mixed droplets of the same composition. The kinetics of the ripening depends on various parameters. The major ones are the nature and solubility of the oils, the nature and concentration of the surfac-

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FIG. 10 Solidiﬁcation and melting of internal and external water phases in a W/O/ W multiple emulsion in which the oil membrane is composed of vaselin oil and lanolin surfactant.

tants, the size of the droplets, and the oil/water ratio. Let us take the example of n-hexadecane–n-tetradecane (50:50 w/w) in water emulsions. As the freezing temperatures of the two oils are different enough, at time t 0 when we put the two O/W emulsions containing the same mass of oil phase together, the thermogram will exhibit three characteristic peaks, as shown in Fig. 11. The ﬁrst peak, around ⫺2°C, is associated with the crystallization of n-hexadecane, whereas the peak around ⫺17°C is related to n-tetradecane crystallization. The peak around ⫺23°C corresponds to the freezing point of the water (the continuous medium). At time t ⬎ t 0, new thermograms are registered. Figure 12 shows thermograms obtained at different times t from 0 to 24 h. The shifts of the oil peaks as well as the areas of those peaks give precise and quantitative information on the concentration ripening. At t large enough (24 h in Fig. 12) the concentration equilibrium is reached and the thermogram exhibits a single peak for the two oils with a more probable temperature at about ⫺9°C. This temperature corresponds to the freezing point of mixed droplets. To evaluate the composition of the droplets it is possible to realize a calibration curve for the system. For that, thermograms were obtained for equilibrated emulsions containing the same ratio of oil phase to water phase as in the emulsion previously described but with a variable composition of the oil phase (variation of the hexadecane/vs tetradecane ratio). From those curves we extracted the temperature of crystallization of the oil droplets

Effects of Cooling–Heating Cycles

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FIG. 11 Crystallization thermogram for the mixed emulsion containing 15 wt% n-hexadecane droplets and 15 wt% tetradecane droplets.

FIG. 12 Crystallization thermograms for the mixed emulsion for different times t.

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FIG. 13 Calibration curve for crystallization temperature of mixed droplets versus percent n-tetradecane.

versus percentage of tetradecane in the oil phase. Those results are reported in Fig. 13. That representation shows a linear evolution. If we now report the temperature obtained in Fig. 12 at 24 h, it is possible to determine that at equilibrium there is 57% tetradecane in the droplet. If all the oil were in the droplets or if the solubilities of the two oils were the same, the temperature should correspond to 50% tetradecane in the droplet. Let us now study the thermograms obtained during the mass transfer. It is obvious from the thermograms that only the peak corresponding to hexadecane shifts to a lower temperature. The position of the tetradecane peak remains constant with t. At the same time, the area of the tetradecane peak decreases signiﬁcantly, clearly indicating that most of the tetradecane diffuses into hexadecane drops, whereas hexadecane diffusion into hexadecane droplets is quite negligible. As the number of moles of oil in a droplet is proportional to the enthalpy of crystallization [23], we calculated the area of the hexadecane peak A with respect to time to quantify the kinetics of diffusion of tetradecane into hexadecane drops. Considering that at t 0 ⫽ 0 the area A 0 is the reference one, we report in Fig. 14 the ratio A/A 0 versus time. This ratio is assumed to vary between 1 (t ⫽ t 0 ) and 0 (t ⫽ t e, end of transfer). The ratio decreases almost exponentially, and t e is reached after approximately 15 h of diffusion. The same kinds of results were reported by Clausse et al. [23] for water-in-oil emulsions, but in that case the equilibrium time was much smaller than in our case (about 1 h).

Effects of Cooling–Heating Cycles

201

FIG. 14 Kinetics of diffusion of n-hexadecane in mixed emulsion.

V. CONCLUSION The purpose of this chapter was to illustrate with examples what goes on when different kinds of emulsions are submitted to regular cooling and heating. We focused on liquid–solid transitions, the most obvious of the expected phenomena. Numerous techniques allow qualitative information to be obtained about phenomena such as droplet composition or composition ripening. However, most of them have to be used in very dilute conditions, far from real application conditions. We have shown that calorimetry is a powerful tool for the study of those systems because it does not require dilution and the results obtained give quantitative information. Therefore, it appears to be one of the most efﬁcient techniques for studying phenomena within emulsions, such as composition ripening and phase transitions.

REFERENCES 1. BP Binks, JH Clint, PDI Fletcher, S Rippon, SD Lubetkin, PJ Mulqueen. Langmuir 15:4495–4501 (1999). 2. L Taisne, P Walstra, B Cabane. J Colloid Interface Sci B 184:378–390 (1996). 3. D Clausse. J Dispersion Sci Technol 20(1/2):315–316 (1999). 4. J Avendano Gomez, JL Grossiord, D Clausse. Entropie 224/225:98–104 (2000). 5. S Raynal, JL Grossiord, M Seiller, D Clausse. J Controlled Release 26:129–140 (1993).

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6. S Raynal, I Pezron, L Potier, D Clausse, JL Grossiord, M Seiller. Colloids Surf A: Physicochem Eng Aspects 91:191–205 (1994). 7. NN Li. AIChE J 17(2):459–463 (1971). 8. Kuswandi, JL Grossiord, D Clausse. Rec Progr Ge´n Proc 13:277–284 (1999). 9. D Clausse, I Pezron, S Raynal. Cryo-Letters 16:219–230 (1995). 10. S Matsumoto. ASC Symp Ser 272:415–436 (1987). 11. N Garti, S Magdassi. J Colloid Interface Sci 104:587 (1985). 12. JL Grossiord, M Seiller, F Puisieux. Rheol Acta 32:168–180 (1993). 13. RP Cahn, NN Li. Separ Sci 9(6):505–519 (1974). 14. JP Dumas. PhD Thesis, Pau, 1976. 15. L Dufour, R Defay. Thermodynamics of Clouds, Academic Press, New York, 1963. 16. H Pruppacher, D Klett. Microphysics of Clouds and Precipitation, Reidel, Dordrecht, 1980, pp. 162–180. 17. AP Gray. In: Analytical Calorimetry, Vol. 1, (RJ Porter, JF Johnson, eds.) Plenum Press, New York, 1968, p. 209. 18. D Clausse, JP Dumas, F Broto. CR Acad Sci 279:415–418 (1974). 19. JP Dumas, D Clausse, F Broto. Therm Acta 13:261–275 (1975). 20. D Clausse. In: Encyclopedia of Emulsion Technology, Vol. 2, Applications (P Becher, ed.), Marcel Dekker, New York, 1985, pp. 77–157. 21. F Broto, D Clausse. J Phys C: Solid State Phys 9:4251–4257 (1976). 22. O Sassi, I Sifrini, JP Dumas, D Clausse. Phase Transitions 13:101–111 (1988). 23. D Clausse, I Pezron, A Gauthier. Fluid Phase Equil 110:137–150 (1995).

6 Thermal Analysis of Self-Assembling Complex Liquids DONATELLA SENATRA Department of Physics—INFM Group, University of Florence, Florence, Italy

I. Introduction II.

The A. B. C.

DSC Approach DTA and DSC From ∆T to ∆Q The DSC signal (dH/dt)

204 204 205 207 213

III. Phase Diagrams

214

IV.

217 217 217 221

DSC Analysis of Microemulsions A. Standard reference liquids B. Thermal cycles C. Sample weight and thermal rate

V. Phase Transitions A. First-order phase transitions: melting endotherms study B. Interphasal water C. Structural transitions associated with the interphase region VI. VII.

DSC-ENDO Spectra: Deuterated Components

233

First-Order Phase Transitions: Freezing Exotherms Study

236

VIII. Higher Order Phase Transitions IX.

221 222 226 229

239

The Percolation Transition

241

References

244

203

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I. INTRODUCTION This chapter deals with the use of differential scanning calorimetry (DSC) in the study of some of the properties of self-assembling thermodynamically stable, multicomponent systems that appear to the naked eye as homogeneous and monophasic. Typical examples are micellar and microemulsion systems [1]. Both of these liquids are characterized by the presence of a dispersed phase, whether in the form of aggregates or droplets (diameter ⬇10 nm), a dispersing medium, and a large interphasal area that becomes increasingly important as the ‘‘particle’’ size decreases. From a microscopic point of view, these systems are heterogeneous. To understand their thermodynamic stability, the equilibrium condition valid for heterogeneous systems in the condensed state must be considered. In other words, the system as a whole is assumed to be closed, which means that it may exchange only energy with the surrounding world. In this closed system there is a dispersed phase that behaves as an open system and may therefore exchange both energy and matter with the surrounding bulk medium. The equilibrium condition implies thermal, mechanical, and chemical equilibrium. In an equilibrium system, only reversible processes can take place. The question of the inﬂuence of temperature on the heat effect due to chemical reactions is outside the scope of this chapter. By introducing the enthalpy state function (H) deﬁned by H ⫽ E ⫹ pV, where E is the system’s total energy, p the pressure, and V the volume, and by using the condensed state condition (∆V ≅ 0), it follows from the ﬁrst and second laws of thermodynamics that at constant pressure, ∆H ⫽ ∆Q and a change in the enthalpy equals the change in the heat (Q) released or absorbed by the system during any thermal process. Since the heat change or the heat content at a given transition, in the frame of the reversible processes taking place in an equilibrium system, is the fundamental parameter to deal with in this study, we have found the ‘‘probe’’ for testing some of the main properties of our liquid multicomponent systems. It is the bulk behavior of the massive phases, phase transitions, and the role of the interphasal region. The main problem is how to measure the heat associated with a given thermal event. The extent to which we can rely on the measured heat exchange depends on the particular instrument used, on the calibration procedure followed, and on some experimental ‘‘considerations’’ that must be taken into account.

II.

THE DSC APPROACH

‘‘Thermal analysis’’ refers to the group of methods in which some physical property of a sample is continuously measured as a function of temperature while the sample is subjected to heating or cooling at a controlled rate (dT/dt). The temper-

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ature change is the driving force that determines the ability of a material to transfer heat to or accept heat from other materials or sources. The effect of heat can be wide-ranging, and it causes changes in many properties of a sample. In thermal analysis, changes in weight form the basis of thermogravimetry (TG), while measurements of energy changes form the basis of differential thermal analysis (DTA) and differential scanning calorimetry (DSC). Thermomechanical analysis (TMA) follows dimensional changes as a function of temperature. DTA and DSC are the most widely used techniques for investigating phase changes and phase equilibria, structural changes, thermal stability, qualitative analysis, quantitative analysis of mixtures, quality control as an assessment of purity, hydration, solvation and coordination effects, thermodynamic studies, and the determination of thermal constants. The range of materials that can be studied by thermal methods includes biological materials, building materials such as concretes and cements, ceramics and glasses, fats, oils, soaps and waxes, fuels and lubricants, liquid crystals, polymers and plastics, pharmaceuticals, textiles and ﬁbers, and so on. Before entering the speciﬁc argument about the application of DTA-DSC techniques to multicomponent liquids consisting of water or oil droplets coated with a surfactant shell and dispersed into an oil or water continuous phase, we consider some technical details of these two thermal methods of analysis [2].

A. DTA and DSC The techniques of DTA and DSC are not identical. Let us consider the essential difference between them. In DTA, the heat changes within the material are monitored by measuring the difference in temperature (∆T ) between a sample and an inert reference. In a classical DTA equipment both the sample (S) and the reference (R) are heated by the same furnace (Fig. 1a). The temperature sensors are inserted directly into the sample and reference, while in a modiﬁcation of classical DTA, called Boersma DTA (Fig. 1b) they are in contact with the container but not with the materials under test. The temperature difference between the sample and the inert reference is recorded as a function of temperature (T) or time (t). In DSC, the sample and the reference materials are provided with their own separate furnaces as well as with their own separate temperature (T) sensors. In DSC, the sample and reference are maintained at identical temperatures by controlling the rate at which heat is transferred to them (Fig. 1c). Differential scanning calorimetry differs from differential thermal analysis in that instead of allowing a temperature difference to develop between the reference and the sample, the former measures directly the energy that has to be applied to keep the temperature the same, that energy being the amount of heat that must be supplied during an endothermic process (∆H ⬍ 0), for example, the melting of a substance, or subtracted during an exothermic process (∆H ⬎ 0), when the

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FIG. 1 Instrumental setup for thermal analysis. (a) Classical DTA; (b) modiﬁed DTA; (c) DSC, two furnaces. The parameters R, S, T R, T S, and ∆T are deﬁned in the text.

thermal energy is, for instance, released as the material crystallizes from the melt. If ∆H ⬎ 0, the sample heater is energized and a corresponding signal is obtained; if ∆H ⬍ 0, the reference heater is energized in order to compensate for the temperature difference between the furnace of the sample and that of the reference until the temperatures of the two heat sources become equal again. The second process gives a signal opposite that of the ﬁrst. Since the energy inputs are proportional to the magnitude of the thermal energies involved in the transition, the records give the calorimetric measurements directly. The latter aspect of DSC measurements is one of the greatest advantages of this technique. For this reason, this type of calorimeter is called power-compensated DSC. Typical DTA and DSC recordings are depicted in Figs. 2a and 2b, respectively. There is a third type of process, heat ﬂux DSC, in which the electronic response of the instrument is coupled with the heat ﬂow across an interface while

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FIG. 2 (a) Typical DTA recording. The temperature difference (∆T) between sample and reference is plotted on the ordinate axis. (b) Typical DSC recording. The differential heat input (mW) is plotted on the ordinate axis. In both cases, the abscissa can be either time or temperature.

both the sample and the reference are in close contact with the latter. The interface is usually a sapphire disk in which both the sample and reference are inserted in their own housings surrounded by thermocouples embedded in the same disk. In this case, both the sample and reference are contained in a single furnace as in DTA, and the temperature difference (Ts ⫺ Tr ) is related to the instantaneous rate of heat generation (dH/dt) by the sample through an equation that links together the temperature differences between the sample, the reference, and the instrument heat source at a temperature T0, the thermal rate applied (dT/dt), the sample heat capacity at constant pressure (C s ), the reference heat capacity (C r ), and the instrument constant (R) that accounts for both the thermal resistivity and the geometry of the calorimetric device. Most of the results reported in the forthcoming sections were obtained with a heat ﬂux DSC thermal analyzer.

B. From ⌬T to ⌬Q It is well known that heat can ﬂow within a system only if energy is transferred because of a temperature gradient from some point at a temperature T 1 to another point at a temperature T 2 with T 1 ⬎ T 2.

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FIG. 3 Newton’s law for the ﬂux of heat through a homogeneous material of cylindrical geometry. The parameters Q, L, A, ∆x, T 1, and T 2 are deﬁned in the text.

With reference to Fig. 3, the amount of heat ﬂux within a time interval ∆t is governed by the relation ∆q kA(T 1 ⫺ T 2 ) ⫽ ∆t L

(1)

where k is the thermal conductivity coefﬁcient of the material constituting the cylinder through which the heat ﬂows, L is the length of the cylinder, and A is its cross-sectional area. In SI units the heat ﬂux is measured in watts and k is therefore expressed in watts per meter per kelvin. By introducing the thermal resistivity R, deﬁned as R⫽

冢冣

∆x 1 k A

(2)

where R is expressed in kelvins per watt (K/W) or in kelvin-seconds per joule (K ⋅ s/J) and ∆x is the thickness of an inﬁnitesimal slab, the rate of heat ﬂux (dq/dt) across ∆x, with ∆T ⬎ 0 can be written as dq ∆T ⫽ dt R

(3)

Equation (3) is known in the literature as Newton’s law. We assume that (1) the heat energy per unit time (dq/dt) is supplied by the instrument source at a temperature T ⫽ T 0; (2) T s is the temperature of the sample and sample pan; (3) (dH/dt) 1 is the instantaneous heat generated (dH/dt ⬎ 0) or

Self-Assembling Complex Liquids

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absorbed (dH/dt ⬍ 0) by the sample because of an exothermic or endothermic process, and (4) (dH/dt) 2 is a term that accounts for the heat transfer to or from the sample, expressed as a function of both the (sample ⫹ sample pan) heat capacity at constant pressure (C s ) and the rate of change of the sample temperature (dT s /dt). Taking into account that the total heat balance must be constant, it follows that

冢冣冢冣

dH dq ⫽ dt dt

⫹

1

dH dt

(4)

2

where dq/dt is the heat supplied per unit time by the furnace. From Newton’s law, the latter is 1 dq ⫽ (T 0 ⫺ T s ) dt R

(5)

The term (dH/dt) 1 is the instantaneous heat due to the sample enthalpic change, and (dH/dt) 2 is the term that accounts for the fact that, depending on whether (dH/dT) 1 is positive or negative, the sample temperature may be increased or decreased. This must be counterbalanced by a cooling device in addition to the thermal resistor of the instrument source. Expressing the sample heat capacity at constant pressure,

冢冣冢冣 dH dT

Cs ⫽

⫽

p

dH/dt dT/dt

(6)

p

and omitting from now on the p subscript, we have

冢冣 dH dt

2

⫽ Cs

dT s dt

(7)

Substituting Eqs. (5) and (7) into Eq. (4), we obtain an expression for the difference between the source temperature T 0 and that of the sample T s, T0 ⫺ Ts ⫽ R

冢冣 dH dt

1

dT ⫹ RC s s dt

(8)

Now we can solve the same problem from the reference side. For the reference we have (dH/dt) 1 ⫽ 0: No change in the heat content occurs in the empty reference pan, and all the heat is used to change the reference temperature T r. However, the reference pan heat capacity C r can differ from that of the sample. Thus, we may write, always according to Newton’s law [Eq. (3)], the analogous expres-

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sion for the reference because the quantity dq/dt is supplied by the same source. We have dq T 0 ⫺ T r ⫽ dt R

(9)

and Eq. (4) for the reference becomes, by substituting (dH/dt) 2 ⫽ C r (dT r /dt), dq dT ⫽ Cr r dt dt

(10)

The latter, with Eq. (9), gives Cr

dT r T 0 ⫺ T r ⫽ dt R

(11)

Therefore, the difference between the source and the reference temperature has the form T 0 ⫺ T r ⫽ RC r

dT r dt

(12)

Subtracting Eq. (12) from (8), we obtain R

冢冣 dH dt

⫽ RC r 1

dT r dT ⫺ RC s s ⫹ (T r ⫺ T s ) dt dt

(13)

By adding to both sides of Eq. (13) the quantity RC s dT r /dt and rearranging, it follows that R

dH dT d ⫽ (T r ⫺ T s ) ⫹ R r (C r ⫺ C s ) ⫹ RC s (T r ⫺ T s ) dt dt dt

(14)

where the subscript 1 has been omitted. Equation (14) expresses the instantaneous rate of heat generation by the sample as a function of the ‘‘measured’’ temperature difference between sample and reference, taking into account other parameters such as the heat capacities for both the sample and reference, the thermal rate (dT r /dt ⫽ dT/dt), and the instrument constant R. As a further step we must understand the meaning of the three terms on the right-hand side of Eq. (14) and also try to recognize which of them can be experimentally handled to optimize the heat ﬂux DSC measurements. In Eq. (14), apart from the ﬁrst term on the right, whose meaning is obvious, the second term represents the baseline displacement from the electric zero level, while the third, multiplied by the constant R and the sample heat capacity, is the term responsible for the thermal peak in the DSC recordings. In a pure DTA

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setup, this term represents the slope at any point of the peak [2]. Since the products RC r,s have the dimension of time (τ), i.e., RC r,s ⫽ τ, where the dimensions of τ are (K ⋅ s/J)(J/K) ⫽ s, we can rewrite Eq. (14) as follows: dT d dH ⫽ ∆T ⫹ (τ r ⫺ τ s ) ⫹ τ s (∆T ) R dt dt dt

(15)

From Eq. (15) it emerges that the R(dH/dt) term depends on the temperature difference between the sample and the reference, on the thermal rate dT/dt, on ∆τ r,s ⫽ τ r ⫺ τ s, and on τ s ⫽ RC s. In order to understand how ∆τ r,s and τ s can be optimized to improve the quality of the measurements, we must enter the argument from a practical point of view by introducing a given heat ﬂux DCS instrument. From now on we report on the results obatined with a Mettler-Toledo TA 3000 unit equipped with a TC 10A processor and two low-temperature cells, namely a DSC 30 and a DSC 30 Silver. As stated earlier, we cannot have any heat ﬂux without ∆T ≠ 0. The latter condition is fulﬁlled in this DSC instrument in such a way that, assuming T 0 ⫺ T r ⬎ 0 (see Fig. 4), the reference temperature lags behind the source temperature by the quantity T 0 ⫺ T r ⫽ τ LAG

dT dt

(16)

In Eq. (16), the time constant is called the ‘‘tau lag’’; it depends on the particular instrument used. Moreover, Eq. (16) follows directly from Eqs. (9)–(12) with dT r /dt ⫽ dT/dt, the latter being the applied thermal rate. The value of the tau lag constant is usually provided with the DSC equipment. However, this time constant can be optimized experimentally by repeating the same measurement

FIG. 4 Heat ﬂux DSC. Relation between the furnace temperature (T 0 ) and reference temperature (T r ). [See Eq. (16) in the text for further explanation.]

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without changing anything but the thermal rate. The calculated value τ* is given by the relation τ* ⫽ τ LAG ⫹ 60

T1 ⫺ T2 dT 1 /dt ⫺ dT 2 /dt

(17)

where T 1 and T 2 are the melting temperatures of a standard, whether a solid or a liquid, measured at two different thermal rates, dT 1 /dt and dT 2 /dt, with dT 1 /dt ⬎ dT 2 /dt; the number 60 transforms the time unit to seconds. Usually, dT 1 /dt ⫽ 8–11 K/min and dT 2 /dt ⫽ 1–2 K/min. Several measurements must be performed and the average value used. For the low-temperature range, this procedure must be repeated with a component such as n-pentane, which has a melting temperature of ⬃143 K. Therefore, to assess the instrument behavior within the working temperature interval, the average of the two τ* values can be evaluated and used in the conﬁguration list. The latter value represents the time constant, in seconds, required to equilibrate the temperature difference between the furnace and the DSC sensor. Going back to Eq. (15), we will try to understand how it is possible to optimize the second term on its right-hand side, ∆τ r,s (dT/dt). The latter can be optimized in two steps: 1. 2.

By compensating for the weight difference between the crucibles that will be used for the measurement By compensating for the difference arising from the sample’s thermal conductivity

In the ﬁrst case, a measurement must be performed with two ‘‘empty’’ crucibles, both for the reference and the sample, within the temperature interval that will be used in the ﬁnal DSC measurement. The measurement can be stored and the result thereafter subtracted from the ﬁnal DSC analysis obtained by using the same crucibles for the reference and sample and, obviously, the same scan speed. Such a procedure is known as blank correction. In the second case, a measurement must be performed by ﬁlling both the reference and sample pans with a ‘‘reference’’ sample. By ‘‘reference sample’’ we mean exactly the system under test, provided it has previously been ascertained that within the temperature interval required to perform the correction of the time constant no transitions of any order are occurring in the sample. A relation similar to Eq. (17) is used. However, in this second case a time constant (τ**) is evaluated with both pans ﬁlled with the ‘‘reference’’ system. We have τ** ⫽ τ LAG ⫹ 60

T1 ⫺ T2 , dT 1 /dt ⫺ dT 2 /dt

with

dT 1 dT 2 ⬎ dt dt

(18)

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The tau lag constant (τ*) must therefore be replaced with the τ** value. Greater details about this topic are given later. The main problem relates to the availability of a standard for the system as a whole. Practically, the inability of a sample to follow a given thermal program can be tested experimentally from the steplike pattern occurring at the end of the dynamic part of the DSC recording, between the latter and the isothermal part (ISO): The larger the step, the worse the situation. This means that the sample temperature lags too much behind the furnace temperature. In other words, in a melting analysis, for example, the sample ends with T s ⬍⬍ T r, while during a cooling test, the sample ends with T s ⬎⬎ T r. These problems can be overcome by reducing the sample mass or by lowering the thermal rate and by careful control of the τ* constant. An example of the steplike pattern at the end of the dynamic part of a DSC recording is reported in Section IV.C. The third term on the right-hand side of Eq. (14) or (15) contains another time constant called the ‘‘tau signal,’’ τ s ⫽ RC s. The latter can also be experimentally evaluated and therefore optimized. Before entering into this argument we must discuss how the heat ﬂux DSC instrument handles the dH/dt signal.

C. The DSC Signal (dH/dt) If we assume that the second term on the right-hand side of Eq. (14) or (15) is a known constant evaluated as discussed in the previous section, we get d dH ∆T ⫽ ⫹ C s (∆T ) dt R dt

(19)

By introducing the sensitivity of the thermocouples (S), deﬁned as ∆V ⫽ S ∆T, where ∆V is a voltage difference, we may write ∆T ⫽

∆V S

d d(∆V)/dt dS/dt ∆T ⫽ ⫺ ∆V dt S S2

(20a)

(20b)

We recall that S is the thermometric sensitivity of the DSC sensor that converts the thermocouple voltage (∆V) to the temperature difference ∆T. Since the second term on the right-hand side of Eq. (20b) can be disregarded, we obtain, by substituting (20a) and (20b) into (19), ∆V ⫹ RC s d dH ∆V C s d ⫽ ⫹ ∆V ⫽ (∆V) dt RS S dt RS dt

(21)

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In Eq. (21), RC s is the already deﬁned ‘‘tau signal’’ (τ s ); its value, given in the instrument handbook, can be inserted in the conﬁguration list. The tau signal accounts for the type of crucible used (whether aluminum, gold, or glass). The product RS is called the calorimetric sensitivity and is replaced with E. Both R and S depend on temperature. The calorimetric sensitivity E can be divided into two terms, one of which, E IN, does not depend on temperature, while the other, E REL, does depend on temperature, and its temperature dependence is contained in the TA processor as a polynomial, E REL ⫽ A ⫹ BT ⫹ BT 2 Therefore the T dependence of the relative calorimetric sensitivity is directly governed by the instrument’s software. The heat ﬂow to the sample (dH/dt) is given by dH ∆V ⫹ τ s d ∆V/dt ⫽ dt E IN E REL

(22)

The E IN part of the E constant can be experimentally determined through a careful calibration procedure, by measuring the latent heat of pure indium pellets in a melting DSC run. This procedure deﬁnes the heat ﬂux calibration. It requires that several measurements be made of the constant E IN, each time using a new, previously unmelted indium pellet. Thereafter the average value can be inserted into the conﬁguration list. We recall that with the standard sensor in the ‘‘medium’’ sensitivity, the measuring range is 60 mW, with a calorimetric sensitivity of 11 µV/mW and 2400 points/K; in the ‘‘high’’ sensitivity position, the measuring range is 17 mW and the number of points per kelvin rises to 8500. Unless speciﬁed, the medium sensitivity setup is used in the DSC measurements reported in this chapter. The tau signal τ s can be assessed by using a crucible ﬁlled with a sample of the system under test. By performing an isothermal measurement it must be veriﬁed how quickly the baseline is reached by the DSC signal. Such a procedure is essential in the study of chemical reactions, but it can be used to improve the DSC measurements in the study of other processes as well.

III. PHASE DIAGRAMS As already mentioned in the Introduction, micelles and microemulsions are complex multicomponent ﬂuids consisting of two liquids, namely water and oil, and a surface-active agent (for a three-component system). For a four-component system, in addition to the surfactant a cosurfactant is also added (usually an alcohol). In systems containing more than four components, some salt is added, solubilized in either water or oil.

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The composition of a multicomponent system is depicted by points on the plane of an equilateral triangle for three components and of a regular tetrahedron for four components. In the ﬁrst case, the apices of the equilateral triangle correspond to pure components, the points on its sides to two-component systems, and the points inside the triangle to ternary mixtures. Since the composition is generally expressed as a fraction or percent (molar volume, weight), the sides of the triangle are divided into 10 (or 100) parts, and straight lines parallel to the respective sides are drawn through the points of division. The ratios of the components are determined either on the basis of the fact that the sum of perpendiculars dropped from any point onto the sides of an equilateral triangle equals its altitude, taken equal to 1 (or 100), or that the sum of lines drawn from any point inside an equilateral triangle, parallel to its sides, up to their intersection with another side of the triangle equals a side of the triangle, which is taken equal to 1 (or 100). Both methods give the same result, since the sides and the altitudes of an equilateral triangle are proportional to one another. Moreover, 1. A straight line parallel to the side opposite a given apex is a line representing a constant concentration of the component to which this apex corresponds. 2. A straight line passing through the apex of the triangle corresponding to a given component is a line with a constant ratio between the other two components. Points 1 and 2 follow directly from the proportionality of perpendiculars dropped from any point of a line to the corresponding sides of the triangle. In the case of the regular tetrahedron describing the composition of four-component systems, the length of its edges is taken as 100%, while its apices correspond to the pure substances. The tetrahedron edges depict the binary systems, its faces the ternary ones. Planes parallel to the faces correspond to systems containing a constant percent of the component opposite this face. The latter feature is quite often used to construct ‘‘pseudoternary’’ phase diagrams in which one apex of an equilateral triangle represents, for instance, the amount of surfactant ⫹ cosurfactant in a given and ﬁxed molar, weight, or mass ratio or percent, while the other components, namely the water and the oil, are represented on the other two remaining apices. In the latter case, the rules given for ternary systems apply. The conﬁned domains depicted in Fig. 5 represent the regions where macroscopically homogeneous and single-phase systems are found. However, these domains do not necessarily represent micellar or microemulsion systems. The characterization of such systems requires a great deal of experimental work, usually interdisciplinary. Structural properties can be investigated by small-angle neutron scattering (SANS) [3–5] or by quasi-elastic light scattering (QELS) [6–8]. Interphasal properties can be studied by dielectric spectroscopy and electrical conductivity mea-

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FIG. 5 Phase diagrams. (a,b) Pseudoternary phase diagrams of two four-component systems. The continuous line encloses the domain within which monophasic, homogeneous samples are conﬁned. PP′ lines are experimental paths followed in the DSC study by adding water to samples characterized by the constant ratio (S ⫹ COS/O) of 0.70 and 0.68 for systems (a) and (b), respectively. The compositions are given in Table 2. (c) Phase diagram of a three-component system with perﬂuoropolyether (PFPE) oil (O), PFPE surfactant (S), and water (W). The composition of the system along the dilution line W/S ⫽ 11 is given in Table 4.

surements, ﬂuid properties by viscosity measurements [9–12], and basic thermodynamic behavior by differential scanning calorimetry (DSC) [13–14]. In laboratory practice, samples may be prepared by weighing the components. Sometimes, mostly when dealing with volatile components or strongly hygroscopic surfactants, it is difﬁcult to dose exact amounts of any given component in preparing a sample. If one starts with a basic stock solution and thereafter proceeds to add ﬁxed

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amounts of a component to it, it is easier to follow the evolution of the system behavior and thus to understand its properties as a function of the change of only one component. The latter procedure becomes increasingly important as we approach the border of the monophasic domain of the given system.

IV.

DSC ANALYSIS OF MICROEMULSIONS

Three main topics are fundamental to DSC study of microemulsions: 1. Standard reference liquids 2. Thermal cycles 3. Sample weight and thermal rate

A. Standard Reference Liquids The melting temperatures (T m ) and the enthalpy of melting (∆H m ) values of the pure liquid components are necessary to identify the different contributions of each of the system’s components to the DSC spectrum. The literature data for both T m and ∆H m must be used as reference values for testing whether the instrumental setup is working properly in order to identify the different peaks in the thermal spectrum. However, for quantifying the contribution of each component, it is better to use as standard values for both T m and ∆H m the experimentally measured values of the pure bulk compounds used to formulate a given system. Another procedure that may help in identifying the thermal events is the substitution of a given component by the corresponding deuterated one, provided that the melting temperature of the latter differs by about 3–4 K from that of the normal liquid. One precaution must be followed in applying this procedure: The substitution of one of the microemulsion components by its deuterated counterpart may modify the monophasic domain of the system phase diagram, so one must ascertain that even if the proportions between the components are the same, one is working far from the boundary of the monophasic region across which a phase transition to lyotropic mesophases or macroscopic phase separation may occur. The melting spectra of systems with deuterated components are given later. Some melting temperatures and enthalpy values of liquids commonly used in the formulation of microemulsions are listed in Table 1. The compositions of the systems analyzed in this work are given in Tables 2, 3, and 4.

B. Thermal Cycles As shown in Fig. 6, during a melting or freezing thermal process, a temperature difference develops between the sample and the reference. Therefore, it is important, in a dynamic DSC measurement (as a function of temperature), both to precede and to follow the thermal analysis with an isothermal period (ISO) of

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TABLE 1 Melting Temperatures and Enthalpy Values Compound

Formula

MW

MP (K)

∆H (J/g)

C 5H 12 C 6H 6 C 6H 14 C 7H 8 C 8H 18 C 10H 22 C 12H 26 C 16H 34 H 2O D 2O H 2O C 16D 34

72.5 78.11 86.18 92.14 114.23 142.28 170.34 226.41 18.016 20.029 18.016 329.248

143.3 278.53 177.7 178.01 165.7 243.3 263.4 292.9 273.0 276.82 263.0 286.0

116.69 127.40 151.75 74.35 89.73 202.25 216.27 235.44 333.42 313.54 312.38 —

n-Pentane Benzene n-Hexane Toluene Isooctane n-Decane n-Dodecane n-Hexadecane Water Heavy water Interphasal water (n-Hexadecane) d34

TABLE 2 Composition of Four-Component W/O Microemulsionsa System 1 2

Oil (%) Dodecane 57.22 Hexadecane 57.73

Surfactant (%)

Cosurfactant (%)

Dispersed phase (%)

K-oleate 15.30 K-oleate 14.94

n-Hexanol 25.03 n-Hexanol 24.35

Water 2.45 Water 2.98

Component proportions: surfactant/oil ⫽ 0.2 g/mL; cosurfactant/oil ⫽ 0.4 mL/mL. Percentages are by weight.

a

TABLE 3 Composition of Three-Component W/O Microemulsions System

Φa (mL/mL)

W 0b (mol/mol)

T dp (K)

0.35 0.35 0.31

40.8 40.7 37.0

300 312 306

Water–Na(AOT)c –decane D 2O–Na(AOT)–decane Water–Na(AOT)–isooctane Volume fraction (water ⫹ surfactant)/total. Molar fraction water/surfactant. c Sodium di-2-ethylhexyl sulfosuccinate. d Percolation temperature. a

b

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TABLE 4 Composition of Perﬂuoropolyether W/O Micromulsions Along the Dilution Line W/S ⫽ 11a Φb,c

%W

%S

%O

0.205 0.327 0.395 0.462 0.501

3.95 6.37 7.80 9.20 10.05

14.05 22.86 27.90 33.00 36.03

82.00 70.77 64.30 57.80 53.92

T p (K)d 305.5 292.3 289.5 285.5 282.3

⫾ ⫾ ⫾ ⫾ ⫾

0.2 0.3 0.3 0.3 0.3

a

W/S molar fraction. Percentages are by weight. W ⫽ water; S ⫽ PFPE surfactant; O ⫽ PFPE oil (see Ref. 28). c Φ-volume fraction (W ⫹ S)/total. d Percolation temperatures from Ref. 34. b

at least 10 min at the starting temperature as well as at the ﬁnal temperature reached in the experiment in order to allow the sample temperature (T s ) to approach that of the reference and to ensure that the dynamic part of the DSC recording is performed between two equilibrium temperatures. Utilizing a given thermal cycle may help in confronting the data, testing the reproducibility of the measurements, gaining evidence as to whether repeated thermal cycles do affect the thermal results, and controlling the sample’s thermal history. Examples of typical thermal cycles for DSC analysis of microemulsion systems are plotted in Figs. 7 and 8. Obviously, the highest temperature reached

FIG. 6 Temperature difference between the sample and the reference pans when a melting or freezing thermal event occurs in the sample. (From Ref. 13.)

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FIG. 7 Example of a thermal cycle that can be applied for DSC analysis of microemulsion systems. Each thermal run is preceded as well as followed by an isothermal period. (L ⫽ liquid; S ⫽ frozen solid). (From Ref. 13.)

FIG. 8 Typical thermal cycle for the study of W/O microemulsions exhibiting percolative behavior. The cycle starts with an isothermal period of 20 min at a temperature equal to the percolative temperature T p evaluated by dielectric and conductivity measurements. After the DSC-EXO measurement, a second isotherm of 40 min follows on the frozen sample. The heating measurement, DSC-ENDO, ends with a third isotherm at a temperature T L ⬍ T p at which the sample is again in the liquid state. The last measurement (C p Run) completes the thermal analysis. The thermal rate dT/dt of the latter run is higher than the 2 K/min rate used in both the exothermic and endothermic stages. Thermal rates varying from 4 to 10 K/min are applied depending on the surfactant used to formulate the system. (From Ref. 14.)

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in the heating part of the measurement must not exceed the maximum temperature at which the microemulsion is still stable.

C. Sample Weight and Thermal Rate In a multicomponent system such as a microemulsion, several plateaus of the type shown in Fig. 6 may occur. The larger the amount of a given component involved in a thermal event, the larger will be the difference between the reference and sample temperatures. Therefore a careful choice of the sample weight for reasonably good temperature accuracy is necessary. If small samples (2–6 mg) are used and low thermal rates (⬍1–4 K/min) are applied, the overall sample temperature may have a better chance to approach that of the reference, which is the parameter plotted on the abscissa of the DSC recording in a dynamic measurement. If relatively large samples (8–20 mg) are used, the degree of accuracy of the measured temperatures of the thermal processes as well as those of the measured enthalpies will obviously decrease. In the latter case, a low (1–2 K/ min) thermal rate is required. The extent to which the temperature difference between sample and reference has been minimized can always be checked as reported in the previous section. The effect of the thermal rate on the DSC recordings is depicted in Fig. 9 for a water–hexadecane system (Table 2). The thermal rate, basically, does not affect the amount of information linked with ﬁrst-order phase transitions such as a melting or freezing process, because these are rateindependent thermal events. The change of the dT/dt parameter can indeed be used as a tool for testing whether a recorded thermal transition is of the ﬁrst order. A low thermal rate is fundamental if high temperature accuracy is required. However, as stated earlier, this parameter is not critical in the case of ﬁrst-order transitions but it becomes critical if higher order phase transitions are investigated and also if thermal history dependent phenomena are studied [14]. In the latter case, a reference thermal cycle must be followed throughout the experiment and a low thermal rate must be applied both upon freezing of the liquid samples and upon their melting. Last but not least, it should be pointed out that as dH/dt is substantially a function of both (∆T) r,s and dT/dt, the higher the latter the larger will be the output signal of the DSC measurement. In other words, the output DSC signals are proportional to the applied thermal rate. A high thermal rate (10–30 K/min) may decrease the resolution of two adjacent peaks. At a very low thermal rate (⬍1–2 K/min), small thermal events (⬍0.5 mW) may become difﬁcult to detect.

V. PHASE TRANSITIONS The following main processes can be investigated by DSC in microemulsion systems.

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FIG. 9 The effect of different thermal rates on the DSC spectra recorded upon the melting of a previously frozen sample. First-order phase transitions are rate-independent. However, the smaller the ﬁnal step from the dynamic to the isothermal part of the measurement (iso.T in time units), the lower will be the difference between the sample and reference temperatures. Water–hexadecane sample with C w ⫽ 0.25. (a)–(d), dT/dt ⫽ 1, 2, 4, and 8 K/min. Composition is given in Table 2. Symbols ∆H h,w,b,x are used to identify the thermal peaks due to the melting of hexadecane (h), water (w), K-oleate–hexanol–water mixture (b), and hexanol (x). (From Ref. 13.)

1. 2. 3.

First-order phase transitions associated with the freezing and/or melting of the system’s liquid components that behave as massive phases Structural transitions associated with the system’s interphasal region because of a change in the surface-to-volume ratio of the dispersed phase Higher order phase transitions such as glass and percolation transitions

A. First-Order Phase Transitions: Melting Endotherms Study First-order phase transitions, as is well known, are characterized by a continuous change in the Gibbs energy and by a stepwise change in its ﬁrst derivatives, as

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volume and entropy. A latent heat of transition (T ∆S) is associated with these transitions. At the transition temperature, the speciﬁc heat at constant pressure diverges because of the absorption (or release) of latent heat at constant temperature. Since the transition must be a reversible process, the transition temperature is the only one at which a liquid phase can be in equilibrium with its solid counterpart and vice versa. By studying the DSC behavior upon the melting of previously frozen microemulsion samples, their melting spectra are obtained (DSC-ENDO), as shown in Figs. 10a and 10b for four- and three-component systems, respectively [13–16]. The identiﬁcation of the various thermal contributions shows that both the dispersed and dispersing liquids behave as massive bulk phases, as indicated by their melting at the melting temperatures of the corresponding pure liquids.

FIG. 10 (a) Melting endotherms of four-component W/O microemulsions (Table 2). Curve 1, water–dodecane sample, C w ⫽ 0.293. Curve 2, water–hexadecane sample, C w ⫽ 0.291. Surfactant and cosurfactant are the same in both systems. (From Ref. 15.) (b) Melting endotherms of three-component systems (Table 3). Curve 1, water–isooctane system. Curve 2, heavy water–decane system.

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The formation of a microemulsion as a distribution of droplets of either oil or water dispersed in a continuous water or oil phase can be justiﬁed in terms of the concentration and interacting energies of the only surfactant at the water– oil or oil–water interphase, under the assumption that the dispersed liquid behaves as a bulk massive phase [17–19]. Therefore the results plotted in Fig. 10 offer rather direct veriﬁcation of the above working hypothesis. The enthalpy values associated with the water endotherm allow evaluation of the free water fraction (i.e., melting at 273 K) as well as of the amount of water bound to the surfactant hydrophilic groups. The latter information results from the difference between the a priori known water content of the sample, from which the expected enthalpy value (∆H 0w ) can be estimated, and the amount of water that was found to melt at 273 K. The latter is obtained from the measured enthalpy (∆H w ) value associated with the experimentally recorded DSC peak. Worked examples are given at the end of the next paragraph. If the surfactant is insoluble in both the water and the oil, then the enthalpy evaluated from the oil melting endotherm conﬁrms that all the oil has melted. However, if the surfactant is partly soluble in the oil phase, as reported for the water component, the evaluated enthalpy offers an estimate of the percentage of free oil (i.e., melting at the bulk oil T m ) as well as of the amount of oil trapped within the surfactant hydrophobic tails [14]. Example 1. A four-component system consists of n-hexadecane (O), n-hexanol (CoS), K-oleate (S), and water (W). (The composition is given in Table 2.) The proportions by weight between the components are S/CoS ⫽ 0.6; CoS/O ⫽ 0.4; (S ⫹ CoS)/O ⫽ 0.68. The sample weighs 8.099 mg and has a water concentration C w ⫽ 0.169. The analysis is summarized in Table 5. The columns designate the following parameters: (1) weight percent of each components in the stock solution; (2) percent composition of the DSC sample; (3) weight of each DSC sample component. The enthalpy analysis results are in columns 4– 8. Thermal rate applied: dT/dt ⫽ 8 K/min. For evaluation of the enthalpies, the following symbols are used. ∆H Ti ⫽ measured reference enthalpy of pure bulk component i (J/g component i) ∆H oi ⫽ a priori expected enthalpy value for the known amount of i in the sample ( J/g of i in the sample) ∆H Si ⫽ experimentally measured enthalpy value (J/g sample); ∆H i ⫽ enthalpy evaluated for component i and expressed in joules per gram of component i Free i ⫽ fraction of free, not bound, component i in the DSC sample The different enthalpic contributions are obtained as follows: ∆H oi ⫽

∆H Ti ⫻ % i ⫽ ∆H Ti ⫻ C i 100

(23)

57.73 24.35 14.94 2.98

Component

O CoS S W

49.44 20.85 12.80 16.91

2 Sample (%)

Composition

4.004 1.688 1.037 1.370

3 Sample component (mg) 235.41 150.52 — 333.26

4 ∆H iT (J/g)

Worked Example for a Four-Component System (Example 1)

1 Stock solution (%)

TABLE 5

116.39 31.38 — 56.35

5 ∆H oi (J/g)

116.040 16.618 — 23.510

6 ∆H iS (J/g)

Enthalpy analysis

234.71 79.70 — 139.51

7 ∆H i (J/g)

99.70 52.95 — 41.86

8 Free-(i) %

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TABLE 6 Worked Example for a Three-Component System (Example 2)a Composition

Component O S W a

Enthalpy analysis

1 Sample (%)

2 Sample component (mg)

T i

3 ∆H (J/g)

o i

4 ∆H (J/g)

5 ∆HiS (J/g)

6 ∆Hi (J/g)

7 Free-i (%)

59.28 16.30 24.42

6.532 1.796 2.691

89.73 — 333.26

53.19 — 81.38

28.07 — 65.66

47.35 — 268.88

52.77 — 80.68

Notations and symbols as in Table 5.

∆H i ⫽

∆H S i ⫻ DSC sample wt weight of i in DSC sample

(24)

∆Hi ⫻ 100 (25) ∆H Ti Example 2. A three-component system is made up of isooctane (O), Na(AOT) (S), and water (W). The composition is given in Table 3. Following the scheme of Example 1, the results of the DSC analysis are summarized in Table 6. Notations and symbols are as in Table 5. The weight of the DSC sample is 11.02 mg; C w ⫽ 0.269; dT/dt ⫽ 4 K/min. The analysis reported in Table 6 shows that the AOT surfactant is soluble in both the water and oil phases. As much as 47.23% of the oil is in fact trapped between the surfactant’s hydrophobic tails. The accuracy of the measurements was estimated to be on the order of 1% for the measured enthalpies and ⫾0.5 K for the measured temperatures. For higher accuracy, a sample weight of 4–5 mg and a scan speed heating rate of 1–2 K/ min should be used. However, in a case where the thermal peaks are well separated from each other and the heat content involved in the thermal events is well above 0.5 mW, an increase in the accuracy would not contribute substantially to the amount of physical information obtained. Percent of i free fraction ⫽

B. Interphasal Water The study of the enthalpic changes associated with the melting of water in W/O systems, as a function of the increase in the sample water content (C, weight fraction of added water), is very useful for distinguishing between different forms of water, namely free (melting at 273 K) and interphasal (melting at 263 K) [15,20–22]. The presence of a water fraction melting at 263 K was ﬁrst evidenced in a

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four-component water–dodecane system (Table 2) characterized by a constant mass fraction (surfactant ⫹ cosurfactant)/dodecane ⫽ 0.7 and investigated relative to increasing water concentration in the interval 0.1007 ⱕ C ⬍ 0.4. For water concentrations in the interval 0.1007 ⱕ C ⬍ 0.22, the experimentally evaluated enthalpic changes associated with the melting of the dodecane oil were found to be higher than the a priori expected ones, just if an amount of oil larger than that really contained in the sample had melted (Fig. 11). To isolate the endothermic event superimposed on that of the oil, another microemulsion was formulated by substituting the decane oil with n-hexadecane. The latter was chosen because its melting at 291 K was assumed not to interfere with any of the thermal events due to water in the temperature interval of interest. In the case of water–hexadecane samples (Table 2), within the concentration

FIG. 11 Enthalpic changes (∆H) versus increasing water content (C) in the case of the water–dodecane system (Table 2). Experimentally measured enthalpies of (䊉) dodecane and (䊊) water expressed in joules per gram of sample. ∆Ho d and ∆Ho w are the expected values calculated a priori for the melting of the known amounts of the two components in the samples. Bars are standard errors of the mean. (From Ref. 15.)

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range 0.105 ⱕ C ⬍ 0.2, an evident endothermic contribution due to water was found to develop at T ⫽ 263 K (Fig. 12) in correspondence with the temperature at which the melting of the dodecane occurred in the previous system (Fig. 13). Analysis of the enthalpies showed a linear relationship between the measured enthalpic changes and the concentrations of both the oil and water (Fig. 14). The values of the oil enthalpy (∆H h ) prove that all the oil contained in the sample has melted (Table 5, column 8). The latter ﬁnding conﬁrms that in this system both the surfactant and the cosurfactant are insoluble in the oil phase or do not interact with the hexadecane in a way detectable by DSC. As far as the water phase is concerned, it must be pointed out that the measured ∆H w value never equals the expected ∆H 0w value corresponding to the sample’s known water content. Part of the water is, in fact, bound to the hydrophilic groups of the surfactant and, for example in the case of our four-component system, part of the water is also involved in the thermal events occurring in the low-temperature part of the DSC spectrum (see Fig. 15, curve 5). In the case of our threecomponent systems, the information about the amount of water not behaving as free, but linked with the system’s interphase region, is obviously more immediate.

FIG. 12 Endothermic contribution due to the melting of interphasal water at T ⫽ 263 K. Water–hexadecane system (Table 2), C w ⫽ 0.105. Inset shows a close-up of the 263 K peak. (From Ref. 13.)

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FIG. 13 Curves a–c: Melting spectra of water–hexadecane samples (see Table 2) with increasing water content showing that the 263 K peak is the ﬁrst thermal event associated with the melting of a water fraction (curve b). Concentrations (expressed as weight fraction of water) are C a ⫽ 0.071, C b ⫽ 0.108, C c ⫽ 0.290. Curve d: DSC endotherm of a water– dodecane sample (see Table 2). In the latter case the melting of the oil hides the interphasal water thermal event. C d ⫽ 0.275. Thermal rate 4 K/min. Symbols of enthalpies are the same as in Fig. 9. (From Ref. 22.)

C. Structural Transitions Associated with the Interphase Region The appearance of the 263 K endothermic peak was found to correspond to the ﬁrst formation of droplets consisting of an interphasal corona of amphiphiles enclosing a water core. This conclusion is supported by the results gathered by studying the water–hexadecane system along a line starting from the oil-rich side (see Fig. 5b) of the pseudoternary phase diagram and moving toward the zero oil vertex, by adding water to samples characterized by a constant mass ratio (surfactant ⫹ cosurfactant)/oil ⫽ 0.68. The concentration interval studied crosses the point P′ (see Fig. 5b), which is on the border between the microemulsion monophasic domain and the multiphase region in which macroscopic phase separation occurs [23]. The study of the monophasic domain limiting concentration has shown pretransitional effects linked with structural rearrangements preceding the macro-

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FIG. 14 The linear relationship between the measured enthalpic changes and the water concentration (C) is shown for the water–hexadecane system (see Table 2). ∆H sh, and ∆H sw are the least squares ﬁt regression lines for the experimental points of (䊊) hexadecane and (䊉) water, respectively. Dashed lines are 5% conﬁdence intervals for the experimental lines. Heavily marked open circles (near the C axis) are ∆H values due to water melting at 263 K. ∆H oh and ∆H ow as in Fig. 11. (From Ref. 15.)

scopic phase separation into a liquid crystalline mesophase (LC) and a W/O isotropic phase. This process was investigated by DSC analysis by studying the upper isotropic phase after the initial formation of a birefringent LC lens on the bottom of a test tube with a total water concentration C Tot ⫽ 0.372. In this case the DSC spectrum shows the only interphasal water endothermic peak at 263 K, the disappearance of the surfactant contribution, and the oil thermal event (Fig. 15, curve 1). Further addition of water to the sample increases the bottom LC phase and decreases the upper isotropic one. However, DSC analysis of the latter shows that both the water and oil thermal peaks begin to grow again (Fig. 15, curves 2 and 3), up to water contents of the original sample at which a monophasic LC mesophase develops. The trend of the measured enthaplies (∆H h,w ) versus C, within the concentration interval investigated, is reported in Fig. 16, where on the left-hand side (C ⬍ 0.3) are plotted the data collected on monophasic isotropic samples and

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FIG. 15 Water–hexadecane system (Table 2). DSC-ENDO spectra of the upper isotropic phase of biphasic samples with increasing water concentration of the sample as a whole. Curve 1: C Tot ⫽ 0.372, the ﬁrst appearance of a birefringent liquid crystalline lens. Curve 2: C Tot ⫽ 0.388. Curve 3: C Tot ⫽ 0.419. Curve 4: Melting endotherms of the liquid crystalline bottom mesophase of a sample with C Tot ⫽ 0.419. ∆H x and ∆H b are the thermal contributions of the n-hexanol and the water–K-oleate–hexanol mixture, respectively. (From Ref. 23.) Curve 5: DSC-ENDO spectrum of the ternary mixture n-hexanol–Koleate–water. The proportions between surfactant and cosurfactant are the same as those used to formulate the four-component W/O microemulsions.

on the right-hand side (0.316 ⬍ C ⬍ 0.42) those pertaining to the isotropic part of biphasic samples. In order to study the thermal behavior of biphasic samples for any concentration tested (C Tot ), a large sample was formulated, stirred, divided into subsamples, and thereafter stored for 1 year at T ⫽ 301 K to allow both the completion of the phase separation process and time for the two phases to reach an equilibrium state. In the case of monophasic isotropic samples, the behavior of ∆H h and ∆H w

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FIG. 16 Water–hexadecane system (see Table 2). Behavior of the measured enthalpies of (䊊) hexadecane (∆H h ) and (䊉) water (∆H w ) as a function of increasing water concentration (C) in the interval 0.105 ⱕ C ⬍ 0.420. The linear relationship holds, as shown in Fig. 14, within the interval 0.105 ⱕ C ⬍ 0.3. Pretransitional effects occur in the range 0.316 ⱕ C ⱕ 0.372; phase separation develops in the interval 0.372 ⱕ C ⬍ 0.42. In the latter range, the linear relationship still holds for the isotropic upper phase of biphasic samples until the transition occurs toward a monophasic liquid crystalline mesophase. (Redrawn from Ref. 23.)

as a function of increasing water concentration suggests that the added water is approximately partitioned with a constant ratio between bulk and interphase, since, as for stability requirements, an increase in water content is accompanied by an increase in the number of hydrophilic groups at the water–oil interphase. When the interphase reaches the maximum extension allowed by thermodynamic stability, the observed linear relationship fails and the system must undergo a transition to a structure with a lower surface-to-volume ratio, leading, upon further addition of water, to macroscopic phase separation. When the linear relationship fails, the enthalpy values of both the water and the oil tend to saturate. As soon as phase separation has occurred, the oil enthalpy rises linearly and the bestﬁt regression line reverses its slope, while the water enthalpy line starts rising

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from the lowest possible value, which is not ∆H w ⫽ 0 but the one associated with the 263 K water endothermic peak. Since the formation of a lyotropic mesophase is accompanied by a reduction in the surface of the system’s total interphase, both parts of the biphasic samples may still exist. Just because of the above process, some of the surfactant molecules, by leaving the system’s interphase, become newly available for stabilizing the newly formed LC structure as well as the isotropic W/O microemulsion upper phase. This process lasts until free surfactant molecules are available in the system as a whole. Therefore, by DSC analysis, it is possible to follow the partitioning of the different components in either phase of biphasic samples and also to detect the changes occurring at the level of the system’s interphase region.

VI.

DSC-ENDO SPECTRA: DEUTERATED COMPONENTS

The use of a deuterated component with a melting temperature differing from the one of the ordinary (not deuterated) component is a tool for identifying the thermal events in DSC spectra. This procedure works because the dispersed phase in microemulsion systems maintains its droplet identity independently of the continuous oily phase, provided that the interphase region of the system is not modiﬁed. That is, the same surfactants are adopted for both systems. As shown in Fig. 17a, the substitution of ordinary dodecane with ordinary hexadecane does

FIG. 17 (a) Comparison between the thermal endotherms of water–dodecane (continuous line) and water–hexadecane (dotted line) microemulsion samples. C 1 ⫽ 0.195, C 2 ⫽ 0.197. The two spectra differ only by the thermal event associated with the melting of the oil. (From Ref. 13.) (b) Similar comparison for three-component W/O microemulsions. Curve 1: Water–isooctane system. Curve 2: Water–decane system. The surfactant, NaAOT, is the same in both samples. Compositions are given in Tables 2 and 3.

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not affect the thermal contribution of the dispersed water phase. As a matter of fact, the DSC recordings differ only in the thermal events associated with the melting of the oils. The same applies to three-component systems as depicted in Fig. 17b. In the latter case, the substitution was performed to avoid thermal processes that could interfere with the ones related to the water phase. If the problem is the identiﬁcation of a speciﬁc thermal event, the substitution of one of the system components may be very effective, as shown in Fig. 18, where the DSC spectra of a H 2O–hexadecane and a D 2O–hexadecane microemulsion are presented. In the latter case, the aim was to ascertain that the 263 K thermal event was unambiguously due to the dispersed phase, whether water or heavy water [24]. The deuteration of one or more of the system’s components may become necessary to ﬁt some of the requirements of a given experimental study as for instance, in SANS measurements or low resolution NMR. Therefore the DSCENDO analysis may be carried out just to check whether the deuteration procedure has affected the system in some way. Figure 19 presents an example for the water–hexadecane microemulsion (Table 2). The effect of the substitution of water with ‘‘heavy water’’ in the case of a three-component system is given in Fig. 20. The aim of the latter modiﬁcation was to realize a system in which, upon the freezing of the liquid samples, the thermal events associated with the freezing

FIG. 18 The use of heavy water for identifying the 263 K thermal event ﬁrst observed in the water–hexadecane system. Composition is given in Table 2. (From Ref. 24.)

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FIG. 19 The effect of the deuteration observed by DSC. The basic system is water– hexadecane (see Table 2). (a) Sample with normal undeuterated components; (b) deuterated oil; (c) deuterated water and oil. (From Ref. 21.)

FIG. 20 The effect of deuteration on a three-component microemulsion. Comparison between the melting spectra of a water-decane (1) and a heavy water–decane (2) microemulsion sample (see Table 3). The two DSC recordings differ only in the thermal event associated with the dispersed phase, water, or heavy water. The two systems contain the same decane oil, therefore the thermal peak due to the melting of the latter, occurs at the same melting temperature in both cases. (From Ref. 14.)

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of both the oil and water did not overlap each other because of the overcooling phenomenon [14].

VII. FIRST-ORDER PHASE TRANSITIONS: FREEZING EXOTHERMS STUDY The analysis by DSC of the freezing behavior of liquid microemulsion samples (DSC-EXO spectra) was ﬁrst undertaken for checking on whether it were possible to distinguish the interphasal water endothermic peak from that of the dodecane in the water–dodecane system. As shown in Fig. 21, the DSC-EXO recordings conﬁrm the presence of a thermal event superimposed on that of the dodecane [13,15]. Since then, DSC-EXO analysis has been carried out as a standard procedure for all the systems studied. Besides the overcooling phenomenon due to the liquid nature of the system’s components, the above investigation demonstrated that the free water fraction of the sample maintains its liquid state down to temperatures near the homogeneous nucleation temperature of water (⬇233 K) without requiring a quenching procedure, even with applied thermal rates as low as 0.1 K/min (Fig. 22).

FIG. 21 Freezing spectrum of a water–dodecane sample with C ⫽ 0.106. The presence of a thermal event (*)—(later identiﬁed as due to interphasal water)—partially hidden by the oil freezing peak is quite evident. In the study of the melting behavior of the same system, summarized in Fig. 11, in the concentration interval 1.007 ⱕ C ⬍ 0.22, the enthalpic contribution due to the melting of the dodecane gave the surprising result that more oil than that contained in the samples had melted. The latter paradox was solved by substituting the dodecane with hexadecane (see Figs. 12 and 14). In this way the presence of a fraction of water melting at 263 K and freezing at 251 K could be ascertained. Symbols are the same as in Fig. 9.

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FIG. 22 (a) Melting and (b) freezing peaks due to the free water part of a water–isooctane microemulsion (see Table 3). Both the melting and freezing temperatures are evaluated with the onset method. First asterisk shows the intersection point of the evaluated regression line with the experimentally recorded baseline; the second asterisk marks the tangent to the experimental curve inﬂection point. Thermal rate: 2 K/min.

FIG. 23 (a) Evolution of the DSC-EXO spectra of a water–isooctane microemulsion (see Table 3) sample as a function of increasing water concentration. Note that the dispersed phase freezes into a liquid oil matrix. (b) Melting endotherms of the corresponding samples. dT/dt ⫽ 1 K/min.

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FIG. 24 (a) Freezing DSC spectra of the Water–hexadecane system (see Table 2) versus concentration. Note the dispersed phase freezing into a frozen oil matrix. The corresponding melting endotherms are plotted in Fig. 13, curves a, b, and c. (b) DSC-ENDO (1) and EXO (2) spectra of a water–dodecane microemulsion (see Table 2), C ⫽ 0.252. The freezing of the oil at T ⬇ 258 K does not prevent the water from overcooling to a lower temperature. (From Ref. 22.)

The evolution of the DSC-EXO spectra for a three-component water–isooctane microemulsion (Table 3) as a function of the water concentration is reported in Fig. 23, where, for the sake of comparison, the DSC-ENDO spectra are also shown. The same analysis is reported for four-component microemulsions in Fig. 24. In the case of the water–dodecane system, as shown in Fig. 24a for a sample with a high water concentration (C ⫽ 0.252), the freezing of the oil (T fz ≅ 258 K) does not prevent the free water fraction of the sample from freezing at the lower temperature of ⬇248 K. (See also Fig. 21 for a sample of the same system with C ⫽ 0.150.) The study of the thermal behavior of microemulsions upon freezing of the liquid samples has shown that the freezing temperature of neither the water nor the oil depends on the temperature at which the DSC-EXO study began or on the sample’s thermal history. Moreover, for any concentration tested, the massive phases always freeze at the same temperature, provided that the same thermal rate is applied. It has been experimentally veriﬁed that the scan speed does not signiﬁcantly affect the freezing temperatures until it changes in the interval 0.1– 10 K/min. If dT/dt ⬎ 10 K/min, the instrument thermal control no longer works

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properly. In other words, the difference between the source and reference temperatures and that between the reference and sample temperatures become too large to allow reasonable thermal control, while the available low-temperature range decreases drastically.

VIII.

HIGHER ORDER PHASE TRANSITIONS

Whereas ﬁrst-order phase transitions are characterized by a continuous change in the Gibbs free energy, volume [(∂G/∂p) T], and entropy [(∂G/∂T )p], secondorder phase transitions are distinguished by a stepwise change in (∂2 G/∂p 2 )T ⫽ (∂V/∂p)T ⫽ ⫺ γV, (∂2 G/∂T 2 ) p ⫽ ⫺Cp /T, and (∂G/∂p ∂T) ⫽ (∂V/∂T) p ⫽ αV, where γ and α are the isochoric pressure and isobaric expansion coefﬁcients, respectively. In second-order transitions, the ﬁrst derivatives of a thermodynamic parameter are continuous, but the second derivatives with respect to the corresponding parameter change in steps. Such transitions are not attended by a heat effect and are characterized by a change in the heat capacity and in the expansion and pressure coefﬁcients, which means that the coexisting phases differ not in volume and their store of energy but in the values of their derivatives. The glass transition (GT) is the most typical second-order transition, because the heat capacity of the glass is always lower than that of the liquid at the same

FIG. 25 The glass transition (GT) of the perﬂuoropolyether oil (Galden LS/215, Ausimont, Bollate-Milan, Italy) used to formulate the PFPE microemulsions (see Table 4). Curve 1, upon freezing; curve 2, upon melting. The GT is observable also in PFPE–water– oil microemulsions. (From Ref. 28.)

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temperature and no latent heat is needed to stop molecular motion. Moreover, since the freezing of molecular motion is time-dependent, the GT is considered an irreversible process. The microemulsion state has been used to detect the glass transition of the water dispersed phase upon rapid freezing of the samples [25– 27]. The GT is due to the freezing of large-scale molecular motions without changes in structure. The GT temperature is the main characteristic of both amorphous solid and liquid states. By DSC, however, one can observe the GT upon both freezing and heating analysis (see Fig. 25). Such behavior results from the considerable temperature dependence of the relaxation times of large-scale molecular motions. In other words, the glass–liquid transition occurs at an easily

FIG. 26 Perﬂuoropolyether W/O microemulsions (Table 4). Top: Energy balance analysis. Variation of the total enthalpy measured upon freezing the liquid samples as a function of the volume fraction Φ ⫽ (water ⫹ surfactant)/total. ∆H is expressed in joules per gram of sample. Bottom: Trend of ∆H w associated with the free water fraction of the sample, as a function of Φ. In both cases the samples belong to the dilution line with W/S ⫽ 11. ∆H is expressed in joules per gram of water.

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detectable transition temperature even if the GT is, thermodynamically, an irreversible process. For sake of completeness, we report in Fig. 26 some results of DSC analysis performed on ﬂuorinated W/O microemulsion (see Table 4) samples belonging to the dilution line W/S ⫽ 11 [28].

IX.

THE PERCOLATION TRANSITION

The thermodynamic stability of heterogeneous systems in the condensed state requires the existence of mechanical, thermal, and chemical equilibria. Chemical equilibrium implies that the chemical potential of each component in the system is the same in both the droplet interphase and the massive phase. Therefore, the thermodynamic equilibrium condition imposes a continuous exchange of matter within the system. Considering W/O microemulsions as self-assembling complex liquids of two phases in which one is electrically conducting and the other is either nonconducting or possesses a much lower degree of electrical conductivity, it follows that the mechanism of electrical conduction and transport properties can be described in terms of the percolation of the electrically conducting phase (water ⫹ surfactant) through the nonconducting oily phase. The percolative behavior of the system depends on the degree of connectivity of the conductive phase within the insulating one; the connectivity depends on the concentration by volume of the conductive components (number of droplets), which in turn depends on the dimension of the conducting regions (clusters of droplets) with respect to the mean free path of the charge carriers as well as on the presence of short-range interactions between the globules [29–37]. Short-range interactions favor the clustering process via the aggregation of the dispersed droplets of the conducting phase, eventually leading to a path connecting the system (percolation transition). The development of short-range interactions depends on the number of droplets, that is, on the volume fraction Φ. However, it has been shown that in W/O microemulsions [33,34] a percolative behavior may also develop as a function of temperature for a given ﬁxed Φ value. The latter ﬁnding facilitates the study of the percolation transition by thermal analysis methods [37]. Upon a rise in temperature, a transition occurs from a regime of transport dominated by droplet motion and cluster rearrangement to one dominated by the motion of the charge carriers within a connected cluster of droplets. This transition results in a steep increase in charge carrier diffusion. The latter depends via a power law on the rate of cluster rearrangement. Whether or not a system percolates can be established only by verifying whether the experimental data obey the

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scaling laws that describe percolative processes obtained from critical phenomena theories [29–31]. The study of the percolation transition in liquid systems versus temperature by means of a dynamic type of thermal analysis presents some difﬁculty, because the only available tool to prime the transition is the thermal rate. To detect the percolation transition, the thermal cycle depicted in Fig. 8 may be followed. It allows control of the system thermal history from the starting temperature T ⬇ T p up to the percolation transition (C p Run). With the aim of not interrupting the temperature control of the system, the instrumental setup was modiﬁed to allow reﬁlling the liquid nitrogen Dewar without removing the DSC low-temperature head while the instrument is in a standby state [16]. In such a way, not only are the sample temperatures continuously monitored, but also the calibration assessment of the instrument does not change. The last measurement, called C p Run, must be performed by applying a thermal rate different from the one used in the preceding DSC-EXO and DSC-ENDO measurements. To trigger the percolation transition, a thermal rate higher than the one used in both the freezing and melting studies is required. The latter was found to depend on the surfactant used, i.e., on the type of interphase the surfactant builds up. Typical DSC recordings at the percolation transition are shown in Fig. 27a. The shape of the DSC recordings is always the same—a more or less peaked trend depending on how well the threshold temperature was included in the temperature range studied. The variation of the speciﬁc heat at constant pressure, as a function of temperature, is shown in Fig. 27b. The speciﬁc heat was evaluated following the procedure described in Eqs. (17) and (18). In the former case, the blank correction was used by compensating, within the temperature range of interest, for the weight difference between the reference and sample pans. In the second case, the reference crucible was also ﬁlled with a sample of the system tested and the τ** constant was evaluated. The microemulsion system can be used as a standard because 1.

2.

Microemulsion samples give reproducible thermal results and overlapping DSC spectra, even after a period of years, provided the same crucible plus sample is used and is kept well sealed. This may be easily tested by weighing the sample pan at any time. If one does not follow the thermal cycle of Fig. 8 for the liquid sample, then the only change in the thermal rate results in a perfectly ﬂat, neat, and eventless line. Therefore the τ** constant value can be inserted in the conﬁguration list for the C p Run.

The ﬁnding reported in point 1 applies because, due to the modiﬁcation of the instrumental setup described previously, the calorimetric assessment of the low-temperature DSC head can be easily checked at any time.

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FIG. 27 (a) The percolation transition as revealed by DSC: raw recordings. Curve 1, water–Na(AOT)–decane system; curve 2, D 2O–Na(AOT)–decane system; curve 3, water–Na(AOT)–isooctane system (see Table 3). (b) Speciﬁc heat as a function of temperature (dT/dt ⫽ 8 K/min). Curve 1, D 2O–Na(AOT)–decane system; curve 2, water– Na(AOT)–isooctane system. (From Ref. 16.)

In the C p evaluation, the dispersion of the data is rather large because the thermal event is usually a very small one in terms of the energies involved (ⱕ0.5 mJ/s). It may happen that, although in the raw DSC recording the transition is detectable, the signal-to-noise ratio in the speciﬁc heat evaluation is indeed comparable with that of the transition itself! Another improvement in the instrumental ‘‘answer’’ may be achieved by evaluating τ s. By reducing the time required by the DSC signal to reach the baseline, the temperature interval available for the evaluation of the speciﬁc heat increases. An example of the application of this procedure is shown in Fig. 28 for a perﬂuoropolyether (PFPE) microemulsion sample with Φ ⫽ 0.395 (see Table 4) and T p ⫽ 289.5 K. For percolative temperatures lower than 289 K, the evaluation of C p fails. Depending on the thermal rate used, the available temperaturerange for the DSC measurement is conﬁned between an upper temperature at which the system is not in the microemulsion state and a lower temperature at which the sample, albeit liquid, is in the overcooled state. If the last melting component is water, then at T ⱕ 280 K, for instance, the DSC measuring tempera-

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FIG. 28 PFPE system (see Table 4). The change in C p at the percolation transition for the sample with Φ ⫽ 0.395 and T p ⫽ 289.5 K (dT/dt ⫽ 4 K/min). (From Ref. 28.)

ture range would fall within an interval in which there is competition between the overcooling and percolative phenomena, besides the increase in the density of water. Therefore, the percolation transition may become difﬁcult to detect, and in any case it would fall within the ‘‘lost’’ temperature interval (⬇20 K), required to stabilize the DSC signal. The percolation transition presents a notable thermal hysteresis: It may require up to 24 h to observe the transition on the same sample again, even following the same thermal cycle of Fig. 8. Another interesting peculiarity observed in all the W/O microemulsion samples that exhibit percolative behavior and are listed in Tables 3 and 4, is a spreading in the thermal events due to the freezing of the dispersed phase. The latter behavior, described in detail in Refs. 14, 16, and 28, was found to depend on the temperature at which the DSC study began (ﬁrst isothermal period), that is, on whether the temperature was at, below, or above T p. This unusual freezing behavior was explained in terms of the size of the domains formed by the water when it froze. At T ⫽ T p the domain is linked with the size of the cluster connecting the system as well as with the sizes of small, unconnected clusters of droplets. At T ⬎ T p, the system is multiconnected. For temperatures well below T p only one exothermic peak is associated with the dispersed phase, as shown in Figs. 21–24.

REFERENCES 1. S Martellucci, AN Chester, eds. Progress in Microemulsion. Ettore Majorana Int Sci Ser Vol. 41, Plenum Press, New York, 1989.

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7 Water Behavior in Phospholipid Bilayer Systems MICHIKO KODAMA and HIROYUKI AOKI Department of Biochemistry, Okayama University of Science, Okayama, Japan

I. Classiﬁcation of Water Molecules Based on Ice-Melting DSC Curves A. Nonfreezable interlamellar water B. Freezable interlamellar water and bulk water II.

Estimation of the Number of Differently Bound Water Molecules Based on a Deconvolution Analysis of Ice-Melting DSC Curves A. Deﬁnitions B. Deconvolution analysis C. Estimation of the number of differently bound water molecules D. Water distribution diagrams

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III. Relationship Between Lipid Phase Transitions and Ice-Melting Behavior in Lipid–Water Systems

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IV.

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V. Ice-Melting Behavior for a Minute Amount of Freezable Interlamellar Water VI.

Analysis of Water Molecules in the Gel Phase of Lipid–Water Systems A. DPPC–water system B. DMPE–water system C. DPPG–water system

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VII. Subgel Phases in Lipid–Water Systems VIII. Analysis of Water Molecules in the Subgel Phases of Lipid–Water Systems A. DPPC–water system B. DMPE–water system IX.

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References

292

I. CLASSIFICATION OF WATER MOLECULES BASED ON ICE-MELTING DSC CURVES Studies of the interaction of lipid and water molecules are the subject of many investigations and have been performed with many techniques such as X-ray diffraction [1–8], NMR spectroscopy [9–11], and differential scanning calorimetry (DSC) [12–24]. DSC has been frequently used to investigate the mode of bonding between water molecules and organic and inorganic substances. In this case, the thermal behavior associated with the melting of ice and sometimes with the freezing of water is measured. First, we discuss how the water molecules in multilamellar dispersions of lipid–water systems are classiﬁed according to their ice-melting behavior (i.e., the appearance of an endothermic peak related to the melting of ice) as revealed in the heating mode of DSC. Next, we discuss how the number of water molecules in the different bonding modes is estimated from the ice-melting DSC curves.

A. Nonfreezable Interlamellar Water A characteristic feature of DSC is its ability to distinguish clearly between freezable water, for which ice-melting behavior is observed, and nonfreezable interlamellar water, for which it is not observed even at temperatures low enough to form ice. As is well known, the structure of ice is characterized by networks of hydrogen bonds formed among neighboring water molecules. Therefore, the point to note is that the water molecules present as nonfreezable water cannot participate in the formation of such hydrogen bonds even when cooled to extremely low temperatures. For the systems studied here, water molecules that exist in regions between adjacent lipid headgroups in an intrabilayer [23] are considered to behave as nonfreezable water. This is because the water molecules, even in the liquid state, are conﬁned within the narrow intrabilayer region as a result of their hydrogen bonding to carbonyl ester groups of the lipid. Also, water molecules that are bound to lipid headgroups in an interbilayer region so tightly that they cannot

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form hydrogen bonds with their neighboring water molecules can be taken as nonfreezable water. However, if these water molecules have the freedom required for the formation of water–water hydrogen bonds, they are present as either freezable or nonfreezable water depending on the strength of the resultant hydrogen bonds. When the hydrogen bonds are weak, the energy necessary to break them is too small to be detected by DSC, so the involved water molecules are counted as nonfreezable water. All the nonfreezable water in the systems studied in this investigation is found in regions between lamellae and so is designated as nonfreezable interlamellar water.

B. Freezable Interlamellar Water and Bulk Water On the other hand, there are two types of freezable water. One exists in the interbilayer region [23] but keeps the degree of freedom necessary for its molecules to at least reorient themselves in order to form icelike hydrogen bonds. This water is designated freezable interlamellar water. The second type of freezable water exists outside the bilayers and is designated as bulk water. However, the structure of ice derived from freezable interlamellar water is presumed to be far different from that of hexagonal ice, while ice derived from bulk water is close to the most ordered hexagonal ice. The structural difference in the ice, based on some assumptions, is reﬂected in its melting behavior shown in Fig. 1. The ice obtained from freezable interlamellar water begins to melt at temperatures as low as ⫺45 to ⫺35°C and continues to melt up to about 0°C. In contrast, the ice derived from bulk water melts in a narrow temperature range around 0°C. The ice-melting behavior observed over a wide temperature range below 0°C suggests that the mode of hydrogen bonding in the ice formed by freezable interlamellar water molecules changes continuously in such a way that it approaches more closely that of hexagonal ice the more remote the water molecules are from the bilayer surfaces.

II.

ESTIMATION OF THE NUMBER OF DIFFERENTLY BOUND WATER MOLECULES BASED ON A DECONVOLUTION ANALYSIS OF ICE-MELTING DSC CURVES

A. Deﬁnitions As discussed above, the water molecules in lipid–water systems are classiﬁed into three types: nonfreezable interlamellar, freezable interlamellar, and bulk water. A correlation between the numbers of water molecules of these three types at a desired total water content is given by the equation N T ⫽ N I(nf) ⫹ N I(f) ⫹ N B

(1)

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FIG. 1 Ice-melting DSC endotherm of a lipid–water system showing the variation of the apparent excess heat capacity (∆C P) as a function of temperature t.

where N T is the total number of water molecules per lipid molecule and N I(nf), N I(f), and N B are the numbers per lipid molecule of nonfreezable interlamellar, freezable interlamellar, and bulk water molecules, respectively. N T is estimated from the amount of water added to a sample. When a molar mass is used, N T is the sum of the molar numbers (per mole of lipid) of the three types of water and is equal to the water/lipid molar ratio, N w, for samples of varying water contents. In the present study, N T and N w are treated separately. By using the known melting enthalpy of hexagonal ice, 1.436 kcal/mol water, Eq. (1) is replaced by 1.436 (N T ⫺ N B) ⫽ 1.436 (N I(nf ) ⫹ N I(f ) )

(2)

In Eq. (2), each term of 1.436 ⫻ N is expressed in kilocalories per mole of lipid. We assume that bulk water in the systems studied here behaves as free water. On this basis, the ﬁrst term, 1.436 N T, represents the melting enthalpy, ∆H T, for N T mol of water added to 1 mol of lipid, assuming that the water is all present as bulk water, and hence is a theoretical value. The second term, 1.436 N B, corresponds to the melting enthalpy, ∆H B , for N B mol of water actually present as bulk water per mole of lipid and is experimentally determined from the ice-melt-

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ing DSC curve. However, the ﬁrst and second terms on the right side of Eq. (2) are not comparable to the ice-melting enthalpies for N I(nf) mol of nonfreezable interlamellar water and N I(f ) mol of freezable interlamellar water, respectively. So, Eq. (2) may be written as ∆H T ⫺ ∆H B ⫽ 1.436 (N I(nf) ⫹ N I(f) )

(3)

On the other hand, Eqs. (1)–(3) are limited to a certain water content of a lipid– water system. A more detailed picture is shown in Fig. 2, which takes into account the variation in water content. In this ﬁgure, the theoretical (∆H T ) and experimental (∆H B) ice-melting enthalpies for the bulk water given in Eq. (3) are plotted against N w for comparison. Furthermore, the ∆H B curve is drawn for two typical cases, (a) limited hydration and (b) inﬁnite hydration. The points to note in Fig. 2 are that (1) the bulk water appears for the ﬁrst time at the N w value where the

FIG. 2 Comparison of ice-melting enthalpy curves of ∆H B and ∆H T for bulk water per mole of lipid. The ∆H B curve is an experimental one determined by DSC, and the ∆H T curve is a theoretical one obtained by assuming that all the water added is present as free water. In this ﬁgure, the ∆H B curve consists of the curves a and b for limited and inﬁnite hydration, respectively. N W is the water/lipid molar ratio. N W (a) is the water/lipid molar ratio when the maximum amount of interlamellar water is reached in a lipid–water system.

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∆H B curve intersects the abscissa and N B at each N w is calculated from ∆H B /1.436; (2) the enthalpy difference, ∆H T ⫺ ∆H B , between the theoretical and experimental curves corresponds to 1.436 N I, where N I ⫽ N I(nf) ⫹ N I(f ) in Eq. (3), so for each Nw NI is calculated as equal to (∆H T ⫺ ∆H B)/1.436. ∆H B curve a is parallel to the theoretical curve, indicating that the total (nonfreezable plus freezable) amount of interlamellar water reaches a maximum at the N w value of the intersection point, denoted as N w (a), and so N w (a) just gives the maximum amount of interlamellar water; above N w (a), all the water added exists as bulk water outside the lamellae. Thus, such a parallel curve proves a limited uptake of the interlamellar water. On the other hand, ∆H B curve b, which is not parallel to the theoretical curve, indicates an inﬁnite uptake of the interlamellar water. Thus, some of the water added beyond the intersection point exists as bulk water, and the remainder increases the amount of interlamellar water.

B. Deconvolution Analysis* As discussed above, N B and N I are estimated from the enthalpy ∆H B, which is experimentally determined from the ice-melting DSC curve. So it is understandable that ∆H B is a chief determinant in the accuracy of this method. From this viewpoint, to determine ∆H B as accurately as possible, a deconvolution analysis was used to separate the ice-melting DSC curve into two components (or peaks), broad and sharp, for the freezable interlamellar and bulk water, respectively, because the two components overlap at their basis. Furthermore, the broad component was deconvoluted into multiple components. The purpose is not only to improve the accuracy of the deconvolution analysis but also to estimate N I(nf) and N I(f) given in Eq. (3). The deconvolution was performed by using a computer program for multiple Gaussian curve analysis. An example of the deconvolution analysis is shown in Fig. 3. In the present deconvolution, the ice-melting DSC curve was deconvoluted into the minimum number of components by applying the conditions that (1) the theoretical curve given by the sum of individual deconvoluted curves is best ﬁtted to the experimental DSC curve and (2) both the half-height width and the midpoint temperature of each deconvoluted curve are maintained almost constant throughout all the deconvolutions for varying water contents. The standard deviations of the present deconvolutions are about 0.1–0.3 kcal/(K ⋅ mol).

C. Estimation of the Number of Differently Bound Water Molecules In Fig. 3, deconvoluted curves are compared with the experimental DSC curve. The deconvoluted curve IV is for the bulk water, and the deconvoluted curves I, * See also Refs. 18–22.

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FIG. 3 Example of a deconvolution analysis of an ice-melting DSC. The deconvoluted curves I, II, and III are for the freezable interlamellar water, and the deconvoluted curve IV is for the bulk water. The deconvoluted curves and their sum (the theoretical curve) are shown by dotted lines, and the experimental DSC curve is represented by a solid line.

II, and III are for the freezable interlamellar water. Therefore, the melting enthalpy of the deconvoluted curve IV gives the enthalpy ∆H B in Eq. (3), so it was used to estimate N I from (∆H T ⫺ ∆H IV )/1.436 as discussed above. In Fig. 4, the ice-melting enthalpy for the freezable interlamellar water, denoted as ∆H I(f), which is given by the sum of the individual melting enthalpies of the deconvoluted curves I, II, and III, is plotted against N w and is compared with the ∆H T and ∆H B (a) curves shown in Fig. 2. The ∆H I(f) curve intersects the abscissa at the N w value denoted as N w (b), above which freezable interlamellar water appears. Therefore, for N w ⬍ N w (b) (I), all the water added is present as nonfreezable interlamellar water, and so N I(nf) at each N w is equal to N w. Here, if we assume limited uptake of the nonfreezable interlamellar water, then N w (b) gives the maximum number of nonfreezable interlamellar water molecules. This assumption seems to be reasonable, because the van der Waals interaction force operating between the lipid hydrocarbon tails restricts expansion of their headgroups, resulting in a limited space for the intrabilayer regions. Accordingly, the maximum value of N I(nf) is equal to N w (b). For N w (b) ⬍ N w ⱕ N w (a) (II), i.e., in the absence

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FIG. 4 Comparison of ice-melting enthalpy curves of ∆H B and ∆H I(f) for bulk and freezable interlamellar water per mole of lipid. The ∆H B and ∆H I(f) curves are determined from the deconvoluted ice-melting curves for the bulk and freezable interlamellar water, respectively. N W (a) and N w (b) are water/lipid molar ratios at the maximum amounts of freezable and nonfreezable interlamellar water, respectively. The designations I, II, and III represent the three regions N w ⬍ N w(b) (i.e., in the presence of only nonfreezable interlamellar water), N w(b) ⬍ N w ⬍ N w(a) (i.e., in the presence of nonfreezable and freezable interlamellar water), and N w ⬎ N w(a) (i.e., in the presence of nonfreezable and freezable interlamellar and bulk water), respectively.

of bulk water, N I(f) at each N w is calculated by subtracting N w(b) from N w. For N w ⬎ N w (a) (III), i.e., in the presence of bulk water, N I(f) is obtained by subtracting N w (b) from the N I value calculated from (∆H T ⫺ ∆H IV )/1.436 at each N w. The estimations of N I(nf), N I(f ), and N B for varying water contents are summarized as follows: 1. 2. 3.

For N w ⱕ N w (b) (I), N I(nf) ⫽ N w, N I(f) ⫽ 0, N B ⫽ 0. For N w (b) ⬍ N w ⱕ N w (a) (II), N I(nf) ⫽ N w (b), N I(f ) ⫽ N w ⫺ N w (b), N B ⫽ 0. For N w ⬎ N w (a) (III), N I(nf) ⫽ N w (b), N I(f) ⫽ N I (⫽N w ⫺ N B) ⫺ N w (b), N B ⫽ ∆H IV /1.436.

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FIG. 5 Water distribution diagram for limited hydration of a lipid–water system. The cumulative number of water molecules (per molecule of lipid) in different bonding modes is plotted against the water/lipid molar ratio (N w).

D. Water Distribution Diagrams Values of N I(nf), N I(f), and N B obtained according to the above calculations were used to construct a water distribution diagram for limited hydration of a lipid– water system (Fig. 5), where the cumulative number of molecules of water (⫽N I(nf ) ⫹ N I(f) ⫹ N B) per molecule of lipid is plotted against N w. The diagram provides much information such as (1) the number of water molecules in different binding modes at each N w; (2) the mode, whether limited or inﬁnite, for the uptake of the water molecules; and (3) the N w value at which the system is fully hydrated.

III. RELATIONSHIP BETWEEN LIPID PHASE TRANSITIONS AND ICE-MELTING BEHAVIOR IN LIPID–WATER SYSTEMS Lipid–water systems usually exist in either a gel or a liquid crystal phase depending on temperature. In this case, the gel-to-liquid crystal phase transition of

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the lipid is observed by DSC. However, the systems are occasionally present in a semicrystalline or crystalline phase, generally called the subgel phase (for diacylphosphatidylcholine, see Refs. 1, 14–16, 24–26; for diacylphosphatidylethanolamine, Refs. 18–20, 27–32; for diacylphosphatidylglycerol, Refs. 33–39), which transforms to either the gel or the liquid crystal phase on heating. If the ice-melting DSC peak (whether broad or sharp) is successively followed by the gel-to-liquid crystal phase transition, the melting behavior is known to be derived from the water molecules of the gel phase. If no phase transition is observed at a temperature higher than that of the ice melting, then the ice is assigned to one of the liquid crystal phases. Furthermore, if the phase transition of either the subgel to gel or subgel to liquid crystal follows the ice-melting peak or thermal event, the ice is assigned to one of the subgel phases. On this basis, we measured the ice-melting behavior of both the gel and subgel phases and constructed the water distribution diagrams of both phases according to the method discussed above. In this chapter, our recent results are referred to with a view to answering the following questions: 1. 2. 3.

IV.

Is there any difference between neutral and acidic phospholipids in the mode of incorporation of water molecules between their lamellae? What is the role of water molecules in the lipid phase transitions such as gel to liquid crystal, subgel to gel, and subgel to liquid crystal? What is the role of water molecules in the conversion of the gel to the subgel phase?

EXPERIMENTAL TECHNIQUES

Phospholipids are major components of biomembranes and constitute a fundamental part of their bilayer structure. The phospholipids used in the present study are dipalmitoylphosphatidylcholine (DPPC) and dimyristoylphosphatidylethanolamine (DMPE) as neutral lipids and dipalmitoylphosphatidylglycerol (DPPG) as an acidic lipid. The polar headgroups of these lipids are compared in Fig. 6 [40–43]. It is worthy of note that these headgroups provide many binding sites for a water molecule on the surface of a bilayer. On the other hand, phosphatidylcholine (PC) and phosphatidylethanolamine (PE) constitute the majority of the total phospholipids in biomembranes and are present as dipolar zwitterions at neutral pH. Phosphatidylglycerol (PG) is a ubiquitous phospholipid in mitochondrial and chloroplast membranes and is negatively charged at neutral pH. Since these lipids have charged groups, electrostatic forces operate not only between adjacent headgroups in an intrabilayer (intermolecular force) but also between adjacent bilayers (intersurface force), although the forces are opposite in sign or direction for the neutral and acidic lipids. Furthermore, results of X-ray crystallographic studies previously reported by other workers should be mentioned here.

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FIG. 6 Difference in the polar headgroups of diacylphosphatidylcholine (PC), diacylphosphatidylethanolamine (PE), and diacylphosphatidylglycerol (PG).

Thus, two adjacent PC molecules in an intrabilayer are linked to each other via a water-based hydrogen bond [41,44]. However, PE molecules in an intrabilayer interact directly via a hydrogen bond formed between the amino group of one molecule and the phosphate group of an adjacent molecule [41,42,44]. For PG used in Na ⫹-PG, the counterions are present in a layer sandwiched by the headgroups of adjacent bilayers [45]. On the other hand, the present lipids have different chain lengths. This is because when the dimyristoylphosphatidylcholine (DMPC) system is used in place of the DPPC system, its subgel phase exists at temperatures below at least 0°C (i.e., it is impossible to measure the ice-melting curve for the subgel phase). Similarly, when the dipalmitoylphosphatidylethanolamine (DPPE) system is used in place of the DMPE system, the system requires much longer periods (at least 40 days) for completion of the conversion of the gel to the subgel phase by annealing. The water distribution diagram shown in Fig. 5 was composed of the results of at least 30 samples of a lipid–water mixture containing from 0 to at least 40 wt% water. The value of N T in Eq. (2), determined by weighing both the lipid and water, is also a dominant factor in the accuracy of the present method, similarly to the value of ∆H B discussed above. From this viewpoint, samples of varying water content were prepared in the present study by successive additions of the desired amounts of water to the same dehydrated lipid. Thus, only the weight of water was changed throughout the preparation of a series of samples. The dehydrated lipid was prepared as follows. A lipid (approximately 30 mg) in a high pressure crucible cell was dehydrated under high vacuum (10 ⫺4 Pa) at room temperature for at least 3 days until no mass loss was detected by electroanalysis. The crucible cell containing the dehydrated lipid was sealed off in a dry box ﬁlled with dry

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N 2 gas and then weighed with a microbalance. All the samples were weighed after adding the desired amounts of water and annealed by repeating thermal cycling at temperatures above and below the lipid phase transition until the same transition behavior was attained. After the annealing, the loss of water in the samples was checked with the microbalance [13,21].

V. ICE-MELTING BEHAVIOR FOR A MINUTE AMOUNT OF FREEZABLE INTERLAMELLAR WATER Figure 7 shows a series of typical DSC curves for samples of the DPPC–water mixture with increasing water content expressed as [(g water)/(g lipid ⫹ g water)] ⫻ 100 and designated as W H2O. The ice-melting peaks are followed by two lipid transition peaks of the gel (L β′)-to-gel (P β ′) and subsequent gel (P β ′)-to-liquid crystal phase transitions, generally called the T p and T m transitions, respectively.

FIG. 7 A series of DSC curves of the DPPC–water system ranging in water content from 11.5 wt% (N w ⫽ 5.3) to 40.9 wt% (N w ⫽ 28.2).

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FIG. 8 Variation of the broad component of ice-melting DSC curves at low water contents up to 20.1 wt% for the gel phase of the DPPC–water system. Water contents (wt%) are a, 11.5 (5.3); b, 12.6 (5.8 7); c, 12.8 (5.9 8); d, 13.1 (6.2); e, 14.1 (6.7); f, 14.8 (7.0); g, 16.1 (7.8); h, 17.4 (8.6); i, 20.1 (10.2), where the numbers in parentheses are the corresponding N w values.

In Fig. 8, enlarged scale ice-melting peaks are compared for W H2 O ⬍ 20 wt%, where the water content is successively changed at short intervals of about 1 wt%. A characteristic feature of this ﬁgure is that the broad components of icemelting peaks d–i cannot be superimposed on one another. Only at water contents less than 13 wt% (i.e., N w ⬍ 6) is such a superposition observed. This phenomenon indicates that the interbilayer freezable water molecules interact with one another in different hydrogen bonding modes and their bonding modes become closer to that of free water with increasing water content. Furthermore, it is suggested that the hydrogen bonding mode of the freezable water molecules existing in interbilayer regions is little affected by the addition of more interlamellar water. On the other hand, as discussed later, the freezable interlamellar water of the DPPC–water system begins to appear at N w ⬃ 5 (W H2O ⬃ 11 wt%); therefore, N w(b) ⬃ 5. However, as shown in Fig. 8, the ice-melting behavior (curves a–c)

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for 5 ⬍ N w ⬍ 6 is different from that (curves d–i) for N w ⬎ 6. Thus, a broad, low, ﬂat peak extending over a fairly wide temperature range is observed for a very small amount of freezable interlamellar water (N w ⫽ 5.3, W H2O ⫽ 11.5 wt%) (curve a). Yet, even though the amount of freezable interlamellar water is slightly less than one molecule of H 2 O per molecule of lipid (N w ⫽ 5.9 8, W H2O ⫽ 12.8 wt%) (curve c), the melting peak is broader and is not ﬁtted to similar peaks observed for N w ⬎ 6. Furthermore, the thermal behavior is observed to depend on the procedure used for the cooling of the sample, as shown in Fig. 9. Thus, when the sample is cooled to ⫺60°C at a rate higher than 1°C/min, its heating curve shows an exothermic phenomenon at temperatures just below the ice-melting peak (Fig. 9, curve a). The exothermic peak completely disappears after annealing at temperatures around ⫺40°C (exothermic temperatures), but the resulting ice-melting peak is still broad (Fig. 9, curve b). In contrast, no exothermic peak is observed when the sample is cooled at a rate as slow as 0.2°C/min (Fig. 9, curve c). Such phenomena are characteristic of freezable interlamellar water in amounts of less than one molecule per molecule of lipid, namely, for

FIG. 9 Characteristic behavior of ice-melting DSC curves at a water content of 12.8 wt% (N w ⫽ 5.9 8) for the gel phase of the DPPC–water system. Curves a, b, and c are explained in the text.

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5 ⬍ N w ⬍ 6. By assuming multiple sites on the bilayer surface to which the water molecules can bind, it is suggested that one molecule of H 2O per molecule of lipid of freezable interlamellar water is not enough to cover all the binding sites. As a result, a localized increase in the transformation of the water molecules into ice on cooling would occur on the bilayer surface, resulting in a broadening of the ice-melting peak. Presumably, the hydrogen bonds in such localized ice are unstable or metastable, and so the exothermic peak due to the stabilization is observed upon heating. On this basis, it is suggested that one molecule of H 2O per molecule of lipid is a critical amount required for the freezable interlamellar water to form icelike hydrogen bonds between lamellae.

VI.

ANALYSIS OF WATER MOLECULES IN THE GEL PHASE OF LIPID–WATER SYSTEMS

A. DPPC–Water System According to the method discussed above, the ice-melting DSC peaks for N w ⬎ 6 (W H2O ⬎ 13 wt%), characterized by similar shapes, are deconvoluted. In Fig. 10, typical results of the deconvolution analysis are compared at water contents of 16.1, 20.1, and 22.1 wt%. On the whole, the number of deconvoluted curves increases and the area of each curve becomes larger with increasing water content. The broad peak for the freezable interlamellar water is shown to be ﬁnally deconvoluted into four curves—I, II, III, and IV—which successively appear with increasing water content. A deconvoluted curve V for the bulk water is observed at water contents of 20.1 and 22.1 wt%. In Fig. 11 the ice-melting enthalpies ∆H I, ∆H II, ∆H III, and ∆H IV of the respective deconvoluted curves I, II, III, and IV are plotted against N w, together with the sum of these enthalpies, ∆H I(f). Similarly, in Fig. 12 the ice-melting enthalpy ∆H V of the deconvoluted curve V, comparable to ∆H B in Eq. (3), is plotted against N w. To make clear the relationship between the ice-melting enthalpies for the freezable interlamellar and bulk water, the ∆H B (⫽∆H V ) and ∆H I(f) curves are compared in Fig. 13. Furthermore, Table 1 summarizes values of ∆H I(f) and ∆H B per mole of lipid at varying water contents (W H2O) shown together with the corresponding water/lipid molar ratios (N w). First, focusing on Fig. 11, it is seen that with increasing water content, the ∆H I, ∆H II, ∆H III, and ∆H IV curves appear in this order and reach maxima in the same order. Every curve gently increases before arriving at a plateau, so that the ∆H I(f) curve also shows the same behavior. Consequently, N w (⬃15) at the beginning of the plateau of the ∆H I(f ) curve is higher than that (⬃10) predicted from the extrapolated (dashed) lines. On the other hand, the ∆H I(f ) curve intersects the abscissa at N w ⬃5. Therefore, the limiting, maximum number of nonfreezable interlamellar water molecules for the gel phase of the DPPC–water system is 5 H 2 O per molecule of lipid.

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FIG. 10 Deconvolution analysis of ice-melting DSC curves for the gel phase of the DPPC–water system. Water contents (wt%); a, 16.1 (7.8); b, 20.1 (10.2); c, 22.1 (11.6). The numbers in parentheses show the corresponding N w values. The deconvoluted curves I–V and their sum (the theoretical curve) are shown by dotted lines and the DSC curves by solid lines.

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FIG. 11 Plots of ice-melting enthalpies for freezable interlamellar water versus N w in the gel phase of the DPPC–water system. ∆H I(f) is the sum of the individual enthalpies of the deconvoluted curves I, II, III, and IV for the freezable interlamellar water shown in Fig. 10.

Next, the ∆H B curve is also shown (Fig. 12) to increase gently up to N w ⬃15, after which it increases linearly and parallel to the theoretical ∆H T line. Accordingly, the amount of total interlamellar water is the same for water contents above the boundary N w (⬃15), indicating the appearance of a fully hydrated gel phase. In this case, the maximum amount of total interlamellar water can be determined graphically by extrapolating the linear ∆H B curve to N w below 15. Thus, N w of the intersection point just corresponds to the maximum number of interlamellar water molecules, i.e., 10 H 2 O per molecule of lipid for the DPPC–water system. Focusing on the nonlinear increase observed for both the ∆H I(f ) and ∆H B curves, it is seen from Fig. 13 that the phenomenon for both curves takes place in the same water content region, 8 ⬍ N w ⬍ 15. Therefore, it is understandable that the deviations of the ∆H I(f ) curve from the extrapolated ideal (dashed) line is caused by the bulk water that appears although the limiting, maximum amount of interlamellar water is not yet reached (in other words, the gel phase is not

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FIG. 12 A plot of the ice-melting enthalpy ∆H B for the bulk water versus N w in the gel phase of the DPPC–water system. The theoretical ∆H T curve is shown for comparison.

FIG. 13 ∆H T, ∆H B , and ∆H I(f) curves for the gel phase of the DPPC–water system. Hatch lines within the range 8 ⬍ N w ⬍ 15 represent the pre-region (see text).

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Table 1 Ice-Melting Enthalpies of Freezable Interlamellar and Bulk Water, ∆H I(f) and ∆H B , Respectively, per Mole of Lipid and the Numbers of Nonfreezable and Freezable Interlamellar and Bulk Water Molecules, N I(nf), N I(f), and N B , respectively, per Lipid Molecule at Varying Water Contents (W H 2 O) in the Gel Phase of the DPPC–Water System Ice-melting enthalpy (per mole of lipid) (kcal)

W H2O System a b c d e f g h i j k l m n o p

Number of water molecules (per molecule of lipid)

(wt%)

Nw

∆H I(f)

∆H B

N I(nf)

N I(f)

NB

12.6 12.8 13.1 14.1 14.8 16.1 17.4 20.1 22.1 24.1 26.0 28.9 31.9 35.0 37.9 40.9

5.9 6.0 6.2 6.7 7.0 7.8 8.6 10.2 11.6 12.9 14.3 16.6 19.1 21.9 24.8 28.2

0.45 0.98 1.34 1.80 2.44 3.31 4.18 5.03 5.35 5.75 5.85 5.85 5.85 5.85 5.85 5.85

0 0 0 0 0 0 0.50 1.29 3.05 4.96 6.48 9.85 12.85 17.10 21.58 26.01

5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0

0.9 1.0 1.2 1.7 2.1 2.8 3.4 4.1 4.5 4.9 5.0 5.0 5.0 5.0 5.0 5.0

0 0 0 0 0 0 0.2 1.1 2.1 3.1 4.3 6.6 9.1 11.9 14.8 18.2

fully hydrated). This indicates the existence of a speciﬁc region (8 ⬍ N w ⬍ 15), taken as a pre–region [6,8,9,21,22] and designated by hatch lines in Fig. 13. In this region, the bulk water content likewise increases, little by little, until the maximum amount of freezable interlamellar water is reached. Above this amount, all the added water is present as bulk water, so that the ∆H B curve becomes parallel to the straight ∆H T line. Furthermore, a point to notice in Fig. 13, except for the pre-region, is the difference in slope between the linear curves of ∆H I(f) (N w ⬍ 8) and ∆H B (N w ⬎ 15). Thus, although the ∆H I(f) curve is also linear at N w values below the preregion, it is not parallel to the ∆H T line and therefore not parallel to the linear ∆H B curve at N w values above the pre-region. The slopes of the linear curves of ∆H B and ∆H I(f ) are characterized only by the bulk and freezable interlamellar water, respectively, and so give individual molar ice-melting enthalpies for both types of water. On this basis, the individual average molar melting enthalpies for the bulk and freezable interlamellar water were estimated from the slopes of the respective straight ∆H B and ∆H I(f) lines obtained by a least squares method.

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The average melting enthalpy for the bulk water is 1.420 kcal/mol H 2 O and is very close to the known value estimated from the ∆H T line. For the freezable interlamellar water, the estimated average melting enthalpy is 1.201 kcal/mol H 2 O and is smaller than that for the bulk water. The above estimates evidence a difference in the molar ice-melting enthalpy between the freezable interlamellar and bulk water, and this difference is related to different hydrogen bond modes for the two types of water. Again, we remark on the linear relationship between ∆H I(f ) and N w observed at water contents below the pre-region. This indicates that the molar melting enthalpy for the freezable interlamellar water is nearly the same for 5 ⬍ N w ⬍ 8. However, this result does not agree with our analysis because the multiplecomponent deconvolutions of the ice-melting peak for the freezable interlamellar water suggest the existence of water molecules in different hydrogen bond modes. The values of N I(nf ), N I(f), and N B for varying water contents were estimated according to the method discussed above, and the results are summarized in Table 1. Furthermore, in Fig. 14, the cumulative values of N I(nf), N I(f), and N B are

FIG. 14 Water distribution diagram for the gel phase of the DPPC–water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted against N w .

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plotted against N w. On the basis of the water distribution diagram, the following results are obtained for the gel phase of the DPPC–water system: 1. The limiting, maximum numbers of water molecules are approximately 5 H 2 O and 5 (⫽ 10 ⫺ 5) H 2 O per molecule of lipid for the nonfreezable and freezable interlamellar water, respectively. 2. These maximum values are reached at water/lipid molar ratios of approximately 5 and 15, respectively. 3. The pre-region exists in the range of ⬃8 ⬍ N w ⬍ ⬃15 before the attainment of full hydration of the gel phase.

B. DMPE–Water System [21] A series of ice-melting DSC peaks for the DMPE–water system is shown in Fig. 15. In this ﬁgure, the ice-melting curve c at N w ⬃ 3 is shown to deviate from

FIG. 15 A series of ice-melting DSC curves at varying water contents for the gel phase of the DMPE–water system. Water contents (wt%): a, 2.3 (0.8); b, 6.0 (2.25); c, 8.0 (3.1); d, 10.2 (4.0); e, 12.2 (4.9); f, 14.1 (5.8); g, 16.1 (6.8); h, 18.1 (7.8); i, 20.0 (8.8); j, 22.0 (10.0); k, 25.0 (11.8); l, 28.0 (13.7); m, 32.0 (16.6). The numbers in parentheses show the corresponding N w values.

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similar shapes observed for N w ⬎ 3. This is the same phenomenon as that observed in the DPPC–water system (see Fig. 8), for which the amount of freezable interlamellar water is less than 1 H 2 O per molecule of lipid. Deconvolution results of the ice-melting curves are compared at different water contents in Fig. 16. The broad peak for the freezable interlamellar water is shown to be ﬁnally deconvoluted into three curves designated I, II, and III. In Fig. 17, the estimated sum of the ice-melting enthalpy ∆H I(f) for the freezable interlamellar water is plotted against N w and is compared with the ∆H B curve obtained from the deconvoluted curve IV for the bulk water, together with the ∆H T line. A gentle increase with water content is observed for both the ∆H I(f) and ∆H B curves over the N w range from approximately 4 to 10, indicating the existence of a pre-region similar to that observed for the DPPC–water system. Except for the pre-region, both the ∆H I(f ) and ∆H B curves are linear for N w ⬍ 4 and N w ⬎ 10, respectively. The

FIG. 16 Deconvolution analysis of ice-melting DSC curves for the gel phase of the DMPE–water system. Water contents (wt%): a, 10.2 (4.0); b, 12.2 (4.9); c, 14.1 (5.8); d, 22.0 (10.0). The numbers in parentheses show the corresponding N w values. The deconvoluted curves (I–IV) and their sum (the theoretical curve) are shown by dotted lines and the DSC curves by solid lines.

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FIG. 17 Comparison of ∆H T, ∆H B , and ∆H I(f) curves for the gel phase of the DMPE– water system.

linear ∆H I(f) line intersects the abscissa at N w ⫽ 2.3, whereas the linear ∆H B line extrapolated to N w ⬍ 10 intersects the abscissa at N w ⬃ 6. Thus, the maximum numbers of interlamellar water molecules are estimated to be 2.3 H 2O and 3.7 (⫽ 6 ⫺2.3) H 2 O per molecule of lipid for the nonfreezable and freezable interlamellar water, respectively. On the other hand, similarly to the case of the DPPC– water system, the linear ∆H B line is almost parallel to the straight ∆H T line, in contrast to the linear ∆H I(f) line, which is characterized by a slope of 1.283 kcal/ mol H 2 O. The N I(nf), N I(f), and N B values at varying water contents were calculated from Eq. (3). Table 2 summarizes data concerning ∆H I(f) and ∆H B and also values of N I(nf), N I(f ), and N B at increasing water contents (W H2O) shown together with

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Table 2 Ice-Melting Enthalpies of Freezable Interlamellar and Bulk Water, ∆H I(f) and ∆H B , Respectively, per Mole of Lipid and the Numbers of Nonfreezable and Freezable Interlamellar and Bulk Water Molecules, N I(nf), N I(f), and N B , Respectively, per Lipid Molecule at Varying Water Contents (W H 2 O) in the Gel Phase of the DMPE–Water System Ice-melting enthalpy (per mole of lipid) (kcal)

W H2O System a b c d e f g h i j k l m

Number of water molecules (per molecule of lipid)

(wt%)

Nw

∆H I(f)

∆H B

N I(nf)

N I(f)

NB

2.3 6.0 8.0 10.2 12.2 14.1 16.1 18.1 20.0 22.0 25.0 28.0 32.0

0.8 2.2 5 3.1 4.0 4.9 5.8 6.8 7.8 8.8 10.0 11.8 13.7 16.6

0 0 1.09 2.45 3.41 3.90 4.34 4.56 4.85 4.98 5.06 5.02 5.11

0 0 0 0 0.25 1.05 1.97 3.04 4.28 5.76 8.21 11.13 15.07

0.8 2.2 5 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3

0 0 0.8 1.7 2.4 2.8 3.1 3.4 3.5 3.7 3.7 3.7 3.7

0 0 0 0 0.2 0.7 1.4 2.1 3.0 4.0 5.8 7.7 10.6

the corresponding N w values for the gel phase of the DMPE–water system. The water distribution diagram is shown in Fig. 18 for the gel phase of the DMPE– water system.

C. DPPG–Water System [22] A series of typical ice-melting DSC peaks for the DPPG–water system are compared in Fig. 19A. However, the onset temperature of the sharp peak of icemelting endotherms is about 3–4°C lower than that of the corresponding peak for the neutral lipid systems discussed above. In other words, the temperature axis of the sharp peak is shifted by 3–4°C to the lower temperature side. This suggests that the bonding mode of the freezable interlamellar water is very close to that of the bulk water. Accordingly, the deconvolution of the sharp peaks of the DPPG system was performed by setting up a new Gaussian curve other than that for the bulk water, as shown in Fig. 19B. Furthermore, the water content of this system was continuously changed up to 90 wt% (N w ⫽ 374) to investigate whether the hydration is limited or inﬁnite. In Fig. 20, curves of ∆H T, ∆H I(f), and ∆H I(nf ) are compared up to N w ⫽ 250.

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FIG. 18 Water distribution diagram for the gel phase of the DMPE–water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted versus N w .

The water distribution diagram of this system is shown over the wide N w range up to 400 in Fig. 21A. In addition, for comparison with the DPPC and DMPE systems, an enlarged scale diagram of the DPPG system up to N w ⫽ 50 is shown in Fig. 21B. A characteristic feature of this diagram is the inﬁnite uptake of freezable interlamellar water, i.e., inﬁnite hydration of DPPG bilayers, in contrast with the limited hydration of the neutral lipid bilayers discussed above. Thus, as shown in Fig. 20, the linear ∆H B line observed for N w ⬎ 150 is not parallel to the straight ∆H T line, showing an increase in the enthalpy difference between the ∆H T and ∆H B given in Eq. (3) with increasing water content. This is reﬂected in the ∆H I(f) curve, which continues to increase up to N w ⫽ 400. Furthermore, it is shown by this ﬁgure that the bulk water of this system begins to appear at N w ⬃ 35, which is quite a bit higher than the corresponding N w values of approximately 8 and 4 for the DPPC and DMPE systems, respectively. These facts indicate that both the freezable interlamellar and bulk water continuously increase over the wide N w range (35–400) investigated, as shown in Fig. 21. In this case,

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FIG. 19 (A) A series of ice-melting DSC curves at varying water content for the gel phase of the DPPG–water system. Water contents (wt%): a, 8.1 (3.6); b, 11.9 (5.6); c, 14.1 (6.8); d, 16.0 (7.9); e, 18.0 (9.1); f, 21.1 (11.1); g, 23.9 (13.0); h, 27.0 (15.3); i, 29.9 (17.7); j, 34.9 (22.1); k, 39.9 (27.4); l, 44.9 (33.7); m, 49.9 (41.2). The numbers in parentheses show the corresponding N w values. (B) Deconvolution analysis of ice-melting DSC curve j shown in (A). The deconvoluted curves (I–V) and their sum (the theoretical curve) are shown by dotted lines, and the DSC curve is represented by a solid line.

FIG. 20 Comparison of ∆H T, ∆H B , and ∆H I(f) curves for the gel phase of the DPPG– water system.

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FIG. 21 Water distribution diagram up to (A) N w ⫽ 400 and (B) N w ⫽ 50 for the gel phase of the DPPG–water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted versus N w .

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the overall regions for N w ⬎ ⬃ 35 would be taken as the pre-region, since there is no saturation point for the hydration of the gel phase.

VII. SUBGEL PHASES IN LIPID–WATER SYSTEMS In Fig. 22, three typical types of DSC curves are shown for the DMPE–water system at the same water content. A distinct difference in the thermal behavior is observed not only for the phase transition of the lipid but also for the melting of the ice. Figure 23 shows a schematic diagram of relative enthalpy (∆H ) versus temperature (t) curves that was constructed on the basis of the transition enthalpies and temperatures associated with the lipid phase transitions shown in Fig. 22. By reference to the diagram, it becomes apparent that the DMPE–water system can be present in two phases, designated the L- and H-subgel phases, other than the gel phase at temperatures where the hydrocarbon chains of the lipids are in a solid-like state and the thermodynamic stability of these phases increases

FIG. 22 Three typical types of DSC curves of the DMPE–water system at the same water content (W H 2 O ⫽ 25.0 wt%, N w ⫽ 11.8). The phase transition peaks of the lipid are characterized as (a) gel to liquid crystal, (b) L-subgel to gel followed by gel to liquid crystal, and (c) H-subgel to liquid crystal.

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FIG. 23 Schematic diagram of the relative enthalpy (∆H ) versus temperature (t) for the DMPE–water system, constructed from the transition enthalpies and temperatures associated with the lipid phase transitions shown in Figs. 22a–22c. The system is also present in the H- and L-subgel phases, which are different from the gel phase.

in the order gel ⬍ L-subgel ⬍ H-subgel. The designations L and H for the subgel phases are due to their transitions, which appear, respectively, at temperatures lower and higher than that of the gel-to-liquid crystal phase transition. As shown in Fig. 24, similar behavior is observed for the DPPC–water system, although the H-subgel phase is missing in this system. To date, many studies on the stability of the gel phase have been performed for various phospholipids (PC, Refs. 1, 14–16, 24–26; PE, Refs. 18–20, 27–32; PG, Refs. 33–39), and it is generally accepted that the gel phase is a metastable state. Thus, the gel phase, which is ﬁrst realized by cooling the liquid crystal phase to temperatures below that of the phase transition, converts into more stable phases, generally called subgel phases. In this conversion, lateral packings of the lipid molecules in the intrabilayer are changed with a view to enhancing the van der Waals interaction force operating between the hydrocarbon chains [46,47]. In fact, the difference in the van der Waals interaction energy between the gel and subgel phases calculated from the chain–chain separation is consistent with the calorimetric enthalpy difference between the two phases [30,33,39]. However, such a conversion is achieved only when the thermal annealing adopted for the gel phase is adequate. Therefore, it is necessary to search for adequate annealing conditions relating to a temperature range and a time period. In the case of the DMPE–water system,

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FIG. 24 Two typical types of DSC curves of the DPPC–water system at the same water content (W H 2 O ⫽ 28.0 wt%, N w ⫽ 15.9), characterized by the lipid phase transitions of (a) gel to liquid crystal and (b) L-subgel to gel followed by gel to liquid crystal.

the annealing condition is different for the respective conversions to the L- and H-subgel phases [18–20]. Thus, the conversion to the L-subgel phase is achieved by annealing at temperatures of ⫺5 to ⫹5°C for periods of 2–4 weeks (depending on the water content of the sample). For the conversion to the H-subgel phase, two steps of annealing at different temperatures are necessary; the gel sample is kept at around ⫺60°C for at least 5 h (nucleation) and is then kept at a temperature just below the gel-to-liquid crystal phase transition for about 24 h (nuclear growth). For the DPPC–water system, a two-step annealing for the processes of nucleation at ⫺60°C and nuclear growth at 4°C is required to complete the conversion to the L-subgel phase [16]. For a DPPC sample that is not fully hydrated, a long period of annealing, up to 3 weeks, is required for the process of nuclear growth. Accordingly, the lipid phase transitions for the DMPE system shown in Figs.

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22a, 22b, and 22c are from the gel, L-subgel, and H-subgel to the respective liquid crystal phases, and the transitions for the DPPC system shown in Figs. 24a and 24b are from the gel and L-subgel to the respective liquid crystal phases. The difference in the ice-melting behavior observed in Figs. 22 and 24, respectively, indicates the difference in the state of the water molecules between the gel and subgel phases of solidlike hydrocarbon chains. The ice-melting endotherm for the L-subgel phase of the DMPE system in Fig. 22b is characterized by a shoulder peak at around ⫺5°C, and the endotherm for the H-subgel phase (Fig. 22c) is characterized by an enlarged sharp peak at around 0°C. Similarly, the ice-melting endotherm for the L-subgel phase of the DPPC system in Fig. 24b presents a shoulder peak at around ⫺5°C. Such differences are reﬂected in the ∆H B and ∆H I(f ) curves and the water distribution diagram for the subgel phases of the DPPC and DMPE systems.

VIII.

ANALYSIS OF WATER MOLECULES IN THE SUBGEL PHASES OF LIPID–WATER SYSTEMS

A. DPPC–Water System Gel samples with varying water contents of the DPPC system were annealed according to the procedure described above. DSC curves for the resultant Lsubgel phase are compared at varying water contents in Fig. 25. Furthermore, to make clear the difference in the ice-melting behavior between the gel and subgel phases, the results of the deconvoluted ice-melting curves are compared for the two phases at the same water content in Fig. 26. Compared with the individual deconvoluted curves for the gel phase, the areas of the deconvoluted curves I, II, and III for the L-subgel phase decrease, respectively, but that of the deconvoluted curve IV increases. Consequently, as shown in Fig. 27, the ∆H I(f) curve for the subgel phase is lower than that for the gel phase (dashed lines) over all water contents tested, and the intersection point of the extrapolated linear ∆H I(f ) line with the abscissa gives approximately 6 H 2 O per molecule of lipid as the maximum number of nonfreezable interlamellar water molecules for the L-subgel phase of the DPPC system. This limiting value is larger by 1 H 2 O per molecule of lipid than the corresponding value for the gel phase. Furthermore, as shown in Fig. 27, ∆H B for the subgel phase increases along a curve nearly the same as that of ∆H B for the gel phase (dashed lines), although there are some inconsistencies in the pre-region. This indicates that the amount of total (nonfreezable plus freezable) interlamellar water is nearly the same for the gel and subgel phases at each N w. The water distribution diagram for the L-subgel phase was prepared from the estimated values of N I(nf), N I(f), and N B , and the resultant diagram is shown in Fig. 28. The amount of nonfreezable water for the L-subgel phase is

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FIG. 25 (A) A series of DSC curves of the DPPC–water system for samples thermally annealed according to the procedure described in the text. Water contents are from 10.8 wt% (N w ⫽ 4.9) to 35.0 wt% (N w ⫽ 21.9). (B) Ice-melting curves and lipid transition peaks of L-subgel to gel phase are compared, in an enlarged scale. Water contents (wt%): a, 10.8 (4.9); b, 12.8 (6.0); c, 16.1 (7.8); d, 17.4 (8.6); e, 20.1 (10.2); f, 22.1 (11.6); g, 23.8 (12.8); h, 24.8 (13.7); i, 28.0 (15.9); j, 31.1 (18.4); k, 35.0 (21.9). The numbers in parentheses show the corresponding N w values.

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FIG. 26 Comparison of deconvoluted ice-melting curves between (a) L-subgel phase and (b) gel phase of the DPPC–water system at the same water content (W H 2 O ⫽ 28.0 wt%, N w ⫽ 15.9). The deconvoluted curves (I–V) and their sum (the theoretical curve) are shown by dotted lines and the DSC curves by solid lines.

greater by approximately one H 2O per molecule of lipid than that for the gel phase over all water contents at N w ⬎ 6. The extra nonfreezable interlamellar water, characteristic of the L-subgel phase, is shown to arise from the freezable interlamellar water present in the gel phase. Furthermore, it is seen from Fig. 26 that the bonding mode of a great part of the freezable interlamellar water of the L-subgel phase is very close to that of the bulk water.

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FIG. 27 ∆H B and ∆H I(f) curves for the L-subgel phase of the DPPC–water system. For comparison, corresponding curves for the gel phase are shown by dashed lines.

FIG. 28 Water distribution diagram for the L-subgel phase of the DPPC–water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted versus N w .

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FIG. 29 A series of DSC curves of the DMPE–water system for samples (N w ⬎ 10) annealed according to the procedure described in the text. Water contents (wt%): a, 21.1 (9.4); b, 25.5 (12.1); c, 28.2 (13.9); d, 30.7 (15.6). The numbers in parentheses show the corresponding N w values. The ice-melting curves are followed by the lipid phase transitions of L-subgel to gel and gel to liquid crystal.

B. DMPE–Water System* In Fig. 29, DSC curves of the DMPE system for the L-subgel phase obtained by annealing are compared at different water contents for N w ⬎ 10, because conversion of the gel to both L- and H-subgel phases (which are different in stability) is observed only when the gel phase is not fully hydrated (N w ⬍ 10). In Fig. 30, deconvoluted ice-melting curves are compared for the L-subgel and gel phases at the same water content, as an example. A marked enlargement of the deconvoluted curve III for the freezable interlamellar water is observed in the L-subgel phase, similarly to that observed for the L-subgel phase of the DPPC system * See also Refs. 18–20.

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FIG. 30 Comparison of deconvoluted ice-melting curves between (a) L-subgel and (b) gel phases of the DMPE–water system at the same water content (W H 2 O ⫽ 22.0 wt%, N w ⫽ 10.0). The deconvoluted curves (I–IV) and their sum (the theoretical curve) are shown by dotted lines and the DSC curves by solid lines.

shown in Fig. 26. Simultaneously, a decrease of the deconvoluted curve IV for the bulk water is observed in the L-subgel phase. In Fig. 31, a ∆H B vs. N w curve for the L-subgel phase of the DMPE system is shown, along with the corresponding curve for the gel phase (dashed lines). The amount of bulk water for the Lsubgel phase is shown to be smaller by approximately one molecule of H 2 O per molecule of lipid than that for the gel phase over all water contents at N w ⬎ 10.

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FIG. 31 Comparison of ∆H B and ∆H I(f) curves for the L-subgel phase of the DMPE– water system at N w ⬎ 10. Corresponding curves for the gel phase are shown by dashed lines.

The maximum total amount (nonfreezable plus freezable) of interlamellar water estimated from the extrapolated line is approximately 7 H 2 O/lipid for the Lsubgel phase, which is larger by 1 H 2 O/lipid than that (6 H 2 O/lipid) for the fully hydrated gel phase. Furthermore, the ∆H I(f ) vs. N w curve for a fully hydrated Lsubgel phase shown in Fig. 31 is almost identical with the corresponding curve for the gel phase (dashed lines). On this basis, although there are no data for N w ⬍ 10 (i.e., it is impossible to estimate from the value of N w where the ∆H I(f ) curve intersects the abscissa), the maximum amount of freezable interlamellar water for the L-subgel phase is evaluated to be comparable to that for the gel phase, i.e., approximately 3.7 (⫽ 6 ⫺ 2.3) molecules of H 2 O per molecule of lipid. Consequently, the maximum amount of nonfreezable interlamellar water for the L-subgel phase is estimated to be approximately 3.3 (⫽ 7 ⫺ 3.7) molecules of H 2 O per molecule of lipid and is found to increase by about 1 H 2 O/lipid compared with the gel phase (2.3 H 2 O/lipid). The increment of nonfreezable interlamellar water is comparable to that observed for the L-subgel phase of the

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FIG. 32 Water distribution diagram for the L-subgel phase (N w ⬎ 10) of the DMPE– water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted versus N w .

DPPC system. Accordingly, it is suggested that in the conversion of the gel to the L-subgel phase, one molecule of H 2 O per molecule of lipid of the freezable interlamellar water present in the gel phase changes to nonfreezable interlamellar water in regions between the lipid headgroups in the resultant subgel phase. However, such a migration of water molecules would induce an empty space in the interbilayer regions, and this space would be ﬁlled by an infusion of the bulk water existing outside the bilayer. As a result, compared with the gel phase, the amount of bulk water of the L-subgel phase is less by one molecule of H 2 O per molecule of lipid and the amount of freezable interlamellar water is the same, as shown by a comparison of the water distributions in Figs. 18 and 32 for the two phases. However, no participation of bulk water in the conversion of the gel to the L-subgel phase by annealing is observed for the DPPC system, differently from the DMPE system. On the other hand, complete conversion of the gel to the H-subgel phase by

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annealing was observed even at a low water content at which only nonfreezable interlamellar water is present in the gel phase (i.e., in the absence of freezable interlamellar and bulk water). This is contrasted with the conversion to the Lsubgel phase discussed above. An example of deconvolution analysis of the icemelting peak for the H-subgel phase is shown in Fig. 33, and curves of ∆H B vs. N w and ∆H I(f) vs. N w for this phase are shown in Fig. 34, along with the corresponding curves for the gel phase. In Fig. 33, the deconvoluted curves I and II are not observed for the H-phase. Accordingly, the extrapolated ∆H I(f) line for

FIG. 33 Deconvoluted ice-melting curves of (a) H-subgel phase and (b) gel phase of the DMPE–water system at the same water content (W H 2 O ⫽ 22.0 wt%, N w ⫽ 10.0). The deconvoluted curves (I–IV) and their sum (the theoretical curve) are shown by dotted lines and the DSC curves by solid lines.

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FIG. 34 ∆H B and ∆H I(f) curves for the H-subgel phase of the DMPE–water system. Corresponding curves for the gel phase are shown by dashed lines.

the H-subgel phase is shown to intersect the abscissa at an extremely low N w value of around 0.3, indicating that there is almost no nonfreezable interlamellar water for this phase. In contrast, the deconvoluted curve IV for bulk water shown in Fig. 33 is markedly enlarged for the H-subgel phase, so that the ∆H B curve for this phase is noticeably higher than that for the gel phase (dashed lines) over all water contents studied. The extrapolated linear ∆H B line for the H-subgel phase, which is parallel to the ∆H T line, gives the maximum amount of total interlamellar water as approximately 1.3 H 2 O/lipid. Consequently, the amount of freezable interlamellar water is estimated to be approximately 1 (⫽ 1.3 ⫺ 0.3) H 2 O/lipid for the fully hydrated H-subgel phase. The water distribution diagram for the H-subgel phase is shown in Fig. 35. In the conversion of the fully hydrated gel to the H-subgel phase, as many as 4.7 (⫽ 6 ⫺ 1.3) interlamellar water molecules per molecule of lipid are excluded outside the bilayers and present as bulk water in the resultant H-subgel phase. The 4.7 H 2 O/lipid comes from 2.0 (⫽ 2.3 ⫺ 0.3) nonfreezable interlamellar water molecules plus 2.7 (⫽ 3.7 ⫺ 1) freezable interlamellar water molecules present in the gel phase.

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FIG. 35 Water distribution diagram for the H-subgel phase of the DMPE–water system. The cumulative numbers of water molecules (per molecule of lipid) present as nonfreezable and freezable interlamellar water and as bulk water are plotted versus N w .

IX.

ROLE OF WATER MOLECULES IN PHASE TRANSITIONS OF LIPIDS

Finally, we discuss the role of interlamellar water in lipid phase transitions. As shown in Fig. 36, the phase behavior of the lipid in the DMPE–water system is complex in the absence of freezable interlamellar water [21]. Presumably, in a region of such low water content, the lipid bilayers exist as hydrated crystals containing only nonfreezable interlamellar water. However, with the appearance of freezable interlamellar water (curves d–m), the lipid phase transition comes to be characterized by a certain peak that is gradually shifted to lower temperatures with increasing water content and ﬁnally converges to a ﬁxed temperature, generally ascribed to the gel-to-liquid crystal phase transition. Such phase behavior suggests that freezable interlamellar water is absolutely necessary for the formation of the gel phase of lipid–water systems. In this respect, another noticeable point is that the ﬁxed peak of the gel-to-liquid crystal transition is obtained above a certain water content where a maximum uptake of the freezable interlamellar

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FIG. 36 Variation of the transition peak of gel to liquid crystal phase with increasing water content for the DMPE–water system. Water contents (wt%); a, 2.3 (0.8); b, 6.0 (2.25); c, 8.0 (3.1); d, 10.2 (4.0); e, 12.2 (4.9); f, 14.1 (5.8); g, 16.1 (6.8); h, 18.1 (7.8); i, 20.0 (8.8); j, 22.0 (10.0); k, 25.0 (11.8); l, 28.0 (13.7); m, 32.0 (16.6). The numbers in parentheses show the corresponding N w values.

water is attained (curves j–m). Thus, as shown for the DMPE system in Fig. 37, both the lipid transition temperature and the half-height width of the transition peak are constant for N w ⬎ 10, at which the limiting, maximum amount of freezable interlamellar water is reached. A similar role for the freezable interlamellar water is observed for the DPPC–water system. Thus, as shown in Fig. 38, ﬁxed transition peaks are obtained not only for the main transition (P β ′ gel to liquid crystal) but also for the pretransition (L β ′ gel to P β′ gel) at water contents above

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FIG. 37 Variation with increasing N w of the temperature (t m) of the gel-to-liquid crystal phase transition and of the half-height width (∆T 1/2) of its transition peak in the DMPE– water system.

the limiting point (N w ⬃ 15–16) of the freezable interlamellar water shown in Fig. 14. Furthermore, focusing on the pretransition in Fig. 38, it is noticeable that a growth of the transition peak from a trace up to a ﬁxed large peak takes place in the pre-region of 8 ⬍ N w ⬍ 15 shown in Fig. 14. Considering that the pretransition is a phenomenon characteristic of tilted hydrocarbon chains adopted by a lipid that has bulky headgroups [48], the growth of the pretransition peak in the pre-region suggests that the hydrocarbon chains of DPPC become more tilted up to N w ⬃ 15 at the saturation point of the lipid with freezable interlamellar water. Furthermore, from the standpoint of water, it is suggested that the appearance of bulk water in the pre-region—namely, prior to the limiting uptake of the freezable interlamellar water—is caused by a change in the bilayer lamellae from planar to curved surfaces and ﬁnally to a vesicular form [6,8,9,21,22]. Presumably, the water trapped within regions between adjacent vesicular assemblies behaves like bulk water. However, such structural changes in the pre-region would induce higher surface curvatures of the bilayer, resulting in looser packing of the hydrocarbon chains and consequently in weaker

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FIG. 38 A series of DSC curves focusing on the lipid transitions of the L β′ gel to P β′ gel and P β′ gel to liquid crystal phases of the DPPC–water system. Water contents (wt%): a, 12.6 (5.9); b, 12.8 (6.0); c, 13.1 (6.2); d, 14.1 (6.7); e, 16.1 (7.8); f, 17.4 (8.6); g, 20.1 (10.2); h, 22.1 (11.6); i, 24.1 (12.9); j, 26.0 (14.3); k, 31.9 (19.1); l, 35.0 (22.0); m, 38.9 (25.9). The numbers in parentheses show the corresponding N w values.

van der Waals interaction energies for them. Therefore, to compensate for the energy loss, the hydrocarbon chains would adopt more tilted positions in order to shorten the chain–chain separation related to the van der Waals energy [30,33,39]. This seems to be the reason for the appearance of the pretransition peak and its saturation observed in the pre-region. On the other hand, as discussed above, the L-subgel phase of the DPPC–water system involves the extra nonfreezable interlamellar water up to one molecule of H 2 O per molecule of lipid, compared with the gel phase. This nonfreezable interlamellar water comes from the freezable interlamellar water present in the gel phase, indicating the critical role of this freezable water in the conversion of the gel to the L-subgel phase. In fact, as shown in Fig. 25B, the conversion to the L-subgel phase by annealing is not realized for a gel sample at N w ⬍ 5 (see curve a), i.e., when there is no freezable interlamellar water (see Fig. 14). Furthermore, as shown in Fig. 25B, the ﬁxed peak of the L-subgel-to-gel phase transition is observed above N w ⬃ 12–13 where the subgel phase is fully hydrated (see

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Fig. 28), although the N w value is lower than the corresponding N w ⬃ 15–16 for the gel phase (see Fig. 14). This fact indicates that both the fully hydrated subgel and gel phases are characterized by limiting, ﬁxed peaks of their transitions to the respective high temperature phases. This is because, after the attainment of the fully hydrated gel and subgel phases, lateral packings of lipid molecules in a bilayer are unchangeable, even though the water content is further increased [49]. Finally, the most stable H-subgel phase of the DMPE system, which directly transforms to the liquid crystal phase, is discussed from the standpoint of the interlamellar water. As shown in Fig. 35, the H-subgel phase is characterized by a much smaller amount of interlamellar water compared with the L-subgel and

FIG. 39 Variation of a lipid transition peak with increasing water content for the DPPG– water system. Water contents (wt%): a, 23.9 (12.0); b, 29.9 (17.7); c, 39.9 (27.5); d, 49.6 (40.7); e, 60.0 (62.1); f, 69.9 (96.1); g, 74.9 (123.0); h, 80.0 (166.0); i, 85.0 (235.0); j, 90.0 (373.0). The numbers in parentheses show the corresponding N w values.

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gel phases (see Figs. 18 and 32), and so conversion of the gel to the H-subgel phase by annealing accompanies the exclusion of the interlamellar water. Accordingly, the conversion does not require the presence of freezable interlamellar or bulk water in the gel phase, in contrast with the conversion of the gel to the Lsubgel phase. In fact, the conversion is accomplished, even for a gel sample containing as little as 5 wt% water (N w ⫽ 1.8) where only nonfreezable interlamellar water is present (see Fig. 18). In addition, a ﬁxed transition peak to the liquid crystal phase is observed for the fully hydrated H-subgel phase, like the transitions for the fully hydrated gel and L-subgel phases in the DPPC and DMPE systems. However, as shown in Fig. 39, a ﬁxed transition peak is not observed for the inﬁnitely hydrated DPPG gel phase (see Fig. 21), and the hydration results in disruption of the multilamellar vesicles into unilamellar vesicles in a dilute aqueous region [22,43,50–53].

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.

MJ Ruocco, G Shipley. Biochim Biophys Acta 691:309 (1982). TJ McIntosh, SA Simon. Biochemistry 25:4058 (1986). TJ McIntosh, SA Simon. Biochemistry 25:4948 (1986). JM Seddon, G Cevc, RD Kayer, D Marsh. Biochemistry 23:2634 (1984). RP Rand, VA Parsegian. Biochim Biophys Acta 988:351 (1989). G Klose, B Ko¨nig, HW Meyer, G Schulze, G Degovics. Chem Phys Lipids 47:225 (1988). MC Wiener, RM Suter, JF Nagle. Biophys J 55:315 (1989). JF Nagle, R Zhang, T Stephanie-Nagle, W Sun, HI Petrache, RM Suter. Biophys J 70:1419 (1996). K Gawrisch, W Richter, A Mo¨ps, P Balgavy, K Arnold, G Klose. Studia Biophys 108:5 (1985). J Ulmius, H Wennerstro¨m, G Lindblom, G Arvidson. Biochemistry 16:5742 (1977). EG Finer, A Darke. Chem Phys Lipids 12:1 (1974). D Chapman, RM Williams, BD Ladbrooke. Chem Phys Lipids 1:445 (1967). M Kodama, M Kuwabara, S Seki. Thermochim Acta 50:81 (1981). M Kodama, H Hashigami, S Seki. Thermochim Acta 88:217 (1985). M Kodama. Thermochim, Acta 109:81 (1986). M Kodama, H Hashigami, S Seki. J Colloid Interface Sci 117:497 (1987). M Kodama, S Seki. Adv Colloid Interface Sci 35:1 (1991). M Kodama, H Inoue, Y Tsuchida. Thermochim Acta 266:373 (1995). H Aoki, M Kodama. J Thermal Anal 49:839 (1997). H Takahashi, H Aoki, H Inoue, M Kodama, I Hatta. Thermochim Acta 303:93 (1997). M Kodama, H Aoki, H Takahashi, I Hatta. Biochim Biophys Acta 1329:61 (1997). M Kodama, J Nakamura, T Miyata, H Aoki. J Thermal Anal 51:91 (1998). JF Nagle, MC Wiener. Biochim Biophys Acta 942:1 (1988). SC Chen, JM Sturtevent, BJ Gaffeny. Proc Natl Acad Sci USA 77:5060 (1980).

Water in Phospholipid Bilayer Systems 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.

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HH Fuldner. Biochemistry 20:5705 (1981). DG Cameron, HH Mantsh. Biophys J 38:175 (1982). H Chang, RM Epand. Biochim Biophys Acta 728:319 (1983). HH Mantsch, SC Hsi, KW Butler, DG Cameron. Biochim Biophys Acta 728:325 (1983). S Mulukutla, GG Shipley. Biochemistry 23:2514 (1984). DA Wilkinson, JF Nagle. Biochemistry 23:1538 (1984). J Silvius, PM Brown, TJ O’Leary. Biochemistry 25:4249 (1986). PM Brown, J Steers, SW Hui, PL Yeagle, JR Silvius. Biochemistry 25:4259 (1986). DA Wilkinson, TJ McIntosh. Biochemistry 25:295 (1986). AE Blaurock, TJ McIntosh. Biochemistry 25:299 (1986). KK Eklund, IS Salonen, PKJ Kinnunen. Chem Phys Lipids 50:71 (1989). IS Salonen, KK Eklund, JA Virtanen, PKJ Kinnunen. Biochim Biophys Acta 982: 205 (1989). RM Epand, B Gabel, RF Epand, A Sen, SW Hui, A Muga, WK Surewicz. Biophys J 63:327 (1992). M Kodama, T Miyata, T Yokoyama. Biochim Biophys Acta 1168:243 (1993). M Kodama, H Aoki, T Miyata. Biophys Chem 79:205 (1999). R Harrison, GG Lunt. Biological Membranes, 2nd ed., Blackie, London, 1980, p. 68. GG Shipley. In Handbook of Lipid Research, Vol. 4 DM Small, ed., Plenum Press, New York, 1986, p. 97. JM Boggs. Biochim Biophys Acta 906:353 (1987). M Kodama, T Miyata. Colloid Sur A 109:283 (1996). H Hauser, I Pascher, RH Pearson, S Sundell. Biochim Biophys Acta 650:21 (1981). I Pascher, S Sundell, K Harlos, H Eibl. Biochim Biophys Acta 896:77 (1987). JF Nagle, DA Wilkinson. Biophys J 23:159 (1978). DA Wilkinson, JF Nagle. Biochemistry 20:187 (1981). TJ McIntosh. Biophys J 29:237 (1980). G Cevc, D Marsh. Biophys J 47:21 (1985). D Atkinson, H Hauser, GG Shipley, JM Stubbs. Biochim Biophys Acta 339:10 (1974). H Hauser, F Paltauf, GG Shipley. Biochemistry 21:1061 (1982). H Hauser. Biochim Biophys Acta 772:37 (1984). M Kodama, T Miyata. Thermochim Acta 267:365 (1995).

8 Heat Evolution of the Self-Assembly of Amphiphiles in Aqueous Solutions DOV LICHTENBERG, ELLA OPATOWSKI, and MICHAEL M. KOZLOV Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel

I. Introduction II.

General Theoretical Considerations A. The origin of self-assembly B. Factors determining the cmc C. ITC measurements, major ﬁndings, and interpretation D. Enthalpy associated with dissolving hydrocarbons E. The enthalpy of micelle formation

III. Experimental Titration Protocols, Procedures, and Interpretation of Data A. Determination of the heat evolution of the self-assembly of surfactants B. Partitioning of solutes between membranes and aqueous solutions C. The heat evolution of bilayer–micelle phase transformation in mixtures of phospholipids and detergents IV. Heat Evolution of the Transfer of Amphiphilic Molecules Between Aggregates and Water A. Heat of micellization and its dependence on temperature and composition B. Heat of partitioning of amphiphiles between lipid bilayers and aqueous media C. Heat of phase transformations in mixtures of bilayer-forming and micelle-forming amphiphiles V. Concluding Remarks References

296 297 297 298 300 301 303 305 305 309 312 316 316 321 328 331 332 295

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I. INTRODUCTION A common feature of all amphiphiles is their tendency to self-assemble in aqueous solutions above a critical concentration, denoted as the critical aggregation concentration or, for micelle-forming amphiphiles (surfactants), the critical micellar concentration, abbreviated cmc [1–3]. The structure of the resultant aggregates depends on the molecular geometry of the amphiphiles and varies from micelles of various geometries (e.g., spheres, ellipsoids, or rods) to bilayers, cubic, or hexagonal phases [4,5]. The driving force for the self-assembly is the hydrophobic effect resulting from interplay between entropic and enthalpic contributions to the free energy of the process. Although the entropic effects are believed to be the leading ones in most cases, the enthalpy associated with the self-assembly is of fundamental interest because it reﬂects the energetics of the many molecular interactions involved in the process. This enthalpy is a complex and not fully understood function of the molecular structure of the amphiphile, the composition of the aqueous medium, and the temperature. In reviewing the existing data, we try to contribute to the understanding of these relationships. The enthalpy of micellization of many surfactants in aqueous solution has been determined in the past, using mostly cell type and ﬂow microcalorimeters [6–8]. These determinations were based on measurements of the excess heat associated with dilution of a surfactant from a concentration above the cmc to a concentration below the cmc, which results in demicellization of the preexisting micelles. One difﬁculty with these determinations relates to the dependence of the heat evolution (∆Q) on the initial and ﬁnal concentrations, probably due to secondary self-aggregations of the surfactants at high concentrations and/or premicellar dimer formation at low surfactant concentrations [6,9]. These difﬁculties are at least partially responsible for the lack of consistent data on the thermodynamics of micelle formation [6]. Recent advancements in the sensitivity of microcalorimeters made it possible to study low surfactant concentrations, thus improving the quality of data obtained through dilution experiments (see below). In this review we address the scope, the limitations, and the difﬁculties associated with interpretation of high sensitivity isothermal titration calorimetry (ITC) in studying aqueous solutions of amphiphiles. In reviewing the existing knowledge, we ﬁrst present the theoretical background required for interpretation of the results of ITC experiments. Then we describe the experimental approaches and protocols that can be used to 1.

2.

Obtain reliable heats of formation of micelles and other self-assemblies in aqueous media. We also show how these approaches can be used to estimate the cmc of the surfactants. Determine the partitioning of amphiphiles between amphiphilic self-assemblies and aqueous media.

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3. Determine the heat associated with the composition-induced transformations between various phases. Finally, we summarize and discuss some of the results obtained thus far regarding these issues. This presentation is neither comprehensive nor objective. Its general theme is to describe the scope of ITC and draw awareness of its limitations in studying the self-assembly of amphiphiles in aqueous solutions.

II.

GENERAL THEORETICAL CONSIDERATIONS

A. The Origin of Self-Assembly The chemical potential of a surfactant monomer in a dilute aqueous solution µ w is given by µ w ⫽ µ 0w ⫹ kT ln D′w

(1)

where µ is the standard chemical potential of a surfactant monomer in the aqueous medium and D′w is the mole fraction of the surfactant in the solution. Similarly, the chemical potential of a surfactant molecule in a micelle is given by 0 w

µ m ⫽ µ 0m ⫹

D′ 1 kT ln m m m

(2)

where µ 0m is the standard chemical potential of surfactant molecules in the micelle, m is the aggregation number, and D′m is the mole fraction of aggregated surfactant. At equilibrium, when micelles and monomers coexist, µ w ⫽ µ m the aqueous concentrations of the aggregated (D′m) and unaggregated (D′w) surfactant are related by ∆G 0mic ⫽ µ0m ⫺ µ 0w ⫽ kT [ln D′w ⫺ ln(D′m) 1/m ⫹ ln m 1/m]

(3)

where ∆G 0mic ⫽ µ 0m ⫺ µ 0w denotes the difference of the standard chemical potentials. For most surfactants, m is sufﬁciently large to make the contribution of lnm1/m negligible so that ∆G 0mic ⫽ kT [ln D′w ⫺ ln(D′m) 1/m]

(4)

This means that at any given temperature, for any given total detergent concentration (D′t ⫽ D′w ⫹ D′m), the relationship between the concentrations of monomeric surfactant (D′w) and micellar surfactant (D′m) is determined by the difference in standard chemical potentials, ∆G 0mic , according to ∆G 0mic D′w ⫽ exp (D′m)1/m kT

(5)

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B. Factors Determining the cmc The cmc of a surfactant is commonly deﬁned as being that total detergent concentration at which micelle formation is already considerable (experimentally detectable) but most of the surfactant is still monomeric (D′w ⬎ D′m), so that the concentration of monomers is still close to the total detergent concentration (D′w ⬇ D′t ⫽ cmc′). It is therefore convenient to deﬁne cmc′ [1] by the equation ∆G 0mic ⫽ kT ln(cmc′)

(6)

This deﬁnition along with Eq. (3) determines the micellization in terms of the value of cmc′, cmc′ ⫽

D′w m 1/m (D′m) 1/m

(7)

Notably, the law of mass action, mD w s D m

(8)

deﬁnes micellization in terms of an equilibrium constant K: K⫽

D′m m(D′w) m

(9)

Rewriting Eq. (7) as (cmc′) m ⫽

(D′w) m m D′m

(10)

and comparing it with Eq. (9) yields an expression that connects K with cmc′: K⫽

1 (cmc′) m

(11)

This means that exact determination of the cmc is theoretically sufﬁcient for determination of both ∆G 0mic [Eq. (6)] and K [Eq. (11)]. The distribution of surfactant molecules between micelles and monomers depends also on the aggregation number m [Eq. (7)]. This dependence is schematically depicted in Fig. 1 in terms of the dependence of D w and D m on the total surfactant concentration D t, as computed on the basis of Eq. (7) for a surfactant with cmc ⫽ 1 mM, assuming two aggregation numbers: m ⫽ 10 (solid lines) and m ⫽ 100 (dashed lines). As evident from this ﬁgure, at that total concentration deﬁned by Eq. (7) as the cmc (1 mM in Fig. 1), both D w and D m depend on the aggregation number. Thus, if the cmc is deﬁned according to Eq. (7), the apparent cmc, at which micelles begin to form, depends on the aggregation number. Furthermore, the actual partitioning of surfactant molecules between micelles

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FIG. 1 Dependence of the concentrations of monomeric (D w) and micellar (D m) surfactant on the total concentration of a surfactant of cmc ⫽ 1 mM as computed from Eq. (7) assuming m ⫽ 100 (broken line) and m ⫽ 10 (solid line).

and soluble monomers at other concentrations depends on m such that at m ⫽ 100 the ‘‘breaks’’ in the curves are much more pronounced than at m ⫽ 10 and the monomer-to-micelle transition resembles a ﬁrst-order phase transition. This means that exact determination of the partitioning of surfactant between micelles and monomers (especially around the cmc) can be used to estimate not only the value of ∆G 0mic but also the aggregation number (m) and the association constant (K). In addition, accurate determination of the cmc as a function of temperature can be used to evaluate the excess molecular enthalpy of micellization, ∆H 0mic according to van’t Hoff’s equation [1,10], ∆H 0mic ⫽ kT 2

d ln(cmc) dT

(12)

Hence, determination of the cmc and its dependence on temperature are theoretically sufﬁcient for complete characterization of the thermodynamics of micelle formation: For any given temperature, ∆G 0mic can be calculated directly from the (temperature-dependent) cmc, ∆H 0mic (which is also temperature-dependent) can

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be computed from the ﬁrst derivative of the cmc with respect to temperature, the molecular heat capacity, ∆C 0P,mic can be computed from the ﬁrst derivative of ∆H 0mic with respect to temperature, ∆C 0P,mic ⫽

d ∆H 0mic dT

(13)

and the molecular entropy of micellization, ∆S 0mic , can then be computed from the Gibbs–Helmholtz equation, ∆G 0mic ⫽ ∆H 0mic ⫺ T ∆S 0mic

(14)

C. ITC Measurements, Major Findings, and Interpretation Calorimetric titration yields reliable determination of both ∆H 0mic and the cmc as well as a reasonable approximation for the micelle-to-monomer ratio in the range of the cmc (see below). The data obtained by this method can thus be used to fully characterize the system according to Eqs. (12)–(14). Two major ﬁnding of ITC measurements are that 1.

2.

∆S 0mic , which is regarded as being the major contributor to the ‘‘hydrophobic effect’’ [1], is positive throughout the range of temperature up to 100°C [10]. This result is likely to be due to the elimination of ordered hydration shells around the hydrophobic parts of monomeric amphiphiles when the monomers self-assemble into micelles. The sign of ∆H 0mic depends on temperature. For many surfactants, micellization is exothermic only at relatively high temperatures and endothermic at low temperatures [11,12].

In relating to the heat evolution of micellization, it is important to note that the above discussion addresses the changes in the free energy only in terms of the sum of changes in the entropy and enthalpy of the system due to removal of surfactant molecules from the aqueous medium into a micelle. From Eqs. (14) and (4) it follows that ∆H 0mic ⫺ T ∆S 0mic ⫽ kT ln

冤(D′D′) 冥 m

w 1/m

(15)

On the other hand, partitioning of amphiphile is also dependent on the concentration-dependent entropy of translation (∆S trans), which always favors dissociation of micelles, reducing the ‘‘ordering’’ introduced into the system by aggregation of monomers into micelles. The heat associated with micellization is therefore the sum of two entropic terms of opposite sign,

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∆H 0mic ⫽ T(∆S 0mic ⫹ ∆S trans)

301

(16)

where ∆S trans (the entropy associated with translation) is deﬁned as ∆S trans ⫽ k ln

冤(D′D′) 冥 m

w 1/m

(17)

D. Enthalpy Associated with Dissolving Hydrocarbons In terms of molecular interactions, demicellization is analogous to dissolving hydrocarbons in water, which has been viewed [13] as being a two-step process: 1. Breaking van der Waals attraction interactions between hydrocarbon molecules, which is endothermic. 2. Hydrating the individual hydrocarbon molecules in the dilute aqueous solutions, which has been shown to be exothermic [13]. Hence, ∆H solution ⫽ ∆H vdW ⫹ ∆H hydration

(18)

∆H vdW can be regarded as being analogous to the endotherm associated with evaporation of the hydrocarbon, ∆HvdW ≅ ∆Hevap

(19)

A major contributor to the heat of hydration (∆H hydration) relates to the hydrogen bonds that link individual water molecules to each other in the absence of solutes (∆H ww). This arrangement is disrupted by any solute dissolved in water. For nonpolar solutes, such as a hydrocarbon, the expected net result of breaking the water structure is an increase in the enthalpy of the solution. Nonetheless, the heat of hydration can be regarded as being the sum of two enthalpy terms, one of which, ∆H ww, relates to the water–water hydrogen bonds that were present in the aqueous solution in the absence of the hydrocarbon and were broken by the hydrocarbon, whereas another term, ∆H cw, relates to the molecular interactions that exist in the system only in the presence of the hydrocarbon [1,14]. ∆H hydration ⫽ ∆H cw ⫹ ∆H ww

(20)

Combining Eqs. (18)–(20) yields ∆H solution ⬇ ∆H cw ⫹ (∆H evap ⫹ ∆H ww)

(21)

Both ∆H evap and ∆H ww are positive (endothermic), whereas ∆H cw may be either positive or negative. This means that while the solubility of a hydrophobic mole-

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cule in water is associated with a heat loss due to reduction of both water–water hydrogen bonds and lipid–lipid van der Waals interactions, the solubility is also associated simultaneously with some heat gain due to water–hydrocarbon interactions and/or the strengthening of water–water hydrogen bonds in comparison with the system that exists in the absence of hydrocarbon (see below). In fact, the absolute value of the enthalpy associated with the overall process of dissolving hydrocarbons in water at 25°C, ∆H solution, is an order of magnitude smaller than that of the heat of their evaporation, which is always endothermic (Table 1). This must mean that solvatation (hydration) of the hydrocarbons is exothermic and of the same order of magnitude as the heat of evaporation. It can therefore be concluded that the new bonds created in the presence of hydrocarbons (∆H cw) are enthalpically more beneﬁcial than the hydrogen bonds between the water molecules that break down as a consequence of the introduction of a hydrocarbon chain into water (∆H ww). This ﬁnding has been previously explained in terms of the strength of the water–water hydrogen bonds at the surface of the cavity created by a nonpolar solute [13,14]. Rearrangement of these water molecules may be sufﬁcient to regenerate the broken hydrogen bonds, and the newly formed hydrogen bonds may be stronger than before. The data given in Table 1 show that the absolute values of both the experimentally determined heat of evaporation and the computed heat of hydration are larger for hexane than for pentane. Similar results were observed for alkylbenzenes (Table 1). In the temperature range of 15–35°C, ∆H solution increases (becomes more endothermic) with increasing temperature. In both series, when the chain length increases, the absolute value of ∆H evap increases more than the absolute value of ∆H hydration , so the overall process of dissolving the hydrocarbon in water becomes more endothermic (or less exothermic) upon increasing the chain length. The same trend was obtained for a larger series of short-chain alkanes as well as for alkyl alcohols (Table 2) [1]. Notably, dissolving alcohols of chain length greater than 2 was always more exothermic than dissolving the corresponding

TABLE 1 ∆H Values That Relate to Dissolving Hydrocarbons in Water Compound Pentane Hexane Toluene Ethylbenzene Propylbenzene Source: Ref. 13.

∆H solution (kJ/mol) ⫺2.0 0.0 1.7 2.0 2.3

⫾ ⫾ ⫾ ⫾ ⫾

0.2 0.2 0.1 0.1 0.1

∆H evaporation (kJ/mol) 26.7 31.6 38.0 42.3 46.2

⫾ ⫾ ⫾ ⫾ ⫾

0.2 0.1 0.1 0.1 0.1

∆H hydration (kJ/mol) ⫺28.7 ⫺31.6 ⫺36.3 ⫺40.2 ⫺43.9

⫾ ⫾ ⫾ ⫾ ⫾

0.3 0.2 0.2 0.1 0.1

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TABLE 2 Dependence of ∆H solution on the Chain Length of Hydrocarbons and Alcohols as Measured at 25°C Alkane

∆H solution (kJ/mol)

Alkanol

∆H solution (kJ/mol)

C2 H6 C3 H8 C 4 H 10 C 5 H 12

⫺10.42 ⫺7.09 ⫺3.33 ⫺2.09

C 2 H 5 OH n-C 3 H 7 OH n-C 4 H 9 OH n-C 5 H 11 OH

⫺10.13 ⫺10.09 ⫺9.378 ⫺7.79 (7.95)

Source: Refs. 1 and (in parentheses) 15.

parafﬁns, probably due to the contribution of hydrogen bonds of the hydroxyl group with water.

E. The Enthalpy of Micelle Formation Assuming that the differences between the interactions of the headgroups of amphiphiles with water in the monomeric and micellar forms are smaller than those between the respective interactions of the hydrophobic chains, it follows that the overall heat associated with micelle formation can be treated similarly to the solubility of hydrocarbons, i.e., in terms of the interplay between three major contributing stabilizing interactions, 1. Van der Waals interactions between hydrophobic moieties in the aggregates (∆H vdW ), which favor micellization 2. Hydrogen bonds between water molecules (∆H ww), which also contribute to micelle formation 3. Hydration of hydrophobic moieties and consequent formation of strong hydrogen bonds (∆H cw), which, according to Gill et al. [13], should strongly favor transition of surfactant molecules into the water (i.e., favors demicellization) Accordingly, ∆H demic ⫽ ∆H cw ⫹ (∆H vdW ⫹ ∆H ww)

(22)

The observed exothermic nature of demicellization of many surfactants at low temperatures (around 25°C) (see above) must mean that the heat gain associated with hydration of the hydrophobic moieties (possibly due to stronger hydrogen bonds in the water [14]) is greater than the sum of heat losses associated with reduction of the original hydrogen bonds in the water and disruption of the van der Waals interactions between hydrophobic moieties in the aggregates. Elevation of the temperature is likely to result in reduction of all the stabilizing energies. The observed endothermic nature of demicellization at high temperature

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(see below) must therefore mean that ∆H cw becomes reduced more than the sum of the other two contributing factors. One possible explanation of this behavior is that the excessive attractive energy is indeed due to ‘‘stronger hydrogen bonding’’ and that this binding is affected by increasing the temperature more than the other interactions are. As a consequence, the heat of demicellization at high temperature is governed by the latter forces, which favor micellization, so that demicellization becomes endothermic. This is schematically depicted in Fig. 2.

FIG. 2 Schematic explanation for the dependence of the heat of demicellization on chain length and temperature. The bold arrows represent the overall enthalpy of demicellization, the dotted arrows represent the excess enthalpy of hydration of the hydrophobic moieties of the amphiphiles, and the dashed arrows represent the sum of enthalpies resulting from van der Waals interactions between hydrophobic moieties in the aggregates and from hydrogen bonds between water molecules.

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A similar rationale may explain the effect of chain length on the heat of demicellization of surfactant micelles. Speciﬁcally, chain elongation is likely to enhance all the stabilizing energies represented in Eq. (22), but not necessarily to the same extent. The ﬁnding that chain elongation makes demicellization less exothermic (or more endothermic) indicates that upon increasing the chain length ∆H cw increases less than the other two attractive interactions, as illustrated in Fig. 2.

III. EXPERIMENTAL TITRATION PROTOCOLS, PROCEDURES, AND INTERPRETATION OF DATA The general protocol of an ITC experiment involves titration of a small volume, v t, of a solution of a certain composition into a cell containing a much larger volume, v c , of another solution. Simultaneously, a volume v t is removed from the cell so as to maintain a constant volume of solution in the cell, while the temperature is kept constant either by cooling the cell when the reaction is exothermic or heating it when the reaction is endothermic.

A. Determination of the Heat Evolution of the SelfAssembly of Surfactants Surfactant solutions may contain monomers and micelles. In addition, under certain conditions the solution may contain premicellar aggregates and/or aggregates of very high aggregation numbers due to ‘‘secondary aggregation’’ at high surfactant concentrations [16]. A surfactant solution with a concentration D t higher than the cmc contains at least two species, i.e., monomers of a concentration only slightly higher than the cmc (D w ≅ cmc mM) and micelles of a concentration of D m ⫽ (D t ⫺ cmc) mM. Upon dilution, both the micelles and monomers are diluted. If the surfactant concentration in the cell is lower than the cmc, the dilution results in dissociation of micelles into monomers (complete dissociation being obtained when the ﬁnal concentration D t is lower than the cmc). The heat involved can thus be described as being due to three processes: dilution of monomers, dilution of micelles, and dissociation of micelles into monomers. ∆Q ⫽ ∆Q mono ⫹ ∆Q mic ⫹ ∆Q demic

(23)

When demicellization occurs, the heats of dilution of both monomers and micelles usually make only a minor contribution to the overall evolution of heat. In the following discussion we neglect these contributions. However, a more accurate evaluation of the heat of demicellization must be based on independent determination of the contribution of the heat of monomer dilution, which can be experimentally measured by dilution of a solution of a concentration below the cmc. This, of course, is possible only when the heat of dilution of monomers is

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sufﬁciently large to be experimentally detected. Determination of the heat associated with micelle formation is possible only if the calorimetric titrations cause the surfactant to be repartitioned between its aggregated and monomeric forms. This requires that in one of the two solutions to be mixed in the calorimetric cell the surfactant concentration must be above the cmc, whereas in the other solution the concentration must be below the cmc. (Mixing two dilute monomeric solutions of concentrations below the cmc will not result in micellization, whereas mixing two concentrated solutions each of which already contains micelles will not result in demicellization.) Accordingly, mixing two appropriately selected solutions in the calorimeter results in the dissociation of micelles into monomers, and the measured heat evolution can be used to compute the heat of demicellization, as described below. In general, after a surfactant solution of volume v t and concentration D t is injected into a cell of volume v c containing a surfactant of concentration D 0, the amount of surfactant in the cell, a 1, is given by a1 ⫽ D0 vc ⫹ Dt vt

(24)

and the concentration Dl is D1 ⫽

D0 vc ⫹ Dt vt vc ⫹ vt

(25)

After evacuation of a volume v t , the remaining fraction of surfactant in the cell will be given by D⫽

vc vc ⫹ vt

(26)

and the remaining amount will be a′1 ⫽ (D 0 v 0 ⫹ D t v t ) D

(27)

The concentration and amount of surfactant in the calorimetric cell following subsequent steps of titration can be computed similarly (see below). In practical terms, two protocols are commonly used for the determination of ∆H, ‘‘inﬁnite dilution’’ and inﬁnitesimal dilution.

1.

‘‘Inﬁnite Dilution’’

The ‘‘inﬁnite dilution’’ protocol involves titration of a concentrated amphiphile solution with D t ⬎ cmc into a cell containing no amphiphile, namely D 0 ⫽ 0. After titration, the concentration in the cell is D 1 ⫽ D t v t /(v c ⫹ v t), where D 1 ⬍ cmc. Since v c ⬎⬎ v t, this protocol is denoted as ‘‘inﬁnite dilution’’ and the heat evolution of the process reﬂects demicellization of all the micelles that were present in the titrated volume. The major contribution to the heat of dilution (∆Q) is the heat of demicellization of (D t ⫺ cmc)v t moles of surfactant. Hence,

Amphiphiles in Aqueous Solutions

∆Q ⫽ (D t ⫺ cmc) v t ∆H demic

307

(28)

If a series of one-step titration experiments are conducted using a constant volume of titrant but different concentrations D t , the experimentally observed dependence of ∆Q on D t can be used to evaluate ∆H demic and the cmc from the slope and intercept of the linear dependence ∆Q ⫽ D t ∆H demic ⫺ cmc ∆H demic vt

(29)

When such a linear dependence is observed experimentally, it can be used to determine both ∆H demic and the cmc (see Fig. 3). By contrast, when the titrated (micellar) solution contains micelles that undergo secondary aggregation and/ or when the ‘‘inﬁnitely diluted’’ (supposedly monomeric) solution contains premicelles (dimers, etc.), the line describing ∆Q ⫽ f(D t) will deviate from linearity.

FIG. 3 Schematic description of the expected dependence of the heat of demicellization on the total surfactant concentration in inﬁnite dilution experiments.

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For the range of D t where ∆Q is a linear function of D t, as long as the concentration in the cell is lower than the cmc, all the injected micelles will dissociate into monomers and the observed heat will remain constant [as given by Eq. (28)]. Upon subsequent steps of titration of surfactant into the cell, the total concentration in the cell will increase, but since some of the detergent is removed after each titration step, the amount of surfactant in the cell after n steps of titration will be smaller than nv t D t. After the ﬁrst step of titration and removal of a volume v t , the amount of surfactant left in the cell, as given by Eq. (27), will be a′1 ⫽ D t v t D

(30)

The amount of surfactant added in the second step of titration is again D t v t, so that after the second addition (prior to the removal of the excess volume v t ) the amount of surfactant in the cell is given by a 2 ⫽ D t v t D ⫹ D t v t ⫽ D t v t (D ⫹ 1)

(31)

After removing the excess volume, the amount of surfactant in the cell is a′2 ⫽ D t v t (D ⫹ 1)D ⫽ Dv t (D 2 ⫹ D)

(32)

Hence, D′2 ⫽

ct v t 2 (D ⫹ D) vc

(33)

Similarly, after a series of n subsequent steps of titration and evacuation, D′n ⫽

Dt vt n (D ⫹ D n⫺1 ⫹ . . . ⫹ D 2 ⫹ D) vc

(34)

This concentration can be expressed as the sum of a geometric series, Dn ⫽

Dt vt 1 ⫹ Dn D vc 1⫺D

(35)

As long as D n is much smaller than the cmc, computation of D n is of minor importance, because essentially all the micellar surfactant in the titrated solution will become dissociated. Only when D n approaches the cmc must determination of ∆H demic take into account the change in the concentration of micelles in the cell. Under these conditions, the heat evolution is given by ∆Q ⫽ [(D n ⫺ cmc) ⫺ (D n⫺1 ⫺ cmc)]v c ∆H demic

(36)

and interpretation of ITC experiments conducted in this concentration range can be used to determine the cmc.

Amphiphiles in Aqueous Solutions

2.

309

Inﬁnitesimal Dilution

In another series of experiments, small volumes of aqueous solutions containing no surfactant are injected into the cell. When the initial concentration in the cell (D 0) is lower than the cmc, the (relatively low) heat of dilution of monomers can be determined. When D 0 ⬎⬎ cmc and v c ⬎⬎ v t, the titration results in partial demicellization, the titrated volume becomes saturated with monomeric surfactant, and the total amount of surfactant that becomes dissociated equals v t cmc so that ∆Q ⫽ v t cmc ∆H demic

(37)

Hence, as long as the concentration in the cell remains much higher than the cmc, ∆Q can be expected to be independent of the surfactant concentration in the cell unless at that concentration the cell contains ‘‘secondary aggregates.’’

B. Partitioning of Solutes Between Membranes and Aqueous Solutions Similar to the partitioning of solutes between water and oil, partitioning of amphiphiles (including surfactants at concentrations below the cmc) between water and aggregates, such as bilayer membranes, can in principle be measured by ITC using three different protocols. Experimentally, the least suitable protocol is the injection of a small volume of the solute into a cell of large volume containing the aggregates. The use of this protocol for detection of the heat of partitioning of detergents with low cmc’s between membranes and water is problematic, because the concentration of the titrated detergent solution in these cases may have to be higher than the cmc to enable detection of the heat associated with partitioning. As a consequence, dilution of the titrated solution will cause demicellization accompanied by partitioning, which complicates the measurement of the heat of the latter process. Nonetheless, for certain surfactants the detection of the heat evolution of the partitioning is possible by titration of a detergent solution below the cmc. In those cases this protocol yielded reliable information [17,18]. Similarly, its use for studying the partitioning of other solutes (e.g., alcohols) is limited by the heat associated with dilution of the solute in the cell prior to partitioning. Accordingly, most of the investigators who studied the heat of partitioning used the ‘‘incorporation’’ protocol based on the injection of a small volume containing aggregates into a large volume of dilute solute (e.g., alcohol or detergent). Using this protocol, the heats of dilution (and/or demicellization) are minimal, and the measured heat can be interpreted in terms of the insertion of solute into the added aggregates.

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As long as the partitioning of solute between aggregates and water obeys a constant partition coefﬁcient (i.e., as long as the solute in the aggregates does not change the partition coefﬁcient), the following relationship is valid: K⫽

Sa Sw ([A] ⫹ S a)

(38)

where S a and S w are the concentrations of solute that reside in the aggregates and water, respectively, and [A] is the concentration of the aggregates. For [A] ⬎⬎ S a, K⫽

Sa (S T ⫺ S a) [A]

(39)

where S T is the total concentration of the solute in the cell. Rewriting Eq. (39) results in Sa ⫽

K [A] ST 1 ⫹ K [A]

(40)

The amount of solute that becomes transferred from water into the added aggregates is given by v c S a, and the heat associated with this process can be expressed by ∆Q ⫽ ∆H w→a v c S a

(41)

Inserting Eq. (40) into Eq. (41) and rewriting it results in the equation

冢

1 1 1 ⫽ ⫹ ∆Q v c S T ∆H w→a v c S T ∆H w→a

冣冢冣 1 K[A]

(42)

Hence, in principal, the description of 1/∆Q as a function of 1/[A] for a constant S T yields interpretable values of the slope and intercept. K can then be computed from the ratio intercept/slope ⫽ K, and ∆H w→a can then be computed from the intercept and the known values of S T and v c (Fig. 4). Alternatively, Heerklotz et al. [19] introduced a new protocol denoted as a ‘‘release’’ protocol. In this protocol a dispersion of mixed vesicles containing surfactant in the bilayer (and monomeric surfactant) is injected into a cell containing buffer. This titration results only in a partial release of the surfactant into the buffer. The latter two protocols should, of course, give the same ∆H values (∆H w→a ⫽ ⫺∆H a→w) unless the solute cannot cross the membrane within the time scale of the ITC experiment. Comparison of the data obtained by the ‘‘incorporation’’ and ‘‘release’’ protocols therefore yields information on whether the partitioning of solute represents a state of equilibrium or is kinetically controlled.

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FIG. 4 Schematic presentation of the effect of the concentration of the aggregates on the heat associated with partition of an amphiphile into aggregates. The experimental protocol involves stepwise addition of the aggregates into the surfactant solution (S T ⬇ constant). U denotes the ratio U ⫽ 1/(v c S T ∆H w→a) [see Eq. (42)].

In all the experimental protocols, the heat evolution (∆Q) is a product of the standard molar enthalpy of association (∆H w→a) and the change in the number of aggregate-associated molecules of solute (∆n w→a). When the latter factor is a welldeﬁned function of the partition coefﬁcient K, ∆Q is a well-deﬁned function of ∆H w→a and K. The most straightforward way to interpret the results of an ITC experiment is to determine K in an independent experiment. This can be done by determining the concentration of solute in the aqueous solution (S w), using equilibrium dialysis or independent ITC experiments designed speciﬁcally to determine the solute concentration in a system containing aggregates and solutes. Such experiments were based on the solvent-null method of Zhang and Rowe [20], which is conducted by titration of a solute of a concentration S tit into a mixture of aggregates with the same solute. In the latter mixture, the total concen-

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tration of solute in the cell, S t, is a sum of the solute concentrations in the solution, S w, and in the aggregate, S a . When S tit ⬍ S w, S a will decrease due to repartitioning of the solute into the medium, whereas when S tit ⬎ S w, some of the added solute will repartition into aggregates. Only when S tit ⫽ S w no repartitioning will occur, and the titration will be isocaloric. Hence, S w can be determined from a series of titration experiments with different S tit values. When the heat of dilution of the added solute does not contribute signiﬁcantly to the overall heat of titration, such experiments can be used to determine the partition coefﬁcient, K. Furthermore, even when the heat of dilution does contribute to the overall heat, S w (and K ) can still be evaluated from the solvent-null method by conducting a series of control experiments in which solutions of different S tit values are titrated into a solution containing no aggregates. From the latter series of experiments, the heat associated with the dilution can be determined, so that the heat associated with aggregate–solute interactions can be evaluated. When the latter, corrected value of ∆Q becomes zero, S tit ⫽ S w, and K can be computed from the values of S w and S a (S a ⫽ S T ⫺ S w). Alternatively, the heat evolution obtained upon sequential titration steps can be used to estimate both ∆H w→b and K if it is assumed that both of these factors are concentration-independent. Under this assumption, ∆Q for each titration step can be related to ∆H w→b and K: ∆Q ⫽ f(∆H w→b, K ) [17,18]. Under conditions of sequential titration of vesicles into a solution of the amphiphile, the difference in ∆Q between consecutive titration steps is particularly sensitive to the value of K (e.g., large K values produce a fast decrease in the titration peaks), whereas the plateau level of the cumulative heat of reaction is essentially determined by ∆H w→b. Consequently, K and ∆H w→b are not strongly coupled, so their determination is quite unambiguous [21].

C. The Heat Evolution of Bilayer–Micelle Phase Transformation in Mixtures of Phospholipids and Detergents Due to their cylindrical molecular shape [4,22], most phospholipids tend to aggregate along ﬂat surfaces. Consequently, in aqueous solutions they spontaneously form bilayer structures. By contrast, amphiphiles of ‘‘conical shape’’ form micelles. Figure 5 depicts, in the form of a schematic phase diagram, the type of aggregates in a mixture of a micelle-forming amphiphile (detergent) and a bilayerforming amphiphile, such as a phospholipids [23]. As seen in this scheme, when the ratio of nonmonomeric detergent to phospholipid is lower than R sat e , the mixture contains bilayer vesicles and monomers, and when the ratio is higher than another critical value, R sol e , the mixture contains micelles and monomers, whereas in the range of R e between the latter two critical ratios, vesicles, micelles, and monomers coexist.

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313

FIG. 5 A schematic phase diagram for detergent–lipid mixtures. The bold lines describe the dependence of D sat and D sol on lipid concentration. The slopes of these lines represent the maximal values of R e in vesicles (R esat ) and the minimal value of R e in mixed micelles sat sol (R sol e ), respectively. The intercepts of the lines (D w and D w ) represent the respective (extrapolated) values of monomer concentrations. The broken lines denoted by I, II, and III illustrate the three protocols of ITC experiments as described in the text.

Isothermal titration calorimetric studies of the transfer of molecules between these phases have been conducted using various experimental protocols. Three such protocols are indicated in Fig. 5. Protocol I. Injection of buffer into a mixed micellar solution, which results in the transfer of micellar detergent from mixed micelles into water and, subsequently, in the transformation of mixed micelles into mixed vesicles followed by extraction of detergent molecules from these vesicles into aqueous solution. Protocol II. Injection of pure PC vesicles into a cell containing detergent at a concentration c 0 either below or above the cmc. When c 0 ⬍ cmc, detergent will partition between the added vesicles and the aqueous media, whereas when c 0 ⬎ cmc the added vesicles may be solubilized by the detergent. Protocol III. Injection of detergent (of varying concentrations) into a cell containing pure PC vesicles, which results in partitioning of the added detergent between vesicles and water and subsequently causes partial solubilization of the vesicles when R e approaches the value R sat e . The three phases present in the phase diagram are characterized by their compositions. The aqueous solution of surfactant monomers is characterized by the deter-

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gent concentration in the water, D w, whereas the mixed micelles and vesicles are characterized by the ratios R em ⫽ N Dm /N Lm and R be ⫽ N Db /N Lb , respectively. The equilibrium of each mixture is determined by an equation of state that relates to the intensive thermodynamic parameters. The variables changing along the phase diagram are the compositions. Therefore, the equations of state that determine the behavior of the mixture are given by the functions R me (D w) in the micellar range of the phase diagram, R be (D w) in the vesicular range, and the relationships between the compositions of all three phases in the range of coexistence of micelles and vesicles [24]. The energetics of the process of self-assembly are determined by the energetics of transition of the different components between the different phases. Considering the changes in enthalpy as characteristics of the transition, the relevant values for our analysis are 1. 2. 3.

The molar enthalpy of transition of detergent from mixed micelles to water, (R em, D w) ∆H m→w D The molar enthalpy of transition of detergent from mixed micelles to mixed (R em, R be) vesicles, ∆H m→b D The molar enthalpy of transition of lipid from mixed micelles into vesicles, (R em, R be) ∆H m→b L

Notably, all these enthalpies depend on the composition of the corresponding phases and consequently can have different values for different points of the phase diagram. Titration of the mixture within the range of coexistence results in considerable exchange of the two amphiphiles between mixed micelles and mixed vesicles. In addition, surfactant molecules may be transferred from the aqueous solution into the aggregates, or vice versa. Although the enthalpic consequence of this repartitioning is signiﬁcant, its effect on the concentration of monomeric surfactant (D w) is relatively small. For the sake of simpliﬁcation, we assume that within the range of coexistence the aqueous concentration of monomeric detergent resol mains constant and equal to D*w ⫽ (D sat w ⫹ D w )/2. Under this assumption, supported by theoretical considerations (see below), the heat of one titration step can be presented as follows: First we consider a solution of a titrant that contains both lipid at a concentration c L and detergent at a concentration c D. The total number of lipid molecules in the system is the sum of lipid molecules in bilayers and micelles, N L ⫽ N bL ⫹ N Lm

(43)

Detergent molecules also reside in the water at a concentration D *w. Hence, b sol m N D ⫽ D*w v ⫹ R sat e NL ⫹ Re NL

(44)

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315

The changes in the total volume and in the total numbers of lipid and detergent molecules are given by dN L ⫽ c L v t ,

dv ⫽ v t ,

dN D ⫽ c D v t

(45)

Combining these equations with Eqs. (43) and (44), we obtain expressions for the changes in the numbers of molecules of lipid and detergent inside the micelles and the vesicles: dN Lm ⫽

c D ⫺ D*w ⫺ c L R sat e vt ∆R e

(46)

dN bL ⫽

c L R sol e ⫹ D* w ⫺ cD vt ∆R e

(47)

dN Dm ⫽ R sol e

c D ⫺ D*w ⫺ c L R sat e vt ∆R e

(48)

dN bD ⫽ R sat e

c L R sol e ⫹ D* w ⫺ cD vt ∆R e

(49)

sat where ∆R e ⫽ R sol e ⫺ Re . The resulting heat accompanying one injection is therefore given by

∆Q m→w ⫽ [∆H m→w (R sol (1, D*w ) cmc] D e , D* w )D* w ⫺ ∆H D vt 1 sat sat m→b sat [∆H Lm→b (R sol (R sol ⫹ e , R e ) ⫹ R e ∆H D e , R e ) D* w] ∆R e

冤

冥

R sat e sat sol m→b sat [∆H Lm→b (R sol (R sol e , R e ) ⫹ R e ∆H D e , R e )] ∆R e ⫹ c D [∆H m→w (1, D*w ) ⫺ ∆H m→w (R sol D D e , D* w )]

⫹ c L ∆H Lm→b (1, R sat e )⫹

⫺ cD

冢冣

1 sat sat m→b sat [∆H Lm→b (R sol (R sol e , R e ) ⫹ R e ∆H D e , R e )] ∆R e

(50)

In the ﬁrst of the ﬁve terms on the right-hand side of Eq. (50), we take into account that the concentration of the detergent in the titrant, c D, can be higher than the cmc, so that after injection the pure micelles undergo monomerization, (1, D*w ). The ﬁrst two which is related to the molar heat of transition, ∆H m→w D terms in the total heat, Eq. (50), are independent of the concentrations in the titrant (c D and c L); the third contribution is proportional to the concentration of lipid c L; and the last two contributions are proportional to the concentration of detergent, c D, in the titrant. This feature makes it possible to design experimental investigations of the molar heats of transition of the two components inside the range of coexistence. This may be done by determination of ∆Q for several values

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of c L and c D according to protocols II and III, respectively. Consideration of the slopes and intercepts of the dependence of ∆Q on c L and c D allow determination of the values of the molar heats [25]. Thus, in the range of coexistence we can determine not only the heat of transfer of detergent between aqueous solution and aggregates but also the heat of transition of lipid and detergent between the sat m→b sat (R sol (R sol mixed vesicles and the mixed micelles, ∆H m→b L e , R e ) and ∆H D e , R e ).

IV.

HEAT EVOLUTION OF THE TRANSFER OF AMPHIPHILIC MOLECULES BETWEEN AGGREGATES AND WATER

A. Heat of Micellization and Its Dependence on Temperature and Composition Although the change in entropy is the main driving force for micellization, the enthalpy of micellization may also contribute signiﬁcantly to the Gibbs energy of this process, particularly in the case of amphiphiles with long alkyl chains. As described earlier, micellization is often endothermic at low temperatures but exothermic at higher temperatures. Comprehensive evaluation of the inﬂuence of the molecular structure of amphiphiles on the heat of their micellization therefore requires comparison of the heat associated with micellization of the various amphiphiles as a function of temperature. Since the experimental protocols yield information on the heats of demicellization, the data cited below refer to ∆H demic . Most of the data published thus far on the effects of molecular structure on the heat evolution relate to a constant temperature (usually 30 ⫾ 5°C). At this temperature, demicellization may be either endothermic or exothermic, depending on both the chain length and the headgroup of the surfactant. Examples are given in Tables 3–5 for three series of surfactants (alkyltrimethylammonium bromides in Table 3, alkyl-N-acetylamino saccharides in Table 4, and alkyl oligoethylene oxides in Table 5). The data given in these tables can be used to evaluate the effects of elongation of the hydrocarbon chain on ∆H demic , ∆G demic

TABLE 3 Thermodynamic Parameters and cmc for Three Alkyltrimethylammonium Bromides at 30°C Surfactant

Cn

cmc (mM)

∆H demic (kJ/mol)

∆G demic (kJ/mol)

T ∆S demic (kJ/mol)

DTAB TTAB CTAB

C 12 C 14 C 16

15.98 (17.85) 3.98 (3.31) 1.03 (0.95)

5.1 (1.8) 8.5 (7.4) 13.9 (8.6)

20.5 24.0 27.4

⫺15.4 ⫺15.5 ⫺13.5

Source: Refs. 26 and (in parentheses) 27.

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317

(computed from the cmc value of the surfactant), and T ∆S demic (computed from the values of ∆H demic and ∆G demic at the given temperature). The general ﬁnding of these studies is that the major driving force for micellization is entropic, whereas the enthalpy associated with micellization can either add to this driving force (as for the trimethylammonium bromides listed in Table 3 and for most of the carbohydrate-derived surfactants of Table 4) or have the opposite effect (as for the C n Em surfactants of Table 5). Another generalization that can be drawn from Tables 3–5 is that increasing the chain length lowers the cmc and makes demicellization either less exothermic or more endothermic [28]. For the three cationic surfactants of Table 3, the effect of chain elongation on ∆H demic is sufﬁcient to explain the effect of the chain length on the cmc, whereas the entropic term associated with demicellization of these surfactants remains almost constant. Table 4 presents the thermodynamic parameters that relate to demicellization of four groups of nonionic surfactants in which alkyl chains are linked through N-acetyl amine bonds to different sugar headgroups at 40°C. It is obvious from these data that demicellization of the surfactants of these series is either endothermic or exothermic, depending on the chain length and headgroup. Similar to the previous example, for each series of surfactants with a given headgroup, elongation of the chain results is higher (more positive) molar enthalpy of demicellization; that is, micellization becomes more exothermic. As to the effect of the head-

TABLE 4 Thermodynamic Parameters for Four Series of Nonionic CarbohydrateDerived Surfactants in Which the Alkyl Chains are Linked Through an N-Acetyl Amine Bond to Different Sugar Headgroups at 40°C Compound Headgroup

Cn

cmc (mM)

∆H demic (kJ/mol)

∆G demic (kJ/mol)

T ∆S demic (kJ/mol)

Glucitol

C8 C 10 C 12 C8 C 10 C 12 C8 C 10 C 12 C8 C 10 C 12

21 2.0 0.18 21 2.9 0.26 24 3.3 0.31 35 4.6 0.45

⬎⫺0.9 2.6 7.2 —a 3.0 7.7 ⬎⫺1.1 1.9 6.6 ⫺2 1.4 5.3

20.4 26.6 32.8

⫺21.5 ⫺24 ⫺25.6

25.6 31.9 20.1 25.3 31.4 19.1 24.4 30.4

⫺22.6 ⫺24.2 ⫺21.2 ⫺23.4 ⫺24.8 ⫺21.1 ⫺23.0 ⫺25.1

Glucose

Lactitol

Lactose

a

Endothermic. Source: Ref. 28.

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group (for any given chain length), it appears that increased hydrophilicity of the surfactant, as expressed by higher cmc values, results in less exothermic micellization. The same trend was observed when the sugar moiety was linked to the hydrocarbon chain through an N-propionyl amine bond [28]. Similar to the surfactants of Table 3, when C n ⱖ 10, micellization of surfactants of these series is enthalpically favorable. Again, the enthalpy of micellization becomes more exothermic upon elongation of the chain length whereas the entropic term remains almost constant. Different results were obtained for the nonionic surfactants composed of hydrocarbon chains of varying length Cn linked by an ether bond to polyethylene oxides of two different lengths, E 5 and E 6 (Table 5). For each of these surfactants, the published values of the cmc vary over a large range. Hence, the values given in this table for ∆G demic and T ∆S demic can only be regarded as rough estimates of the actual values. Yet it is clear from these data that the entropically driven micellization of the surfactants of Table 5 occurs in spite of them being endothermic (i.e., enthalpically unfavorable). Interestingly, in these series of surfactants ∆H demic is affected much less than T ∆S demic by the chain length of either the hydrocarbon chain or the polyethoxy headgroup. As for other groups of surfactants, elongation of the hydrocarbon chain makes demicellization less exothermic, whereas elongation of the headgroup makes it more exothermic. However, in contrast to the surfactants in Tables 3 and 4, the entropic term of the surfactants of Table 5 exhibits strong dependence on the hydrocarbon chain length. Chain elongation results in large values of T ∆S demic (i.e., micellization becomes more favorable entropically). In addition, chain elongation reduces the enthalpic driving force against micellization, but this effect is much smaller than that observed for the surfactants of Tables 3 and 4. TABLE 5 Thermodynamic Parameters for a Series of Nonionic Surfactants C n E m as Measured at 25°C on a Thermal Analysis Monitor Surfactant Cn Em C6 E5 C8 E5 C 10 E 5 C 12 E 5 C8 E6 C 10 E 6 C 12 E 6 a

∆H demic (kJ/mol)

∆G demic (kJ/mol)

T ∆S demic (kJ/mol)

⫺15.2 ⫺14.46 (15.9) a ⫺13.3 ⫺13.46 b ⫺19.68 c ⫺14.67 c ⫺14.79 b

15.0–15.4 21.1–21.6 26.8–28.3 34.0

⫺30.2 (⫺30.6) a ⫺35.56 (⫺36.06) a ⫺40.1 (⫺41.6) a ⫺47.5

33.8

⫺48.6

cmc (mM) 107–130 9–11 0.6–1.1 0.058

0.064

Values in parentheses from Ref. 30. From Ref 31. c From Ref 32. Source: Ref. 29 except as noted. b

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For many series of surfactants, demicellization is associated with an exothermic contribution of the headgroup and an endothermic contribution of the tail [28]. Hence, at a certain temperature these two contributions may cancel each other, leading to zero transition enthalpy (∆H demic ⫽ 0). A systematic study devoted to the effect of temperature on the thermodynamics of demicellization revealed, for the four studied surfactants (SDS, sodium cholate, sodium deoxycholate, and octylglucoside), that demicellization becomes less exothermic (or more endothermic) as the temperature increases [11]. By contrast, the cmc goes through a minimum at the temperature where ∆H demic ⫽ 0 (Fig. 6). The latter ﬁnding was explained by Paula et al. [11] in terms of van’t Hoff’s

FIG. 6 The enthalpy of demicellization and the cmc of selected surfactants as a function of temperature. (Data taken from Ref. 11.)

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law [Eq. (12)], ∂(∆G demic /RT) ∆H demic ∂ ln cmc ⫽⫺ ⫽ ⫽0 ∂T ∂T RT 2

(51)

Speciﬁcally, at the temperature where ∆H demic ⫽ 0, the ﬁrst derivative of the cmc with respect to temperature equals zero, indicating a minimal value of the cmc. It should be noted that both the cmc and ∆H demic values given in Fig. 6 are less accurate for the bile salts than for SDS and octylglucoside because micellization of bile salts exhibits signiﬁcantly broader transitions between monomers and micelles due to the much smaller aggregation numbers of these surfactants (see above). In an attempt to gain an understanding of the effect of the structure of surfactants on the temperature dependence of ∆H demic , we studied a series of three alkyl glucosides of different chain lengths (Opatowski et al, Heat capacity of micelle formation of alkyl glucosides, in preparation). The temperature dependence of ∆H demic obtained for the three studied alkylglucosides with different chain lengths (C 7, C 8, and C 9) are depicted in Fig. 7. Each

FIG. 7 The enthalpy of demicellization of three alkylglucosides of different chain lengths (C 7, C 8, and C 9) as a function of temperature. The lines plotted through the point where T ⫽ 25°C and ∆H demic ⫽ 0 are parallel to the respective experimental lines.

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of these dependences can be characterized by its slope and by the temperature T 0 at which micelle formation is isocaloric (∆H demic ⫽ 0). It is obvious from Fig. 7 (and the table given as an inset to this ﬁgure) that the increase in chain length n CH2 results in lower values of T 0 and larger slopes of the apparently linear dependence of ∆H demic on temperature (i.e., in increased ∆C P). Notably, the value of ∆C P appears to depend linearly on the chain length [∆C P /n CH2 ⫽ 0.048 ⫾ 0.008 kJ/(mol ⋅ K)], as in other hydrophobic systems with varying chain length [12]. To explain the differences among the values of T 0 of the three studied alkyglucosides, we note that for the studied alkanes (e.g., Table 2), T 0 is almost constant and equal to T alk 0 ⬇ 25°C [13]. Hence, the difference in T 0 relates to the headgroups. Figure 7 shows that at a temperature T ⫽ T alk 0 ⫽ 25°C, the values of ∆H demic of the three studied alkylglucosides are close (⫺7.1 to ⫺9.0 kJ/mol). Because the alkyl chains are assumed not to contribute to ∆H demic at this temperature, we propose that the major contributor to ∆H demic at 25°C relates to headgroup– headgroup interactions. Assuming that the enthalpy associated with the latter interactions is temperature-independent, we can present the temperature dependence of ∆H demic in terms of the dependence term that relates to the alkyl chains. This term is given for each of the surfactants of Fig. 7 by the computed lines that intersect ∆H demic ⫽ 0 at 25°C. These lines supposedly represent the temperature dependence of the enthalpy that relates solely to the sum of all the enthalpic terms that relate to the interactions of the alkyl groups. However, many more data are required to assess this hypothesis and its generality.

B. Heat of Partitioning of Amphiphiles Between Lipid Bilayers and Aqueous Media In the presence of amphiphilic bilayers, such as phospholipid vesicles or biological membranes, water-soluble amphiphiles partition between the bilayer and the aqueous media. Many studies have been devoted to the partitioning of alcohols between bilayers and water as well as to the enthalpy associated with the introduction of alcohols into bilayers, the effects of the alcohols on the physical properties of the bilayers, and the dependence of all these factors on the structure and properties of both the bilayers and the alcohols. The heat associated with the incorporation of three different short-chain alcohols into DMPC bilayers at 26°C and 40°C are given in Table 6. As is obvious from these data, the incorporation of the alcohols into the bilayers, as measured at both temperatures, is endothermic and only slightly dependent on the chain length. The molar enthalpies associated with the incorporation of the alcohols into the bilayers at any given temperature are of the same magnitude as but of opposite sign to the enthalpies associated with transferring the alcohols from their pure liquid state into buffer (Table 2). Notably, the transfer of alcohol molecules

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TABLE 6 ∆H 0incorporation of Alcohols of Different Chain Lengths into DMPC Vesicles at 26°C and 40°C a ∆H 0incorporation (kJ/mol) Alcohol

26°C

40°C

Ethanol Propanol Butanol

16 16.1 18

8 9.8 10

a Note that ∆H 0incorporation is also denoted as ∆H w→b. Source: Ref. 33.

from water into bilayers (Table 6) is somewhat less endothermic than their transfer into pure liquid alcohol (Table 2). According to Trandum et al. [33], this difference may relate to dehydration of the alcohols upon association with the lipid bilayers. (‘‘Dehydration of alcohol is the predominant contributor to ∆H 0incorporation.’’) Different results were obtained for the partitioning of long-chain alcohols between DPPC vesicles and aqueous solutions (Table 7). In this system, at 45°C the DPPC bilayers are in their liquid crystalline phase, similar to DMPC at 25°C. The heat evolution in this system exhibited much greater dependence on the chain w→b length, ∆H alcohol (the enthalpy associated with transferring a solute molecule from water into lipid bilayers) being more exothermic for the longer alcohols. This difference may result from different changes in lipid–lipid interactions within the lipid bilayer due to the introduction of alcohols of different chain lengths. Partitioning of the alcohols can be described in terms of a chain-length-dependent partition coefﬁcient, which increases with the chain length of the alcohol (Table 7). This increase in partitioning is accompanied by more negative enthalpy. The strong chain length dependence of the enthalpy of partitioning of alcohols into lipid bilayers is not consistent with purely hydrophobic interactions, which relate only to dehydration of nonpolar moieties by removal from water. This has been interpreted by Rowe et al. [34] in terms of some speciﬁc interactions between the alcohols and the lipid moieties and/or changes in speciﬁc interactions among lipid molecules due to the introduction of alcohol molecules into the bilayers. This interpretation is supported by the ﬁnding that the sign of enthalpy at 45°C changes from positive to negative with increasing chain length, for which the most straightforward interpretation is that short-chain alcohols disrupt the lipid–lipid interactions in the bilayer whereas the longer chain alcohols enhance and participate in such interactions.

6.7 ⫺5.0 ⫺8.8 ⫺16.7

C6 C7 C8 C9 ⫺7.5 ⫺12.6 ⫺15.9

48°C ⫺7.9 ⫺14.7 ⫺18.0

50°C ⫺0.8 ⫺10.5 ⫺16.7 ⫺20.1

⫺0.8 ⫺14.7 ⫺19.3

55°C

53°C

(kJ/mol)

DPPC

a The lipid bilayers were made of DPPC or DPPC/cholesterol ⫽ 4/1. Source: Ref. 34.

45°C

∆H w→b alcohol

⫺11.3 ⫺20.1 ⫺20.9

60°C 839 2150 1.81 ⫻ 10 4 5.55 ⫻ 10 4

K, 45°C

296 1615 7657 2.7 ⫻ 10 4

K, 45°C

67 42 28 8

w→b ∆H alcohol (kJ/mol), 45°C

DPPC/cholesterol ⫽ 4/1

Thermodynamic Parameters for the Partitioning of Alcohols into DPPC Bilayers a at Different Temperatures

Alcohol Cn

TABLE 7

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w→b The temperature dependence of ∆H alcohol is such that upon an increase in temperature, the introduction of alcohols into the DPPC bilayer becomes more exothermic (Table 7). Counterintuitively, the partition constant was found to be only slightly dependent on temperature [34]. Further work will be needed to conﬁrm and explain these ﬁndings. The data given in Table 7 also show that inclusion of cholesterol in DPPC bilayers reduces the bilayer/water partitioning of the alcohols (at 45°C) and makes the introduction of alcohols into the bilayers more endothermic. Both these effects are particularly pronounced for short-chain alcohols. These results are consistent with the interpretation that short-chain alcohols disrupt the packing within bilayers, reducing the energy of the interactions between lipid chains [33,34]. In the absence of cholesterol this reduction of stabilizing interaction overcomes the effect of the alcohol–bilayer interaction only for alcohols with chain lengths of six carbon atoms or less, whereas in cholesterol-containing membranes, in which the packing is tighter, even the introduction of nonanol is endothermic. As a consequence, the dependence of the enthalpy on the chain length is greater than in the absence of cholesterol. Recent studies demonstrate that both the partition coefﬁcient and the enthalpy associated with the introduction of octanol into bilayers depend on the composition (and physical properties) of the bilayers. From the data depicted in Table 8, it appears that the variation of the enthalpy is relatively small and that no obvious w→b correlation can be deﬁned between the partition coefﬁcient and ∆H alcohol . More data are needed to gain an understanding of this process and its dependence on factors such as lipid acyl chain unsaturation. Several systematic studies addressed the enthalpy associated with the introduction of surfactants into phospholipid bilayers and phospholipid–detergent mixed micelles. These include several investigations of the enthalpy of partitioning of the nonionic surfactant octylglucoside (OG) into PC bilayers. The results of these studies (Table 9) reveal that, similar to the partitioning of alcohols, increasing the temperature results in more exothermic introduction of OG into lipid bilayers.

TABLE 8 Partitioning of Octanol into Different Lipid Bilayers at 45°C Lipid Dilinoleylphosphatidylethanolamine (DLPE) Dioleylphosphatidylglycerol (POPG) Dipalmitoylphosphatidylcholine (DPPC) Dioleylphosphatidylcholine (DOPC) Stearoylarachidonylphosphatidylcholine (SAPC) Source: Ref. 34.

K ⫻ 10 ⫺4 1.19 1.29 1.81 1.98 2.12

w→b ∆H alcohol (kJ/mol)

⫺5.0 ⫺6.7 ⫺8.8 ⫺8.0 ⫺5.4

⫾ ⫾ ⫾ ⫾ ⫾

0.4 0.8 2.5 0.4 0.4

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TABLE 9 Enthalpies Associated with the Transfer of OG from Water into Aggregates, ∆H Dw→a (Micelles, Mixed Micelles, and Other Bilayers), at 27°C and 70°C

Aggregate OG micelles OG–PC mixed micelles Dimiristoyl PC (DMPC bilayer) Soybean PC bilayer Palmitoyloleyl PC (POPC bilayer) POPC bilayer (30 nm) diluted POPC bilayer (200 nm) diluted POPC bilayer (400 nm) diluted POPC/POPG bilayer (75:25) POPC/cholesterol bilayer (95:5) POPC/cholesterol bilayer (50:50) bilayer Egg–PC bilayer (30 nm) diluted Egg–PC bilayer a

K (M ⫺1) a at 27°C 39 [18]

75 [18] 77 [18] 88 [35] 120 ⫾ 10 [17] 130 ⫾ 5 [17] 120 ⫾ 10 [17] 100 [17] 110 [17] 90 [17] 78 [17] 40 [25]

∆H Dw→a (kJ/mol) a At 27°C

At 70°C

6.3, 7.0 [11], 7.1 [24] 7.3 [25] 12.7 [18] 5.6 [18] 7.11 [35] 5.4 [17] 7.3 [17] 7.9 [17] 6.7 [17] 7.3 [17] 9.4 [17] 6.2 [17] 10.0 [25]

⫺8.6, ⫺8.2 [11], ⫺8.8 [24] ⫺9.03 [18] ⫺8.9 [18]

Sources as noted.

The value of the partition coefﬁcient increases with decreasing surfactant concentration. Furthermore, similar to the heat of micelle formation, transfer of OG molecules into the bilayers is endothermic at room temperature but exothermic at high temperature (Table 9). The enthalpy at any given temperature depends on the composition and size of the vesicle bilayers (Table 9). Thus, at room temperature, the introduction of OG into POPC bilayers appears to become more endothermic as the size of the vesicles increases as well as when either POPG or cholesterol is included in the POPC vesicles. However, even when the bilayers contain relatively high cholesterol concentrations, ∆H Dw→a is only a factor of up to 2 larger than the heat of micellization of pure OG (Table 9). Notably, the enthalpy associated with transfer of OG from water into DMPC or POPC bilayers at 27°C is somewhat more positive than the heat of transfer into micelles. As a result, the transfer of OG from micelles into bilayers at 27°C is endothermic (see below). The systematic studies of Keller et al. [18] revealed that the partition coefﬁcient that describes the partitioning of OG into PC bilayers remains almost constant throughout the temperature range of 28–50°C (K ⫽ 120 ⫾ 10 M ⫺1), whereas ∆H Dw→b decreases linearly with increasing temperature (from 5.2 kJ/mol at 28°C to ⫺1.05 kJ/mol at 45°C). Such linear regression indicates that the molar heat capacity (∆C p) for transfer of OG from water into bilayers is large and nega-

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tive [∆C p ⫽ ⫺0.314 kJ/(mol ⋅ K )]. Such large ∆C p values are usually considered to be ﬁngerprints of the hydrophobic effect, similar to the results obtained for the incorporation of other amphiphilic compounds into model membranes [36,37]. Reaction enthalpies close to zero at 25°C and large negative heat capacities are also typical for the transfer of hydrophobic molecules from aqueous phase into organic environment (see above). In recent studies we investigated the heat evolution obtained upon stepwise dilution of OG–PC mixed micelles. This process ﬁrst results in extraction of OG from mixed micelles to the aqueous solution, which subsequently results in transformation of the mixed micelles into vesicles, and thereafter in extraction of OG from the bilayers to the water. Our major ﬁndings were that 1. 2.

3.

The heat associated with the dilution varied from one step to the next. Dilution was isocaloric at about 40°C, exothermic at temperatures below 40°C, and endothermic above 40°C, similar to the dilution of pure detergent micelles. The absolute value of the heat evolution, measured at any temperature, was larger in the range of coexistence than in either the vesicular or micellar range.

To interpret these results, we ﬁrst note that in the ‘‘pure phase,’’ where only one lipidic aggregate is present, the heat is due to the extraction of OG from either micelles or vesicles into the aqueous solution. Given the similar temperature dependence of the range of coexistence, it follows that this heat also relates to the extraction of OG from mixed aggregates into water. This means that the heat associated with this process is much greater than the heat associated with the transformation of micelles into vesicles. This interpretation also means that dilution of lipid–detergent mixtures in the range of coexistence results in the extraction of more OG into the diluting aqueous medium than similar dilution of a pure (micellar or vesicular) phase. Assuming that the molar enthalpy of extraction at any temperature (∆H Da→w) is constant implies that the heat associated with each titration step is determined only by the number of OG molecules that become extracted from the mixed aggregates into the water, ∆n Da→w. For any assumed value of ∆H Da→w , the observed ∆Q can be used to compute ∆n Da→w as a function of added aqueous solution. This in turn can be used to compute the dependence of the OG/PC ratio in mixed aggregates (R e) on the concentration of monomeric OG. This dependence is, of course, a function of the value assumed for ∆H Da→w . sol Since the phase boundaries, R sat e and Re , are particularly sensitive to the value of ∆H Da→w, these independently determined boundaries can be used to estimate ∆H Da→w from the best ﬁt between their computed and experimental values [24]. The best ﬁt between our ITC data and the phase boundaries yields the ‘‘equation of state’’ depicted in Fig. 8. This ﬁt was obtained for ∆H extraction ⫽ 7.1 kJ/ mol [24]. This value is similar to that of ∆H demic obtained for pure OG at 28°C

Amphiphiles in Aqueous Solutions

FIG. 8 (R e).

327

Dependence of the monomer concentration of OG on the OG/PC effective ratio

(Table 9). The more detailed experimental approach used to estimate the enthalpy of transferring individual OG and PC molecules from micelles to vesicles at 28°C (see experimental protocols in Section III.C and Ref. 25) yielded estimates for the ∆H values associated with transferring OG from both bilayers and micelles into water (∆H Db→w and ∆HDm→w, respectively) as well as for the much smaller heat ). Similar exassociated with transferring OG from micelles to bilayers (∆H m→w D periments are presently under way in our laboratory with other surfactants to test whether the heat associated with extracting surfactant molecules from lipidic aggregates into water is always much greater than the heat associated with the transfer of surfactant molecules between different types of aggregates. An interesting feature of the equation of state (Fig. 8) is that within the range of coexistence the concentration of monomeric OG is not constant. The observed increase of D w within this range is apparently inconsistent with the simplest thermodynamic expectations. This contradiction can, however, be explained by more sophisticated considerations [38]. The heat evolution of transfer of a surfactant molecule from water into bilayers depends on the hydrophobicity of the surfactant. As an example, octyl thioglucoside (OTG) is a more hydrophobic surfactant than OG. Its cmc (9 mM) is lower than that of OG, and its partition coefﬁcient between bilayers and water (240

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M ⫺1) is higher than that of OG (120 M ⫺1) [17]. Thermodynamic analysis of the OTG–POPC system is more complex than analysis of the OG–lipid system because the partition enthalpy for the transfer of OTG from the aqueous phase to the membrane apparently depends on the mole fraction of detergent in the membrane [17]. Titration of SUV into OTG solutions below D 0w results in partitioning of the detergent into the SUV bilayers without affecting the integrity of the bilayers. Under these conditions, the apparent reaction enthalpy increased almost linearly with OTG concentration [17]. Speciﬁcally, ∆H Dw→b varied linearly with the mole fraction of OTG in the membrane, being exothermic at low OTG/POPC ratios but endothermic when the bilayer contained more OTG, approaching values that are similar to the heat of micellization (∆H mic ⫽ 4.6 kJ/mol) at OTG concentrations close to D 0w . Interestingly, according to Wenk and Seelig [17], the partition coefﬁcient K is constant and independent of the presence of cholesterol in the bilayer throughout the temperature range 28–45°C. The nonionic detergent octaethylene oxide dodecyl ether (C 12 EO 8) is even more hydrophobic than OTG (cmc ⫽ 0.11 mM). Thermodynamic parameters that relate to this surfactant are compared with those of OTG and OG in Table 10. The only conclusions that can be drawn from this comparison are that increasing the hydrophobicity of the surfactant results in lower cmc values, more endothermic micellization, and higher values of the surfactant’s partitioning into bilayers. By contrast, no simple relationship between the nature of the surfactants and the heat involved in transferring them into bilayers can be derived. An understanding of the factors that govern the enthalpy associated with transfer of amphiphiles into membranes requires more information on the enthalpy of this process for these and other surfactants under different conditions.

C. Heat of Phase Transformations in Mixtures of Bilayer-Forming and Micelle-Forming Amphiphiles The heat associated with the transformation of bilayers into micelles is a sum of the heats associated with the transfer of lipid molecules from micelles into bilayers (∆Q Lm→b) and the respective heat of transfer of detergent (∆Q m→b D ). In addi-

TABLE 10 Critical Micelle Concentration and Enthalpies Associated with Micellization and with the Transfer of Detergent Molecules into POPC Bilayer and Partition Coefﬁcient Values Surfactant

cmc (mM)

∆H mic (kJ/mol)

K (M ⫺1)

∆H Dw→b (kJ/mol)

OG OTG C 12 EO 8

≅23 [11] 9 [17] 0.11 [41]

6.2 [11] 4.6 [39] 15.9 [31]

120 [21] 240 [17] 3900 [41]

5.44 [21] ⫺0.08–(⫹0.6) [17] 31.4 [41]

Amphiphiles in Aqueous Solutions

329

tion, the concentration of monomeric detergent (Dw) varies slightly within the range of coexistence, where the phase transformation occurs [25]. The composition-induced transformation between vesicles and mixed micelles is therefore accompanied by redistribution of surfactant between aggregates and water. As discussed above, the heat associated with transferring surfactant molecules between different types of aggregates is much less than the heat associated with their transfer from lipid aggregates into water (i.e., ∆H Dm→b ⬍ ∆H Da→w). As a consequence, although the variation of Dw in the range of coexistence is small, ∆Q Da→w cannot be neglected. The overall ∆Q therefore depends on at least three individual unknown molar enthalpies (∆H Dm→b , ∆H Lm→b , and ∆H Da→w). Determination of these unknown factors therefore requires a combination of a series of experimental protocols. The general expression for ∆Q [Eq. (50)], which relates to the heat evolution of one titration step within the range of coexistence, is valid for all the experimental protocols. When lipid vesicles are titrated into a mixture of lipids and detergent within this range (protocol II), the heat is given by

冢

∆Q coex ⫽ D w V t ∆H Dm⫺w ⫹ ⫹ V t c L R sat e

冢

m⫺b ∆H m⫺b ⫹ R sat L e ∆H D ∆R e

m⫺b ∆H m⫺b ⫹ R sat L e ∆H D ∆R e

冣

(52)

冣

where V t and c L are the volume and concentration, respectively, of the titrated lipid [25,40]. Similarly, the heat evolution of one step of titration of detergent into the mixed system (protocol III) is given by ∆Q coex ⫽ (D w ⫺ cmc)V t ∆H Dm⫺w ⫹ D w V t ⫺ cD Vt

冢

m⫺b ∆H m⫺b ⫹ R sat L e ∆H D ∆R e

冢

m⫺b ∆H m⫺b ⫹ R sat L e ∆H D ∆R e

冣

(53)

冣

When the cmc of the surfactant is very low, both D w and the cmc are approximately equal to zero. The variation of Dw that accompanies the phase transformation is small, and its contribution to the heat evolution is negligible, so that and ∆H Dm→b can be straightforwardly estimated from two experiments that ∆H m→b L each yield a value of ∆Q for a given concentration of the surfactant. Namely, Eq. (52) yields the simpliﬁed equation

冤

冢

∆Q coex ⫽ V t c L R sat ∆H Dm→b 1 ⫹ e

冣冢

冣冥

R sat 1 e ⫹ ∆H m→b L ∆R e ∆R e

(54)

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and Eq. (53) yields ∆Q coex ⫽ ⫺V t c D

1 m→b (∆H m→b ⫹ R sat L e ∆H D ) ∆R e

(55)

This is the case for the nonionic detergent C 12 (EO) 8. Given the very low cmc of this detergent (0.11 mM), when it is added to phospholipid vesicles it partitions almost completely into the vesicle bilayers (D b ⬎⬎ D w). Hence, combining Eqs. (54) and (55) enables the computation of the heats of phase transformations and ∆H Lm→b). Using this strategy, Heerklotz et al. [41] concluded that for (∆H m→b D C 12 (EO) 8 at 25°C, transferring detergent from micelles to bilayers is endothermic (∆H m→b ⫽ 10 kJ/mol), whereas transferring lipids from micelles to bilayers is D exothermic (∆H Lm→b ⫽ ⫺2.5 kJ/mol). For the more general case, when cmc ≠ 0, determination of the relevant molar enthalpies requires more experimentation. In this case, two series of experiments can be conducted according to protocols II and III, using varying concentrations of lipid and detergent (c L and c D, respectively). The results of these experiments can then be interpreted in terms of Eqs. (52) and (53) to yield the relevant molar enthalpies as described above. Using this approach we found [25], in good agreement with our expectation, that transferring detergent molecules from micelles to bilayers is endothermic (∆H Dm→b ⫽ 2.7 kJ/mol) whereas transferring ‘‘curvophobic’’ lipid molecules from curved micelles into relatively ﬂat bilayers is exothermic (∆H Lm→b ⫽ ⫺2.5 kJ/mol). The observed enthalpies can be used to describe the packing tendency of various amphiphiles in general and particularly that of various phospholipids. No other straightforward method is available for experimental evaluation of this characteristic attribute of membrane phospholipids. Another potentially useful approach based on ITC experiments is to determine the enthalpy difference between two different states by comparing the heat evolution of transferring both these states into a common state. As an example, phospholipid vesicles of different sizes differ in their enthalpy level. Solubilization of a given amount of phospholipid by a given micelle-forming surfactant results in mixed micelles whose properties are independent of the size of the solubilized vesicles [42]. This can be used to estimate the enthalpy difference between vesicles of various sizes by determining the difference between the heats of solubilization of these vesicles, as illustrated in Fig. 9. Using this approach we found that at 27°C the enthalpy difference between small and large POPC (liquid crystalline) vesicles is merely 0.724 kJ/mol, compared to an enthalpy difference of 10.5 kJ/ mol found for DPPC (gel phase) vesicles [43]. A similar approach can be used to study other characteristics of lipid bilayers and membranes. For example, in a membrane composed of two phospholipids, these two components may be either mixed or phase-separated in the plane of the membrane. Differentiating between these two possibilities can be based on

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331

FIG. 9 A schematic diagram for the enthalpy of large unilamellar vesicles (LUVs) and small unilamellar vesicles (SUVs) with respect to mixed micelles.

a comparison between the heat of solubilization of the studied membrane and the heat associated with solubilizing a mixture of two populations of vesicles each composed of one of the components. Since solubilization of vesicles and subsequent equilibration of the resultant mixed micellar systems are believed to be rapid, a comparison of ∆Q of solubilizing the mixed lipid system with that of solubilizing the mixture of vesicles can be used to estimate the heat associated with mixing the two lipids in the mixed bilayer. The feasibility of this approach has yet to be investigated.

V. CONCLUDING REMARKS Isothermal titration calorimetry is a very potent tool in the ﬁeld of self-assembly of amphiphiles. Given the recent improvements of the sensitivity of this technique, it can be used to investigate many processes of interest in this ﬁeld. The possibility of using a variety of experimental protocols increases conﬁdence in the experimental evidence. In conjunction with other, independent techniques,

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ITC can yield answers to speciﬁc questions that cannot be addressed by any other technique. Thus, ITC studies of the dilution of detergents can be used not only to determine the enthalpy of micelle formation but also the detergent’s cmc and hence the free energy difference. Thus, ITC experiments are sufﬁcient for complete characterization of the thermodynamics of micellization. Other processes that have been studied by ITC include the partitioning of amphiphilic molecules between water and lipid bilayers and the compositionally induced vesicle–micelle phase transition. The examples presented above are of several studies that demonstrate the potential of ITC measurements. Thus far, this potential has been only partially exploited and only for a limited number of amphiphilic systems. Present and future research in this ﬁeld will undoubtedly make much more use of this potent method. This will hopefully clarify many of the fundamental questions to which we presently have only partial answers.

ACKNOWLEDGMENTS We thank the Israel Science Foundation, founded by the Israel Academy of Science and Humanities—Centers of Excellence Program, for ﬁnancial support, and the members of the center devoted to self-assembly of mixtures of amphiphiles, D. Andelman, A. Ben Shaul, S. Safran, and Y. Talmon, for helpful discussions.

REFERENCES 1. C Tanford. The Hydrophobic Effect, Plenum Press, New York, 1981. 2. K Shinoda, T Nakajawa, B Tamamushi, T Isemura. Colloid Surfactants, Academic Press, New York, 1963. 3. P Mukerjee. The nature of the association equilibria and hydrophobic bonding in aqueous solutions of association colloids. Adv Colloid Interface Sci 1:241–275 (1967). 4. JN Israelachvili, Intermolecular and Surface Forces, Academic Press, London, 1985. 5. SM Gruner, MW Tate, GL Kirk, PTC So, DC Turner, DT Kaene, CPS Tilcock, PR Cullis. X-ray diffraction study of the polymorphic behavior of N-methylated dioleoylphosphatidylethanolamine. Biochemistry 27:2853–2866 (1988). 6. H Hoffmann, W Ulbricht. In: Thermodynamic Data for Biochemistry and Biotechnology (H Hinz, ed.), Springer-Verlag, Berlin, 1986. 7. L Benjamin. Calorimetric studies of the micellization of dimethyl-n-alkylamine oxides. J Phys Chem 68:3575–3581 (1964). 8. P Stenius, S Backlund, O Ekwall. In: Thermodynamic and Transport Properties of Organic Salts (P Franzosini, M Sanesi, eds.), IUPAC Chem Data Ser 28, Pergamon, Oxford, 1980, p. 295. 9. R De Lisi, G Perron, J Paquette, JE Desnoyers. Thermodynamics of micellar systems: Activity and entropy of sodium decanoate and n-alkylamine hydrobromides in water. Can J Chem 59:1865–1871 (1981). 10. A Moroi. Micelles: Theoretical and Applied Aspects, Plenum Press, New York, 1992.

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11. S Paula, W Sus, J Tuchtenhagen, A Blume. Thermodynamics of micelle formation as a function of temperature: A high sensitivity titration calorimetry study. J Phys Chem 99:11742–11751 (1995). 12. M Okawauchi, M Hagio, Y Ikawa, G Sugihara, Y Murata, M Tanaka. A light-scattering study of the temperature effect on micelle formation of N-alkanoyl-N-methylglucamines in aqueous solutions. Bull Chem Soc Jpn 60:2718–2725 (1987). 13. SJ Gill, NF Nichols, I Wadsoe. Calorimetric determination of enthalpies of solution of slightly soluble liquids. II. Enthalpy of solution of some hydrocarbons in water and their use in establishing temperature dependence of their solubility. J Chem Thermodyn 8:445–452 (1976). 14. HS Frank, MW Evans. Free volume and entropy in condensed systems. III. Entropy in binary liquid mixtures; partial molar entropy in dilute solutions; structure and thermodynamics in aqueous electrolytes. J Chem Phys 13:507–532 (1945). 15. I Johnson, G Olofsson. Solubilization of pentanol in sodium dodecylsulphate micelles. J Chem Soc Faraday Trans 1 85:4211–4225 (1989). 16. DM Small. In: Bile Acids: Chemistry, Physiology and Metabolism, Vol. 1. (P Nair, D Kritchevsky, eds.), Plenum Press, New York, Chapter 8 (1971). 17. M Wenk, J Seelig. Interaction of octyl-β-thioglucopyranoside with lipid membranes. Biophys J 73:2565–2574 (1997). 18. M Keller, A Kerth, A Blume. Thermodynamics of interaction of octyl glucoside with phosphatidylcholine vesicles: Partition and solubilization as studied by high sensitivity titration calorimetry. Biochim Biophys Acta 1326:178–192 (1997). 19. HH Heerklotz, H Binder, RM Epand. A release protocol for isothermal titration calorimetry. Biophys J 76:2606–2613 (1999). 20. F Zhang, ES Rowe. Titration calorimetric and differential scanning calorimetric studies of the interactions of n-butanol with several phases of dipalmitoylphosphatidylcholine. Biochemistry 31:2005–2011 (1992). 21. M Wenk, T Alt, A Seelig, J Seelig. Octyl-beta-D-glucopyranoside partitioning into lipid bilayers: Thermodynamics of binding and structural changes of the bilayer. Biophys J 72:1719–1731 (1997). 22. JN Israelachvili, S Marcelja, RG Horn. Physical principles of membrane organization. Quart Rev Biophys 13:121–200 (1980). 23. D Lichtenberg. Liposomes as a model for solubilization and reconstitution of membranes. In: Handbook of Nonmedical Applications of Liposomes, Vol. 2, Models for Biological Phenomena (Y Barenholz, DD Lasic, eds.), CRC Press, Boca Raton, FL, 1996, p. 199. 24. E Opatowski, MM Kozlov, D Lichtenberg. Partitioning of octyl glucoside between octyl glucoside/phosphatidylcholine mixed aggregates and aqueous media as studied by isothermal titration calorimetry. Biophys J 73:1448–1457 (1997). 25. E Opatowski, D Lichtenberg, MM Kozlov. The heat of transfer of lipid and surfactant from vesicles into micelles in mixtures of phospholipid and surfactant. Biophys J 73:1458–1567 (1997). 26. PR Majhi, SP Moulik. Energetics of micellization: Reassessment by a high-sensitivity titration microcalorimeter. Langmuir 14:3986–3990 (1998). 27. SP Moulik. Micelles: Self-organized surfactant assemblies. Curr Sci India 71:368– 376 (1996).

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28. JM Pestman, J Kevelam, MJ Blandamer, HA van Doren, RM Kellogg, JBFN Engberts. Thermodynamics of micellization of nonionic saccharide-based N-acyl-N-alkylaldosylamine and N-acyl-N-alkylamino-1-deoxyalditol surfactants. Langmuir 15: 2009–2014 (1999). 29. O Ortona, V Vitagliano, L Paduano, L Costantino. Microcalorimetric study of some short-chain nonionic surfactants. J Colloid Interface Sci 203:477–484 (1998). 30. K Weckstrom, K Hann, JB Rosenholm. Enthalpies of mixing a non-ionic surfactant with water at 303.15°K studied by calorimetry. J Chem Soc Faraday Trans I 90: 733–738 (1994). 31. G Olofsson. Microtitration calorimetric study of the micellization of three poly(oxyethylene) glycerol dodecyl ethers. J Phys Chem 89:1473–1477 (1985). 32. JM Corkill, JF Goodman, JR Tate. Calorimetric determination of the heats of micelle formation of some non-ionic detergents. Trans Faraday Soc 60:996–1002 (1964). 33. C Trandum, P Westh, K Jorgensen, OG Mouritsen. A calorimetric investigation of the interaction of short chain alcohols with unilamellar DMPC liposomes. J Phys Chem B 103:4751–4756 (1999). 34. ES Rowe, F Zhang, TW Leung, JS Parr, PT Guy. Thermodynamics of membrane partitioning for a series of n-alcohols determined by titration calorimetry: Role of hydrophobic effects. Biochemistry 37:2430–2440 (1998). 35. M Wenk, J Seelig. Vesicle–micelle transformation of phosphatidylcholine/octylbeta-D-glucopyranoside mixtures as detected with titration calorimetry. J Phys Chem B 101:5224–5231 (1997). 36. PL Privalov, SJ Gill. The hydrophobic effect: A reappraisal. Pure Appl Chem 61: 1097–1104 (1989). 37. RL Baldwin. Temperature dependence of the hydrophobic interaction in protein folding. Proc Natl Acad Sci USA 83:8069–8072 (1986). 38. Y Roth, E Opatowski, D Lichtenberg, MM Kozlov. Phase behavior of dilute aqueous solutions of lipid–surfactant mixtures: Effects of ﬁnite size of micelles. Langmuir In press. (1999). 39. JC Brackman, NM van Os, JBFN Engberts. Polymer–nonionic micelle complexation. Formation of poly(propylene oxide)-complexed n-octyl thioglucoside micelles. Langmuir 4:1266–1269 (1988). 40. MM Kozlov, E Opatowski, D Lichtenberg. Calorimetric studies of the interactions between micelle forming and bilayer forming amphiphiles. J Thermal Anal 51:173– 189 (1998). 41. HH Heerklotz, H Binder, G Lantzsch, G Klose, A Blume. Thermodynamic characterization of dilute aqueous lipid/detergent mixtures of POPC and C 12 EO 8 by means of isothermal titration calorimetry. J Phys Chem 100:6764–6774 (1996). 42. GC Kresheck, HB Long. Determination of the relative molal heat content of dipalmitoylphosphatidylcholine vesicles in the various physical states. Colloids Surf 30: 133–143 (1988). 43. D Lichtenberg. Size-dependent properties of phosphatidylcholine unilamellar vesicles. In: Supramolecular Structure and Function, 5th ed. (G Pifat-Mrzljak, ed.), Ruder Boskovic Institute, Croatia, 1997.

9 Calorimetric Methods for the Study of Adsorption of Surfactants at Solid/Solution Interfaces ´ N KIRA ´ LY ZOLTA Szeged, Hungary

Department of Colloid Chemistry, University of Szeged,

I. Introduction II.

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Classiﬁcation of Calorimeters A. Isotherm power compensation calorimetry B. Isoperibolic heat ﬂux calorimetry

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III. Enthalpies of Displacement Obtained with Different Microcalorimetric Methods A. Deﬁnition of the enthalpy of displacement B. Immersion microcalorimetry C. Batch sorption microcalorimetry D. Titration sorption microcalorimetry E. Flow sorption microcalorimetry F. Noncalorimetric enthalpies of displacement

339 340 341 343 344 346 349

IV. Literature Survey on Calorimetric Studies of Surfactant Adsorption on Solid Substrates

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References

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I. INTRODUCTION The adsorption of surfactants at solid/solution interfaces has long been the subject of extensive experimental and theoretical research. Various aspects have been addressed, among them the composition and structure of the adsorption layer, the mechanism of the adsorption (different stages), the kinetics, the thermodynamics 335

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(driving force), the nature of the solid surface (charged, uncharged, hydrophilic, hydrophobic, modiﬁcations, roughness, porosity), the nature of the surfactant (ionic, nonionic, HLB number, chain length, headgroup effect, stereochemistry), and experimental conditions (pH, temperature, salinity). The ﬁrst step in the quantiﬁcation of adsorption phenomena is the determination of the adsorption isotherms (material balance or mass exchange). Today, measurements of adsorption isotherms are supplemented by a variety of experimental techniques. Among the various methods available, calorimetry is the most powerful tool for elucidating the thermodynamic properties of surfactants at solid/solution interfaces (enthalpy balance or heat exchange). By means of calorimetry, the sign and magnitude of the enthalpies associated with the adsorption process are measured directly. Differential molar enthalpy data provide information on how strongly the adsorbate is bound to the surface, on intermolecular interactions in the adsorption layer, on surface heterogeneity, and on phase transitions or other structural changes within the adsorption layer. Heat capacities, obtained from the temperature dependence of the enthalpy data, are particularly sensitive to such changes. A combination of the enthalpy isotherm with the Gibbs free energy (conveniently obtained from the adsorption isotherm) allows calculation of the entropy function, thereby resulting in a full description of the adsorption process by means of thermodynamic potential functions. However, characterization of the structure of the adsorption layer at a molecular level requires complementary measurements with the use of more structure-sensitive methods such as ellipsometry, neutron reﬂection, the force balance technique, atomic force microscopy, and spectroscopy. The aim of this chapter is to describe the fundamentals of calorimetric methods currently available for determining the enthalpies of displacement of water by surfactants at solid surfaces. Typical applications of these techniques are reported and commented on. Finally, an extensive list of references is provided, with speciﬁcations of the particular systems studied.

II.

CLASSIFICATION OF CALORIMETERS

The adsorption of surfactants on solid surfaces is usually associated with the release of heat to, or the absorption of heat from, the surroundings. This heat can be measured by allowing the adsorption process to occur inside a sample cell (sorption vessel) located in the ‘‘measuring block’’ of a calorimeter. Although a large variety of instruments are available commercially, home-made calorimeters may possess particular advantages for special applications. The new production techniques, and especially the rapid progress in electronics, mean that modern calorimeters permit accurate and reliable measurements, usually controlled by an external computer, which also furnishes the possibility of fast data processing. In general, calorimeters can be classiﬁed on the basis of the measuring princi-

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ple, the mode of operation, and the construction principle [1,2]. Since the material balance of the adsorption process is measured at constant temperature (adsorption isotherm), the enthalpy balance of the adsorption is also to be determined at constant temperature (enthalpy isotherm), allowing the calculation of differential molar enthalpies as a function of, say, surface coverage. The mode of operation of a sorption calorimeter is therefore either isothermal or isoperibolic. As far as the measuring principles are concerned, thermoelectric compensation and heat conduction calorimeters currently predominate, though a number of combinations exist among the various measuring principles, modes of operation, and construction principles [1,2]. As for the construction principle, calorimeters may be either single or twin. In differential calorimetry, two equal, independent measuring units (sample and reference) are situated symmetrically in the same thermostat, with their thermoelectric detector piles are connected in opposition. A twin calorimetric system is free from ﬂuctuations in zero reading and is unaffected by variations in the thermostat temperature. The twin arrangement improves the sensitivity over that of the single conﬁguration.

A. Isotherm Power Compensation Calorimetry In isotherm power compensation calorimetry [3–5], the inactive reference cell is maintained throughout at the temperature of the thermostat, while in the active sample cell the heat of the thermal event (adsorption) is compensated internally by Peltier cooling (if exothermic) or by Joule heating (if endothermic). To this end, the temperature of the sample is continuously monitored relative to that of the reference, and every small deviation is corrected by means of a closed-loop control system (Fig. 1). The values of the current temperature of the sample and the set temperature of the reference are fed through a comparator into an electrical control unit, which activates the Peltier cooler or the Joule heater in the sample cell if its temperature deviates from the desired temperature. Thermoelectric compensation can be applied in various conﬁgurations. The best performance is achieved when the Peltier cooler cools the sample cell at a constant rate while a feedback circuit activates the electric heater to maintain the sample cell at the same temperature as that of the reference cell. In the absence of thermal events, the feedback power is constant and a resting calorimeter baseline is obtained. Exothermal or endothermal effects produced by the sample are compensated for by temporarily reducing or increasing, respectively, the feedback power, which causes deﬂections from the resting baseline until the temperature balance is restored. The power compensation appears as a calorimetric peak. If the product of the voltage U(t) and the current I(t) is recorded continuously during time t (calorimeter power signal), then the electrically generated compensatory heat, Q ⫽ ∫ U(t)I(t)dt (i.e., the area under the calorimetric peak), is equal to, but opposite in sign to, the heat evolved during the thermal event in the sample cell.

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FIG. 1

The closed-loop control system of a power compensation calorimeter.

B. Isoperibolic Heat Flux Calorimetry In isoperibolic heat ﬂux calorimetry [6–8], the temperature differences along the heat-conductive connections between the sample cell and its surroundings (a constant-temperature bath) are continuously monitored during time t with respect to the reference cell, which is also connected to the thermostat (Fig. 2). The occurrence of thermal events (adsorption or desorption) in the sample cell either increases (exothermic process) or decreases (endothermic process) the temperature of the sample, which generates an equalizing heat ﬂux dQ/dt either toward the inﬁnite heat sink or in the reverse direction. The heat ﬂow takes place through extremely sensitive thermopile blankets until equilibrium is reached. Upon establishment of the new equilibrium state, the temperature difference ∆T (t) vanishes and the entire system reverts to the initial temperature. The heat exchanged, Q ⫽ K ∫ ∆T (t)dt, is equal to the heat produced or absorbed by the sample. The constant K is proportional to the (ﬁnite) thermal resistance of the heat-conductive connections between the sample cell and the thermostat. The results (calorimetric peaks) are quantiﬁed by electrical calibration, where known power values are passed through built-in resistors. Other measuring principles, for instance the monitoring of thermoelectric compensation applied to the reference element, may also be used in isoperibolic operation. Formally, the major difference between isothermal and isoperibolic operations is that the thermal resistance between the measuring system and the constant-

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FIG. 2 Heat ﬂow calorimeter in a twin arrangement.

temperature surroundings is inﬁnitesimally small for the former, whereas it is of ﬁnite magnitude for the latter. Therefore, although the surroundings and the measuring system in isothermal calorimeters have practically the same temperature during the thermal event produced by the sample, independently of time, in isoperibolic calorimeters the temperature of the measuring system changes in time until the heat exchange with the surroundings is accomplished. It should be noted that only quasi-isothermal operations may take place, because heat transport is not possible in the absence of (at least small) temperature differences. Commercially available power compensation and heat ﬂux calorimeters are competitive in stability, accuracy, and sensitivity, fractions of a millijoule being detectable with good reproducibility. Although thermoelectric compensation is more efﬁcient in time (larger power values are detected in shorter time intervals), the kinetics of adsorption may impose limitations on this advantage.

III. ENTHALPIES OF DISPLACEMENT OBTAINED WITH DIFFERENT MICROCALORIMETRIC METHODS Calorimeters can be classiﬁed further in terms of the choice of methodology (technical characteristics). Modern calorimeters are supplied with standard mea-

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suring units and optional accessories so that the experimentalist can select the preferred conﬁguration for a particular application. There are four major techniques for study of the adsorption of surfactants from solutions on solid surfaces: immersion, batch, titration, and liquid ﬂow methods [9]. Although the designation ‘‘microcalorimeter’’ should be avoided, as it does not reveal whether the term ‘‘micro’’ refers to the size of the device, the sample container, or the quantity of heat measured, the term ‘‘microcalorimetry’’ is often used in studies of adsorption phenomena when the overall heat evolved is not more than a few hundred millijoules. Of course, the magnitude of the measured heat is dependent not only on the strength of the adsorption but also on the total surface area of the solid present in the calorimeter vessel. As far as the duration of an adsorption calorimetric experiment is concerned, the recorded phenomenon may require a few minutes to several hours, depending on the kinetics of adsorption.

A. Deﬁnition of the Enthalpy of Displacement Adsorption from solution may be represented by a stoichiometric displacement reaction between molecules of the adsorbed solvent (water, component 2) and the solute (surfactant, component 1) [10–12]: (1)l ⫹ r(2) s ⫽ (1) s ⫹ r(2) l

(1)

where superscripts s and l refer to the adsorption layer and the bulk liquid phase, respectively, and r is the amount of solvent displaced by 1 mol of solute at concentration c l . We deﬁne the differential molar enthalpy of displacement (∆2l h l ) as the difference between the partial molar enthalpies (h i) of the two components in the adsorption layer and the equilibrium bulk solution [10–12]: ∆ 21 h 1 ⫽

冢

冣

∂(∆ 21 H ) ∂Γ 1s

⫽ (h 1s ⫺ h 1l ) ⫺ r(h 2s ⫺ h 2l )

(2)

T,p,a s

where ∆ 21 H is the integral enthalpy of displacement and Γ s1 is the amount of solute actually present in the adsorption layer. In the case of dilute solutions and preferential adsorption of the solute, the real amount adsorbed, Γ s1, is practically equal to the surface excess concentration, Γ 1, the latter being an experimental quantity [13]. The integral enthalpy of displacement, ∆ 21 H, is deﬁned [11] as the enthalpy change of the adsorbed phase when the pure solvent (component 2) initially ﬁlling the adsorption space is displaced (partly or totally, depending on the experiment) by the solute (component 1), itself provided by a solution in which its ﬁnal concentration is c 1 . This enthalpy change is equal to the difference between the enthalpies of formation of the phases adsorbed from the solution and from the pure solvent, respectively. In general, calorimetric enthalpies of displacement are measured with reference to the equilibrium bulk solution, which

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can then be transferred to other reference states, e.g., the solute at inﬁnite dilution or the pure components [11]. For further details concerning thermodynamic quantities of displacement, the reader is referred to earlier works [10–12,14].

B. Immersion Microcalorimetry A typical immersion experiment may be described [15–18]. The solid sample is outgassed in a glass bulb that has a capillary break-seal. The sealed ampoule is attached to a push-rod, which may also be used to drive a stirrer, and placed in the immersion liquid inside the calorimeter vessel (Fig. 3). Depression of the plunger breaks the seal, the solid is wetted by the surrounding liquid, and the heat evolved is detected. The experimental heat Q exp comprises three components, only one of which is relevant to the immersion effect. The correction term Q corr originates from the breaking of the ampoule and the subsequent heat of evapora-

FIG. 3 Immersion microcalorimetry setup. (Adapted from Ref. 18.)

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tion [15–18]; it can be determined in a separate blank experiment by using an empty bulb. The dilution term ∆ dil H is related to the change in the bulk composition upon adsorption. It can be determined by breaking ampoules containing appropriate volumes of concentrated surfactant solutions into the solvent to give ﬁnal concentrations in the same range as in the case of the adsorption experiments. The dilution term may be given by ∆ dil H ⫽ n 1 [∆h(c 1) ⫺ ∆h(c 01)] where n 1 is the number of moles of surfactant remaining in solution after adsorption and the enthalpy terms in the brackets are the molar heats of dilution of a concentrated solution of surfactant to the ﬁnal (c 1 ) and initial (c 01) surfactant concentrations in the adsorption experiments [19,20]. Depending on the solid-toliquid ratio, the equilibrium concentration c 1 may differ signiﬁcantly from the initial concentration c 01. In general, c 1 ⬍ c 01 due to the partition of the surfactant molecules between the adsorption layer and the bulk phase (adsorption). The equilibrium composition can be determined by a suitable analytical method (spectrophotometry, differential interferometry, differential refractometry), or it can be calculated by an iteration procedure (described in Section III.D) from the separately measured adsorption isotherm. The enthalpy of immersional wetting is then calculated as ∆ w H ⫽ Q exp ⫺ Q corr ⫺ ∆ dil H, which may be expressed per unit mass or unit surface area of the solid. If the immersion experiment is repeated at different solution concentrations, the enthalpy isotherm of immersion, ∆ w H vs. c l , is obtained. For immersion calorimetry, the presentation of the results is often more appropriate in terms of the relative enthalpy of immersion, ∆ 21 H w, which, for dilute solutions, is equal to the integral enthalpy of displacement ∆ 21 H d , more generally obtained from batch or ﬂow sorption microcalorimetric measurements. The relative enthalpy of immersion is deﬁned as the enthalpy of immersion in the solution minus the enthalpy of immersion in pure solvent 2: ∆ 21 H w ⫽ ∆ w H(c 1 ) ⫺ ∆ w H 02, where ∆ w H 02 ⬅ ∆ w H(c l ⫽ 0). The size of the immersion cell may lie in the range 1–100 mL, depending on the calorimeter design. The immersion method is usually less satisfactory for study of the adsorption of surfactants than other calorimetric methods, for several reasons. Among others, the initial and ﬁnal states of the adsorbent may lack reproducibility, due to improper sample preparation, poor wetting, slow equilibration, etc. The heat correction terms are likewise often ill-deﬁned. Further, the relative enthalpy of immersion is obtained by taking the difference of two large quantities, and this difference may be comparable in magnitude with the dis-

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turbing heat effects. Even though considerable efforts have been made to improve the accuracy of immersion calorimetry, including the design of vacuum-tight immersion vessels, the use of improved bulb-breaking devices, and the introduction of various kinds of agitation techniques [16,17,21], immersion calorimetry still cannot compete in accuracy with the titration and ﬂow sorption calorimetric methods. Further limitations include the facts that only one heat effect can be measured in each experiment and that this technique cannot be applied for the study of desorption processes. Nevertheless, immersion calorimetry is unique in that it is the only method that is able to detect the enthalpic interaction between a bare surface and a solution. Further, the method can be applied advantageously to study adsorption phenomena on ﬁne powders, including the swelling of clays.

C. Batch Sorption Microcalorimetry Formally, the technical procedure of the immersion method described in Section III.B can be applied to measure the relative enthalpy of immersion in a single step instead of in two steps. In this case, a suspension of the adsorbent in the solvent is sealed in the bulb and thermally equilibrated with the surrounding solution in the calorimeter vessel [22]. When the ampoule is broken, the solution mixes with the solvent and the adsorption proceeds until a new equilibrium state is attained. The experiment is then repeated in the absence of the solid in order to determine Q corr ⫹ ∆ dil H, the heat attributable to the breaking of the ampoule plus the enthalpy of dilution of the solution in the solvent. The relative enthalpy of immersion is calculated as ∆ 21 H w ⫽ Q exp ⫺ Q corr ⫺ ∆ dil H Similar calorimetric enthalpies can be obtained, but now in simultaneous adsorption and blank experiments, by using a rotating block calorimeter in a twin arrangement [23]. The block consists of a sample cell and a reference cell; each cell has two compartments, the contents of which mix when the block is rotated. During the experiment, the surfactant solution mixes with the adsorbent slurry in the sample cell, and the same amount of surfactant solution mixes with the diluent in the reference cell. Hence, the heat evolved, Q exp, is measured with respect to the heat of mixing, ∆ dil H, so that ∆ 21 H w is obtained directly. An application of the above-mentioned blank correction and the measurement in a differential arrangement takes into account the enthalpy of dilution of a (concentrated) mother surfactant solution to the initial concentration but not to the equilibrium concentration of the adsorption. Correction for the dilution due to adsorption requires considerations similar to those described under immersion calorimetry in Section III.B.

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D. Titration Sorption Microcalorimetry In the titration operation mode (also referred to as a batch method), a feed solution of surfactant is introduced in a number of successive steps into the microcalorimetric cell, where the solid material is maintained in suspension by effective agitation [9,16,18,24–28]. The size of the titration vessel varies from 2 to 100 mL, depending on the calorimeter design. One possible setup is outlined in Fig. 4. In the initial state, the solid is suspended in pure solvent under stirring. A portion of the mother solution from an external reservoir is then delivered through an efﬁcient heat exchanger by means of a pump or a motor-operated syringe. The aliquot of the titrant and the rate of injection can be adjusted as required. Upon injection of the titrant,the overall enthalpy change ∆ inj H is measured. After ther-

FIG. 4

Batch (titration) microcalorimetry setup. (Adapted from Ref. 18.)

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mal equilibration, the next portion is added, and the procedure is repeated several times (typically 10–20 steps). A full experiment is so designed that at the end of the experiment the equilibrium concentration in the suspension slightly exceeds the critical micelle concentration, cmc. The mother solution is therefore at a concentration above the cmc, whereas the concentration in the sorption vessel during the experiment is mainly below the cmc. It follows that a dilution enthalpy ∆ dil H is involved in the experiment. This quantity consists of the enthalpy of demicellization, the enthalpies of dilution of the micelles and the monomers (depending on the stage of the titration), and the enthalpy of dilution due to adsorption [18,25–28]. ∆ dil H can be measured in a series of blank experiments, i.e.,in the absence of the solid, but otherwise under the same experimental conditions. However, during the blank titration experiment, the equilibrium concentration c 1 in the calorimeter vessel is equal to the total surfactant concentration c 01. In contrast, c 1 is unknown during the sorption titration experiment. Fortunately, the separately determined adsorption isotherm Γ 1 vs. c 1 allows the calculation of c 1 in the titration vessel via a mathematical iteration routine. For dilute solutions, the amount adsorbed in a static system may be given by [13,29] Γ1 ⫽

V0 0 (c 1 ⫺ c 1 ) ma s

(3)

where V 0 is the volume of the solution, m is the mass of solid of speciﬁc surface area a s, c 01 is the initial (or total) surfactant concentration in the sorption vessel, and c 1 is the equilibrium concentration of the surfactant in the supernatant. Under the calorimetric conditions, V 0 and c 01 gradually increase as the titration proceeds, but their values are readily calculated, at any stage of the experiment, from the total amount of titrant added. According to Mehrian et al. [27], Eq. (3) can be solved by iteration to obtain c 1 . Values of c 1 are generated periodically, starting from zero, say, and using sufﬁciently small concentration increments. After each cycle, the resulting Γ 1 vs. c 1 values are compared with the adsorption isotherm. If the values do not satisfy the isotherm simultaneously, the Γ 1 vs. c 1 pair is rejected and the iteration proceeds until the isotherm is satisﬁed within a certain error. A graphical method is described by Partyka et al. [25]. The bulk dilution term was very thoroughly analyzed by Zajac et al. [30]. For each titration step, the pseudo-differential molar enthalpy of displacement may be obtained from [27,30] ∆ 21 h 1 ⫽

∆ inj H ⫺ ∆ dil H ∆Γ 1

(4)

where ∆Γ1 is the change in the amount adsorbed during the given titration step. If the succeeding enthalpy differences ∆ inj H ⫺ ∆ dil H are summed in the concen-

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tration range of interest, the cumulative (or integral) enthalpy isotherm of displacement, ∆ 21 H vs. c 1, is obtained. Titration calorimetry allows a number of successive heat determinations in a single experiment using the same solid sample. The method is particularly well suited to follow adsorption phenomena on ﬁne particles (typical colloids). In the case of suspensions, stirring is of crucial importance. The problem of ﬁnding a compromise between sufﬁcient mixing and minimum mechanical heat evolution was recently solved by employing a magnet-driven propeller with a rapid–slow reciprocating motion [9,16,24–26] or a circular horizontal disk moving up and down at low frequency [27]. The accuracy of titration calorimetry may be seriously affected by the change in the rheological properties of the suspension upon adsorption. Aggregation–disaggregation and change in viscosity may cause changes in the thermal power dissipated by constant-rate stirring. There are other disadvantages of the titration method. The heat of dilution (correction term) may be comparable in magnitude with the corresponding heat relating to the adsorption process. Further, the evaluation of raw data requires the adsorption isotherm, which must be determined in a separate experiment. Titration microcalorimetry is unsuitable (or less suitable) for following desorption phenomena because only a limited concentration range can be covered by back-titration with the solvent. The adsorption of ionic surfactants on charged surfaces in a static system may give rise to a drift of the solution pH or salinity [31]. This effect may be inﬂuenced by the liquid-to-solid ratio, which increases continuously as the titration proceeds. In contrast, the equilibrium pH and salinity can readily be held constant by using the method of ﬂow frontal analysis [31]. In any case, to obtain reliable differential enthalpy data, adsorption and calorimetric measurements should be performed under identical, or at least very similar, experimental conditions.

E. Flow Sorption Microcalorimetry The experimental protocol of ﬂow sorption microcalorimetry is closely related to that of ﬂow frontal analysis solid/liquid chromatography applied at low pressure [10,12,32–36]. The sorption vessel (a small chromatographic column) is loaded with the solid material (typically 0.05–0.4 g) and placed inside the measuring block of the calorimeter. Initially, pure solvent (water) is percolated through the column (by using a micropump) until thermal equilibrium is reached. The liquid ﬂow is then switched to that of a dilute surfactant solution in continuous operation. As the new solution enters the column, surface-bound water molecules are displaced by adsorbing surfactant molecules until the new equilibrium state is established. The replacement experiment is successively repeated up to the desired concentration (say, slightly beyond the cmc) by using small concentration increments, and the associated heat effects ∆ dis H are recorded for each step. Typi-

Surfactants at Solid/Solution Interfaces

347

cally, the cmc is reached in 10–20 concentration steps. One of the major advantages of ﬂow sorption microcalorimetry over the other methods is that the exit port of the calorimeter can be connected to a suitable analytical device (spectrophotometer or differential refractometer) for the continuous monitoring of surfactant concentration. A fully automated measuring system designed for simultaneous measurements of the material balance and the enthalpy balance of adsorption is shown in Fig. 5 [35]. Typical instrumental response curves (calorimeter signals and refractive index detector signals) are illustrated in Fig. 6. From the concentration waves (breakthrough curves), the retention volumes and hence ∆Γl , the amounts successively adsorbed on the same solid sample, can be calculated [37–39]: ∆Γl ⫽

Q v ∆c 1 t CR ⫽ CR ∆c1 ma s ma s

(5)

where Q is the (constant) ﬂow rate, ma s is the surface area of the solid in the column, ∆c 1 is the concentration difference for the step c′1 → c″1 , t CR is the corrected retention time (t R ⫺ t D, the retention time minus the dead time), and v CR is the corrected retention volume (v R ⫺ v D, the retention volume minus the dead volume). It should be noted that the Γ l terms in Eq. (3) (static system) and Eq. (5) (dynamic system) are completely equivalent [37]. Strictly speaking, Γ l is the

FIG. 5 Apparatus for ﬂow sorption microcalorimetry simultaneously with ﬂow frontal analysis solid/liquid chromatography. L1–L6, solutions; D1, D2, degassers; 7PV, electric seven-port valve; PC1, PC2, personal computers; MP, HPLC micropump; PR, pressure regulator; 6WV, six-way valve; L, loop; T1, T2, thermostats; TAM, microcalorimeter; COL, column; RID, refractive index detector; SC, RID sample cell; RC, RID reference cell; A, ampliﬁer; FM, ﬂowmeter; W, waste. (Adapted from Ref. 35.)

348

Kira´ly

FIG. 6 Instrumental response curves (calorimeter signals and refractive index detector signals) of the step-by-step displacement of water (2) by n-octyltrimethylammonium bromide (1) on Vulcan 3G graphitized carbon black at 298.15 K. The adsorption path is followed by the desorption path. The concentration increments are indicated in the ﬁgure in mmol/dm 3.

volume-reduced surface excess concentration Γ (v) 1 , which in dilute solutions and for preferential adsorption of the solute over the solvent becomes equal to the real amount adsorbed, Γ 1s [13]. Although the breakthrough curves closely mimic the concentration proﬁle, an exact correction for the dilution effect in the liquid ﬂow experiment is less straightforward than in a batch experiment [11,14]. However, in dilute solutions and for closely spaced concentrations, the heat of mixing at the interface between replacing and replaced solutions can be neglected to a fairly good approximation

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349

[11,14]. The blank experiments required for this correction can be performed by using glass pearls [34] or Teﬂon powder [40], which are inert solids with small speciﬁc surface areas, as the column packing materials. If the step-by-step displacement enthalpies and the amounts adsorbed are collected after k ⫽ 1, . . ., K steps and the cumulative data are gathered, the integral enthalpy isotherm of displacement, ∑ k ∆ dis H k ⫽ ∆ 21 H vs. c l and the adsorption isotherm ∑ k ∆Γ 1,k ⫽ Γ 1 vs. c 1 are obtained. Alternatively, the measured heat can be divided by the amount adsorbed for each step: ∆ 21 h 1 ⫽

∆(∆ 21 H ) ∆Γ 1

(6)

where ∆(∆ 21 H ) ⫽ ∆ dis H. The pseudo-differential molar enthalpies of displacement ∆ 21 h 1 obtained in this way are essentially free of systematic errors. Systematic errors in the calculation of ∆ 21 h 1 may arise from a combination of separately measured enthalpy and adsorption isotherms. A further advantage of ﬂow sorption microcalorimetry is that the reversibility of the adsorption process can be readily checked by using successive concentration steps in the opposite direction (desorption path). Repeated one-step adsorption/one-step desorption jumps, i.e., starting from and returning to the solvent for each step, offer an alternative to the step-by-step method [41]. In general, the ﬂow sorption calorimetric assembly requires a stable, constant ﬂow rate (about 10 cm 3 /h) and essentially zero pressure drop along the column. Flow resistance variation through the sample bed limits the performance of the method. Therefore, coarse particles (ⱖ40 µm) are mainly used as the column packing material. Fine particles may pass through or block the ﬁlter of the column. A sorption vessel has been designed that is claimed to yield good baseline stability even at high pressure (up to 100 bar) and elevated ﬂow rates [42]. Application of this HPLC calorimeter vessel may offer new perspectives in sorption calorimetric studies. Since the chromatographic effect (retention) plays a dominant role in ﬂow sorption microcalorimetry, Eq. (5) can be advantageously used to estimate what systems can be studied and under what experimental conditions (mass of the solid, ﬂow rate, and concentration increments). This aspect is particularly important in the case of surfactants with low cmc values, because the retention time for a small concentration step can be unreasonably high (1 day or even more) for an ill-designed experiment.

F.

Noncalorimetric Enthalpies of Displacement

The differential molar enthalpy of displacement can be approximated by the isosteric heat of adsorption, ∆ st h 1 . This indirect (noncalorimetric) method is based on measurement of the adsorption isotherms at neighboring temperatures. For

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350

adsorption from dilute solutions, where the solvent may be regarded as in the pure state in the liquid phase, the Clausius–Clapeyron equation reads [11,43,44] ∆ 21 h 1 ⫽ ⫺RT 2

冢

∂ ln c 1 ∂T

冣

⫽ ∆ st h 1

(7)

p, Γ 1 , Γ 2 , pH, salinity

This approximation should be applied with reservation for several reasons. Among others, the activity coefﬁcient of the solute may change with temperature, even at inﬁnite dilution; the only quantity (Γ 1 ) that can be experimentally determined may be insufﬁcient to specify the surface composition (little is known about Γ 2), so Γ 1 /Γ 2 may not be independent of temperature; and the nature and number of the active sites of the adsorbent, hydration of the solid surface and hydration of the surfactant molecules may also be sensitive to temperature variations. In any case, a direct calorimetric experiment is always safer.

IV.

LITERATURE SURVEY ON CALORIMETRIC STUDIES OF SURFACTANT ADSORPTION ON SOLID SUBSTRATES

The adsorption of surfactants on solid surfaces takes place in essentially two distinct stages. In the ﬁrst stage, at low concentrations, surfactant molecules adsorb in direct contact with the solid surface via either Coulombic attraction, hydrogen bonding, or van der Waals forces. In the second stage, at higher concentrations, these adsorbate molecules induce surface aggregation at the ‘‘critical surface aggragate concentration’’ (csac ⬍ cmc), and the cooperative adsorption levels off near the cmc. A variety of surface aggregate structures may exist, such as globular micelles, full bilayers, patchy bilayers, half-cylindrical aggregates, or even full cylinders [45–48]. For illustration, our recent results on the adsorption of a nonionic surfactant (N, N-dimethyldecylamine-N-oxide) on hydrophilic (CPG silica glass) and hydrophobic (Vulcan 3G graphitized carbon black) surfaces are displayed in Fig. 7. The corresponding integral enthalpy isotherms of displacement are given in Fig. 8 [36]. On the hydrophilic surface of CPG silica, weakly adsorbed surfactant molecules at low concentrations induce surface aggregation at higher concentrations as the cmc in the bulk solution is approached (S-type isotherm). In contrast with the hydrophilic substrate, the hydrophobic surface of V3G strongly adsorbs surfactants at high dilutions in water. The adsorption proceeds further with increasing concentration until it turns to a plateau value (LS-type isotherm). The differential enthalpies of displacement ∆ 21 h 1 ⫽ ∆(∆ 21 H )/∆Γ 1 are plotted in Fig. 9 as a function of surface coverage Γ 1 (upper graph) and of solution concentration c 1 (lower graph) [36]. It is seen from the ﬁgure that the differential molar enthalpy functions undergo dramatic changes at the csac; the functions turn from an exo-

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FIG. 7 Adsorption isotherms of N,N-dimethyldecylamine-N-oxide from aqueous solutions on CPG silica glass (䊊) and Vulcan 3G graphitized carbon black (䊐) at 298.15 K.

FIG. 8 Cumulative enthalpy isotherms of displacement of water by N,N-dimethyldecylamine-N-oxide onto CPG silica glass (䊊) and Vulcan 3G graphitized carbon black (䊐) at 298.15 K.

352

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FIG. 9 Differential molar enthalpies of displacement of water by N,N-dimethyldecylamine-N-oxide on CPG silica glass (䊊) and Vulcan 3G graphitized carbon black (䊐) at 298.15 K.

thermic to an endothermic direction. It is interesting to note that the points indicated in the ﬁgure are raw experimental data, obtained directly from simultaneous adsorption and calorimetric measurements, and were not calculated from smoothed curves. The enthalpies of surface aggregate formation are 9.2 kJ/mol on CPG and 9.0 to 3.5 kJ/mol on V3G, which are close to the corresponding enthalpy of micelle formation in the bulk solution, ∆ mic h ⫽ 9.6 kJ/mol [36]. The close agreement is calorimetric evidence that the driving force of surface

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353

TABLE 1 Literature Relating to Calorimetric Studies of Surfactant Adsorption on Solid Substrates Surfactant Alkyl polyoxyethylenes Alkylbenzene polyoxyethylenes

Alkylsulﬁnylalkanols n-Octyl β-d-monoglucoside N,NDimethyldecylamineN-oxide n-Decylmethylsulfoxide Alkyltrimethylammonium halides

Alkylpyridinium chlorides

Alkylbenzyldimethylammonium bromides Tetrabutylammonium nitrate Aerosol OT

Adsorbent

Reference

Silica (gel) Graphitized carbon black Silica (gel) Quartz Alumina Titanium dioxide Tin dioxide Sandstone Kaolin Bentonite Activated carbon Reverse phase silica gel Graphitized carbon black Silica glass Graphitized carbon black

41, 19, 18, 18, 59 59 59 24 24, 58 25, 33, 63 36, 36

50–52, 64 20, 51, 53, 54 25, 28, 31–33, 55–60, 62 31

Silica glass Graphitized carbon black Carbon black

36, 64, this work 36, this work 65,a 66 a

Silica (gel) Graphitized carbon black Reverse-phase silica gel Kaolinite Na-, Fe-, Al-montmorillonite Bentonite, illite Bentonite, hectorite Silica (gel)

26, 28, 33, 58, 60, 67, 68 35 33, 58, 60 43,a 69, 70 a 71, 72 70a 73 44,a 52, 59, 74, 75

Alumina Titanium dioxide Tin dioxide Kaolinite Sepiolite Bentonite, illite Silica Quartz Bentonite, hectorite Silver iodide

59, 74 59, 74 59, 74 27, 43,a 69, 70a 75 70 a 76 77 73 43 a

Silica (gel), alumina, Reverse-phase silica gel

33, 58 58

61 62 58, 60 41, 64

Kira´ly

354 TABLE 1 Continued Surfactant Aerosol OT (from toluene) Sodium alkylsulfates

Sodium hexanoate Sodium oleate Sodium alkylbenzenesulfonates

Sodium alkylxylenesulfonates Zwitterionics (betaines) a

Adsorbent

Reference

Silica (gel), alumina, Reverse-phase silica gel Silica (gel) Reverse-phase silica gel Scheelite, calcite Alumina Zirconium dioxide Graphitized carbon black Graphitized carbon black Scheelite, calcite Sandstone Kaolin Alumina Activated carbon Zirconium dioxide Alumina

33, 58 33, 33, 22 26 77 20 78 22 24, 24 61, 62 77 23

58

Silica (gel)

28, 30, 79

58 58

34, 61 62

Isosteric heats.

aggregation is similar in nature to the driving force of aggregate formation in the bulk solution, predominantly attributed to entropically driven hydrophobic interactions. Obviously, the structure of the surface aggregates in a particular interfacial environment must be in some respect distorted in comparison with that in the bulk solution; this is reﬂected by the difference between the corresponding enthalpies of aggregate formation. A review providing insight into the contribution of calorimetry to the revelation of surfactant adsorption phenonomena will be published shortly [49]. Table 1 provides a list of references to the particular systems studied so far.

ACKNOWLEDGMENT I thank the Alexander von Humboldt Foundation for a research fellowship at the Technical University of Berlin and the Hungarian Scientiﬁc Foundation (grant OTKA T025002) for ﬁnancial support.

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2. E Calvet, H Prat, HA Skinner. Recent Progress in Microcalorimetry, Pergamon Press, Oxford, UK, 1963. 3. JJ Christensen, JW Gardner, D Eatough, RM Izatt, PJ Watts, RM Hart. Rev Sci Instrum 44:481–484 (1973). 4. RM Izatt, EH Redd, JJ Christensen. Thermochim Acta 64:355–372 (1983). 5. T Wiseman, S Williston, JF Brandts, LN Lin. Anal Biochem 179:131–137 (1989). 6. J Suurkuusk, I Wadso¨. Chem Scripta 20:155–163 (1982). 7. MG Nordmark, J Laynez, A Scho¨n, J Suurkuusk, I Wadso¨. J Biochem Biophys Methods 10:187–201 (1984). 8. I Wadso¨. Thermochim Acta 85:245–250 (1985). 9. J Rouquerol. Pure Appl Chem 57:69–77 (1985). 10. GH Findenegg. Calorim Anal Therm 16:1–11 (1985). 11. R Denoyel, F Rouquerol, J Rouquerol. J Colloid Interface Sci 136:375–384 (1990). 12. Z Kira´ly, I De´ka´ny, E Klumpp, H Lewandowski, HD Narres, MJ Schwuger. Langmuir 12:423–430 (1996). 13. Z Kira´ly, I De´ka´ny. Colloid Polym Sci 266:663–671 (1988). 14. GW Woodbury Jr, LA Noll. Colloid Surf 28:233–245 (1987). 15. S Partyka, F Rouquerol, J Rouquerol. J Colloid Interface Sci 68:21–31 (1979). 16. J Rouquerol, Thermochim Acta 96:377–390 (1985). 17. DH Everett, AG Langdon, P Maher. J Chem Thermodyn 16:981–992 (1984). 18. R Denoyel, F Rouquerol, J Rouquerol. In: Proceedings of the 2nd Engineering Foundation Conference on Fundamentals of Adsorption, (AI Liapis, ed.), Am Inst Chem Eng, New York; 1987, pp. 199–210. 19. MJ Hey, JW MacTaggart, CH Rochester. J Chem Soc Faraday Trans 1 80:699–707 (1984). 20. A Gellan, CH Rochester. J Chem Soc Faraday Trans 1 81:1503–1512 (1985). 21. G Della-Gatta. Thermochim Acta 96:349–363 (1985). 22. W von Rybinsky, MJ Schwuger. Ber Bunsenges Phys Chem 88:1148–1152 (1984). 23. A Sivakumar, P Somasundaran, S Thach. J Colloid Interface Sci 159:481–485 (1993). 24. J Rouquerol, S Partyka. J Chem Biotechnol 31:584–592 (1981). 25. S Partyka, M Lindheimer, S Zaini, E Keh, B Brun. Langmuir 2:101–105 (1986). 26. S Partyka, E Keh, M Lindheimer, A Groszek. Colloid Surf 37:309–318 (1989). 27. T Mehrian, A de Keizer, AJ Korteweg, J Lyklema. Colloid Surf 73:133–143 (1993). 28. S Partyka, M Lindheimer, B Faucompre. Colloid Surf 76:267–281 (1993). 29. DH Everett. Pure Appl Chem 58:967–984 (1986). 30. J Zajac, C Chorro, M Lindheimer, S Partyka. Langmuir 13:1486–1495 (1997). 31. R Denoyel, J Rouquerol. J Colloid Interface Sci 143:555–571 (1991). 32. R Denoyel, F Rouquerol, J Rouquerol. In: Adsorption from Solution (RH Ottewill, CH Rochester, AL Smith, eds.), Academic Press, London, 1983, pp. 225–234. 33. LA Noll. Calorim Anal Therm 16:12–19 (1985). 34. NM van Os, G Haandrikman. Langmuir 3:1051–1056 (1987). 35. Z Kira´ly, GH Findenegg. J Phys Chem 102:1203–1211 (1998). 36. Z Kira´ly, GH Findenegg. Langmuir (2000, in press). 37. HL Wang, JL Duda, CJ Radke. J Colloid Interface Sci 66:153–165 (1978). 38. CS Koch, F Ko¨ster, GH Findenegg. J Chromatogr 406:257–269 (1987).

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10 Microcalorimetric Control of Liquid Sorption on Hydrophilic/Hydrophobic Surfaces in Nonaqueous Dispersions ´ NY Department of Colloid Chemistry, University of Szeged, IMRE DE´KA Szeged, Hungary I. Introduction II.

Adsorption and Heat of Immersion on Solids in Pure Liquids and Binary Liquid Mixtures A. Heat of immersion at solid/liquid interfaces B. Adsorption of binary liquid mixtures on dispersed solid particles C. Combination of adsorption excess isotherms and enthalpy isotherms: new way to determine adsorption capacity D. Adsorption excess and enthalpy isotherms on solids in binary liquids E. Classiﬁcation of enthalpy isotherms

III. Heat of Immersion on Hydrophilic and Hydrophobic Colloidal Particles in Different Liquid Mixtures A. Heat of Wetting in amorphous silica dispersion and on zeolites B. Immersional wetting on nonswelling clay minerals C. Heat of wetting on swelling clay minerals D. Adsorption of n-butanol from water on modiﬁed silicate surfaces IV. Properties of the Adsorption Layer and Stability of Aerosil Dispersions in Binary Liquids A. Inﬂuence of the adsorption layer on the aggregation of aerosil dispersions in binary liquids B. Characterization of the stability of nonaqueous dispersions by calorimetric and adsorption measurements

358 359 359 362 365 367 375 377 377 380 386 392 397 398 401 357

De´ka´ny

358

V. Small-Angle X-Ray Scattering of SiO2 Particles in Binary Liquids References

408 409

I. INTRODUCTION The stabilization of colloidal disperse systems in various liquids is primarily inﬂuenced by the difference between the polarities of the solid particles and the liquid. Thus, metal oxides may be dispersed in aqueous media to form stable hydrosols or in alcohols to produce stable alcosols [1]. Stable dispersions are also obtained in the same way in organic media if the polarity of the surface is altered, i.e., hydrophobized by long alkyl chains, resulting in the establishment of stable organosols or suspensions [2–6]. The determinative factor is the magnitude of the interparticle interaction potential, which can be calculated on the basis of Hamaker constants [7]. The equations describing interaction potential, thus allowing the calculation of interparticle interactions, were formulated by Vold [3] and Vincent [5]. Interparticle interactions and consequently the stability of disperse systems may also be adequately characterized by the properties of the sorption layer formed on the surface of solid particles. When a solid particle is immersed in a liquid and is readily wetted, an exothermic heat of immersion is liberated due to the strong solid–liquid interaction. The reason for this is presumably the formation of an adsorption layer several molecules thick on the surface of the particles. If the particles are well wetted by the given liquid, there is a good chance of obtaining a stable disperse system. If the adsorption interaction between particle and liquid is weak, the heat of wetting is small and the dispersion is unstable because interparticle adhesion forces are larger. Thus, on the basis of the observations mentioned, the stability of a disperse system in a nonelectrolyte (e.g., in an aromatic or aliphatic liquid) is determined by the relationship between wetting and adhesion. According to these observations, the solid–liquid interaction can be quantitatively characterized by the magnitude of the heat of immersion in pure liquids or in mixtures and solutions [8–11]. Further information is obtained if the amount of liquid adsorbed on the surface of the particle is also determined, permitting the combination of the data on heat of immersion with those on the amount of adsorbed liquid. Thus, molar adsorption enthalpies can be given for the characterization of the stabilizing adsorption layer [12–16]. A further beneﬁt of adsorption excess isotherms is that it is possible to calculate from them the free enthalpy of adsorption as a function of composition. When these data are combined with the results of calorimetric measurements, the entropy change associated with adsorption can also be calculated on the basis of the second law of thermodynamics. Thus, the combination of these two techniques makes possible the calculation of the thermodynamic potential functions describing adsorption [14,17–19].

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359

The monitoring of interparticle interactions in disperse systems is very important. One of the simplest methods to achieve this is through the determination of the rheological characteristics of the system, because this property is highly dependent on interparticle adhesion [20–27]. Modern physical methods such as light scattering, small-angle X-ray scattering (SAXS), or small-angle neutron scattering (SANS) obviously yield new information on the structure of disperse systems and the interparticle interactions operative therein [28–30]. On the other hand, direct interparticle interactions in a given liquid or solution may also be determined by surface force microscopy [31–34]. In this chapter, solid–liquid interactions and interparticle interactions are described not only for pure liquids but also for binary mixtures. The reason for this is that in the individual pure liquids, conditions of sorption and wetting are determined by the chemical nature of the components, and it is not easy to systematically vary them (e.g., to change the polarity of the medium). If, however, these pure liquids are combined to yield binary mixtures, the polarity of the medium can be adjusted at will and can be arbitrarily chosen within the limits set by the polarities of the two liquid components. Heat of wetting and consequently the stability of the dispersion can be regulated in a similar way in nonelectrolytes by varying the composition of the mixture so that conditions of sorption and wetting within the limits of miscibility can be adjusted [35–38]. Thus, parallel analysis of adsorption and wetting makes possible a many-sided approach to the stability of disperse systems. Given the knowledge of Hamaker constants, interaction potential functions can be calculated, yielding quantitative data on interparticle interactions. However, calculations of interaction potentials are affected by the composition and thickness of the adsorption layer on the surface of the particles. Quantitative information on the adsorption layer makes possible an even more precise calculation of these interactions [29–39].

II.

ADSORPTION AND HEAT OF IMMERSION ON SOLIDS IN PURE LIQUIDS AND BINARY LIQUID MIXTURES

A. Heat of Immersion at Solid/Liquid Interfaces A simple and straightforward way for quantifying the solid–liquid interfacial interaction is immersion microcalorimetry. In the course of this measurement, the surface previously heat-treated in vacuo is brought into contact with the pure wetting liquid [8,9,40]. It is advisable to choose a liquid of different polarity, so that the extent of the hydrophobicity or hydrophilicity of the surface can be estimated from the magnitude of the heat of wetting. Thus, the wetting a hydrophilic surface with a polar liquid liberates a large exothermic enthalpy of wetting, and

360

De´ka´ny

FIG. 1 Schematic picture of immersional wetting (solid/gas into solid/liquid) in pure liquids.

wetting a hydrophobic surface with a polar liquid produces a smaller heat effect (Fig. 1). When a solid adsorbent is immersed in a binary mixture, the heat of wetting is greatly affected by the composition of the bulk phase, and values intermediate between the heat effects of wetting ∆ w H 02 and ∆ w H 01, measured in the pure components 2 and 1, respectively, are obtained. This is the so-called immersion technique, which supplies direct information on the strength of the solid–liquid interaction with the mixture (Fig. 2) [41–44]. When ∆n 1 moles of component 1 of the binary mixture is added to the suspension made up in the liquid mixture with molar amount n ⫽ n 1 ⫹ n 2 (i.e., to the solid/liquid interface), the original composition x 1 is changed to x*1 and consequently the composition of the interfacial layer is shifted by the value ∆x 1s ⫽ x 1s* ⫺ x 1s . The amount of adsorbed material present in the interfacial layer is therefore n s* ⫽ n s1* ⫹ n 2s*, where n 1s* and n 2s* are the material contents of the adsorption layer of components 1 and 2, respectively. The changes in composition in the bulk phase (∆x 1) and in the interfacial phase (∆x 1s ) bring about a change in the so-called enthalpy of displacement, ∆ 21 H, which is the difference between the heats of wetting characteristic of the two states with different compositions (Fig. 3). When the change in composition is started from component 2 (∆ w H 02), increasing x 1 in the direction x 1 → 1, the isotherm of enthalpy of displacement ∆ 21 H ⫽ f(x 1) is obtained (Fig. 4) [12–14].

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FIG. 2 Schematic picture of immersional wetting (S/G into S/L) in binary liquid mixtures. n o and x 01 are the liquid material amount and mixture molar fraction, respectively, in the initial state. In equilibrium state: liquid material amount n, mixture molar fraction x 1, surface layer amount n s .

FIG. 3 Schematic picture of the heat evolution (enthalpy of displacement ∆ 21 H ) in the solid/liquid adsorption layer. After adding component 1 (∆n 1) to the liquid mixture, the composition of the bulk and the adsorption layer will be exchanged (notation with *).

362

De´ka´ny

FIG. 4 Schematic representation of the enthalpy of displacement isotherm in binary mixtures in the case of U-shaped adsorption excess isotherms.

B. Adsorption of Binary Liquid Mixtures on Dispersed Solid Particles When solid particles are dispersed in liquid medium, solid–liquid interfacial interactions will cause the formation of an adsorption layer, the so-called lyosphere, on their surface. The material content of the adsorption layer is the adsorption capacity of the solid particle, which may be determined in binary mixtures if the adsorption excess isotherm is known [45–50]. Due to adsorption, the initial composition of the liquid mixture, x 01, changes to the equilibrium concentration x 1. This change, x 01 ⫺ x 1 ⫽ ∆x 1, can be determined by simple analytical methods. The relationship between the reduced adsorption excess amount calculated from the change in concentration, n σ(n) ⫽ n 0 (x 01 ⫺ x 1), and the material content of the 1 interfacial layer is given by the Ostwald–de Izaguirre equation [46–49]: n σ(n) ⫽ n 1s ⫺ n s x 1 ⫽ n s (x s1 ⫺ x 1) ⫽ f(x 1) 1

(1)

where n 0 is the total amount of liquid mixture in the disperse system, n 1s ⫹

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n s2 ⫽ n s is the material content of the adsorption layer, and x 1s ⫽ n 1s /n s is the composition of the interfacial layer. Given the knowledge of the adsorption excess isotherm n σ(n) ⫽ f(x 1), the so-called individual isotherms are given by the 1 equations [46–48]. n s1 ⫽

s r*n σ(n) ⫹ n 1,0 x1 1 x 1 ⫹ r*x 2

(2)

s n 1,0 x 2 ⫺ n σ(n) 1 x 1 ⫹ r*x 2

(3)

and n s2 ⫽

s where n 1,0 is the adsorption capacity relative to pure component 1 and r* ⫽ V m,2 /V m,1 is the ratio of the molar volumes of the components. In the case of Ushaped excess isotherms, adsorption capacity (n s1,0) can be determined from the linearized Everett–Schay function [49,50]. As soon as the adsorption capacity is s known, the volume of the layer is obtained from the equation V s ⫽ n 1,0 V m,1. The s volume fraction of the adsorption layer, φ 1 can be calculated from the data of excess isotherms by using the equation

φ 1s ⫽

1.

n 1s r*n σ(n) V ⫽ φ 1 ⫹ s 1 m, 1 s n 1, 0 V (x 1 ⫹ r*x 2)

(4)

Free Enthalpy of Wetting of the Solid/Liquid Interface and the Thickness of the Adsorption Layer

The free enthalpy of adsorption of solid/liquid interfaces can be calculated with the Gibbs equation [48–50] and knowledge of the isotherm n σ(n) ⫽ f (x 1): 1 ∆ 21 G ⫽ ⫺ RT

冮

a

n (n) 1 da 1 a 1⫽0 x 2 a 1 1

(5)

where a 1 ⫽ f 1 x 1 is the activity of component 1, which can be calculated with the help of the Redlich–Kister equations [51], given the knowledge of the solid– vapor equilibrium data. Different types of adsorption excess isotherms (U- and S-shaped functions) naturally yield different free enthalpy functions ∆ 21 G ⫽ f(x 1), the course of which is characteristic of the minimum energy of wetting at the solid/liquid interface, a parameter diagnostic of the stability of the disperse system. In calculations of stability for disperse systems, knowledge of the thickness of the stabilizing adsorption layer is highly important [36,39]. If the speciﬁc sur-

De´ka´ny

364

face area (a s) of the particles is known, then the thickness of the layer, t s ⫽ V s / a s, can be calculated from Eq. (4): t s ⫽ r*n 1σ(n)

冢冣冢 V m,1 asx1

φ1 φ ⫺ φ1 s 1

冣

(6)

where φ s1 and φ 1 are the volume fractions of the adsorption layer and bulk phase, respectively, in adsorption equilibrium. The layer thickness t s calculated according to Eq. (6) is nearly constant; in nonideal liquid mixtures, however, its value may be strongly dependent on the composition of the bulk phase [52,53].

2.

Enthalpy of Immersional Wetting in Binary Mixtures

According to Everett’s adsorption layer model [8,10,11,40], the heat of immersional wetting (∆ w H t), a thermodynamic parameter characteristic of the solid– liquid interaction, can be easily calculated when the molar enthalpies, h 1 and h 2, of the components of the system are known. When a solid adsorbent is immersed in a liquid mixture, the amount of which is n 01 ⫹ n 02, the interfacial forces of adsorption cause the formation of an adsorption layer on the surface of the adsorbent, the material content of which is n s ⫽ n s1 ⫹ n 2s . According to Everett [40,50], the change in enthalpy of wetting between the equilibrium and initial states (H e ⫺ H i ) is given by the equation ∆wHt ⫽ He ⫺ Hi ⫽ (n 1 ⫺ n 01) h 1 ⫹ (n 2 ⫺ n 02)h 2 ⫹ n 1s h 1s ⫹ n s2 h 2s ⫹ H se (x 1s ) ⫹ H e (x 1) ⫺ H e (x 01)

(7)

It is assumed in Eq. (7) that the enthalpy of the solid adsorbent is not altered by wetting. The introduction of molar fractions and the material balance n 0 (x 01 ⫺ x 1) ⫽ n s (x 1s ⫺ x 1) brings Eq. (8) to the form ∆ w H t ⫽ n s x s1 (h s1 ⫺ h 1) ⫹ n s x 2s (h 22 ⫺ h 2) ⫹ H se (x 1s ) ⫹ ∆H e (x 1)

(8a)

where ∆H e ⫽ H e (x 1) ⫺ H e (x 01) is the change in the enthalpy of mixing of the bulk phase. When ∆x 1 ⫽ x 01 ⫺ x 1 is known for a given liquid mixture, the function ∆H e (x 1) can be calculated from the functions of enthalpy of mixing described in the literature. If only the change in enthalpy relative to the adsorption layer is to be calculated, then the function ∆ w H t ⫽ f(x 1) has to be corrected by the function ∆H e ⫽ f(x 1). Introducing the volume fractions of the adsorbed layer and the heat of immersion of pure components, Eq. (8a) can be given as follows: ∆ w H t ⫺ ∆H e ⫽ φ 1s ∆ w H 01 ⫹ φ 2s ∆ w H 02 ⫹ H se (x 1s )

(8b)

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C. Combination of Adsorption Excess Isotherms and Enthalpy Isotherms: New Way to Determine Adsorption Capacity The adsorption of binary systems is described by the Ostwald–de Izaguirre equation, which establishes a relationship between the speciﬁc reduced adsorption excess amount (n 1σ(n)) and the material amount in the interfacial layer (n s ⫽ n s1 ⫹ n 2s ) [40–46]: n 1σ(n) ⫽ n 1s x 2 ⫺ n 2s x 1 ⫽ n s (x 1s ⫺ x 1)

(9)

The adsorption volume ﬁlled by the components of the mixture being adsorbed on a solid surface is V s ⫽ n 1s V m,1 ⫹ n s2 V m,2

(10)

In general,

冱n V s i

m,i

⫽ Vs

(11)

where V m,i is the partial molar volume of the components in the adsorption layer. Equation (11) is formally identical with the description of the so-called poreﬁlling model, but it is also applicable for planar nonporous adsorbents, because the thickness of the adsorption layer is determined solely by the range of the forces of adsorption. Thus, the adsorption volume V s designates the volume falling within the range of adsorption forces; in certain regions of the isotherm, its value may be nearly constant, but it may also be a function of equilibrium composition. If molecular sizes within the adsorption space are not identical, i.e., if r* ⫽ s V m,2 /V m,1 ≠ 1, and V s ⫽ n s1,0 V m,1, then Eq. (11) may also be formulated for n 1,0 : n s1,0 ⫽ n 1s ⫹ r*n s2

(12)

Equation (12) already incorporates the assumption that there exists a concentration range where the volume of the adsorption layer—on a constant surface area—is independent of the composition of the bulk phase. However, no statement can yet be made as to whether this layer is monomolecular or multilayered. If the behavior of the bulk liquid and interfacial layer is ideal, the φ1s ⫽ f(x 1 ) function can be calculated from calorimetric data by Eqs. (8b, or 18 and 19). In this case Eq. (4) may be rewritten as [14–16] n 1σ(n) n s1,0 (x 1 ⫺ r*x 2) ⫽ φ s1 ⫺ φ 1 r*

(13)

De´ka´ny

366 s s Since r* ⫽ n 1,0 /n 2,0 ,

n σ(n) 1 s s s ⫽ n 1,0 ⫹ (n 2,0 ⫺ n 1,0 ) x1 φ ⫺ φ1

(14)

s 1

The right-hand side of Eq. (14) is made up exclusively of terms consisting of s adsorption capacities. The intersection of the straight line is n 1,0 and the slope is s s s s n 2,0 ⫺ n 1,0. If r* ⫽ 1 and n 1,0 ⫽ n 2,0, then the second term of Eq. (14) is zero. Knowing the values of the integral exchange enthalpy, the adsorption capacity (n 1s ), and the molar adsorption enthalpy of the layer (h s1, h 2s ), a combination of Eqs. (1) and (8a) and the substitution n 1s ⫽ n 1σ(n) ⫹ n s x 1 (for an ideal adsorption layer and for the case ∆ 21 H se ⫽ 0) yield [14–16,37,38]

冤冢

hs hs ∆ 21 H ∆ w H ⫺ ∆ w H 02 ⫽ ⫽ h 1s ⫺ 2 ⫹ n s h 1s ⫺ 2 σ(n) σ(n) n1 n1 r* r*

冣冥冢冣 x1 n 1σ(n)

(15)

The ideal behavior of the adsorption layer also means that h 1s and h 2s are independent of the concentration of the mixture, a condition that is rarely met. It is apparent from arguments we present later, however, that molar differential exchange enthalpy is constant in a certain range of composition; our assumption therefore has to be accepted. Equation (15) is also a linear function, with intersection b ⫽ h 1s ⫺ h s2 /r* and slope S ⫽ n s (h s1 ⫺ h 2s /r*); i.e., the adsorption capacity is ns ⫽ S/b. Equation (15) was ﬁrst applied for the interpretation of ﬂow microcalorimetric measurements (on dilute solutions only) by Woodbury and Noll [12,13]. If the size of the moles s cules is uniform, n s ⫽ n 1,0 ⫽ n 2,0 , then the slope of Eq. (15) is given by the formula S ⫽ n s1,0 (h 1s ⫺ h s2 /r*) ⫽ ∆ 21 H total ⫽ ∆ w H 01 ⫺ ∆ w H 02

(16)

the slope of the equation yields the total exchange enthalpy of the adsorption displacement process. This value can also be directly determined by calorimetry. In the case of S-shaped excess isotherms, the value of the adsorption azeotropic composition x 1a is known. At the azeotropic point n 1σ(n) ⫽ 0; therefore, x 1 ⫽ x a1, according to Eq. (1). Since x s1 ⫽ n 1s /n s, the adsorption capacity n s can be divided into two terms with the help of the equations [14–16] n 1s ⫽ n s x a1,

n s2 ⫽ n s (1 ⫺ x a1)

(17a)

and s n 1,0 ⫽ n s x 1a ⫹ r*n s (1 ⫹ x 1a)

(17b)

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D. Adsorption Excess and Enthalpy Isotherms on Solids in Binary Liquids 1.

U-Shaped Excess Isotherms and Enthalpy Isotherms

Calculations regarding the composition of the adsorption layer and the determination of adsorption capacity and the heterogeneity of the surface have been discussed in several publications by Everett [40,50], Schay [47–49] Berger and De´ka´ny [52,53], and members of the Polish adsorption school [45,55–57]. The energetics of the exchange (displacement) process taking place in the adsorption layer have been the subject of considerably fewer publications, and these deal mostly with the adsorption of dilute solutions. The change in enthalpy accompanying the adsorption exchange process in organic media on apolar surfaces has been studied in detail by Denoyel et al. [17,18,42], Groszek [41], and Findenegg and coworkers [43,44]. Studies published by Allen and Patel [58] and by Woodbury and coworkers [12,13] include the simultaneous analysis of adsorption excesses and calorimetric data. Billett et al. [8] determined heats of immersion wetting in a system of benzene–cyclohexane/activated carbon in the entire range of mixing, parallel with the determination of adsorption excess isotherms. In this chapter we give a parallel analysis of the liquid sorption excess isotherms and adsorption exchange enthalpy isotherms of benzene–n-heptane and methanol–benzene mixtures on adsorbents with polar and apolar surfaces. Systems with U- or S-shaped excess isotherms were selected. Our aim is to examine the presence and character of a connection between adsorption excess and enthalpy isotherms for the various isotherm types [36]. The determination of enthalpy changes occurring in the course of ﬂow microcalorimetric measurements necessitates a simultaneous analysis of the material balance and enthalpy balance of adsorption. According to De´ka´ny et al. [14–16] and Kira´ly and De´ka´ny [59–61], these relationships, expounded according to either the adsorption layer model or the Gibbs model of adsorption excess amounts, are suitable for the exact determination of changes in exchange enthalpy observable in ﬂowing systems and for the correct interpretation of the sorption exchange process. Adsorption excess isotherms of benzene (1)–n-heptane (2) and methanol (1)– benzene (2) mixtures are shown in Figs. 5 and 6. Both isotherms are U-shaped, with the difference that in the methanol (1)–benzene (2) system methanol is preferentially adsorbed on silica gel. Pretreatment of silica gel by methanol was necessary to eliminate the effect associated with the chemisorption of methanol, so that data reﬂecting only physical adsorption would be measured [14,15]. In the case of benzene–n-heptane mixtures, the excess isotherm on silica gel has no linear region: Parallel with increasing the concentration of component 1 in the bulk phase, the composition of the interfacial layer changes continuously

368

De´ka´ny

FIG. 5 (a) Adsorption excess and (b) enthalpy of displacement isotherms in benzene (1)–n-heptane (2) mixture on silica gel (a s ⫽ 358 m/g).

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FIG. 6 (a) Adsorption excess and (b) enthalpy of displacement isotherms in methanol (1)–benzene (2) mixture on silica gel (a s ⫽ 358 m 2 /g).

De´ka´ny

370

TABLE 1 Results of Analysis of Adsorption Excess and Enthalpy Isotherms on Selected Porous Adsorbents n s1,0 (mmol/g) Adsorbent Silica gel Silica gel Silica gel C 18 Chemviron F400 Printex 300 a

a

Liquid mixture

S,N

Methanol–benzene Benzene–n-heptane Methanol–benzene Methanol–benzene Methanol–benzene

5.31 — 4.80 9.10 1.01

Eq. (15)

⫺∆ 21 H t (J/g)

⫺(h s1 ⫺ h s2 /r*) (kJ/mol)

5.14 2.02 4.10 10.41 1.00

36.71 11.30 9.50 ⫺10.52 ⫺1.23

7.10 5.60 4.00 5.31 ⫺0.50

SN: Schay–Nagy extrapolation method [46–49].

(Fig. 5a). This is well reﬂected by the enthalpy isotherm shown in Fig. 5b, which also indicates a gradual, step-by-step heat exchange and, correspondingly, a gradual process of displacement. Enthalpy changes accompanying the full exchange of the components (∆ 21 H t) are listed in Table 1. These data reveal that the full exchange of n-heptane for benzene on the surface of silica gel is an exothermic process and results in the liberation of ⫺11.3 J/g of heat. In the case of an exchange of molecules in the reverse direction, on the other hand (see the open circles in Fig. 5b), identical but endothermic heat effects are obtained. In the case of the methanol–benzene/silica gel system, adsorption occurs and about 89–90% of the total exchangeable heat (∆ 21 H t) is liberated at the initial section of the isotherms. In that range of composition where the excess isotherm of the methanol (1)–benzene (2) liquid pair is linear (Fig. 6a) (and here the composition of the interfacial layer is nearly constant), some heat effect of exchange is still observable (Fig. 6b). This means that the composition of the interfacial layer is still changing; these changes are too small to be adequately monitored by our analytical methods but are readily detected by calorimetry. This observation is a direct experimental proof for a theoretical statement by Rusanov that, strictly speaking, the composition of the interfacial layer may not be constant within the linear section of the isotherm [39]. The excess isotherm determined on the surface of graphitized carbon has an inverse U-shape, i.e., the adsorption excess for polar methanol is negative within the entire concentration range (Fig. 7a). Accordingly, when the amount of methanol in the mixture is increased from x 1 ⫽ 0 to x 1 ⫽ 1, the effects measured are always endothermic, because the displacement of benzene from the surface is an energy-consuming process (Fig. 7b).

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FIG. 7 (a) Adsorption excess and (b) enthalpy of displacement isotherms in methanol (1)–benzene (2) mixture on graphite (Printex 300) surface.

De´ka´ny

372

2.

S-Shaped Excess Isotherms and Enthalpy Isotherms

An excess isotherm determined in a methanol–benzene mixture on silica gel is U-shaped. If, however, the silica surface is modiﬁed by octadecyldimethylchlorosilane (silica gel C 18) in methanol–benzene mixtures, an S-shaped excess isotherm is obtained, the azeotropic point of which is x a1 ⫽ 0.615 (Fig. 8a). When the displacement process is started from benzene, it can be seen that up to a molar fraction of x 1 ⫽ 0.6 the incorporation of methanol into the adsorption layer results in a change in enthalpy of about 7.35 J/g. However, the displacement of benzene is not yet complete; up to the azeotropic point the adsorption layer will also contain benzene. A common characteristic of the two isotherms presented ⫽ f(x 1) is linear in a very wide range of composiin Fig. 8 is that the isotherm n σ(n) 1

FIG. 8 (a) Adsorption excess and (b) enthalpy of displacement isotherms in methanol (1)–benzene (2) mixture on hydrophobized silica gel (a s ⫽ 312 m 2 /g).

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373

tion (x 1 ⫽ 0.1–0.7), while the enthalpy isotherm ∆ 21 H ⫽ f(x 1) is approximately constant. In other words, within this range of composition, a very small exchange heat effect is produced; consequently the composition of the layer is not constant. The maximum value of the enthalpy isotherm is at the azeotropic composition; further heat effects are endothermic, and the integral enthalpy isotherm therefore exhibits a tendency to decrease. Endothermic effects occurring from x 1 ⫽ 0.6 to x 1 ⫽ 1 are associated with the displacement of benzene from the adsorption layer. The azeotropic composition of the excess isotherm determined on Chemviron (Union Carbide USA) activated carbon, an adsorbent with a large speciﬁc surface area, is x 1a ⫽ 0.095, indicating that the adsorption layer still contains a little methanol (Fig. 9). This methanol is bound to the polar regions of the surface of the adsorbent, as shown by the exothermic heat effect detectable from x 1 ⫽ 0 to x 1 ⫽ 0.1.

FIG. 9 (a) Adsorption excess and (b) enthalpy of displacement isotherms in methanol (1)–benzene (2) mixture on Chemviron F-400 active carbon.

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374

If x 1 ⬎ x 1a, the excess isotherm is practically linear between x 1 ⫽ 0.1 and 0.7, and the enthalpies of exchange measured are moderately endothermic. If the molar fraction of the bulk phase is larger than x 1 ⫽ 0.8, the displacement of benzene by methanol will preferentially occur, resulting in a considerable endothermic effect on the porous apolar surface. When adsorption displacement proceeds from x 1 ⫽ 1 toward x 1 ⫽ 0, the heat effects detected are of a reverse sign in the case of each isotherm. This means that the processes of displacement are reversible to a close approximation. A very little irreversibility was detected only in the case of activated carbon Chemviron, which is probably caused by incomplete displacement of methanol from the micropores by benzene.

3.

The Linearized Functions ∆ 21 H/n σ(n) ⫽ f (x 1 /n σ(n) 1 1 )

The applicability of Eq. (15) for U-shaped excess isotherms is next discussed. Functions ∆ 21 H/n 1σ(n) ⫽ f (x 1 /n σ(n) 1 ) for the case of U-shaped excess isotherms are

FIG. 10 Combination of the adsorption excess amounts and calorimetric data in (䊊) benzene (1)–n-heptane (2) mixture on silica gel (a s ⫽ 358 m 2 /g), and in methanol (1)– benzene (2) mixture on (䉭) silica gel (a s ⫽ 458 m 2 /g and (䊉) silica gel (a s ⫽ 358 m 2 /g).

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shown in Fig. 10. Adsorption capacities (n s) obtained in this representation as the ratio of the slope n s (h s1 ⫺ h s2 /r*) and the intersection (h 1s ⫺ h 2s /r*) are identical with the values mentioned above. The advantage of Eq. (15) is that the intersection yields the value of (h s1 ⫺ h 2s /r*), and this value is then multiplied by n sl, 0, yielding the calculated value of the total integral exchange enthalpy ∆ 21 H t , which can be compared with the experimentally determined value of ∆ 21 H t (Table 1). The interaction of adsorbents with various surface energies with the liquid components studied are adequately characterized by the differences in molar adsorption enthalpies between components 1 and 2, h s1 ⫺ (1/r*)h 2s , listed in Table 1. In the case of the adsorption of the methanol–benzene liquid pair, these enthalpy differences in the adsorption layer are decreased by the effect of hydrophobization.

E. Classiﬁcation of Enthalpy Isotherms* In the case of adsorption of ideal or quasi-ideal mixtures on adsorbents with polar or apolar surfaces, usually U-shaped excess isotherms are obtained (type I according to the Schay–Nagy classiﬁcation [46–49]. On adsorbents with polar surfaces, in the case of liquid pairs made up of components with a large difference in polarity (e.g., alcohol–benzene), the polar component is preferentially adsorbed on the surface (type II) and again U-shaped excess isotherms are obtained. Thus, in these systems the composition of the interfacial layer (φ s(**) or x 1s ) in1 creases monotonously as a function of equilibrium composition; consequently, according to Eq. (8b), the enthalpy isotherm ∆w H will also be a monotonously increasing function (Fig. 11a). When alcohol–benzene mixtures are adsorbed on adsorbents with low surface energies, S-shaped excess isotherms are measured [15,16,35–38]. When changes in enthalpy accompanying the adsorption displacement process are examined in these systems, the integral exchange enthalpy isotherms usually do not increase monotonously but possess a backward section. After having reached adsorption azeotropic composition, changes in concentration (∆x 1) are accompanied by endothermic heat effects of exchange, and these changes do not follow changes in the composition of the surface layer (Fig. 11b.). For S-shaped excess isotherms (Schay–Nagy types IV and V [46–49]), φ 1s is nearly constant in a relatively wide concentration range, and at ⫽ 0, φ s1 ⫽ φ 1a ⫽ φ 1 , i.e., adsorption azeotropic composition, appears. In this n σ(n) 1 case the value of ∆ w H changes very little in the middle section of the enthalpy isotherm, where φ 1s is constant; then at the azeotropic composition a maximum * See also Refs. 14–16 and 35. ** Notation of the interfacial layer volume fraction is φ s1 , calculated from calorimetric data (see Eqs. 18, 19). This is identical with φ s1, calculated from the excess isotherm.

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FIG. 11 Classiﬁcation of immersional wetting enthalpy isotherms: (a) U-shaped excess isotherm, with corresponding enthalpy of immersion isotherm. (b) S-shaped excess isotherm, with corresponding enthalpy of immersion isotherm.

is observed (∆ w H a). Thus, in the case of S-shaped excess isotherms, integral enthalpy isotherms ∆ 21 H ⫽ f(x 1) have to be divided into two sections at the azeotropic composition φ 1a; 1.

From x 1 ⫽ 0 to x 1 ⫽ x 1a, ∆ 21 H ⫽ (φ 1s ∆ 21 H a)/φ a1

2.

(18)

This section is essentially a version of the total measurable section of Ushaped isotherms, shortened in proportion with φ 1a. From x 1 ⫽ x 1a to x 1 ⫽ 1, the displacement factor can be calculated by the formula

Liquid on Surfaces in Nonaqueous Dispersions

∆ 21 H a ⫺ ∆ 21 H total ⫽ (∆ 21 H a ⫺ ∆ 21 H ) (1 ⫺ φ a1) ⫹ (∆ 21 H a ⫺ ∆ 21 H total)φ 1s

377

(19)

Division of the enthalpy isotherms into two sections can be considered justiﬁed only if the adsorption layer is ideal in the vicinity of azeotropic composition, i.e., ∆ 21 H se ⫽ 0. Displacement enthalpy isotherms calculated according to Eqs. (18) and (19) change parallel with the isotherms φ 1s ⫽ f(x 1) calculated from adsorption measurements [14–16, and 35].

III. HEAT OF IMMERSION ON HYDROPHILIC AND HYDROPHOBIC COLLOIDAL PARTICLES IN DIFFERENT LIQUID MIXTURES Adsorption excess isotherms were determined on hydrophilic and partially hydrophobic layered silicates in methanol–benzene mixtures [62–65]. From these isotherms the free energy of adsorption ∆ 21 G ⫽ f(x 1) that is characteristic of surface polarity is derived [60–62]. Displacement enthalpy isotherms were also determined by immersion microcalorimetry so that the entropy changes could be calculated. The preferential adsorption on adsorbents with different surface hydrophobicities can be properly described by the thermodynamic data of the adsorbed layer [66–69]. When the components in a binary mixture are very different in polarity, as they are in methanol–benzene mixtures, the polarity of the surface can be characterized from the shape of the excess isotherms and the azeotropic composition. The free energy function ∆ 21 G ⫽ f(x 1) calculated from the excess isotherms gives quantitative information about the decrease in free energy due to the displacement [see Eq. (5)], the integral enthalpy isotherms can be determined with microcalorimetry, and the thermodynamic description of the adsorption layer is complete [67–69]. According to Regdon et al. [70,71] and Marosi et al. [72], the displacement enthalpy data give information about the solid–liquid interaction, and the second main law of thermodynamics allows the calculation of the displacement entropy functions. The combination of displacement free energy and enthalpy functions with the excess isotherms gives a new way to determine the adsorption capacities [Eq. (15)]. This combination also gives data (∆ 21 g, ∆ 21 h) that describe the polarity of a surface in a certain liquid mixture [73,74].

A. Heat of Wetting in Amorphous Silica Dispersion and on Zeolites Hydrophilic (A 200) and hydrophobic (R 972) varieties of amorphous SiO 2 (Aerosil derivatives, Degussa AG, Germany) were studied by immersion microcalorimetry in various liquids (methanol, benzene, n-heptane), and the results are listed in Table 2. Clearly, the heat of immersion on the hydrophilic surface (A 200) is

a

40.05 25.7 19.7 25.5

Methanol 19.4 33.8 38.2 33.0

Benzene

⫺∆ w H (J/g)

Aerosil powders were pretreated with methanol before the immersion experiment.

231 120 228 123

a s (BET) (m 2 /g) 8.5 15.1 16.5 17.8

n-Heptane 175 214 86 207

Methanol

84 281 167 268

Benzene

∆ w h (mJ/m 2)

Heat of Wetting on Hydrophilic (A 200) and Hydrophobic (R 972) Aerosils in Selected Liquids

A 200 R 972 A 200/CH 3 OH a R 972/CH 3 OH a

Absorbent

TABLE 2

37 125 72 144

n-Heptane

378 De´ka´ny

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the largest in methanol, moderate in toluene, and the smallest in n-heptane. The heat effect measured in the aromatic solvent benzene is intermediate between the values for toluene and n-heptane. Heats of immersion per unit surface in millijoules per square meter are also given in Table 2 for the various liquids [63,64]. The effect of surface treatment is also easily detected by the determination of heats of immersion. When the surface of the hydrophilic Aerosil is treated with methanol, heats of immersion are changed considerably because SiEOH groups on the surface are replaced by SiEOECH 3 groups. It is revealed by the data in Table 2 that the BET surface is unchanged by methanol treatment; however, the change in enthalpy of wetting per unit surface area of A 200 is signiﬁcantly increased by surface treatment with methanol (surface methylation) in both benzene and n-heptane. The largest value for heat of wetting on the original hydrophilic SiO 2 surface (175 mJ/m 2) is measured in methanol; the heat effect is considerably smaller in benzene, and an effect due solely to dispersion interactions (37 mJ/m2) can be detected in n-heptane (Table 2). Further information on heat alteration of surface energy due to dealumination and on the depolarization of zeolite surfaces can be obtained by the determination of the heat of wetting [65]. The values determined in alcohols of various chain lengths, benzene, and n-heptane are listed in Table 3. The values of speciﬁc heats of immersion (∆ w H ) on Na-Y zeolite are very large in the alcohols; in benzene and n-heptane the wetting effect measured is less signiﬁcant. In each liquid, the values measured on the dealuminated sample are signiﬁcantly lower than those determined on Na-Y zeolite. It is clear from the data of Table 3 that on dealuminated samples the values of heat of wetting in benzene and in n-heptane are nearly identical and do not differ signiﬁcantly from the values measured in methanol and ethanol. In contrast, it can be seen that the effects measured on Na-Y samples in alcohols and benzene are signiﬁcantly higher than those determined in apolar n-heptane.

TABLE 3 Heat of Wetting on Hydrophilic (Na-Y)a and Hydrophobic (Dealuminated) Zeolites in Different Liquids Liquid

Na-Y zeolite, ⫺∆ w H (J/g)

Methanol Ethanol n-Propanol n-Butanol Benzene n-Heptane

214.0 196.5 190.6 175.0 129.5 73.4

a

⫾ ⫾ ⫾ ⫾ ⫾ ⫾

2.4 2.0 2.0 2.8 8.9 7.6

Dealuminated zeolite, ⫺∆ w H (J/g) 41.4 30.1 20.5 16.4 29.1 32.9

⫾ ⫾ ⫾ ⫾ ⫾ ⫾

8.5 8.7 6.7 9.7 6.5 7.6

Na-Y zeolite is a microporous hydrophilic aluminosilicate with high cationic exchange capacity.

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B. Immersional Wetting on Nonswelling Clay Minerals Clay minerals and their modiﬁed (organophilic) derivatives are usually readily dispersed in solvents or solvent mixtures of various polarities. The stability and structure building of these suspensions vary over a wide range, depending on the surface properties of disperse particles and the polarity of solvents. Illite, as a nonswelling mineral of layered structure, plays a very important role in our studies. This special role is due to the fact that both sides of the surface of the silicate lamellae are made up of SiO 4 tetrahedron planar lattices, and this structure— even when hydrophobized—is identical with the surface structures of montmorillonite and vermiculite, both of which are of the swelling type. The swelling clay minerals (e.g., montmorillonites) are of colloidal dimensions (d ⬍ 2 µm) and are therefore able to adsorb signiﬁcant amounts of various molecules, owing to their large speciﬁc surface area. It follows from the above-mentioned structural properties that sorption processes and adsorption capacity will be basically determined by whether the mineral studied is of the swelling or nonswelling type. Several papers on the liquid sorption properties of the hydrophobic clay minerals were published at our institute in Hungary [35–37,67–79]. The adsorption capacities for S-shaped excess isotherms determined on nonswelling illite derivatives were analyzed by using the Schay–Nagy extrapolation and the adsorption space-ﬁlling model. Figure 12 shows the excess isotherms for hydrophilic illite and three gradually organophilized hexadecylpyridinium (HDP) illites in methanol–benzene mixtures. The amount of methanol in the adsorption layer decreases with increasing coverage by HDP cations bonded on the illite surface [75–78]. The sorption exchange process taking place at the solid/liquid interface can be described in thermodynamically exact terms when the activities of the interfacial layer and those of the bulk phase are known. In accordance with the exchange equilibrium at the solid/liquid interface, (1) ⫹ r(2) s s (1) s ⫹ r(2)

(20)

the liquid sorption equilibrium constant is given by the formula K⫽

x s1 f 1s (x 2 f 2) r (x s2 f 2s ) r x 1 f 1

(21a)

Assuming that f 1s /f 2s ≅ 1, i.e., the activity coefﬁcients of the interfacial phase compensate for each other [71,73], K′ ⫽

x 1s (a 2) r (x 2s ) r a 1

(21b)

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FIG. 12 Adsorption excess isotherms on Na-illite and on HDP-illite derivatives in methanol (1)–benzene (2) mixtures. Na, sodium illite; 1, 2, 3, hexadecylpyridinium illites.

If the activity data of the bulk phase are known, the value of K′ can be calculated at a given value of r* ⫽ V m,2 /V m,1 by means of computer iteration [71,73]. The Redlich–Kister equation has proven perfectly reliable for calculating the activities; its application allows the calculation of the activity coefﬁcients of components 1 and 2, and, on this basis, functions a 1 ⫽ f(x 1) and a 2 ⫽ f (x 2) can be given [51]. The applicability of Eq. (21) is demonstrated in Fig. 13. It is revealed by the adsorption equilibrium diagrams that for the adsorption of a liquid pair made up of components signiﬁcantly different in polarity covered by alkyl chains, the value of the equilibrium constant K′ decreases with increasing hydrophobicity of the surface. The excess free energy functions given by integration of the excess isotherms, Eq. (5), reﬂect the extent of the hydrophobization (Fig. 14). Methanol displaces benzene with a maximum change in free energy on sodium illite. The displacement process results in smaller free energy changes on HDP-treated surfaces— the functions shown for the sample with maxima at the azeotropic compositions.

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FIG. 13 Adsorption equilibrium diagrams on solid/liquid interface in methanol–benzene mixtures at different equilibrium constants. K 1 ⫽ 10 3, K 2 ⫽ 10 2, K 3 ⫽ 10, K 4 ⫽ 1, K 5 ⫽ 10 ⫺1. Calculated with Eq. (21).

FIG. 14 Free enthalpy of adsorption on Na-illite and on HDP-illite and on HDP-illite derivatives in methanol (1)–benzene (2) mixtures. Na, sodium illite; 1,2,3 hexadecylpyridinium illites.

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FIG. 15 Immersional wetting enthalpy isotherms on Na-illite and on HDP-illite derivatives in methanol (1)–benzene (2) mixtures. Na; sodium illite; 1,2,3, hexadecylpyridinium illites.

The free energy function for the sample with maximum hydrophobicity changes sign, which means that the displacement of benzene by methanol is not favored. Illites and their organophilic derivatives can be well dispersed in methanol– benzene mixtures; therefore their wetting properties can be studied with batch microcalorimetry [78]. The solid–liquid interaction can be given as ∆ 21 H ⫽ ∆ w H ⫺ ∆ w H 02; its integral isotherm is plotted in Fig. 15. The immersion wetting enthalpy is appreciable on Na-illite. The majority of heat evolution is due to preferential adsorption of methanol (see Fig. 12). The enthalpy change decreases upon hydrophobization, and it becomes endothermic even in x 1 ⬎ 0.5 compositions. The application of Eq. (15) is more favorable, because it clariﬁes the difference between the molar adsorption enthalpies of components (Fig. 16). The parameters of Eq. (15) give the adsorption capacity and the molar wetting enthalpy change. These data show that the change in molar wetting data decreases with increasing hydrophobicity (Table 4).

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FIG. 16 Determination of the adsorption capacities from Eq. (15). 1, Na-illite; 2,3,4, HDP-illites; 5; Na-montmorillonite, all in methanol (1)–benzene (2) mixtures.

TABLE 4 Results of Analysis of Adsorption Excess and Enthalpy Isotherms on Selected Nonswelling Clays Adsorbent Na-kaolinite HDP-kaolinite a Na-illite HDP-illite 1 b HDP-illite 2 b HDP-illite 3 b a b

n s1,0 (mmol/g)

Eq. (15) (mmol/g)

⫺∆ 21 H t (J/g)

⫺(h s1 ⫺ h s2 /r) (kJ/mol)

1.05 2.07 0.84 1.25 1.30 1.42

1.00 1.98 0.85 0.95 1.18 1.38

5.65 0.42 11.10 1.70 1.35 0.85

6.25 1.38 13.65 4.32 3.21 2.27

HDP-kaolinite: 0.048 mmol HDP ⫹ cations/g clay. HDP cation content: HDP-illite 1, 0,097; 2, 0,139; 3, 0,233 mmol/g clay.

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The speciﬁc immersion wetting enthalpies of kaolinite, illite, and their organophilic derivatives were investigated in methanol and benzene in our earlier publications [35,37,38]. These data reveal that the heat of immersion in methanol is the highest in the case of the dialyzed hydrophilic mineral, and with increasing surface modiﬁcation its value decreases. The comparison of immersion wetting enthalpies relative to unit mass of the adsorbent is justiﬁed only when the speciﬁc surface area of the adsorbent is constant. It is also known, on the other hand, that the value of liquid sorption capacity, is a function of surface modiﬁcation: θ 2 ⫽ n 2s a m,2 /a s, where n 2s a m,2 is the hydrophobic surface area and a s is the total surface area of the adsorbent [35,37,38]. If a uniform treatment of immersion wetting data is desirable, it is advisable to relate the wetting enthalpy to the material amount in the interfacial phase, i.e., to use molar immersion wetting enthalpies, ∆ w H m (in kilojoules per mole), in the calculations. In this way the changes in speciﬁc surface caused by disaggregation need not be separately monitored, because our data always refer to enthalpy changes accompanying the sorption of molar amounts of the adsorbed material [62,78,79]. The changes in molar immersion enthalpies, ∆ w H m , that accompany surface modiﬁcation in toluene are presented in Fig. 17 for increasing organophilicity of

FIG. 17 Immersional wetting enthalpies as a function of alkylammonium chain lengths in (䊊) methanol and (䊉) toluene.

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the surface. The ∆ w H m values increase nearly exponentially on the nonswelling HDP illite surface, whereas on HDP-montmorillonite they decrease signiﬁcantly. The difference between these curves is the molar enthalpy of swelling (∆ sw H ). These data reveal that the heat of immersion in methanol is the highest in the case of the dialyzed hydrophilic mineral, and on increasing surface modiﬁcation its HDP ⫹ cation value decreases [75–79].

C. Heat of Wetting on Swelling Clay Minerals When the originally hydrophilic surface is modiﬁed by long alkyl chains [80– 92], heats of immersion display signiﬁcantly greater differences. This is well demonstrated by adsorption and X-ray diffraction measurements in toluene (Table 5). If montmorillonite, a layered silicate, is hydrophobized, then, depending on the length of the alkyl chain (n c ⫽ 12–18), the value of ∆ w H will decrease in polar methanol with increasing alkyl chain length [87–92]. As shown by the data in Fig. 18, the extent of wetting by the polar solvent methanol is nearly exponentially decreased as the increasing number of carbon atoms in the alkyl chain increases. The decrease in heat of wetting by toluene is surprising, as the increased organophilicity of the surface must be associated with an increase in the enthalpy of immersion wetting in the aromatic solvent as was measured in the case of nonswelling HDP-illites. The immersional wetting of hydrophobized montmorillonites in methanol, toluene, and their mixtures gives rise to three types of detector signals, as shown in Figs. 19–21. The isotherm batch microcalorimetry of these hydrophobic clays in methanol yields an exothermic effect, because in these organoclays interlamellar swelling is not very signiﬁcant (d L ⫽ 3.2 nm). Signiﬁcant swelling is observed in toluene; therefore, either endothermal–exothermal signals separated in time are registered within the same measurement or the wetting results in only an

TABLE 5 Interlamellar Sorption and Swelling on Hydrophobic Montmorillonites in Methanol (1)–Benzene (2) Mixtures Organoclay

a

Montmorillonite TDP-montmorillonite HDP-montmorillonite ODP-montmorillonite DMDH-montmorillonite a

Organic cation (mmol/g)

n s1,0 (mmol/g)

d Ldry (nm)

d toluene L (nm)

0.00 0.82 0.85 0.82 0.83

3.44 8.51 8.25 8.33 8.90

1.23 1.84 1.82 1.82 2.91

1.25 3.33 3.86 4.20 4.51

TDP, tetradecylpyridinium; HDP, hexadecylpyridinium; ODP, octadecylpyridinium; DMDH, dimethyldihexadecylammonium.

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FIG. 18 Immersional wetting enthalpies on hydrophobized montmorillonite in toluene as function of surface coverage (θ 2) with hexadecylpyridinium cation.

FIG. 19 Exothermic heat of wetting on hydrophobic (hexadecylammonium) montmorillonite in methanol (d L ⫽ 3.2 nm).

388

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FIG. 20 Endothermic–exothermic heat of wetting on hydrophobic (hexadecylammonium) montmorillonite in toluene (d L ⫽ 3.8 nm). (a) Opening the elastic silicate layer by adsorbed molecules is endothermic. (b) Adsorption in the interlamellar space is exothermic heat effect.

FIG. 21 Endothermic heat of wetting on hydrophobic (octadecylammonium) montmorillonite in 5: 95 methanol–toluene mixture (d L ⫽ 4.6 nm). The swelling effect overcompensate the exothermic adsorption heat in the interlamellar space.

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389

endothermal heat effect [37,38,62,78,79]. In the swelling of clay mineral organocomplexes in organic solvents, however, the amount of energy required for interlamellar expansion (in toluene, d L ⫽ 4.1 nm) may be so high that the exothermic heat effect accompanying the sorption of the liquid penetrating into the interlamellar space cannot compensate for it; therefore, the total heat effect is endothermic, as veriﬁed by Fig. 19. The total endothermic change in enthalpy appears only when the length of the alkyl chain is 2.6–2.8 nm. Thus, the entropy of solvated alkyl chains situated in the expanded interlamellar space may be considerably increased compared to their original state (see Figs. 23–25). It is this increase in entropy that ensures that the change in free enthalpy associated with the process of wetting will have a negative value, i.e., that wetting and swelling will proceed spontaneously. If we investigate the liquid sorption properties of swelling HDP-montmorillonites, we ﬁnd that the enthalpies of wetting in toluene also decrease; what is more, in the case of n c ⫽ 18 or 20 the process of wetting is endothermic, indicating that under the conditions of substantial interlamellar expansion, wetting is an entropy-controlled process. Figure 22 shows the heat effects determined by batch microcalorimetry as a function of the mass of the organocomplex. The points representing different surface hydrophobicities on a swelling organoclay fall on

FIG. 22 Enthalpy of wetting for different masses of hydrophobic montmorillonites— (1) Tetradecylpyridinium and (2) hexadecylpyridinium montmorillonites in methanol and (3) octadecylpyridinium and (4) dimethyldioctadecylammonium montmorillonites in toluene.

390

De´ka´ny

a straight line with a positive slope in methanol, while in the case of dimethyl dioctadecylammonium clay, which swells to a greater extent, the heat evolution decreases with increasing mass of the adsorbent in toluene. The lines do not intersect at the origin because the liquid inﬂux at mass m ⫽ 0 produces 75–78 mJ of heat in the measuring cell. The endothermal effect associated with the swelling of bentonites was ﬁrst pointed out by Zettlemoyer et al. [9], van Olphen [80], and Slabaugh and Hanson [82]. They established that good swelling and gel formation result in small exothermal or exclusively endothermal effects. According to these authors, when the immersion wetting of swelling systems is considered, both the interaction of polar molecules with a silicate surface and the solvation of apolar molecules by alkyl chains as well as the interlamellar expansion have to be taken into account. The ﬁrst two of these interactions are always exothermal, whereas the interlameller expansion may often be endothermal [35,37,78]. Figure 23 shows the degree of swelling for the liquid sorption equilibrium systems ethanol (1)–toluene (2)/hexadecylammonium vermiculite as a function

FIG. 23 The mole fraction of toluene (x s2) in the interfacial layer and the basal spacing (d L) in ethanol (1)–toluene (2) mixtures on hexadecylammonium vermiculite.

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FIG. 24 Orientation of the cationic alkyl chains between silicate layers at high layer charge density (degree of hydrophobization) for different degrees of swelling. (a) Mono˚ nglayer, (b) expanded monolayer, (c) bilayer structure (numbers show the distances in A stro¨m).

of the liquid mixture composition of the bulk phase. It can be established that within the entire series of mixtures the value of d L increases, i.e., the alkyl chains and the silicate layers expand (Fig. 24). The composition of the interfacial layer is therefore also indicated in Fig. 23, and it is apparent that this increase is gradual. This means that the displacement of the polar component (ethanol) from the interlamellar space leads to an increase in basal distance. The same conclusion is demonstrated by Fig. 24, assuming that the orientation of the alkyl chains is perpendicular to the silicate layers. The expansion or contraction of hydrophobized silicate lamellae is well reﬂected by the enthalpy values presented in Fig. 25 as a function of the volume fraction of adsorbed toluene in the interfacial layer (φ s2). It is evident that signiﬁcant swelling occurs only if the interlamellar space of the organoclay is enriched with toluene. For parallel investigation of adsorption and swelling, ﬂow microcalorimetry was used to control the enthalpy of displacement (∆ 21 H ) as a function of the surface layer composition. It is clear

392

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FIG. 25 Basal distance (d L) and enthalpy of displacement at different volume fractions of toluene (φ2 s) in the interfacial layer in ethanol (1)–toluene (2) mixtures on hexadecylammonium vermiculite.

from Fig. 25 that the ‘‘opening’’ of the interlamellar space is an endothermic process, because the expansion and solvation of alkyl chains are entropy-driven effects.

D. Adsorption of n-Butanol from Water on Modiﬁed Silicate Surfaces The structure and the sorption properties of partially hydrophobized silicates (dodecylammonium and dodecyldiammonium vermiculites) were investigated in aqueous solutions of n-butanol. The alcohol is preferentially adsorbed on the surface. The interlayer composition is calculated from adsorption and X-ray diffraction data. In the air-dried state the organic cations lie ﬂat on the interlamellar surface. In aqueous n-butanol solutions, the basal spacing of dodecylammonium vermiculite gradually increases with the extent of n-butanol adsorption because the chains increasingly point away from the surface. The basal spacing of dodecyldiammonium vermiculite is virtually independent of the interlayer composition, because the expansion of the interlayer space is sterically restricted and a

Liquid on Surfaces in Nonaqueous Dispersions

393

FIG. 26 Adsorption excess isotherms for n-butanol–water solutions on (䊊) dodecylammonium vermiculite and (䊉) dodecyldiammonium vermiculite.

relatively rigid structure is formed. The enthalpy of the displacement of water by 1-butanol was determined by ﬂow sorption microcalorimetry [72,93,–96]. Adsorption of n-butanol from water on the surface of vermiculite hydrophobized by alkyl chains of two different structures is illustrated by Fig. 26. It can be established that there is a very large difference between dodecylammonium derivatives with carbon chains of identical lengths but different interlamellar structures. The reason for this is directly shown in Fig. 27, which demonstrates that differences in interlamellar swelling are also quite large. Similarly to adsorption, dodecylammonium (C 12 ⫺ NH 3⫹) vermiculite swells considerably more than dodecyldiammonium [C 12 ⫺ (NH 3⫹) 2] vermiculite. As shown by a detailed discussion in our previous publications [72,93,94], the swelling of the diammonium derivative is limited due to the ‘‘bridges’’ formed by the alkyl chains, and the distance between lamellae is nearly constant (d L ⫽ 2.35–2.45 nm). Thus, this sample has a smaller free interlamellar volume (V int ⫺ V alc) than the dodecylammonium derivative (see Fig. 28b). Figure 29 shows free energy functions on the two different hydrophobic vermiculites, and Fig. 30 shows the ∆G s ⫽ f(x l,r) isotherms, calculated (corrected) according to a dilution term, between the bulk and surface layer [69–74], from known values of the isotherms n σ(n) ⫽ f(x 1,r). It 1 is obvious that the change in free energy that accompanies the adsorption ex-

394

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FIG. 27 Basal spacings of (䊉) dodecylammonium vermiculite and (■) dodecyldiammonium vermiculite in n-butanol–water solutions.

FIG. 28 Schematic representation of the hydrophobic vermiculite at different basal distances: (a) monolayer; (b) ‘‘bridging’’; (c) bilayer orientation.

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FIG. 29 Free enthalpy of adsorption in n-butanol–water solutions on (■) dodecylammonium vermiculite and on (䊉) dodecyldiammonium vermiculite.

FIG. 30 Thermodynamic potential functions of the adsorption layer on dodecylammonium vermiculite in n-butanol–water solutions.

396

De´ka´ny

change process changes parallel with adsorption. On the other hand, it has to be stressed that the value of ∆G s is signiﬁcantly lower in the restrictedly swollen system with lamellae bound together by alkyl chains (∆G s ⫽ 4.1 J/g) than in swollen systems with lamellae that move independently relative to each other (∆G s ⫽ 8.5–10.3 J/g). Enthalpy of displacement isotherms were determined by the ﬂow technique. The heat effects recorded on dodecylammonium and dodecyldiammonium vermiculites are found to be endothermic in both cases, i.e., the measured heat exchange process results in heat extraction. Since the adsorption isotherms unambiguously indicate positive adsorption of n-butanol, the question arises as to why an exothermic exchange enthalpy is not recorded. In our opinion, the reason for this is the endothermic enthalpy of dilution [59–61,69], which overcompensates for the interlamellar adsorption of butanol. When, knowing the adsorption excesses, the enthalpy isotherm ∆ 21 H s ⫽ f(x 1,r) characteristic of the solid/liquid interfacial adsorption layer can be calculated, it is indeed the exothermic adsorption enthalpy isotherm speciﬁc for the surfacial interaction that is obtained (Fig. 30). This measurement suggests that the interlamellar adsorption of n-butanol is thermodynamically preferred and is accompanied by the liberation of a very large amount of heat (∆ 21 H s ⫽ 16.0–16.5 J/g). The ∆Gs and T ∆S s functions are also included in Figs. 30 and 31, in order

FIG. 31 Thermodynamic potential functions of the adsorption layer on dodecyldiammonium vermiculite in n-butanol–water solutions.

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to describe the incorporation of the adsorbate in terms of change in enthalpy also. In Fig. 30, the entropy term of dodecylammonium vermiculite is decreased owing to an increase in the adsorption of butanol (T ∆ 21 S s ⬍ 0). Conversely, in the case of the restrictedly swollen dodecyldiammonium sample, an increase in entropy (T ∆ 21S s ⬎ 0) is observed up to x 1,r ⱕ 0.7, and it is only in the range of adsorption saturation that a decrease in entropy occurs (Fig. 31). This means that in the case of the restrictedly swollen system, water molecules are arranged in the interlamellar space in a more orderly manner (presumably in clusters) than n-butanol molecules. The reason for this is that if ∆S 2(water) ⬎ ∆S 1(n-butanol), then ∆21 S ⫽ ∆S 2 ⫺ ∆S 1 ⱖ 0.

IV.

PROPERTIES OF THE ADSORPTION LAYER AND STABILITY OF AEROSIL DISPERSIONS IN BINARY LIQUIDS

The stability of colloidal disperse systems is basically determined by the adhesive interactions between the particles and by particle–liquid interactions (wetting). The structural building properties of sols and suspensions therefore depend on the magnitude of the energies of these interactions. The state of aggregation of a disperse system can be regulated by altering the adhesive and wetting properties at a constant particle concentration—by selecting a dispersion medium or mixture medium of appropriate polarity or by surface modiﬁcation [27,36,63,64]. The analysis of the sedimentation and rheological properties of a disperse system (sol or suspension) usually yields only qualitative information about the interparticle interactions. However, the solid–liquid interaction, i.e., the heat of wetting, can be accurately determined by microcalorimetry. When the viscosity of a suspension is measured by rotational viscosimetry, the Bingham yield value characteristic of the interparticle interaction can be determined from the so-called ﬂow curves (in a system of a given concentration). The Bingham yield value is measured in non-Newtonian rheological systems and can be used for the calculation of the energy of separation [20–26,97–101] characteristic of adhesive interactions (aggregation). Disperse systems of a great variety of structures aggregated in different ways can be practicably analyzed by small-angle X-ray scattering (SAXS), because the intensity of scattered light is basically determined by the size of the particles and the structural factor characteristic of the system. Thus, SAXS measurements also make possible the determination of structural parameters describing the degree of aggregation of the disperse system studied, which can then be compared with the rheological properties of the suspension and with the wetting characteristics of the particles. A combination of the methods mentioned can greatly increase our knowledge of the stability of structured disperse systems and promote a wider range of practical applications [102].

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A. Inﬂuence of the Adsorption Layer on the Aggregation of Aerosil Dispersions in Binary Liquids From a knowledge of the adsorption, immersion, and wetting properties of solid particles, we have examined the inﬂuence of particle–particle and particle–liquid interactions on the stability and structure formation of suspensions of hydrophobic and hydrophilic Aerosil particles in benzene–n-heptane and methanol–benzene mixtures. For the binary mixtures, the Hamaker constants have been determined by optical dispersion measurements over the entire composition range by calculation of the characteristic frequency (ν k) from refractive index measurements [7,29,36,64]. The Hamaker constant of an adsorption layer whose composition is different from that of the bulk has been calculated for several mixture compositions on the basis of the above results. Having the excess isotherms available enabled us to determine the adsorption layer thickness as a function of the mixture composition. For interparticle attractive potentials, calculations were done on the basis of the Vincent model [3–5,39]. In the case of hydrophobic particles dispersed in benzene–n-heptane and methanol–benzene mixtures, it was established that the change in the attractive potential was in accordance with the interactions obtained from rheological measurements. The Hamaker constant (A) is calculated according to Gregory [103] and Tabor and Winterton [104] by using the equation

冢冣

27 ε⫺1 h νk A⫽ 64 ε⫹2

2

(22)

where h is the Planck constant, ν k is the characteristic frequency, and ε is the relative permittivity of the liquids. The interparticle interaction potential can be described with the help of the Hamaker constant on the basis of the comprehensive work by Hamaker [7] and Visser [105], who developed the calculation of London interactions between macroscopic spherical particles. It was taken into account by Vold [3] that each particle is surrounded by a lyosphere with a thickness t s. The calculation of van der Waals attraction forces between colloidal particles with adsorption layers was developed by Vincent and coworkers [4,5,39], who formulated the following equation for the description of the attraction potential V A: 1 V A ⫽ ⫺ [H ls (A ls1/2 ⫺ A m1/2) 2 ⫹ H p (A p1/2 ⫺ A ls1/2) 2 12 ⫹ 2H pls (A

1/2 p

⫺ A )(A 1/2 ls

1/2 ls

(23)

⫺ A )] 1/2 ls

where A m , A ls , and A p are the Hamaker constants relative to the bulk medium, the lyosphere (adsorption layer), and the particle, respectively, and H ls , H pls are

Liquid on Surfaces in Nonaqueous Dispersions

399

the distance functions [5,29,39]. H pls is the distance function relative to the particle/liquid interface. According to our investigations, Eq. (23) is corrected in the sense that the Hamaker constant A ls is given for the adsorption layer of composition x 1s and—instead of calculating them using a constant, and estimated, layer thickness—t s values derived from adsorption excess isotherms calculated by Eq. (6) and varying as a function of equilibrium composition are used in the H ls functions. Equation (23) allows the calculation of the attraction potential V A at a given interparticle distance h in the entire range of mixture composition; at a given composition, or in a pure liquid, the value of the attraction potential function V ⫽ f (h) can be obtained [29,30,39]. Let us ﬁrst examine the results of the rheological analysis of the hydrophobic Aerosil dispersion R 972 in the entire range of mixture composition of benzene (1)–n-heptane (2) mixtures. The ﬂow curves of a 2 g/100 cm 3 dispersion measured in the pure liquid component are presented in Fig. 32a. The ‘‘ascending’’ and ‘‘descending’’ ﬂow curves obviously do not coincide but form a hysteretic loop; a slight thixotropy is observed. The Aerosil suspensions yield a series of ﬂow curves over the entire mixture composition range, the most characteristic of which are shown in Fig. 32b. Non-Newtonian behavior is observed in the entire mixture composition range; shear stress (τ) increases with the shear gradient (D) in a nonlinear fashion. At very low shearing rates the stress is elastic, and at higher values the behavior is pseudoplastic [99–101]. Based on the Bingham equation τ ⫽ τ B ⫹ η pl D, the plastic viscosity η pl and the Bingham yield value τ B can be calculated from the ﬂow curves [20–27,29,36,39,64]. The dependence of the yield value τ B on the molar fraction of benzene is presented in Fig. 33. Since the yield value is a parameter characteristic of the interparticle interaction [27,29,64], it can be established that the aggregation of silica particles is signiﬁcantly affected by the composition of the mixture medium and that an increase in the fraction of benzene in the mixture results in a decrease in aggregate size—in other words, interparticle adhesion is reduced, which means increased stability. Hydrophobic Aerosil (Degussa AG, Germany) dispersions of various concentrations were studied in methanol (1)–benzene (2) mixtures, in the entire mixture composition range. The 2 g/100 cm 3 dispersion was chosen for detailed analysis. The ﬂow curves of the Aerosil dispersions (Fig. 34) reveal that plastic viscosity and Bingham yield value are the highest in pure benzene, and increases in the molar fraction of methanol in the mixture lead to a decrease in these parameters (Fig. 35). The rheological ﬂow curves reveal that in n-heptane there are strong adhesive interactions between hydrophobic particles. The Bingham yield value (τ B) characteristic of interparticle interactions changes in parallel with the optical density of the suspension (Fig. 36). Aggregation is also demonstrated by the observation that the turbidity of the suspension changes with the composition of the mixture.

400

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FIG. 32 Rheological ﬂow curves of hydrophobic Aerosil (2% m/v) suspensions (a) in benzene (x 1 ⫽ 1) and n-heptane (x 1 ⫽ 0) and (b) in benzene (1)–n-heptane (2) mixtures at different compositions.

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FIG. 33 The Bingham yield values of hydrophobic Aerosil (2% m/v) suspensions in benzene (1)–n-heptane (2) mixtures in the entire composition range.

When attraction potentials are calculated using the Hamaker constants A ls and A m and the layer thickness t s prevailing in the given liquid mixtures, the value of the attraction potential is reduced by the wetting effect of benzene in the benzene–n-heptane mixture series at a constant interparticle distance of 0.1 nm, in complete agreement with our thermodynamic considerations. In the range of x 1 ⫽ 0.4–0.6 for the methanol–benzene liquid pair, the minimal interparticle attraction can also be calculated from the attraction potential function and is found to coincide exactly with the appearance of the Newtonian ﬂow characteristics of the suspension and the minima of the thermodynamic potential functions [36,39,64].

B. Characterization of the Stability of Nonaqueous Dispersions by Calorimetric and Adsorption Measurements The parallel representation of the adsorption isotherms and heats of immersion measured in binary mixtures, presented above, gave information on solid–liquid interfacial interactions. If the stability of disperse systems is approached from the

402

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FIG. 34 Rheological ﬂow curves of hydrophobic Aerosil (2% m/v) suspensions in methanol (1)–benzene (2) mixtures at different compositions.

side of interparticle interactions, the rheological properties of the given colloidal dispersion should be examined. The most straightforward way of doing this is to measure the ﬂow curves of the disperse system in a rotational viscosimeter in mixture media of various compositions. This means that the shearing stress (τ) arising during shearing (D) is plotted against the shear gradient, i.e., the functions τ ⫽ f(D) (ﬂow curves) are determined. If these ﬂow curves are linear and pass through the origin, the liquid studied is Newtonian, whereas in the opposite case, rheological behavior of the non-Newtonian or pseudoplastic type is observed (Fig. 32a). If interparticle adhesion forces increase signiﬁcantly, the dispersion possesses a yield value (Bingham yield value, τ B), meaning that an amount of energy characterized by the value of τ B has to be invested in order to start the ﬂow. Thus, rheological data can be used for the characterization of interparticle interactions on the basis of macroscopic measurements. Let us now examine the relationship between rheological data characterizing interparticle interactions and those obtained by adsorption measurements and calorimetry. Figure 37 displays characteristic data measured in hydrophobic Aerosil in benzene–n-heptane mixtures yielding U-shaped excess isotherms and the cal-

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FIG. 35 The Bingham yield values of hydrophobic Aerosil (2% m/v) suspensions in methanol (1)–benzene (2) mixtures in the entire composition range.

culated functions (Fig. 37a). The aromatic component is positively adsorbed on the surface of the hydrophobic SiO 2 particles, i.e., benzene is accumulated in the interfacial layer. Given the knowledge of the excess isotherm and the activities of the bulk phase, the change in free enthalpy associated with adsorption, i.e., ∆ 21 G ⫽ f(x 1), can be calculated by using the integrated form of the Gibbs equation (Fig. 37b). It can be established that the accumulation of toluene in the interfacial layer produces a signiﬁcant decrease in free enthalpy. In parallel measurements of heats of immersion in the various mixtures, large heat effects are recorded. ∆ w H is obviously much larger in the preferentially adsorbed benzene and in mixtures rich in benzene than in pure n-heptane. The reason for this is that n-heptane is bound to the hydrophobic surface of SiO 2 only by dispersion interactions, whereas the aromatic structure of toluene can be polarized on the hydrophobized SiO 2 surface (Fig. 37c). This concept is also supported by the adsorption layer thickness function t s ⫽ f(x 1) calculated from the adsorption excess isotherm. These calculations were presented in the publications and De´ka´ny [52,53], Marinin et al. [106], and Aranovich [107]. The function ∆ 21 G ⫽ f (x 1) was used for the calculations [52,53]. The results reveal that in n-heptane a monomolecular

404

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FIG. 36 (䊉) Optical density and (■) Bingham yield stress vs. mole fraction of hydrophobic Aerosil (2% m/v) suspensions in benzene (1)–n-heptane (2) mixture.

adsorption layer is formed (Fig. 37e), the heat of immersion is minimal, and consequently interparticle adhesion is maximal (Fig. 37d). An increasing heat of immersion also means an increasing adsorption layer thickness; however, τ B decreases, resulting in lower interparticle adhesion. Thus, in pure toluene, where there is a considerable heat of wetting and the adsorption layer is about 6–7 nm thick, interparticle attraction is quite weak and the suspension is far more stable than in n-heptane. Dispersion of hydrophobic Aerosil in the methanol (1)–benzene (2) liquid pair yields a much more stable system. In this case the excess isotherm is S-shaped. This means that in the molar fraction range of x 1 ⫽ 0–0.35, methanol is positively adsorbed on the surface, whereas in the range of x 1 ⫽ 0.35–1.0, the positive adsorption of benzene is observed. (This section in Fig. 38a indicates negative adsorption with respect to ethanol, as adsorption excesses of component 1 are displayed.) After integration according to the Gibbs equation, the function ∆ 21 G has a minimum in the range of x 1 ⫽ 0.2–0.4, also including the so-called adsorption azeotropic composition (x a1) (Fig. 38b). Measurements of the heat of immer-

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FIG. 37 The solid/liquid interfacial extensive functions and Bingham yield stress for interparticle interactions in hydrophobic Aerosil (2% m/v) suspensions in benzene (1)– n-heptane (2) mixtures in the entire composition range.

406

De´ka´ny

FIG. 38 The solid/liquid interfacial extensive functions and Bingham yield stress for interparticle interactions in hydrophobic Aerosil (2% m/v) suspensions in methanol (1)– benzene (2) mixtures in the entire composition range.

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sion ∆ w H also reveal maximal heat effects in this composition range (Fig. 38c), and this is where the adsorption layer reaches maximal thickness (Fig. 38e). In the azeotropic composition range, the yield value τ B calculated from rheological measurements is zero, i.e., the suspension exhibits Newtonian rheological characteristics (Fig. 38d). Thus, maximal adsorption layer thickness and heat of wetting both indicate that a strong interaction is established between particles and adsorbed solvent molecules, making possible the minimization of interparticle attraction forces. The three parallel series of experiments described above demonstrate that in suspensions of systems with S-shaped excess isotherms, the disperse system may be stabilized in the vicinity of the azeotropic composition, indicated by (1) the minimum of the free enthalpy function, (2) maximal exothermic heat of immersion, (3) maximal thickness of the adsorption layer, and (4) Newtonian rheological properties, i.e., the minimum of interparticle interactions [36,38, 39,64].

FIG. 39 Small-angle X-ray scattering curves of hydrophobic silica in benzene (1)–nheptane (2) mixture in (2% w/v) suspension (a) in n-heptane, (b) in benzene, (c) in x 1 ⫽ 0.7 mixture.

408

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V. SMALL-ANGLE X-RAY SCATTERING OF SiO 2 PARTICLES IN BINARY LIQUIDS Hydrophilic and hydrophobic colloidal SiO 2 particles dispersed in benzene–nheptane mixtures in capillary tubes were studied by small-angle X-ray scattering in a helium atmosphere [107,108]. According to the scattering intensty (I ) vs. wave vector (h) curves in Fig. 39, the difference between hydrophilic and hydrophobic particles is well characterized by the scattering intensities. Correlation length and the course of the distance distribution function P(r) calculated from it yield information on aggregation and on the stability of the disperse system. The rheological ﬂow curves reveal that in n-heptane there are strong adhesive interactions between hydrophobic particles. Aggregation is also demonstrated by the observation that the relative internal surface of the suspension changes with the composition of the mixture. Measurements of wetting and adsorption cor-

FIG. 40 Distance distribution function of hydrophobic silica (R 972) particles in benzene (1)–n-heptane (2) mixture in (2% w/v) suspension. (a) in n-heptane; (b) in x 1 ⫽ 0.7 mixture; (c) in benzene.

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roborate this assumption, since positive adsorption of benzene in the surface layer increases the enthalpy of wetting and decreases the tendency of particles to aggregate. Thus, SAXS measurements also make possible the determination of structural parameters describing the degree of aggregation of the disperse system studied, which can then be compared with the rheological properties of the suspension and with the wetting characteristics of the particles. A combination of the methods mentioned can greatly increase our knowledge of the stability of structured disperse systems and promote a wider range of practical applications [108]. In Fig. 40, the P(r) vs. r distance distribution functions are presented that were calculated from the scattering curves by inverse Fourier transformation [102,108,109]. It can be clearly seen that the numerical values of the functions indicate the differences in the density of aggregates in the liquid mixtures of different polarities. The interparticle interactions are thus regulated via the selective liquid sorption process on the disperse particles, and it can be established that the interfacial layer composition, the layer thickness, and the heat of wetting are crucial factors for the stability of colloidal dispersions in nonaqueous liquids.

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11 The Formation and Transformation of Crystalline Dispersions as Studied by Thermal Analysis ¨ REDI-MILHOFER Casali Institute of Applied Chemistry, HELGA FU The Hebrew University of Jerusalem, Jerusalem, Israel

I. Introduction II.

Theoretical Background A. Nucleation B. Crystal growth C. Flocculation D. Aging: Ostwald ripening and solution-mediated phase transformation

III. Formation and Transformation of Ionic Precipitates from Electrolyte Solutions A. Formation and transformation of amorphous precursor phases B. Nucleation, crystal growth, and solution-mediated phase transformation of crystal hydrates C. Control of crystallization by additives IV. Crystallization in Conﬁned Spaces: Emulsions and Microemulsions A. Emulsions: induced crystallization at the oil/water interface B. Crystallization in microemulsions References

414 415 416 417 417 418 419 420 422 426 434 434 437 445

413

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Fu¨redi-Milhofer

I. INTRODUCTION Methods of thermal analysis date back to the beginning of the 20th century, but only recently, as advanced equipment has made the task of measurement simpler and more rapid, have they become an essential part of the characterization of inorganic and organic compounds. One of the earliest applications was as a tool in phase analysis. In his classical work, Duval [1] gives a compilation of methods suggested for automatic thermogravimetric analysis and describes and evaluates thermolytic curves of some 1200 inorganic compounds. Several excellent monographs describing modern methods of thermal analysis and their application have been published [2,3], along with comprehensive reviews on the thermochemistry of organic, organometallic, and inorganic compounds, including relevant thermodynamic parameters extracted from calorimetric measurements [4,5]. ‘‘Thermal analysis’’ denotes a group of methods and techniques in which a property of a substance is measured as a function of temperature while the substance is subjected to a controlled temperature program. Thus, it is possible to monitor the temperature of the sample [e.g., by differential thermal analysis (DTA) or differential scanning calorimetry (DSC)], its weight loss upon heating [thermogravimetric (TG) and differential thermogravimetric (DTG) analysis] as well as a host of other properties that change with temperature (mechanical strength, morphology, crystal structure, dimensions, etc.). For comprehensive lists and descriptions of available methods see Refs. 2 and 3. Using these methods, information on the thermal behavior of a substance is readily obtained. By employing several methods simultaneously or sequentially to characterize a sample it is possible to obtain complete information about the sequence and thermodynamic parameters (enthalpy, entropy) of decomposition reactions and polymorphic transitions occurring as a consequence of increasing temperature [3]. In addition, complementary methods for physicochemical characterization such as thermal microscopy, X-ray diffraction, and Fourier transform infrared (FTIR) spectroscopy are used. A requirement for obtaining meaningful data is the strict deﬁnition of the experimental conditions employed, particularly those that may inﬂuence the rate of gas diffusion from inside the sample and the rate of heat transport (i.e., the shape and size of the crucible, sample size, heating rate, etc.). Thermoanalytical methods have been frequently employed in the characterization of complex samples such as minerals and clays [6] and carbonate stones used in the construction of monuments [7]. They have become a routine analytical tool for the characterization of new compounds in the pharmaceutical industry, where molecules are frequently prepared as hydrates or pseudosolvates to ensure good water solubility and good stability in moist environments [8]. Biochemical and biological applications of thermal analysis are also the subject of a recent review [9].

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In this chapter we concentrate on applications of thermal analysis in basic and applied research, leading to better understanding of the processes involved in the formation and transformation of crystalline dispersions both from electrolyte solutions and in conﬁned spaces such as emulsions and microemulsions.

II.

THEORETICAL BACKGROUND

Crystalline dispersions are formed by a succession of precipitation processes, nucleation, crystal growth, ﬂocculation, and various aging processes (Fig. 1). In this section we present a short review of the thermodynamic principles that deﬁne these processes. For a comprehensive treatise on the subject the reader is directed to Ref. 10.

FIG. 1 itates.

Processes involved in the formation and transformation of slightly soluble precip-

Fu¨redi-Milhofer

416

A. Nucleation Nucleation is the initial process leading to the formation of a new phase. Classical nucleation theory [11–13] describes homogeneous nucleation as the breakdown of a metastable state that occurs at a critical activation energy, which is achieved at a critical subcooling (in melts) or supersaturation (in solution). The homogeneous nucleus is conceived of as an aggregate of critical size in unstable equilibrium with the parent phase. At concentrations below the critical level the cluster grows or dissociates reversibly, nX s Xn

(1a)

at the critical size irreversible growth commences upon the addition of one more ion or molecule: X n ⫹ X → growth

(1b)

For a spherical nucleus, the energy barrier to nucleation, ∆G0, is simply related to the volume free energy of cluster formation and to the energy required for the formation of a new surface: ∆G 0 ⫽ (4/3) π r3 ∆Gv ⫹ 4π r2 σS/L

(2)

where ∆Gv is the change in the molecular volume free energy associated with cluster formation, σS/L is the cluster/solution (solid/liquid) interfacial energy, and r is the radius of the new nucleus. Maximization of Eq. (2) with respect to r gives, for the critical radius, r* ⫽

2σS/L ⫺2σS/Lv ⫽ ∆ Gv kT ln S

(3)

and for the activation energy, ∆G 0* ⫽

16πσS/L3 16πσS/L3v2 ⫽ 2 2 2 2 3 ∆Gv 3k T ln S

(4)

In Eqs. (3) and (4), v is the molecular volume, k is the Boltzmann constant, T is the absolute temperature, and S is the supersaturation. For constant temperature and pressure, the supersaturation can be deﬁned as the ratio of ionic activity products. Thus, for a binary electrolyte, S ⫽ AP/Ksp, where AP is the ionic activity product in the supersaturated solution and Ksp is the solubility product of the respective solute. Equation (3) is known as the Gibbs–Thompson relation, and Eq. (4) was ﬁrst derived by Gibbs [14] to describe the condensation of droplets from vapor. The rate of nucleation, J, is an exponential function of ∆G0*:

Crystalline Dispersions

J ⫽ Ω exp

417

⫺ 16πσ v * ⫽ Ω exp 冤冤⫺∆G kT 冥 3k T ln S 冥 0

S/L

3

3

3 ⫺2

2

(5)

where Ω is a preexponential factor (1033 ) and all other quantities are deﬁned as above. Equation (5) shows an exponential dependence of the nucleation rate on the supersaturation. A consequence of this dependence is that, ideally, if no catalyzing impurities are present, the rate of nucleation should remain negligibly small until a critical supersaturation, S*, is reached. At this point a sharp increase in the number of particles marks the onset of homogeneous nucleation. If the reaction is conducted in a closed system (with no inﬂow or outﬂow of reagent solutions), at S ⬎ S* the supersaturation is likely to be used up in the creation of new nuclei. The result is a colloidal dispersion that, depending on the electrolytic environment, will either aggregate or form a stable sol. In practice, both in industrial systems and in biological and pathological mineralization, nucleation is usually induced at much lower supersaturations by heterogeneous nuclei that lower the activation energy, i.e., ∆Ghet ⬍ ∆G0*. These can be nonspeciﬁc impurities, which are always present in solution, or templates, which are speciﬁcally added with the purpose of producing a certain kind of precipitate. The number of particles formed by heterogeneous nucleation cannot exceed the number of seeds or impurity particles, which, in aqueous solutions, is estimated to be N ⬃ 106 –107 particles per cubic centimeter.

B. Crystal Growth Crystal growth is visualized as the result of a succession of events, i.e., transport of ions through the solution, adsorption at the solid/solution interface, surface diffusion, reactions at the interface (dehydration, two-dimensional nucleation), and incorporation into the crystal lattice. The rate of crystal growth is controlled by the slowest of these processes, which determines the size and shape of the resulting crystals. The rate-controlling crystal growth mechanism depends on the supersaturation (Fig. 1). At low supersaturation, the rate of growth is likely to be controlled by one or more surface processes, and as a result compact crystals are obtained. At medium supersaturation, the diffusion of ions through the bulk may be rate-controlling, resulting in the development of large dendritic crystals. If the initial supersaturation exceeds S*, crystal growth is almost insigniﬁcant, because the supersaturation is used up in the creation of new nuclei by homogeneous nucleation (Fig. 1).

C. Flocculation* Once formed, particles in solution interact with each other because of Brownian motion. The theory of rapid ﬂocculation was ﬁrst proposed by Smoluchowski, * For a detailed treatise, see Ref. 15.

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who treated the problem as one of the diffusion of spherical particles in an initially monodisperse system, leading, with every collision and in the absence of repulsive forces, to permanent contact [15]. The total number N of particles that are present at time t is given by N ⫽ N0 /(1 ⫹ t/t1/2 )

(6)

where N0 is the initial number of particles and t1/2 is the time necessary to reduce N0 by half. For aqueous dispersions at 25°C, t1/2 ⬇ 2 ⫻ 1011 /N0 s. Thus, in the case of heterogeneous nucleation, t1/2 ⬃ 2 ⫻ 104 –2 ⫻ 105 s, or 5.5–55 h. Apparently, in such systems ﬂocculation is not signiﬁcant in the early stages of precipitate formation but will be preceded by crystal growth [10]. However, if precipitation is initiated by homogeneous nucleation, the number of particles will be larger by several orders of magnitude, in fact ⬃1012 particles per cubic centimeter have been detected experimentally [16]. For that number the half-time of ﬂocculation would be t1/2 ⬃ 0.1 s. With the number of particles only 10 times larger, t1/2 would be approximately 0.01 s, which is within the time scale predicted for induction periods for homogeneous nucleation [10]. Clearly, in the supersaturation region exceeding S*, ﬂocculation of nuclei or primary particles becomes a signiﬁcant factor, occurring in parallel or immediately after nucleation. Homogeneous nucleation thus leads to heavy ﬂocculation unless the particles are charged and therefore stabilized by Coulombic forces or are subjected to repulsive forces arising from solvation, adsorbed layers, etc. For further information, the reader is referred to Ref. 17, a comprehensive treatise covering adsorption at interfaces and the electrical double layer.

D. Aging: Ostwald Ripening and Solution-Mediated Phase Transformation Any two-phase system consisting of a polydisperse precipitate in contact with its mother liquid will be thermodynamically unstable because of its large interfacial area, which is a source of free energy. There are two possible ways for the system to minimize its free energy: (1) Small particles dissolve and large ones grow until, after inﬁnite time, only one large crystal remains, or (2) parts of the crystallites with high energy (edges, corners, dendrite arms) dissolve preferentially and the excess solute is redeposited at surface positions of lower energy. This phenomenon has been termed Ostwald ripening [18,19] and was theoretically treated by several authors [20,21], who showed that it is signiﬁcant even in the early stages of nucleation and crystal growth. This, then, is an important factor (apart from ﬂocculation) that inﬂuences the properties of particles in a nascent crystalline dispersion. Many commonly occurring crystals may exist in a wide variety of forms such as different polymorphs, crystal hydrates, or solvates. For a given set of experi-

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mental conditions such as temperature, pressure, and composition (transition points excluded), only one solid phase will be consistent with the minimum free energy of the system. This phase will be the thermodynamically stable one with the lowest solubility but will not necessarily precipitate ﬁrst from a supersaturated solution. When crystallization of several solid phases is possible, the relative rates of nucleation and crystal growth will determine which form separates ﬁrst [20]. The thermodynamic drive toward minimizing the free energy of the system will then cause the metastable phase to transform into a more stable one. Such a transformation can occur in the solid state by internal rearrangement of molecules. Frequently this occurs as a consequence of heating and can be conveniently studied by DTA, augmented by methods for phase analysis such as X-ray diffraction and infrared spectroscopy. Another route available for phase transformation is aging in contact with a solvent, usually the mother liquid. Such a transformation involves concomitant dissolution of the metastable form and precipitation of the next, more stable form. This phenomenon was observed in the early 1800s and was later formulated as Ostwald’s rule of stages [19]. More recently, Cardew and Davey presented a kinetic analysis [22] that takes into account the rate of dissolution of the metastable phase and the growth rate of the stable phase and shows that the supersaturation proﬁle depends strongly on the relative kinetics of growth and dissolution. It appears that such proﬁles are dominated by a plateau supersaturation, which is the region where the growth and dissolution processes are balanced. This region is determined by the relative surface areas of the phases and their kinetic constants of dissolution (kD) and growth (kG ), respectively. Any change in experimental conditions that inﬂuences either one or both rate constants will then exert an inﬂuence on the rate and possibly on the outcome of the phase transformation.

III. FORMATION AND TRANSFORMATION OF IONIC PRECIPITATES FROM ELECTROLYTE SOLUTIONS The properties of precipitates formed from electrolyte solutions depend on the relative rates of the precipitation processes described in Section II. These in turn depend on a number of experimental factors such as the degree of supersaturation, reactant concentration ratio, temperature, ionic strength, and the presence of impurities or additives in the crystallizing solution. It is therefore essential to design reproducible experimental procedures by which to control these factors. A simple way to control the initial supersaturation and reactant concentration ratio is to rapidly mix equal volumes of known concentrations of the cationic and anionic components of an ionic precipitate (for instance, a solution of calcium chloride and sodium oxalate to obtain calcium oxalate). Knowing the initial concentra-

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tions, precipitation kinetics can then be followed by monitoring the depletion of solution concentration and/or one or more precipitate properties as a function of time. The role of thermal analysis in this context is in the characterization of the solid phase(s) at given time intervals and after termination of the reaction. Several interesting examples follow.

A. Formation and Transformation of Amorphous Precursor Phases The rate and mechanism of nucleation are of prime importance in determining the nature of the ﬁrst solid phase formed from a supersaturated solution. We have seen [Eq. (3)] that the size of the critical nucleus is inversely proportional to the degree of supersaturation. At high supersaturations (S ⱕ S*), where homogeneous nucleation prevails, the critical radius may be rather small, and for crystals with large unit cells (such as hydroxyapatite) it may become smaller than one unit cell [23]. On the other hand, the rate of nucleation increases exponentially with the supersaturation [Eq. (5)]. Under such conditions, poorly crystalline or amorphous particles are formed that enlarge by ﬂocculation rather than by crystal growth (Fig. 1). If the amorphous precipitate contains hydrophilic cations, which in aqueous solution coordinate a number of water molecules (such as calcium or aluminum ions), it will most likely be energetically favorable to incorporate such bound water into the nascent precipitate. Thus, such poorly crystalline precipitates are likely to be highly hydrated; examples are amorphous calcium phosphate [24] and gel-like structures such as Al2O3 ⋅ 3H2O ⋅ H2O, Fe2O3 ⋅ 3H2O ⋅ H2O, or H2SiO3 ⋅ H2O [25]. Thermal analysis gives information on the amount of water incorporated and on the mechanism and strength of bonding. (For a comprehensive discussion of the modes and mechanisms of water incorporation with special regard to inorganic compounds, see Refs. 25 and 26.) Amorphous precipitates tend to be metastable and change in contact with the mother liquid into more stable structures, but nevertheless the history of the sample can in many cases be deduced even after prolonged aging. An interesting example is the formation of hydroxyapatite (HA). A convenient way to prepare stoichiometric hydroxyapatite is to induce precipitation in a nitrogen atmosphere by dropwise addition of a phosphate solution into a calcium hydroxide solution, the molar ratio of the reagents being 1.67 [27]. In the course of such preparations, highly hydrated amorphous calcium phosphate precursors are formed that later transform into HA. Near stoichiometric HA prepared by this method was examined by mass spectrometric temperature-programmed dehydration (MSTPD) analysis [28]. The sample was outgassed at 25°C until the instrument pressure fell to a steady value (⬃10⫺7 torr) and then heated at a rate linear with time while the efﬂuent water vapor was monitored by means of a mass spectrometer (for details of the technique see Ref. 29). Figure 2 shows the

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FIG. 2 Mass spectrometer temperature-programmed dehydration (MSTPD) spectra showing the evolution of water as a function of temperature from (1) hydroxyapatite precipitated from an aqueous solution via an amorphous precursor phase, (2) hydroxyapatite prepared in a hydrothermal bomb, and (3) apatite from a mineral source. (After Ref. 28.)

results (curve 1) compared with those obtained from a sample of HA prepared by the hydrothermal bomb technique [30] (curve 2) and with another one obtained from a mineral source (Holly Springs apatite, curve 3). The interesting part of Fig. 2 lies in the temperature region between 150°C and 300°C, where a very pronounced peak was found for the sample formed via the amorphous precursor phase but none for the hydrothermally prepared or mineral HA. This unique behavior was attributed to the evolution of water from narrow internal micropores that were present only in samples formed by precipitation from aqueous solution via an amorphous precursor phase [28]. These ﬁndings have added signiﬁcance if one considers that in biomineralization (mineralization of bone and teeth) hydroxyapatite is most probably formed in a similar way from body ﬂuids [31]. Temperature-programmed desorption techniques are also successfully used to estimate pore sizes of adsorbents consisting of amorphous materials or arrays of

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poorly oriented crystallites (silica gels, aluminum oxides, active carbons, etc.) [32]. An important class of crystalline compounds that are formed via amorphous precursor phases are zeolites. Zeolites are aluminum silicates with a network of uniform pores of molecular dimensions incorporating exchangeable cations and water. They have numerous applications as adsorbents, catalysts, and membranes. Thermal analysis can give useful quantitative and/or semiquantitative information on the process of water adsorption and desorption and the thermal behavior of different types of zeolites, including information on the pore structure, degree of hydration of cations, interaction of hydrated cations with the aluminosilicate matrix, etc. [25,33–35]. Of particular interest for the present volume is the information that thermal analysis yields on the process of the transformation of amorphous aluminosilicate gel precursors into crystalline zeolite structures [35–37]. Differential thermogravimetric curves of amorphous aluminosilicate gels show endothermic peaks at low temperatures (50–60°C) corresponding to the desorption of loosely held moisture from the inner and outer surfaces of the gels and/ or from the dehydration of Na⫹ ions from residual NaOH (curves 1–3 in Fig. 3). The formation of ordered structural subunits or particles of a quasicrystalline zeolite phase is evidenced by a second endothermic peak in the DTG spectrum that appears between 120°C and 150°C (curves 2 and 3 in Fig. 3). The appearance of this peak was explained by the assumption that the energy needed for the desorption of water molecules from Na⫹ ions positioned in structural subunits similar to those of zeolites is higher than the energy needed for the release of water molecules from the amorphous gel matrix [37]. The relative intensities of the two peaks change as a consequence of the increase in concentration of the quasicrystalline phase in the aluminosilicate matrix (Fig. 3) [35–37]. It was thus possible to use this sensitive method to investigate a number of experimental parameters that inﬂuence the formation of structural subunits that play a decisive role in the nucleation of zeolites from gel systems [35–37].

B. Nucleation, Crystal Growth, and SolutionMediated Phase Transformation of Crystal Hydrates At low and medium supersaturations the number of particles formed depends on the number of heterogeneous nuclei and usually does not exceed 107 cm⫺3 (Fig. 1). Once formed, crystals enlarge by deposition of solute ions at the surface, surface diffusion to a suitable site, and incorporation into the crystal lattice (see also Sections II.A and II.B). Under these conditions strongly hydrated cations are likely to form different crystal hydrates with different solubilities. Crystals thus formed are coarser and contain less—primarily crystalline—water than

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FIG. 3 DTG curves (rate of mass change as a function of temperature; schematic), representing the transformation of amorphous aluminosilicate gels into crystalline zeolite phases. Curve 1 shows a peak characteristic of the amorphous phase (50–60°C); curves 2 and 3 show the progressive appearance of a second endothermic peak (120–130°C), indicating the formation of ordered structural subunits. (Adapted from Ref. 35.)

when crystallization is initiated by homogeneous nucleation. The difference between the amount and mode of binding of water molecules in crystals formed by heterogeneous nucleation and in crystals formed by homogeneous nucleation is illustrated by calcium oxalate precipitates. Calcium oxalate crystallizes in the form of three different hydrates. The thermodynamically stable monohydrate, CaC2O4 ⋅ H2O (COM), crystallizes in the form of monoclinic (⫺101) plates [38]. Two other, metastable, crystal forms are known, the tetragonal calcium oxalate dihydrate [CaC2O4 ⋅ (2 ⫹ x) H2O, x ⱕ 0.5 (COD)] and the triclinic trihydrate [CaC2O4 ⋅ (3 ⫺ x) H2O, x ⱕ 0.5 (COT)]. COM and COD are important as the main constituents of kidney stones [39] and occur in many plants [40], and COT has been extensively investigated in the laboratory [41–44].

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The monohydrate (COM) was one of the ﬁrst compounds studied by thermogravimetric analysis, and it was suggested that it should be used as a calibration standard [1]. Upon heating, it loses water between 100°C and 150°C in one distinct step [1,44]. The anhydrous CaC2O4 decomposes between 300°C and 525°C according to the relation CaC2O4 → CaCO3 ⫹ CO [1,45]. Finally, CaCO3 above 800°C decomposes into CaO ⫹ CO2 [1]. The exact decomposition temperatures depend on the experimental conditions, i.e., the amount of sample, heating rate, size and shape of the crucible, and other factors. Thermograms of COD and COT differ from those of COM and from one another both qualitatively and quantitatively in the part corresponding to dehydration. COT loses water in two distinct steps, i.e., between 75°C and 100°C (about two water molecules) and between 100°C and 200°C (approximately one water molecule), whereas the dehydration of COD starts at 25–30°C and proceeds more gradually [44]. A comparison of the qualitative differences of various dehydration curves gives information on differences in the modes of water incorporation resulting from different modes of crystallization. An example is given in Fig. 4, which shows partial thermogravimetric curves (dehydration only) obtained from calcium oxalate precipitates prepared at different initial reactant concentrations. Curve 1 represents dehydration curves typically obtained from samples of COM of different morphologies formed by heterogeneous nucleation (including compact crystals and dendrites); curve 2 is

FIG. 4 Partial TG curves (dehydration only) showing the loss of water from (1) compact and dendritic crystals of COM and (2) microcrystalline aggregates with the structure of COD, dm1 and dm2 are the total mass loss (i.e., loss of hydration water) corresponding to 1 mol of H2O (dm1 for COM) and 2.5 mol of H2O (dm2 from microcrystalline aggregates) per mole of calcium oxalate. (Adapted from Ref. 44.)

Crystalline Dispersions

425

representative of microcrystalline aggregates initiated by homogeneous nucleation. These aggregates exhibit X-ray diffraction powder patterns characteristic of COD and contain between two and three molecules of water per molecule of calcium oxalate. The gradual loss of water between 25°C and 200°C, shown by their dehydration curve, suggests the presence of different kinds of water bound with a wide spectrum of energies. This can be explained by considering the crystal structure of COD and the size and shape of the microcrystalline aggregates. In the crystal structure of COD [46,47] the calcium atoms are coordinated to six oxalate oxygen atoms and two water oxygens. Additional water molecules (x ⱕ 0.5, see formula given earlier in this section) are included into channels that run throughout the crystal and are formed by the oxalate anions because of their unique positions in the crystal structure. These additional water molecules are structurally disordered, i.e., they do not occupy one stable position within the crystal lattice but occupy different positions and are bound with different energies within the water channels. Additional water molecules may be adsorbed at external and/or internal surfaces of the microcrystalline aggregates and are expected to evolve between 20°C and 100°C depending on the type of bonding [25]. By determining the mass loss due to dehydration (dm1 and dm2 in Fig. 4), it is possible to quantitatively determine the phase composition of mixtures of crystal hydrates provided it was qualitatively ascertained by some other method (for instance, by X-ray powder diffraction). This method has been used to determine the inﬂuence of various experimental parameters on the phase composition of calcium oxalate precipitates. Several examples are given in Figs. 5–9. Figure 5 shows the inﬂuence of the initial reactant concentration, ci , on the water content of calcium oxalate precipitates aged from 3 min to 3 h. Here c* is the concentration that corresponds to S*, the critical supersaturation for homogeneous nucleation. It is seen that at ci ⬍ c* the amount of water corresponded to 1 mol H2O per mole of calcium oxalate, i.e., COM was the prevailing precipitate. This was conﬁrmed by X-ray diffraction powder patterns [44]. However, at ci ⱖ c*, the water content in the precipitates gradually increased to about 2–3 mol H2O per mole of calcium oxalate, and X-ray diffraction powder patterns showed that COD was the prevailing precipitate. This change in composition was matched by signiﬁcant changes in the number, size, and morphology of the particles [44,48]. Thus, the profound inﬂuence of the initial reactant concentrations (i.e., the initial supersaturation) on the properties of the precipitates was conﬁrmed. It is interesting to note that in a number of cases the main characteristics of particle sizes and morphology (i.e., compact crystals, dendrites, microcrystalline aggregates) persist even after aging for 24 h. Thus, it was possible to recognize the heterogeneous/homogeneous nucleation boundary and determine S* from 24 h precipitation diagrams and thus to calculate the interfacial energy of the homogeneous nucleus for several slightly soluble precipitates [49].

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FIG. 5 Schematic presentation of changes of the average water content in crystalline calcium oxalate precipitates as a function of the initial reactant concentrations, [Ca] ⫽ [Ox]. Time of aging in contact with the mother liquid was from 10 min to 3 h. c* denotes reactant concentrations corresponding to S*, as deﬁned in Section II.A (i.e., at c ⱖ c*, homogeneous nucleation prevails). (Adapted from Ref. 44.)

An interesting kinetic study deals with the solution-mediated phase transformation of COT and COD into the thermodynamically stable COM [50]. The experimental conditions were adjusted so that either COT or mixtures of COD and COM crystallized initially as conﬁrmed by X-ray diffraction powder patterns. The systems were then aged in contact with the mother liquid, and the transformation of COT or COD into COM was followed by monitoring the total crystal volume as a function of time (by Coulter counter) and determining (by thermogravimetric analysis) the relative proportion of the crystal hydrates at ﬁxed time intervals. In addition, supersaturation proﬁles (i.e., activity products) were determined by solution calcium analysis. In all cases the transformation was completed within approximately 80–100 h. A schematic presentation of the transformation of COT into COM is shown in Fig. 6. In accordance with the analysis of Cardew and Davey [22] (Section II.D), the activity product (Fig. 6a) exhibits a plateau in the region where the dissolution of COT and growth of COM are balanced (Fig. 6b). Interpretation of the kinetics data showed that dissolution of COT is a ﬁrst-order process (i.e., diffusion-controlled) whereas growth of COM is a second-order process, as was also found in seeded crystal growth experiments [51].

C. Control of Crystallization by Additives Any impurity present in the crystallizing solution (‘‘impurity’’ denoting any ions, small molecules, or macromolecules that are not constituents of the nascent crys-

Crystalline Dispersions

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FIG. 6 Kinetic analysis of solution-mediated phase transformation of in situ precipitated calcium oxalate trihydrate (COT) into calcium oxalate monohydrate (COM). (a) Solution analysis: Variation of ion activity product vs. time. (b) Solid phase analysis: Total crystal volume (curve 1) and volume fractions of COT (curve 2) and COM (curve 3) vs. time. (Schematic presentation adapted from Ref. 50.)

tal phase) may adsorb at the crystal/solution interface and modify the rate of nucleation and/or crystal growth. If adsorption is nonspeciﬁc, the growth process is likely to be retarded, resulting in a reduction in crystal sizes. If the impurity is preferentially adsorbed at selected crystal faces, growth in the direction perpendicular to those faces is slowed down. The result is habit modiﬁcation, with the affected crystal faces appearing larger than usual. Such a case is schematically represented in Fig. 7a, which shows how a platelet-like crystal transforms into a needle when an impurity is adsorbed on its lateral faces. Finally, when the solution is supersaturated to two (or more) crystal polymorphs or different crystal hydrates, an impurity can inﬂuence their relative rates of nucleation and growth by preferentially adsorbing at one of them. In that case, growth of the affected crystal phase will be inhibited, while the other phase(s) can grow faster from the same supersaturation. We may thus experience a change in the crystallizing polymorph. This is schematically shown in Fig. 7b, where phase B grows on account of phase A, which is selectively inhibited by an impurity. By understanding these phenomena, one can hope to design additives to crystallizing systems capable of producing crystals of desired particle sizes and morphology or even to induce growth of a desired crystal polymorph. Control of the crystallizing phase by additives is of considerable importance in the production of specialty chemicals such as pharmaceuticals, dyes, and pesticides [8,22]. The formation of metastable polymorphs and/or higher hydrates is often desired be-

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FIG. 7 Schematic presentation showing (a) control of crystal morphology and (b) control of the crystallizing phase by an additive. (a) Preferential adsorption of an additive at the lateral faces of a growing crystal. This type of interaction results in a change of crystal morphology from platelet to needle-like. (b) In a solution supersaturated to two solid phases (polymorphs), an additive (small circles) preferentially adsorbs at the nuclei of phase A and inhibits their growth. As the supersaturation is essentially unaffected, phase B will grow instead.

cause of their advantageous properties, whereas in other cases metastable phases are undesirable because subsequent phase transformation during storage must be avoided. One of the keys to the understanding of speciﬁc additive–crystal interactions is the structural approach. As early as the 1950s attempts were made to explain crystal habit modiﬁcation by the formation of an adsorbed impurity layer structurally similar to a growing crystal face. Thus, Whetstone [52] showed that habit modiﬁcation of soluble inorganic salts can be achieved by organic dyes if the interatomic distances of the polar groups of the dye match the ionic arrangement of the substrate. This structural approach culminated in the 1980s with the design of ‘‘tailor-made’’ additives for control of the growth and dissolution of organic

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crystals. In their classical work Addadi et al. [53] showed that one can design inhibitors for the engineering of organic crystals with the desired morphologies and moreover for the resolution of conglomerates and enantiomers. It is required that a stereochemical relationship exist between the crystal structure, its modiﬁed morphology, and the molecular structure of the inhibitor. Also, in inorganic crystallization systems, organic macromolecules can exert control over the morphology and nature of the crystallizing phase [54–56]. This ability has been routinely used by living organisms to control the properties of biominerals (calcium carbonate in marine organisms, hydroxyapatite in bones and teeth, etc.) [56,57]. As above, the underlying cause of these effects is speciﬁc molecular recognition based on strict stereochemical correlation between the structures of the affected crystal faces and the molecular structure of the additive, which acts as inhibitor. The macromolecules commonly involved in biomineralization seem to be acidic proteins with arrays of negatively charged (carboxylate and/or phosphate) groups. These macromolecules speciﬁcally recognize crystal faces with characteristic structural motifs emerging at their surfaces [57]. Another factor of importance in selective crystal–additive interactions is the difference in electric charge between different crystal faces, which is caused by differences in their ionic structures. This is particularly evident in some crystal hydrates. Thus, for instance, during growth of some plate-like calcium phosphate crystals (octacalcium phosphate, calcium hydrogen phosphate dihydrate) from electrolyte solution, the largest face may, for most of the time be covered by a hydration layer that shields it from electrostatic interactions [55,58]. As a consequence, small molecules with high charge density exhibit face-selective interactions that result in habit modiﬁcation although there is no long-range structural and stereochemical compatibility with the affected crystal faces [59,60]. The selectivity is due to preferential adsorption of the molecules at the charged side faces of the crystal as a consequence of their inability to penetrate the hydration layer. Other examples of selective interactions of surfactants with calcium oxalate hydrates, are given below. Surfactants are particularly suitable as additives for the control of crystallization because of their speciﬁc molecular structure. A surfactant molecule consists of an ionic or nonionic hydrophillic headgroup coupled with a hydrophobic tail. In a crystallization system the headgroup binds to the crystal surface while the tail provides steric hindrance for the incorporation of growth units into the crystal lattice. As surfactants are relatively inexpensive and readily available in many different designs, they should be regarded as ideal crystallization modiﬁers for industrial applications. The ability of anionic surfactants to control nucleation from solutions supersaturated with different calcium oxalate hydrates will be discussed in some detail. Of all three calcium oxalate hydrates, COD has the lowest crystallization rate. It does not readily crystallize from electrolytic solutions but frequently appears

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in the form of large aggregated crystals in pathological mineral deposits such as occur in crystalluria [61] (the formation of crystals in urine) and kidney stones [39]. It was therefore of interest to understand the reasons for COD crystallization under pathological conditions. One of the apparent reasons is the presence in urine of a large number of soluble organic molecules and macromolecules that can promote crystallization of COD by inhibiting the growth of COM and/or COT nuclei (see Fig. 7b). Because many of the urinary organic molecules and macromolecules have surfactant properties, synthetic surfactants were considered ideal model additives for the study of such interactions [62]. In the ensuing studies, crystallization of COM and COD from solutions containing different concentrations of ionic and/or nonionic surfactants (Table 1) was systematically investigated [62–67]. Qualitative and quantitative information on the precipitate composition was obtained by X-ray powder diffraction and thermogravimetric analysis, respectively. From the thermogravimetric data (see Fig. 4), the amount of water in the precipitate was calculated and translated into weight percent of COD, assuming the formula CaC2O4 ⋅ 2H2O. X-ray powder patterns showed that in the controls (systems without added surfactant) and at low surfactant concentrations [below the critical micellar concentration (cmc)], COM was the prevailing crystallizing phase. This was also true when crystalliza-

TABLE 1 Model Surfactants Used in Crystallization Studies Name Anionic Sodium dodecyl sulfate (SDS)

Formula

Ref.

CH 3E(CH 2)11ESO 4Na

62, 64, 65 62, 63

Sodium dioctylsulfosuccinate (AOT) 62, 66 Sodium cholate

Cationic Dodecylammonium chloride (DDACl) Nonionic Octaethylene glycol Mono-n-hexadecyl ether

CH 3(CH 2)11NH 3Cl

64

C 16H33E(CH 2ECH 2O)8H

65

Crystalline Dispersions

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FIG. 8 Crystallization of calcium oxalates in the presence of anionic surfactants (0.3 M sodium chloride solutions supersaturated to COM and COD, pH 6.5, temperature 37°C). Changes in the mass fraction of COD in the precipitate are shown as a function of the surfactant concentration expressed in multiples of the respective critical micelle concentrations (cmc’s). The mass percent of COD (vertical axis) was calculated from thermogravimetric data assuming a formula C2O4 ⋅ 2H2O for COD. (After Ref. 62.)

tion experiments were carried out in the presence of any concentration of cationic [67] or nonionic [65] surfactant. However, when crystallization was carried out in the presence of an anionic surfactant, an upsurge in COD content was observed at surfactant concentrations close to and/or above the cmc, with the effect decreasing in the order SDS ⬎ sodium cholate ⬎ AOT (Fig. 8) [62–66]. In another set of experiments [68] the kinetics of solution-mediated phase transformation of preprepared, well-deﬁned model COD crystals was investigated in the presence of micellar concentrations of an anionic (SDS) and a cationic (DDACl) surfactant. Figure 9 shows that both surfactants almost completely inhibited phase transformation (SDS was slightly more effective than DDACl [68], which is not shown in Fig. 9). We have thus demonstrated that (1) anionic surfactants can control the composition of crystallizing calcium oxalates (Fig. 8), whereas (2) both anionic and cationic surfactants inhibit the solution-mediated phase transformation of COD into the thermodynamically stable COM (Fig. 9). Both results can be readily explained if one considers the respective adsorption isotherms and adsorption densities of surfactants at COM and COD crystal/solution interfaces (see Fig. 10 and Table 2) [68,69]. Adsorption of surfactants at polar surfaces has been extensively investigated because of the importance of modifying particle surfaces for many industrial applications [70,71]. A number of models have been proposed, most of which are based on experimental and theoretical studies of the adsorption of ionic surfactants at the oxide/water interface [72–75]. All authors agree that at low surfactant concentrations, adsorption at charged surfaces (oxides, salts) is driven by

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FIG. 9 Schematic presentation of the kinetics of solution-mediated phase transformation of preprepared, well-deﬁned COD crystals into COM. tA (horizontal axis) is the aging time. Curves: (1) suspension of COD crystals without surfactant (for control) and (2) in the presence of micellar concentrations of SDS or DDACl. Samples were ﬁltered at different time intervals, and the composition of the solid phase was analyzed by thermogravimetric analysis. (Adapted from Ref. 68.)

electrostatic interactions, resulting in molecular adsorption with the headgroups of individual molecules oriented toward the surface. A subsequent upsurge in the slope of the isotherm is due to the formation of surfactant aggregates in the adsorbed layer caused by hydrophobic tail–tail interactions (see inserts in Fig. 10). Finally, a leveling off of the adsorption, coinciding with the cmc of the surfactant, is ascribed to a constant chemical potential sink caused by the formation of micelles in the bulk solution. The isotherms characterizing adsorption of surfactants at the COM/solution and/or COD/solution interface are in agreement with that general picture [68,69]. As an example, adsorption isotherms of AOT onto COM and COD are shown in Fig. 10. In agreement with the above considerations, the AOT/COM isotherm shows a region of low adsorption and a region of high adsorption with a steep inﬂection between them. In the AOT/COD system the region of low adsorption is not apparent, but the rest of the isotherm is similar. It is important for our argument that the course of the thermogravimetric curves represented in Fig. 8 is in general agreement with the course of the adsorption isotherms (Fig. 10), i.e., the phase change is concomitant with the upsurge in adsorption density. A comparison of the plateau adsorption densities of the investigated surfactants at COM/solution and COD/solution interfaces shows (Table 2) that both anionic surfactants (SDS and AOT) adsorb much more strongly on COM than on COD surfaces, whereas for the cationic surfactant the

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FIG. 10 Schematic presentation of adsorption isotherms (adsorbed amount, Γ, as a function of the equilibrium surfactant concentration, Ceq ) characterizing the adsorption of AOT at the surfaces of (a) COM and (b) COD crystals. Inserts indicate monolayer adsorption at low surfactant concentrations and the formation of a double layer at surfactant concentrations exceeding the cmc of the surfactant. (Adapted from Ref. 69.)

TABLE 2 Plateau Adsorption Densities of Ionic Surfactants at Calcium Oxalate/Electrolyte Solution Interfaces Sorbenta

Sorbatea

Molecules per square nanometer

Ref

COM COD COM COD COM COD

SDS SDS AOT AOT DDACl DDACl

31.9 20.5 14.22 7.45 16.3 13.3

68 68 69 69 68 68

a

For deﬁnitions see text.

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adsorption densities at the surfaces of the two substrates are comparable. It is therefore conceivable that anionic surfactants, when present at micellar concentrations in a solution of calcium oxalate supersaturated with both COD and COM, preferentially adsorb on the faster growing COM nuclei and block their growth, thus enabling the growth of COD crystals (see Fig. 7b). For the cationic surfactant we would not expect such selectivity, because the adsorption densities on the two substrates are comparable. In contrast to nucleation control, inhibition of phase transformation does not require selectivity, as interactions with both substrates (inhibition of dissolution of the metastable phase and growth of the stable phase) may be rate-controlling [22,50] (see also Sections II.D and III.B and Fig. 6). It is therefore not surprising that both the anionic SDS and the cationic DDACl effectively inhibit the transformation of COD into the thermoynamically stable COM (Fig. 9) [68]. The difference between the adsorption densities of anionic surfactants at the surfaces of COM and COD crystals, respectively (Table 2), has been explained [68,69] on the basis of the difference in the crystal structures of the two compounds: COM has negatively charged faces with high charge density [38], whereas COD forms highly hydrated crystals with relatively low surface charge [46,47]. (see Section III.B for a more detailed explanation of the COD crystal structure). In all cases, surfactant adsorption is mediated by calcium ions in the electrolyte solution.

IV.

CRYSTALLIZATION IN CONFINED SPACES: EMULSIONS AND MICROEMULSIONS

In the preceding sections, we discussed the formation and transformation of ionic precipitates from bulk electrolyte solutions. We saw that the rates and mechanisms of the processes governing crystallization (nucleation, crystal growth, ﬂocculation, and aging) depend on the experimental conditions such as supersaturation, temperature, and additives. It has been shown that surfactant micelles have a profound inﬂuence on crystallization, even to the extent of controlling the nature of the crystallizing phase (Fig. 8). In this section, we concern ourselves with crystallization of molecular crystals and/or inorganic clusters within conﬁned spaces and/or at the oil/water interface such as occurs in emulsions and microemulsions.

A. Emulsions: Induced Crystallization at the Oil/ Water Interface The critical supersaturation for nucleation of molecular crystals from a melt or solution is conveniently achieved by cooling the sample until a crystallization temperature, Tc is reached. Another critical point is the melting temperature, Tm ,

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which is obtained by controlled heating of the crystals. The critical supercooling for homogeneous nucleation, T* ⫽ T*m ⫺ T*c , is, like the critical supersaturation S*, a thermodynamic quantity characteristic of the crystallization system. However, it is almost impossible to achieve this degree of supercooling in a bulk melt because of the presence of numerous impurities, which act as heterogeneous nuclei (for a discussion of homogeneous and heterogeneous nucleation, see Section II.A). The effect of these catalytic impurities can be minimized if the sample is broken up into a large number of isolated droplets, which may be achieved by emulsifying. Emulsions thus obtained are micrometer-sized droplets of an organic (oil) phase in water or, vice versa, water droplets in a liquid organic phase (oil) dispersed by an amphiphilic emulsiﬁer. Crystallization from such systems was ﬁrst studied in the context of homogeneous nucleation [76]. Since then, many studies of the crystallization of an oil phase in oil-in-water emulsions [77–81] and of the freezing of water or aqueous solutions dispersed within an oil phase [82–84] have been carried out. In this section we discuss the crystallization of molecular crystals in oil-in-water emulsions; for a review on water-in-oil emulsions, see chapter 5. Most experimental studies on crystallization in emulsions are concerned with nucleation and crystal growth kinetics. In these studies thermal analysis is an indispensable tool. Thus, as a measure of the efﬁcacy of an initiator of heterogeneous nucleation, the supercooling, ∆T ⫽ Tm ⫺ Tc is determined. In many cases Tc is signiﬁcantly higher than T*c . To evaluate ∆T, the system is subjected to cooling and heating cycles and some property is measured as a function of temperature. Alternatively, the variation of the chosen property of the system is followed isothermally as a function of time to evaluate the kinetics of crystallization at constant temperature. For these measurements a number of experimental techniques are available: dilatometry [77], NMR spectroscopy [85], ultrasonic velocity measurements [78,85], and DSC [86], among others. In addition, DTA and DSC are used to yield information on the enthalpies of freezing, ∆Hf , or melting, ∆Hm, and the heat capacity, cp . Nucleation of oil in individual emulsion droplets can be either homogeneous or heterogeneous, with the catalytic impurity distributed throughout the bulk (bulk heterogeneous nucleation) or at the oil/water interface [77–79] (surface heterogeneous nucleation). A fourth mechanism, interdroplet heterogeneous nucleation, has also been proposed [80,81]. It is the third mechanism, interfaceinduced nucleation, that concerns us most in this volume. In 1963 Skoda and Van den Tempel observed [77] that the temperature at which crystallization of triglycerides started in emulsiﬁed systems was invariably lower than in nonemulsiﬁed solutions and depended on the emulsifying agent used. With some emulsiﬁers Tc was so low that the authors assumed the existence of homogeneous nucleation. Other molecules effected a rise in Tc, apparently catalyzing nucleation. It was observed that the catalytic activity was the greater

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the more the molecular structure of the emulsiﬁer resembled that of the crystallizing phase. A mechanism was assumed whereby emulsiﬁer molecules adsorbed at the surface of the oil droplets orient triglyceride molecules close to the surface and thus catalyze nucleation. This structural approach was corroborated by Davey et al. [79], who studied the nature of nucleation catalysis at the oil/water interface using as an example meta-chloronitrobenzene (m-CNB)-in-water emulsions prepared with a wide range of emulsiﬁers. The crystallization temperature, morphology, and crystal orientation at the oil/water interface were determined and correlated to the molecular packing and structure in the amphiphile monolayer at the interface. It was found that nucleation catalysis occurred when the surface area per molecule of the amphiphile approached that of the crystallizing substrate. In addition, in the presence of emulsiﬁers whose molecular structure resembled that of the (020) crystal face, crystals were oriented with that face in the plane of the interface in contact with the aqueous phase. This was proven by X-ray powder patterns, which unequivocally showed preferential crystal orientation. In a recent study by Kaneko et al [78], the dual role of an impurity in emulsion crystallization of n-hexadecane was convincingly demonstrated, thus corroborating earlier bulk crystallization studies showing the dual role of impurities in inorganic crystallization [87]. These authors emulsiﬁed n-hexadecane in water using polyoxyethylene (20) sorbitan mono-dodecanoate (Tween-20) as an emulsiﬁer. Before emulsiﬁcation, a highly hydrophobic food emulsiﬁer, a sucrose polyester with a palmitic acid moiety (P 170), was added to the n-hexadecane. Crystallization was then studied by monitoring changes in ultrasound velocity during temperature changes and in isothermal kinetic experiments. The experiments were based on the fact that ultrasound velocity changes abruptly as a consequence of solid–liquid transformation, showing a sharp increase at the onset of crystallization (for a detailed description of the technique, see Ref. 85). Figure 11 shows that two parameters, Tc and the change in ultrasound velocity, ∆V, could be independently measured in the same experiment. It is seen that while Tc increased, ∆V decreased with increasing concentration of the impurity (for more data see Ref. 78). This result has been interpreted as showing that the impurity induces nucleation when adsorbed at the oil/water interface while at the same time it retards crystal growth. In parallel experiments in a bulk system, there was no detectable effect of the impurity on nucleation, but crystal growth was retarded. Apparently, it is the arrangement of the impurity molecules at the oil/water interface that produces the catalytic effect. The foregoing studies point to conclusions similar to those of the extensive research on induced crystallization of inorganic and organic crystals under closepacked amphiphilic Langmuir monolayers [88–92]. All these studies show that it is possible to design interfaces that will not only catalyze nucleation but will also orient the nascent crystals in a well-deﬁned and reproducible manner. The

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FIG. 11 Schematic presentation of changes in the ultrasound velocity V (arbitrary units) with temperature during the controlled cooling of n-hexadecane in water emulsions, emulsiﬁed with Tween-20. Parameters determined are the crystallization temperature Tc and the magnitude of the change in V due to crystallization (∆V ). Curve 1, control; curve 2, in the presence of an impurity (P-170). (Adapted from Ref. 78.)

underlying mechanisms are geometrical, electrostatic, and stereochemical complementarity between the incipient nuclei and the functionalized substrates [90,92].

B. Crystallization in Microemulsions In contrast to emulsions, which are unstable macrodisperse systems (1–10 µm in droplet diameter), microemulsions are homogeneous, optically transparent, thermodynamically stable systems that can be formed only in speciﬁc ranges of temperature, pressure, and composition. They consist of droplets of water tens of nanometers in size dispersed within an immiscible organic (oil) phase [inverse micelles, or water-in-oil (W/O) microemulsions] or vice versa, oil pools dispersed within an aqueous phase [direct micelles, or oil-in water (O/W) microemulsions]. The droplets are encased in a surfactant shell as in emulsions or, more frequently, in a shell consisting of a suitable surfactant and a cosurfactant (usually an alcohol) and are thus stabilized. Water-in-oil microemulsions are characterized by a micellar core formed by the polar heads of the surfactant protruding into the water droplet, surrounded by a layer of alkyl chains protruding into the surrounding apolar liquid (Fig. 12). The micellar size and shape depend on the nature of the surfactant molecule, the water/surfactant molar ratio, and the presence and location of solutes within the micellar core [93].

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FIG. 12 Schematic representation of the location of solubilizates within water/isooctane microemulsions stabilized with AOT. (a) Without solubilizate; (b) ions and/or ionic clusters located within the water pools; (c) aspartame molecules located at the water/isooctane interface, with the aspartyl end pointing toward the water pool and the phenylalanine end oriented toward the oil phase.

In recent years, W/O microemulsions have found numerous applications as ‘‘microreactors’’ for speciﬁc reactions (for comprehensive reviews, see Refs. 94 and 95). Thus, it has been shown that hydrophilic enzymes can be solubilized without loss of enzymatic activity and used to catalyze various chemical and photochemical reactions [96,97]. Other interesting applications involve the polymerization of solubilizates in microemulsions [98] and the preparation of microporous polymeric materials by polymerization of single-phase microemulsions [99]. Furthermore, microemulsions have been used as microreactors for the synthesis of nanosized particles for various applications [93,95] such as metal clusters (Pt, Pd, Rh, Au) for catalysis [100,101], semiconductor clusters [102–104] (ZnS, CdS, etc.), silver halides [105], calcium carbonates, and calcium ﬂuoride [106]. Recently it was shown [107,108] that it is possible to use W/O microemulsions for the control of polymorphism of water-soluble organic compounds. In most of these applications, one or more reactants are solubilized within a microemulsion and then a reaction is initiated. Depending on its molecular structure,

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a solute may be located at different sites within a microemulsion [93]. The two locations that concern us most in this presentation are within the water pools (Fig. 12b) and at the water/oil interface (Fig. 12c). Experimental studies concerning crystallization from W/O microemulsions use thermal analysis methods to characterize the microemulsions themselves, to determine thermodynamic parameters of crystallization, and to characterize the ﬁnal products. A large number of studies are concerned with the state of water in ionic [109] and nonionic [110] W/O microemulsions. It has been shown that because of the close proximity of the interface, the properties of the water molecules are quite different from those of water in the bulk, and this difference in itself may have a profound effect on the solubilization and crystallization of solutes. The problem is discussed in detail in two other chapters (by Schulz et al. and by Garti et al.) in this book and will not be reiterated here. In this presentation we describe (1) calorimetric studies of the formation of nanosized inorganic crystallites and (2) the use of TG and DSC in the characterization of a water-soluble organic compound crystallized in a W/O microemulsion. The ability to synthesize inorganic crystallites in the size region of tens of angstroms (i.e., hundreds to thousands of atoms) within microemulsions has attracted widespread interest [94,95]. Such crystallites are properly termed clusters, because they have properties intermediate between those of molecules and those of bulk solids [102,104]. They are conveniently prepared by solubilizing a water-soluble metal salt and a reducing agent (for metal clusters) or a water-soluble cationic salt and a water-soluble anionic salt (for metal salts including semiconductors, silver halides, etc.) in two separate microemulsions of the same composition and then mixing the microemulsions. For example, nanosized gold particles were prepared by in situ reduction of tetrachloroauric(III) acid by hydrazine sulfate, both reagents being solubilized in microemulsions of the same composition [101], and silver chloride was prepared by mixing two microemulsions, one containing solubilized AgCl and the other, NaNO3 [105]. As reaction media, water–AOT–hydrocarbon microemulsions are preferred by many investigators [95,104] because (1) AOT self-assembles without cosurfactant, (2) the phase diagrams have relatively large L2 (water-in-oil) regions, and (3) the microemulsions consist of well-deﬁned droplets (water pools). In order to understand why cluster size particles are formed and stabilized within microemulsions, we brieﬂy consider the precipitation reaction: The water-soluble reagents are situated within the water pools of the microemulsions (Fig. 12b) and are randomly distributed among the droplets according to a Poisson distribution [111]. Thus, the reaction that occurs upon mixing is due to exchange between droplets containing different reactants [104]. As in emulsion crystallization (Section IV.A), the effect of heterogeneous nuclei (impurities) is minimized by compartmentalization. Thus, if the nascent salt has a low solubility product and S* is exceeded, particles form by way of homogeneous nucleation. The clusters thus formed would have a tendency to grow by

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ﬂocculation rather than by the addition of ions to the crystal lattice (see Section II.A and Fig. 1). However, because the particles have a large surface-to-volume ratio, they will be protected from ﬂocculation by the adsorption of one of the reactant ions and/or by the surrounding surfactant shell. In a W/O microemulsion stabilized by AOT, the size of the nascent particles is a function of the water pool size, which is given by the equation [104] r ⫽ 0.18w ⫹ 1.5

(7)

where r (in nm) is the hydrodynamic radius and w ⫽ [H2O]/[AOT]

(8)

is the water/AOT molar concentration ratio. So the size of the compartmentalized water droplets can be varied by simply changing w and can then be used to control the size of the precipitating clusters [104]. The enthalpies of precipitation of a variety of nanoparticles in W/O microemulsions have been studied by calorimetry. These include metal particles such as palladium [112] and gold [101], silver halides [105], calcium salts [106], and semiconductors such as ZnS [103]. It was shown that particle formation is an exothermic process, the values of the molar enthalpies, ⫺∆H, increasing with increasing w. In all cases, the values of ⫺∆H for cluster formation in microemulsions were less negative than when the corresponding process was conducted in a bulk aqueous solution. Clearly, submicrometer-sized clusters had higher energies than the corresponding micrometer-sized crystals formed from bulk solutions. In a recent study of the formation of ZnS nanoparticles [103], Arcoleo et al. separated the contribution of the particle size from other contributions to the molar enthalpy by independently measuring particle sizes by UV spectroscopy. (Note that the UV spectroscopic method is based on changes in UV-Vis spectra corresponding to size changes of semiconductor clusters. That is, a shift of λmax toward lower wavelengths is observed with decreasing particle size [103,104].) Thus, it was shown that the ⫺∆H values are indeed a function of particle size, because they increased linearly with increasing λmax. However, at constant λmax (i.e., at the same nanoparticle radius), the ⫺∆H values increased with increasing [S⫺]/[Zn2⫹] molar ratio and depended on the nature of the surfactant stabilizing the microemulsion. This result was interpreted as indicating contributions to the enthalpy from the adsorption of HS⫺ ions at particle surfaces and from particle– surfactant interactions at the oil/water interface [103]. Recently, the possibility of using microemulsions as microreactors for the control of polymorphism of organic compounds, speciﬁcally amino acids and peptides, was demonstrated by Fu¨redi-Milhofer et al. [107,108]. In these experiments, the organic molecules were solubilized in hot microemulsions and crystallized by slow cooling. In some cases, in contrast to the precipitation of ionic clusters (see above), the procedure was most effective when the solute mole-

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cules were situated at the water/oil interface rather than within the water pools of the reversed micelles (Fig. 12c). Thus, the surfactant was brought into intimate contact with the nascent solid phase and could inﬂuence crystal nucleation and growth as in micellar systems (Section III.C and Fig. 7). We used the method to selectively crystallize one of the polymorphs of phenylalanine, whereas a mixture of two different polymorphs crystallizes from bulk aqueous solutions (J Yano, H Fu¨redi-Milhofer, N Garti, unpublished results). We also succeeded in preparing a previously unknown crystal hydrate of the artiﬁcial sweetener aspartame (APM III) by recrystallization from water/isooctane microemulsions stabilized with AOT [107,108]. The latter example is described in more detail below. Aspartame (N-l-α-aspartyl-l-phenylalanine methyl ester; APM) is widely used as an artiﬁcial sweetener because of its high sweetening power (150–200 times sweeter than sucrose), no aftertaste, and relatively good compatibility for human consumption [113]. However, when obtained by conventional recrystallization procedures its crystals tend to have unfavorable morphological characteristics and poor dissolution kinetics. It was therefore of great interest to obtain new crystal forms of aspartame with improved dissolution behavior. The aspartame molecule, HOOCE CH2 E CH(NH2)E CO ENHE CH(COOCH3) ECH2C6H5 is a dipeptide composed of a highly hydrophilic aspartyl residue and a hydrophobic phenylalanine methyl ester entity. In the basic crystal structure [114], the aspartame molecules are arranged in columns formed by an extensive hydrogen bond network, interconnecting zwitterionic N-terminal ends of the aspartyl residue and hydration water molecules. The outer surfaces of the columns are highly hydrophobic, because they are covered with phenyl and methyl groups stemming from the esteriﬁed phenylalanine end. As this columnar structure is probably responsible for the poor dissolution behavior and aspartame’s tendency to form ﬁbers, it was assumed that one way to improve the dissolution behavior would be to disrupt the hydrogen bonding networks by introducing an additive or additional water molecules into its interior. It seemed that a good method to achieve this objective might be the recrystallization of aspartame from a suitable microemulsion. Among a number of microemulsions studied, water/isooctane/AOT microemulsions most effectively solubilized aspartame. At constant temperature and atmospheric pressure, the maximum amount of aspartame that could be solubilized, n(APMs), where n is the number of moles, exceeded by several times the amount that could be dissolved in the same volume of water. Furthermore, n(APMs) depended linearly both on the concentration of AOT and on the amount of free water in the microemulsion; i.e., a linear dependence on w was obtained when w exceeded 10. Thus, we can write n(APMs)/n(AOT) ⫽ Kw

(9)

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where K ⫽ tan α ⫽

冢冣

n(APMs) n(APMs) 1 ⫽ n(AOT) w n H2O

(10)

is the slope of the straight line described by Eq. (9). The respective intercept obtained by extrapolation to w ⫽ 0 gives the n(APMs)/n(AOT) ratio at the water/ oil interface for a given temperature. The relationship is schematically represented in Fig. 13. At 25°C, under the experimental conditions employed in Ref. 108, the n(APMs)/n(AOT) molar ratio at the water/oil interface was 0.16, corresponding to six molecules of AOT per molecule of aspartame. The location of the aspartame molecules at the water/oil interface is probably similar to that depicted in Fig. 12c, i.e., the hydrophobic phenylalanine end points toward the nonpolar medium while the aspartyl end points toward the water pool. Having established that aspartame molecules are located at the water/oil interface, commercial aspartame was then solubilized in a hot microemulsion and recrystallized by cooling [107,108]. Because of the intimate contact with the surfactant during crystallization, the resulting crystal form was expected to be less organized and higher in energy than crystals formed from bulk aqueous solutions. Indeed, after washing the crystals to remove the remaining oil and surfactant a new crystal form, APM III, that shows much improved dissolution kinetics was obtained. The crystals exhibit a distinct X-ray diffraction powder pattern, which is signiﬁcantly different from the patterns of previously known polymorphs of aspartame. However, NMR spectra of the product dissolved in D2O are identical

FIG. 13 Schematic representation of the maximum molar ratio n(APMs)/n(AOT) in water/isooctane/AOT microemulsions as a function of w ⫽ n H2O/n(AOT), where n is the number of moles. At w ⬎ 10 the dependence is linear; the slope, K ⫽ tanα , is given by Eq. (10); and the intercept, y0, is the APM/AOT molar ratio at the water/isooctane interface. (Adapted from Ref. 108.)

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to those of commercial aspartame, indicating that the molecular structure is unchanged. In the following, we give details of the characterization of APM III by DTG and DSC; for further characteristics of the product, see Refs. 107 and 108. Thermal decomposition of aspartame was ﬁrst studied by Chauvet at al. [115], who used thermal microscopy and NMR spectroscopy to identify the decomposition products. According to these authors, TG/DTG and DSC peaks appearing at temperatures lower than 120°C are due to the loss of hydration water, whereas those appearing at higher temperatures are due to decomposition. Two decomposition peaks are apparent in the TG/DTG spectra, the ﬁrst, at 170–200°C, being associated with the evolution of EOCH3 in the course of the formation of diketopiperazine (3-benzyl-2,5-piperazine dione-6-acetic acid), and the second, at 250– 450°C, being due to the decomposition of that compound. In the corresponding temperature range, two endothermic DSC peaks, corresponding to (i) the formation of diketopiperazine (189–191°C) and (ii) fusion of this compound (at 252– 254°C) have been reported in Ref. [115] and a third one (at 322–326°C) corresponding to the decomposition of diketopiperazine, was identiﬁed in Ref. 107. An additional exothermic DSC peak (at 203°C) was obtained when experiments were conducted with an open sample holder and was ascribed to recrystallization of diketopiperazine [115]. Spectra obtained from commercial aspartame (Nutrasweet) and from APM III by TG/DTG and DSC [107] are in general agreement with the above-described analysis, but differences in the curves obtained from different samples are apparent in the region corresponding to dehydration (Fig. 14). The TG/DTG curves show that APM III contains signiﬁcantly more hydration water (7 wt% as opposed to 3.7 wt% in Nutrasweet aspartame and 1.77 wt% reported in Ref. 115), which evolves at lower temperatures (peak temperatures 91°C and 109°C for APM III and Nutrasweet aspartame, respectively). The corresponding endothermic DSC peak for APM III (curve 2 in Fig. 14a) is broader than the one obtained from the commercial sample (curve 1 in Fig. 14a); in fact, it appears to be composed of two peaks, one with a maximum at about 50°C and the other a sharp peak appearing near the boiling point. We therefore concluded [107] that some of the hydration water in APM III is loosely bound while at least part of it is tightly bound crystal water. It should be noted that even when DSC spectra were recorded from ⫺100°C at a rate of 5°C/min, no peak corresponding to free freezing water was detected. Studies of crystallization in emulsions and microemulsions are part of a new area of materials research, the aim of which is to produce advanced inorganic, organic, and inorganic–organic composite materials with well-deﬁned properties. The research has been inspired by biomineralization, i.e., the strategies that living organisms use to form their skeletons or store minerals for various purposes.

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FIG. 14 Partial (a) DSC (rate of heat ﬂow as a function of temperature) and (b) DTG curves (dehydration peaks only) showing the difference between commercial (Nutrasweet) aspartame (curves 1) and aspartame recrystallized from water/isooctane/AOT microemulsions (APM III, curves 2). In diagram (a) the enthalpy changes, ∆H, associated with dehydration were calculated by integration of the respective peak area. Scanning rate 10°C/ min. (Adapted from Ref. 107.)

Remarkably, organisms routinely form tough yet ﬂexible organic–inorganic composite systems (their skeletons) in aqueous environments at relatively low temperatures, i.e., under nondestructive conditions. It is therefore well worth learning more about the strategies employed. The main principles of biomineralization can be discerned from several excellent reviews that are available on the subject [56,57,116,117]. The ﬁrst step in many forms seems to be space delineation by cells. Materials frequently used for this purpose are lipid bilayers either in the cell wall or as a part of matrix vesicles located outside the cell. A less frequently used material is composed of polymerized, water—insoluble proteins and/or polysaccharides [116]. Several mechanisms of crystallization within biological cells or vesicles have been described: 1.

In some cases mineral may form in the center of a vesicle and rapidly spread to form spherulites. This form of mineralization has been observed inside small intracellular vesicles where the crystals function as temporary storage sites for ions important in metabolism [117]. In such cases, the presumed function of the vesicle wall is merely to inhibit further crystal growth.

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2. In other cases (such as in the storage of iron in organisms by the protein ferritin), the membrane walls are probably involved, but the level of nucleation control is limited to spatial constraints and charge and polar interactions [92]. 3. Many biological mineralization processes involve oriented nucleation strictly controlled by organized organic interfaces that interact with the nascent crystals by virtue of structural and stereochemical recognition processes [57,91,92,117]. Clearly, the adaptation of the principles of biomineralization in the laboratory opens exciting new avenues in materials research, speciﬁcally in the development of advanced materials [91,92,94,95]. The main ideas ‘‘borrowed’’ so far from biological organisms are compartmentalization and molecular recognition at organized interfaces, which may be involved in crystal nucleation. There is a vast potential in the use of self-assembling organic materials for the construction of compartments for nucleation and crystal growth. Furthermore, by designing the materials for compartmentalization, it is possible to tailor interfaces to exert control over the crystallization processes. Thus, it should be possible to develop low temperature, nondestructive synthetic routes to advanced materials with special properties such as uniform particle sizes, nanoscale dimensions, tailored morphologies, and/or crystal orientation. In this review we have discussed several examples, many more being available in the cited literature. The potential of this novel approach has yet to be fully realized to satisfy the high demand for advanced materials that exists in many industries (electronics, telecommunication, aerospace, automotive, chemical, food, pharmaceutical, biomaterials and others). In this endeavor, important contributions to the characterization of materials and products as well as to the determination of the energetics and kinetics of reactions are being made by various methods of thermal analysis.

REFERENCES 1. C Duval. Inorganic Thermogravimetric Analysis, 2nd ed., Elsevier, New York; 1963. 2. EL Charsley, SB Warrington, eds. Thermal Analysis: Techniques and Applications, The Royal Society of Chemistry, Cambridge, UK, 1992. 3. F Paulik. Special Trends in Thermal Analysis, Wiley, New York, 1995. 4. MN Jones, G Pilcher. Annu Rep Prog Chem Sect C 84:65–104 (1987). 5. MN Jones, G Pilcher. Annu Rep Prog Chem Sect C 89:235–288 (1992). 6. F Stengele, W Smykatz-Kloss. J Thermal Anal 51:219–330 (1998). 7. LM Barcina, A Espina, M Suarez, JR Garcia, J Rodriguez. Thermochim Acta 290: 181–189 (1997). 8. T Wadsten. J Thermal Anal 47:525–533 (1996). 9. LA Collett, ME Brown. J Thermal Anal 51:693–727 (1998).

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12 Solid-State Transitions of Surfactant Crystals ´ -VINCEKOVIC ´ and VLASTA TOMASˇIC ´ Department NADA FILIPOVIC of Physical Chemistry, Ruer Bosˇkovic´ Institute, Zagreb, Croatia

I. Introduction A. Surfactant crystals B. Thermal behavior of surfactant crystals C. Methods of phase transition analysis II.

Single-Chain Surfactants

451 452 453 455 456

III. Catanionic Surfactants A. Symmetrical catanionic surfactants B. Asymmetrical catanionic surfactants

459 460 466

IV. Double-Chain Surfactants

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References

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I. INTRODUCTION The typical surface-active or surfactant molecule consists of at least one polar hydrophilic part and one apolar hydrophobic part, such as a hydrocarbon or ﬂuorocarbon chain. Although there is normally only one headgroup per surfactant molecule, there are frequently several nonpolar tails. These can be linear or branched, the most common being single and linear. Because of the coexistence of two opposite types of behavior inside the same molecule, surfactants can build different submicroscopic aggregates in water that can organize themselves into various supramolecular structures of macroscopic dimensions and different properties. The variety of supramolecules ranges from micelles to liquid crystalline 451

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phases. In most cases, those structures can transform from one to the other as a result of sometimes subtle changes in the solution conditions (e.g., concentration, electrolyte addition, temperature changes). Literature relating to the phase spectra of surfactants in aqueous and nonaqueous solutions is plentiful. Changes in the structures are manifested by abrupt changes in physical characteristics of the solution (viscosity, conductivity, and other transport phenomena; birefringence; or the existence of characteristic X-ray diffraction patterns) [1]. With decreasing solvent content, interactions between adjacent structures increase, leading to the formation of the liquid crystalline phase. On further decreasing the solvent content, dry surfactant crystals are formed, often via solvent-containing surfactant crystals. The terms liquid crystal, mesophase, or mesomorphic state are used synonymously to describe a number of different states of matter in which the molecular order lies between the almost perfect long-range positional or orientational order of solid crystals and the long-range disorder found in ordinary isotropic liquids. Two main classes of liquid crystals are usually distinguished: lyotropic and thermotropic. In lyotropic mesophases, the combination of order and mobility can be achieved by using a solvent; thermotropic mesophases are based on the temperature-induced mobility of form-anisotropic molecules in the melt. Surfactants can often form both thermotropic and lyotropic liquid crystals; i.e., they possess amphitropic properties [2]. We are interested here only in phase transitions arising solely from the action of thermal energy on single- and double-chain surfactant crystals (synthetic bilayer-forming amphiphiles) and in a novel class of surfactants—catanionic surfactants, which are composed of oppositely charged ionic single-chain surfactants. We do not discuss the vast ﬁeld of molecules of primarily amphiphilic character such as lipids, proteins, and copolymers.

A. Surfactant Crystals Many surfactants in the dry state exist as well-formed crystals. Like most compounds that contain a long hydrocarbon chain, the resulting structures usually appear to be lamellar with alternating head-to-head or tail-to-tail arrangement [3]; i.e., the polar heads and hydrocarbon chains are both arranged in bilayers but segregated from each other. The bilayer structural element of a crystal has macroscopic dimensions in the x and y directions but molecular dimensions in the z direction. Stacking together many bilayers in the z direction forms the bulk crystalline phase. Ordinarily, the atoms in the outer planes do not penetrate signiﬁcantly into the opposing plane of the adjacent bilayer during stacking; i.e., in most surfactant crystals, the functional groups of one layer do not penetrate into the space occupied by the functional groups of another [4]. Most surfactant molecules exist in an extended all-trans conformational structure within perfect single crystals. Structural anisotropy of the cross section of straight-chain lipophilic

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groups is principally responsible for the existence of polymorphism and structural complexity in the crystal states of long-chain molecules [5]. Numerous quantitative variants of the bilayer structure exist in surfactant crystals. One important variable is the tilt angle of molecular pairs with respect to the xy plane of the bilayer, and another is the rotational orientation about the z axis of adjacent molecules. Possible of bilayer arrangements of molecules consisting of one polar group and one or two hydrocarbon chains include bilayer structures with vertical chains or tilted chains, chain penetration structures, and others [6]. Some of the surfactants do not have a bilayer as a basic structural element. Alternative possibilities are interdigitated and monolayer structures. In an interdigitated structure, the head of one molecule is adjacent to the tail of the next one within the structural layer of the crystal, and the surfaces of these structural layers include both the heads and tails of the surfactant molecules [7]. The characteristic of a monolayer structure is that molecules within a monolayer are similarly oriented, but the polar surface of each monolayer lies against the nonpolar surface of the next monolayer [8]. The hydrocarbon chain-packing modes are usually described by means of a subcell, which gives the symmetry relations between equivalent positions in one chain and its neighbors [9,10]. Four types of subcells have been identiﬁed: (1) The planes contain parallel hydrocarbon chains, (2) the chains are perpendicular to each other, (3) the chain axes are crossed, and (4) the chains are packed in a hexagonal lattice. By lateral repetition of the subcell, the entire structure of the chain region is obtained. Structural analysis of normal parafﬁns with more than nine carbon atoms in the chain revealed mainly four possible distinct crystal structures: hexagonal, triclinic, monoclinic, and orthorhombic [11]. Crystal hydrates are formed from strongly polar surfactants whose shape does not allow them to pack densely without water being present. The role of water molecules is to (1) energeticly interact with the polar functional groups and (2) perform a space-ﬁlling function to improve crystal packing. When a molecule can pack nicely in a dense crystal, then crystal hydrates are unlikely [4].

B. Thermal Behavior of Surfactant Crystals Solids and ﬂuids change their structure with temperature as a reaction to speciﬁc thermal molecular motions. Continuous thermal expansion may be followed by abrupt changes in the form of the solid crystalline–solid crystalline transition and melting. Phase transitions are generally accompanied by the cooperative onset of one or several speciﬁc types of molecular movements. In the case of a solid crystalline–solid crystalline phase transition, restricted motions of mainly rotational character occur, while in a melting transition the large scale of intramolecular conformational changes connected with long distance translational diffusion leads to a breakdown of the crystalline lattice.

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Many surfactants undergo polymorphic and melting phase transitions in much the same manner as do most other crystals with hydrocarbon chains, except that they often do not transform directly to an isotropic phase; i.e., they pass through a liquid crystalline phase before reaching the isotropic liquid phase [12]. The general picture of a surfactant crystal phase transition includes the trans to gauche conﬁgurational change for each C EC bond; i.e., the disorder of a low temperature phase, in which the hydrocarbon chains are parallel and, in the all-trans conﬁguration, is attained by a gauche rotation of some C EC bonds. Hydrocarbon chains take up a variety of conformations as a function of temperature. The conformational disordering of the alkyl chains at lower temperature causes the polymorphic transitions in the solid state, while melting mainly implies the bidimensional disordering of the ionic layers from the crystalline to the liquid crystalline organization [13]. As the alkyl chains assume an ordered arrangement with weak intermolecular forces, the thermal liberation of rotational freedom around the chains takes place at a relatively low temperature. Molecular motion within the chain increases gradually as the temperature increases until, at characteristic temperatures, there is a considerable increase in the molecular motion, causing the formation of various polymorphs. Polymorphic crystals may be deﬁned as crystals that are formed from the same molecule and have the same composition but are different in crystal structure. During a phase transition the crystal that exists at low temperatures may be transformed on heating into a different structure. Two different kinds of polymorphs exist; equilibrium and metastable [14,15]. A form that has a range of temperature over which it is stable with respect to other polymorphs is said to be an equilibrium polymorph. An equilibrium polymorph exhibits thermodynamically reversible isothermal phase transitions. Metastable polymorphs are kinetically stable states whose existence depends on the presence of a kinetic barrier to the attainment of equilibrium polymorphs. The transformation of a metastable polymorph to the corresponding equilibrium polymorph is an irreversible process. The packing of hydrocarbon chains into a crystalline alignment is difﬁcult because of the many possible conﬁgurations of the chain units. That difﬁculty is reﬂected in the relatively low melting points and low crystallinity of most hydrocarbons. The melting points of surfactant crystals range from far below 273 K to greater than 623 K. The upper limit of these melting points indicates that the polar groups contribute to crystal stability, because the estimated melting point of linear hydrocarbons of inﬁnitely long chain length is about 417 K [16]. In comparison to most inorganic crystals, surfactant crystals are low melting, and sometimes they do not melt reversibly; i.e., they are not stable at their melting point. Because of molecular structural breakdown, deﬁnitive physical studies cannot be performed. In the case of a surfactant with a liquid crystalline phase, several melting transitions take place, but ﬁnally an isotropic phase will form.

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Generally, in the transformation of a lamellar crystal to a lamellar liquid crystal of the same composition, the average chain length in the bilayers actually decreases because of a change from all-trans to gauche conformations. However, depending on the tilt angle of the chains in the crystal, a net increase or decrease in interlayer spacing is to be expected. In the case of strongly tilted chains, interlayer spacing may increase. Liquid crystals are a state of matter in which liquid-like disorder exists in one or two dimensions. Three types of thermotropic liquid crystalline states are commonly recognized: nematic, smectic, and cholesteric [17]. In the nematic state, the centers of gravity of the elongated molecules are arranged in a nonordered manner, but the long axes are oriented in a deﬁnite direction. The nematic mesophases are the least ordered liquid crystalline phases and are also usually the most stable at high temperatures in thermotropic systems. They are typically the last phase to melt, and when found they usually coexist with an isotropic liquid phase. In the smectic state, the centers of gravity and the ends of the molecules are located in planes equidistant from one another. A number of different types of smectic phases are known, divided into a number of subclasses. The common feature of smectic mesophases is that, apart from the orientational ordering along the directrix, there is a further arrangement of the molecules in layers. According to the molecular order within the layers and the angle of the directrix with respect to the layer, it is possible to differentiate various smectic phases (usually denoted as A, B, C, D, etc.). The cholesteric state can be regarded as twisted nematic. The local directrix in each nematic plane describes a helical pattern. Generally, the thermal behavior of solid crystalline surfactants depends on the molecular packing properties, which include length, branching, and unsaturation of a hydrocarbon chain, polar headgroup, and counterion size. Therefore, it is very difﬁcult to discuss quantitatively the relationship between the geometrical packing property of surfactant molecules and the microscopic and macroscopic rearrangement of molecules caused by heating or cooling. An accurate treatment of a thermal phase transition would require evaluation of a partition function, which involves all the possible contributions to the total energy of a given conﬁguration of the system. These contributions include, in the case of a bilayer, the repulsive excluded-volume interactions, the attractive van der Waals, rotamer, and headgroup interactions. A rigorous statistical-mechanical solution to this problem is extremely complicated, and this is the reason that phase transitions described in the literature are mainly discussed only from a purely phenomenological point of view.

C. Methods of Phase Transition Analysis Methods for the examination of solid-state phase transitions are thoroughly discussed in a review by Threlfall [18]. All solid-state properties of the different

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polymorphic modiﬁcations of a compound will be different, but often only marginally so, to the point of instrumental indistinguishability. For this reason it is important to use a variety of techniques to avoid erroneous conclusions. Techniques that have been available for many years include hot-stage microscopy, thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), differential thermal analysis (DTA), X-ray powder and single-crystal diffraction (XRD), and solubility and density measurements. Techniques that have become readily or more widely available within the past decade are solid-state NMR, diffuse reﬂectance infrared spectroscopy, near-infrared spectroscopy (NIR), Raman spectroscopy, the use of area detectors on a diffractometer, and combined techniques including hot-stage infrared spectroscopy, infrared microscopy, and video recording on the microscope. The same methods can also be used to study the liquid crystalline behavior of a wide class of surfactants, but the outstanding method for a preliminary examination is polarizing microscopy. A polarizing microscope equipped with a heating stage permits qualitative visual observation of the phase transformations that occur when a compound passes through the liquid crystalline state. Very often, a simple observation of morphology and orientation patterns displayed by a thinﬁlm preparation of a liquid crystalline phase is sufﬁcient to establish its main structural type. Differential thermal analysis and differential scanning calorimetry are the most common techniques for studying the thermal phase behavior of surfactants. They yield quantitative data (heat and entropy changes of phase transitions, transition temperatures, speciﬁc heats, and kinetic parameters [19], but do not necessarily identify the nature of the relevant processes. In most cases when the forms are stable to grinding and the transitions are rapid, the resulting curves are reproducible. In other cases, the thermograms obtained may depend on the heating rate; i.e., the apparent location of a thermal event is much inﬂuenced by the heating and cooling rates. Sometimes, the number and intensity of detected thermal events depend on the actual thermal history applied to a sample; i.e., a late run may differ from an earlier one because of tempering on standing with a loss or gain of seed nuclei of other forms. This is sometimes the reason that one has to use exclusively the ﬁrst scan for temperature-induced transitions.

II.

SINGLE-CHAIN SURFACTANTS

A lamellar structure is usually found in crystals of single-chain surfactants [20]. The unit cells of single-chain surfactant crystals typically contain either a pair of molecules or a small number of pairs. In the case of an ionic surfactant, one or more types of ion pairs are found [21]. X-ray diffraction patterns are typical, with long spacing in the ratio 1: 1/2:1/3: 1/4 characteristic of a lamellar structure.

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A structural variation of synthetic single-chain amphiphiles indicates that a certain length of the ﬂexible tail, usually a linear alkyl chain of seven or more C atoms, is required for the formation of a bilayer. The development of the bilayer structure is improved with increasing chain length. A systematic investigation by Skoulios and Luzzati [22] resulted in the well-known model of ionic amphiphilic molecules in which the two polar layers are separated by the hydrocarbon layer. In the liquid crystalline phase, molecules exist in one of an enormous number of conformational states, and they are constantly and rapidly undergoing restructuring among these different conformations. Busico et al. [13] proposed an electrostatic model for both the mesomorphic phase and the isotropic liquid of ionic single-chain surfactants. They concluded that the electrostatic energy alone would mainly account for the stability of the mesomorphic state, because the conformational entropy of the alkyl chains is substantially the same in both states and the residual translational and orientational entropy of a mesomorphic liquid is low. Single-chain surfactants can be classiﬁed in different ways depending on the nature of the hydrophilic or hydrophobic group. According to the number of carbon atoms in the straight aliphatic chains, they range from very short (⬍⬃4) to very long (⬎⬃20) compounds. The common single-chain surfactants are salts of short- and long-chain fatty acids [6,22–28], long-chain primary n-alkylammonium salts [29–31], quaternary ammonium salts [32–34], and synthetic bilayer-forming amphiphiles [35,36]. A design principle of synthetic bilayerforming amphiphiles includes the use of molecular modules: a tail, a connector, a spacer, and a headgroup [35]. In synthetic single-chain surfactants, a ﬂexible alkyl tail (usually a normal alkyl chain, rarely branched, with a vinyl linkage and an ester linkage) with a carbon number of at least 8 is used. A connector is a rigid segment (diphenylazomethine, biphenyl, azobenzene, azoxybenzene, or units composed of two or three benzene rings connected by various atoms or groups) between a tail and a spacer. A spacer is the structural unit between the headgroup and the rigid segment; usually it is a linear methylene chain or an alanyl unit. A hydrophilic head can be cationic (a trimethylammonium group or modiﬁed ammonium group), anionic, nonionic, or zwitterionic. Stable bilayers are obtained when the sum of the tail and spacer carbon numbers is not less than 14 and the tail carbon number is at least 8 [35]. The ﬁrst results of single-chain surfactant thermal phase transitions were reported on anionic single-chain surfactants, metal carboxylates [26–28]. These salts exhibit polymorphism and mesomorphism with two different smectic phases [13]. Salts, which decompose with melting, exhibit only polymorphism. An example is calcium stearate, which decomposes with melting at 423 K and exhibits two reversible polymorphic transformations [26]. Two smectic phases in metal carboxylates are denoted as smectic I (viscous and birefringent with regular layer stacking) and smectic II (ﬂuid and optically isotropic owing to the small dimensions of the liquid crystalline domains; often described in the literature as an

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isotropic liquid). The introduction of a double bond in the proximity of the carboxylate group modiﬁes the thermal stability of the mesomorphic phase [37]. An unusual ability to form a liquid crystalline mesophase with negative anisotropy is shown by short-chain carboxylates [24]. A smectic structure with negative anisotropy is conﬁrmed for all short sodium chain carboxylates. It may be explained by two competing effects, which determine the overall polarizability anisotropy of a material. One is a contribution to a positive anisotropy of the hydrocarbon chains perpendicular to the layers, and the other is a contribution of the layer arrangement to a negative anisotropy. For long chain lengths, the positive polarizability anisotropy contribution is dominant and the birefringence is positive. The n-alkylammonium halides exhibit several successive high entropy phase transitions in the solid state that are reproducible for preheated samples [30]. The room temperature structure is formed by the stacking of double layers of parallel chains in the all-trans conformation facing each other with their methyl ends. The low temperature phases of these salts show a monoclinic or orthorhombic structure, whereas high temperature polymorphs show a tetragonal structure. As shown by wide-line NMR, the molecular mobility increases stepwise in connection with the phase changes in the solid state [34]. X-ray diffractometric investigation shows an intermediate phase, a plastic phase with conformational disordering of the hydrocarbon moieties occurring ﬁrst in a three-step melting. Molten chains in a plastic phase are held together by their ionic end groups packed in crystalline planar arrays [29]. The transitions from the plastic phase to the smectic liquid crystalline phase mainly occur by a bidimensional fusion of the ionic layers. Two smectic phases are found as in alkali metal carboxylates. A comparison of thermodynamic parameters as well as melting and clearing points and transition temperatures between n-alkylammonium salts and various metal carboxylates reveals similarities in their mesomorphic behavior. The crystalline structure of long-chain n-alkyltrimethylammonium halides [32] belongs to the monoclinic form. Ammonium cations and halide anions are bidimensionally extended to form an ionic layer that is sandwiched between the hydrocarbon chain layers. These compounds exhibit one endothermic solid–solid phase transition in the range of temperature 350–400 K. This transition is caused by melting of the hydrocarbon chain layer while the rigid ionic layer retains its regular arrangement. The salts in this phase are not typical mesomorphic salts. Observation with an optical microscope and a thermobalance reveals that this transition is neither a full melting nor a decomposing process. A supercooled state is observed in the cooling process, and complete recovery to the original state is difﬁcult. Single-chain pyridinium surfactants can be prepared by quaternization or protonation of pyridine derivatives [38]. Phase transitions of pyridinium salts are affected by the nature of the headgroup and counterions. Compounds with an N-

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protonated pyridinium show a simple phase transition from the solid state to an isotropic liquid. In the case of N-methylated pyridinium, sometimes a rich polymorphism and mesomorphism are observed. This observation is explained by the relatively high melting points of the protonated derivatives compared with those of the methylated derivatives. The chloride ion as a counterion could be unfavorable for the liquid crystalline formation because of its small radius, which could lead to lesser shielding of the positive charges of the pyridinium ring. The formation of different smectic phases (A, B, C, and H) depends on the nature of the polar headgroup and packing conditions in the lamellar structure. In conclusion, the number and kinds of thermal phase transitions of singlechain surfactant molecules vary from a simple phase transition, the solid crystalline to isotropic liquid, to a complex polymorphism and mesomorphism. More than one thermotropic state may exist in the same system, each being the stable phase within a particular range of temperature (and pressure). Phase transitions are usually reversible through all the intermediate forms to a structure that is thermodynamically stable at room temperature, or they are partially reversible through one or more, but not all, of these transitions, and the room temperature product is an undercooled form of a phase that is stable at some intermediate temperature [26]. The values of phase transition temperatures, the enthalpy and entropy changes of single-chain amphiphiles, increase almost linearly with the number of carbon atoms of the aliphatic chains [32,33], but not always in a straightforward manner [24,28]. It is evident that the longer the alkyl chain, the greater are the area per chain in the layers, the electrostatic energy per mole of ion pairs, and the total conformational entropic gain increases [13,24]. The aging experiments of some crystalline samples after heating demonstrate the slow reversion of metastable forms to stable forms, with both patterns present, superposed on each other [26]. For salts of longer chain fatty acids, the higher the temperature, the more symmetrical (closer to the hexagonal cell) is the shape of the unit cell, and in phases in which the spacing is strongly dependent on temperature the coefﬁcient of linear thermal expansion is negative [22].

III. CATANIONIC SURFACTANTS Phase equilibria of systems containing oppositely charged ionic surfactants have been the subject of extensive experimental and theoretical investigations [39– 61]. Competition between various molecular interactions (van der Waals, hydrophobic, electrostatic, hydration forces, etc.) may result in a variety of microstructures, mixed micelles, vesicles, and catanionic surfactant salts. Mixing aqueous solutions of anionic surfactant with an equivalent amount of cationic surfactant (alkyl chains with more than eight atoms) results in precipitation of

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a new compound, a catanionic surfactant, colloidally dispersed in solution and practically insoluble in water [41,43,60]. The term ‘‘catanionic surfactant’’ has been introduced in addition to the conventional classiﬁcation based on the polar or ionic surfactant headgroup (cationic, anionic, nonionic, and zwitterionic). A catanionic surfactant is an amphiphilic compound that contains both cationic and anionic surfactants in an equimolar ratio with the counterions completely removed. The electrostatic interaction between oppositely charged headgroups neutralizes the surface charge through the formation of tight ionic pairs, forming compounds similar to those of double-chain surfactants. To our knowledge, there are only a few studies of solid-state transitions of symmetrical [62] and asymmetrical [63,64] catanionic surfactants.

A. Symmetrical Catanionic Surfactants Symmetrical catanionic surfactants consist of anionic and cationic surfactants of the same chain length. Alkylammonium alkyl sulfates [such as decylammonium decyl sulfate (DeADeS), dodecylammonium dodecyl sulfate (DDADDS), and tetradecylammonium tetradecyl sulfate (TDATDS)] are prepared by mixing equimolar solutions of alkylammonium chloride and the corresponding alkyl sulfate. The reaction can be represented as Cn H2n⫹1NH3 Cl ⫹ Cn H2n⫹1 SO4 NA → Cn H2n⫹1 NH3 SO4Cn H2n⫹1 ⫹ NaCl

(1)

X-ray diffraction reveals a bilayered structure in agreement with the behavior of other amphiphilic compounds with n-alkyl chains [62]. The double headgroup layer is separated by two parafﬁnic layers composed of an equimolar mixture of cationic and anionic surfactants with saturated portions of chains mostly in the trans conﬁguration with a high degree of molecular parallelism. The trans confor˚ ) in the long mation of chains is indicated by the constant increment (⬃2.5 A spacing of successive even members of the homologous series, which corresponds to the distance between Cn and Cn⫹2 atoms in the alkyl chains [22,65]. Considering the length of fully extended hydrocarbon chains and the shortest distance of an ionic headgroup from the α-carbon atom as well as the value of the basic bilayer thickness, one can conclude that hydrocarbon chains are tilted with respect to the bilayer plane. The symmetrical catanionic surfactants exhibit complex thermal behavior characterized by several successive phase transitions. Three endothermic transitions are displayed by heating: the solid crystalline–solid crystalline, the solid crystalline–liquid crystalline, and the liquid crystalline–isotropic liquid phase. On cooling, all compounds reversibly undergo the isotropic liquid–liquid crystalline transition, while other transitions exhibit peculiar properties. There is no

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FIG. 1 Thermogram of decylammonium decyl sulfate (DeADeS) obtained by differential scanning calorimetry during heating (full line) and cooling (dashed line) scans. T1 represents polymorphic transition, Tm and Ti represent the temperatures of melting and isotropization, while Td and Tc represent the temperatures of deisotropization and crystallization. The lettering a–f denotes the temperatures of diffraction patterns shown in Fig. 3.

corresponding exotherm on the cooling run for the solid crystalline–solid crystalline transition of DeADeS (Fig. 1) or for the liquid crystalline–solid crystalline transitions of TDATDS. All transitions on cooling are located at lower temperatures than the corresponding transitions in the heating scans, indicating a temperature hysteresis. The thermodynamic parameters change almost linearly with the total number of carbon atoms in hydrocarbon chains. The enthalpy increments for transitions are comparable with those for homologous series of n-alkanes, sodium alkyl sulfates, and long-chain alkyltrimethylammonium bromides [22,29–32,66,67], while the entropy change of melting falls within the range of those for stable bilayers of all double-chain amphiphiles, including natural lipids [19]. The phase transition temperatures [the solid crystalline–solid crystalline transition (T1); solid crystalline–liquid crystalline transition (Tm); liquid crystalline–

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FIG. 2 Plots of (䊉) the solid crystalline–solid crystalline and (䊊) solid crystalline– liquid crystalline transition temperatures and (䊐) the temperature of isotropization as a function of the total number of C atoms, 2n, in molecules of symmetrical alkylammonium alkyl sulfate.

isotropic liquid transition or isotropization (Ti ) show a linear dependence (Fig. 2) with increasing n in alkylammonium alkyl sulfates: T1 ⫽ 211 ⫹ 5.4n Tm ⫽ 307 ⫹ 2.1n Ti ⫽ 321 ⫹ 1.5n

(2) (3) (4)

The nature of the transition was studied by XRD and by polarizing microscopy. Characteristic parts of XRD patterns of one of the investigated catanionic surfactants, DeADeS at 293 K (a), 323 K (b), 350 K (c), and 363 K (d), plus immediately after cooling to 293 K (e) and after aging for 4 days at 293 K (f ) are shown in Fig. 3. When heated from room temperature to 323 K, DeADeS undergoes the solid crystalline–solid crystalline phase transition. Two different crystalline phases are denoted as SC1 [room temperature phase (Figs. 3a,f)] and as SC2 [high temperature phase (Fig. 3b)]. A systematic shift of the 001 diffraction lines of the crystalline phase toward smaller Bragg angles—i.e., the increase of basic lamellar thickness and changes in positions and intensities of other diffraction lines—for the SC1 and SC2 phases reveal polymorphism. The sample

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FIG. 3 Characteristic parts of X-ray diffraction patterns of decylammonium decyl sulfate (DeADeS) obtained at different temperatures during heating (a–d) and cooling (e,f ) cycles. (See text.) Phase (䉮) SC1; (䉲) phase SC2.

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FIG. 4 Basic lamellar thickness D (in angstroms) and tilt angle of the chains to the layer plane, α (in degrees) as a function of the number of C atoms in a single alkyl chain in molecules of symmetrical alkylammonium alkyl sulfate polymorph, (䊊) SC1 and (䊉) SC2.

is amorphous for XRD with traces of the SC2 phase at 350 K (Fig. 3c) and completely amorphous at 363 K (Fig. 3d). On cooling to room temperature, the sample is crystalline again, as a mixture of the two phases (SC2 is the dominant phase) (Fig. 3e). After 4 days of aging, only the SC1 phase is recorded (Fig. 3f ). On cooling, both the SC1 and SC2 phases exhibit sharper diffraction lines than before heating (Figs. 3a vs. 3b and 3e vs. 3f ), indicating a more ordered structure. DDADDS and TDATDS show a dependence of the structure on heating similar to that of the DeADeS sample, while on cooling, different kinetics for attaining the starting state are observed [62]. The SC2–SC1 phase transition for DeADeS is kinetically hindered, whereas TDATDS readily converts back to the SC1 phase when cooled to room temperature. After cooling to room temperature DDADDS shows the formation of a phase similar to the SC2 phase (structural parameters slightly different from the initial SC2 phase). The basic lamellar thicknesses D(in angstroms) calculated from XRD using 001 diffraction lines for the SC1 and SC2 phases are shown in Fig. 4. The linear dependence of D(D1 for the SC1 phase and D2 for the SC2 phase) versus the number of C atoms in a single alkyl chain can be expressed by the equations D1 ⫽ 6.57 ⫹ 2.4n

(5)

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465

and D2 ⫽ 6.17 ⫹ 2.5n

(6)

If alkyl chains are in the trans form, the difference between the basic bilayer thicknesses in the SC1 and SC2 phases can be explained by the different tilt angles (α) of the chains with respect to the layer plane. The α value in the lamellae of the SC2 phase (α2 )is somewhat higher than in the lamellae of the SC1 phase (α1 ) (Fig. 4). The linear dependence of α vs. n for the two phases is observed to follow the equations α1 ⫽ 53.3 ⫹ 0.45n

(7)

and α2 ⫽ 54.0 ⫹ 0.73n

(8)

Observation by polarizing microscopy shows typical textures of the smectic A phase between Tm and Ti for all samples. Clearing and transformation to the isotropic liquid are observed approximately 2–7 K above the melting points. The temperature interval within which the liquid crystalline phase exists, ∆T, is narrow, and this interval decreases linearly as the chain length of catanionics increases, according to the equation ∆T ⫽ 14 ⫺ 0.4n

(9)

A transparent liquid exists up to the temperature at which decomposition begins (⬃478 K). On cooling from the isotropic liquid phase, all samples display the focal conical texture of the liquid crystalline phase before crystallization. Nuclear magnetic resonance studies show [68] that the thermotropic transition from the solid to the liquid state in hydrocarbon compounds, which proceeds through intermediate states, results from increased molecular rotation and/or oscillation in the chains at elevated temperatures. The factors determining these phase changes are the state and packing of the chains governed by the balance between cohesive forces and thermal agitation [69]. The transition from the solid to the liquid state includes continuous and discontinuous modiﬁcations in packing during thermal expansion. The electrostatic forces in the ionic layer of catanionic lamellae are very strong compared to the van der Waals forces in the hydrocarbon layer, causing the segregation of ionic and hydrophobic parts. As the alkyl chains take on an ordered arrangement owing to weak intermolecular forces, molecular motions within the chains increase gradually as temperature increases until, at a characteristic temperature, a considerable increase in the molecular motion takes place, causing the formation of various polymorphs. By changing the tilt angle, the organization of the terminal CH3 groups and packing of the chains are altered [70]. It is possible to rationalize the structure of various polymorphs by taking

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into account a change in the organization and packing of chains due to the increase in the tilt angle. As temperature approaches the melting point, a two-dimensional disordering of the ionic layers from the solid crystalline to the liquid crystalline organization takes place [13]. High values of enthalpy and entropy changes corresponding to the melting [62] imply the disordering of the hydrocarbon chains from an alltrans conﬁguration to the liquid crystalline organization (a more disordered organization; i.e., a gauche conﬁguration [71]). An undercooled state is observed in the cooling process; i.e., the time to recovery of the original state depends on chain length.

B. Asymmetrical Catanionic Surfactants Asymmetrical catanionic surfactants consist of anionic and cationic surfactants with different chain lengths. Similar to Eq. (1), the formation of asymmetrical catanionic surfactants from hexadecyltrimethylammonium bromide (CTAB) and an anionic surfactants such as sodium alkyl sulfate (the numbers of carbon atoms per chain being 10, 12, and 14) can be represented as C16 H33 N(CH3 )3 Br ⫹ Cn H2n⫹1 SO4 Na → C16 H33 N(CH3 )3 SO4 Cn H2n⫹1 ⫹ NaBr (10) Thermograms of a series of asymmetrical catanionic salts—hexadecyltrimethylammonium decyl sulfate (CTADeS), hexadecyltrimethylammonium dodecyl sulfate (CTADDS), and hexadecyltrimethylammonium tetradecyl sulfate (CTATDS)—are presented in Fig. 5. Different numbers of endothermic peaks during heating and exothermic peaks during cooling are obtained as the number of carbon atoms in the alkyl sulfates increases. A common feature of all thermograms are transitions corresponding to the solid crystalline–liquid crystalline (Tm ) and liquid crystalline–isotropic liquid (Ti ) transitions in the heating cycle and the isotropic liquid–liquid crystalline (Td ) and liquid crystalline–solid crystalline (Tc ) transitions in the cooling cycle. All liquid crystalline phases show characteristic textures of smectic phases. The temperature interval between the Tm and Ti points increases with increasing number of carbon atoms in the anionic surfactants. Transparent liquid phases exist up to the temperatures at which decomposition has begun. TGA reveals that the decomposition of CTADeS starts at ⬃445 K, that of CTADDS at ⬃465 K, and that of CTATDS at ⬃463 K. Almost all endothermic peaks have corresponding exothermic peaks at lower temperatures, indicating a temperature hysteresis. The exceptions are a small endothermic peak for CTADeS and a transition below Tm for CTADDS; i.e., they do not have corresponding exotherms in the cooling cycle. The phase transition parameters, transition temperatures, and changes in enthalpy derived from DSC heating scans are listed in Table 1, indicating peculiar

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FIG. 5 Thermograms of hexadecyltrimethylammonium decyl sulfate (CTADeS), hexadecyltrimethylammonium dodecyl sulfate (CTADDS), and hexadecyltrimethylammonium tetradecyl sulfate (CTATDS) obtained by differential scanning calorimetry during heating (full line) and cooling (dashed line) scans.

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TABLE 1 Transition Temperatures (T ) and Enthalpy Changes (∆H) of Hexadecyltrimethylammonium Alkyl Sulfate Heating Sample CTADeS

CTADDS

CTATDS

Cooling

T (K )

∆H (kJ/mol)

T (K )

∆H (kJ/mol)

348 361 396 406 426 437 342–348 409 422 443 448 338 362 399 418 447

22.7 0.5 2.9 1.0 11.0 1.0 16.6 12.9 3.2 6.8 1.6 2.6 21.8 8.8 11.1 1.5

312

⫺2.2

339

⫺12.1

407 417 326 389

⫺6.7 ⫺1.1 ⫺11.9 ⫺8.6

441 444 341 349 388 407 413

⫺6.1 ⫺1.4 ⫺13.1 ⫺1.6 ⫺11.1 ⫺4.0 ⫺0.5

properties of the solid crystalline–solid crystalline transitions for each sample. Obviously, the difference in cationic and anionic surfactant hydrocarbon chain lengths differently inﬂuences the number and kinetics of the solid crystalline– solid crystalline transitions. Detailed analyses of the nature of phase transitions obtained by X-ray diffraction and polarizing microscopy are given elsewhere [63,64]. Changes in the positions and relative intensities of the hk0/hkl diffraction lines of all homologs with the change of temperature indicate rearrangements in the crystal lattice, changes in conformation, and/or reorientation of crystal grains, i.e., polymorphism. All polymorphs exhibit a bilayered structure. The changes in the basic lamellar thickness D with the number n of C atoms in sodium alkyl sulfate for different temperatures are presented in Table 2. The variation of the basic lamellar thickness of the room temperature polymorph (SC1 phase) (D1 ) and of the polymorph formed after the ﬁrst endothermic transition (SC2 phase) (D2) with n follows the linear equations D1 ⫽ 25.6 ⫹ 1.0n

(11)

293 K 35.3(2) a 293 K 38.2(2) a 293 K 39.3(2) a

323 K 35.5(2) a 333 K 38.5(3) a 348 K 40.1(3) a

373 K 38.0(3) b 363 K 40.6(3) b 373 K 42.4(3) b

Heating cycle

408 K 42.7(3) b

373 K 38.2(2) b 358 K 40.6(3) b 403 K 42.7(3) b

b

38.2(2) a 373 K 42.4(3) b

323 K 37.6(2) a

350 K 40.0(3),a 42.3(3) b

293 K 35.9(2) c 293 K

Cooling cycle

˚ ), of Hexadecyltrimethylammonium Alkyl Sulfates at Selected Temperatures The Long Spacing, a D (A

The numbers in parentheses are estimated standard deviations to the least signiﬁcant digit. D value for the low temperature solid crystalline phase. c D value for high temperature solid crystalline phase.

a

CTATDS

CTADDS

CTADeS

Sample

TABLE 2

293 K 39.5(4) a

Solid-State Transitions of Surfactant Crystals 469

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and D2 ⫽ 27.1 ⫹ 1.1n

(12)

The constant increment of ⬃0.1 nm in the long spacing of successive members of the homologous series corresponds to half the difference in chain length between Cn and Cn⫹2 and indicates that there is probably no trans conformation of alkyl sulfate chains in hexadecyltrimethylammonium alkyl sulfates. Additionally, X-ray diffraction patterns of hexadecyltrimethylammonium alkyl sulfates in the heating cycle display a superposition of rather sharp diffraction lines on diffuse amorphous maxima, indicating the presence of two phases. One phase is the three-dimensionally ordered crystalline phase, and the other is a disordered one, indicating some kind of a two-dimensionally ordered liquid crystalline phase. The presence of a disordered phase in addition to the ordered phase is not observed in the symmetrical catanionic surfactants [62]. Obviously, there are two parallel mechanisms during the heating cycle: the structural transition of a two-phase system (the appearance of additional periodicity) and the solid crystalline–liquid crystalline transition. The order of appearance of different structures as temperature increases is usually consistent with the gradual breakdown of the long-range molecular order upon heating. As the temperature approaches the melting point, the long-range order gradually decreases. In the cooling cycle, the fraction of the three-dimensionally ordered phase increases, while the fraction of the disordered phase decreases. The kinetics of phase transitions on cooling is different from that on heating. A number of different bilayer phases coexist. In spite of the observed advanced ordering in the crystal lattice, a disordered phase is present again at room temperature. It seems that some thermal activation processes necessary for the transition are kinetically blocked due to steric hindrance. The assumed steric hindrance may occur via molecular conformation changes of the bulky aliphatic chains, rearrangements of the methyl end groups at the lamellae/lamellae interface, and so on. The comparison of the results obtained for asymmetrical and symmetrical catanionic homologs shows that the thermal properties are closely correlated with the extent of symmetry of surfactant molecules. There are two factors contributing to the bilayer stability: the electrostatic interactions between ionic headgroups and the state of packing of the surfactant chains. Since the electrostatic interactions play a signiﬁcant role in bilayers formed from symmetrical and asymmetrical catanionics, the difference between the chain lengths of the cationic and anionic parts of a catanionic molecule leads to a different packing and to more complex thermal behavior. The same chain length of both tails in a symmetrical catanionic bilayer allows denser molecular packing than in a bilayer of asymmetrical catanionic surfactant; i.e., surfactant tails are more ordered in bilayers of symmetrical surfactants. As the difference between the lengths of the tails increases, a poorer hydrophobic match in the bilayer is attained.

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Planar bilayers may undergo strong thermally induced out-of-plane undulations controlled by the bending elasticity. The bending elasticity can be described by the bending modulus, which is, in the case of uncharged bilayers, determined by molecular packing constraints [72]. This is in accordance with the demonstration [73] that the free energy required for bending a bilayer is the sum of the bending and stretching work. The hydrophobic moiety formed by two asymmetrical chains causes successive conformational changes and the formation of several polymorphs in the solid state. The presence of a disordered phase gives some peculiar properties to the asymmetrical catanionic surfactant.

IV.

DOUBLE-CHAIN SURFACTANTS

Synthetic double-chain surfactants have been extensively studied [35,74–89] because they can serve as model systems for the study of natural lipid bilayers, i.e., biological membranes. The hydrophilic group of these surfactants may be cationic (ammonium and sulfonium), anionic (sulfonate, phosphate, and carboxylate), nonionic (polyoxyethylene), or zwitterionic. Double-chain cationic surfactants with a dimethylammonium headgroup are the most extensively studied, but many anionic double-chain surfactants [89] and nonionic oxyethylene oligomers [35] have also been investigated as model bilayer membrane compounds. The essential structural characteristics of synthetic surfactant membranes are very similar to those of biomembranes; the bilayer is formed only when the alkyl chain length exceeds 10 carbon atoms, and its thickness is 3–5 nm depending on the hydrocarbon chain length [79]. A number of double-chain surfactants have been synthesized as analogs of natural lipid molecules, and their thermal behavior in aqueous systems has been examined. Synthetic double-chain surfactants frequently form micelles at very low concentrations, with lower aggregation numbers and a higher degree of counterion dissociation than single-chain surfactants. In general, these surfactants form a lamellar phase as a ﬁrst liquid crystalline phase. The lamellar phase usually borders on an isotropic phase in the phase diagrams of systems based on such surfactants, whereas for single-chain surfactants the lamellar phase is restricted to a rather small concentration range near the surfactant–water side of the corresponding phase diagrams [90]. Dialkyldimethylammonium bromides (which may be considered as a prototype of double-chain surfactants) were prepared by Okuyama et al. [88]. They are the ﬁrst single crystals of a synthetic bilayer compound that were amenable to X-ray structural analysis. The most important aspect in this structure is bending of molecules at the hydrophilic group. This bend usually occurs in such a way that the straight pairs of the chains become unequal in length, thus often causing tilting of the molecule relative to the crystal planes. The chain tilting caused by

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the balance between the molecular cross sections of the two hydrophobic chains and the hydrophilic headgroup displays the hairpin conformational structure [13]. A comparison of the layer thickness with the chain lengths suggests that the chains are tilted with respect to the bilayer surface by 32–47° depending on the alkyl chain length [35]. X-ray data of dioctadecyldimethylammonium chloride (DODMAC) show a typical structure of dialkylammonium salts [4]. Thermal analysis of dry DODMAC crystals reveals a reversible solid crystalline–solid crystalline phase transition at ⬃325 K; i.e., two equilibrium polymorphic forms exist. Melting at ⬃420 K is irreversible and is accompanied by chemical decomposition. Dioctadecylmethylammonium chloride (DOMAC) exhibits an extraordinary crystal structure with respect to both the conformational structure of the molecules and their packing within the crystal structure [4]. Both chains are extended away from the polar hydrophilic group in the crystal, and a curved midchain monolayer structure is formed. DOMAC forms at least one crystal tetrahydrate. Dioctadecylammonium cumene sulfonate (DOACS) is crystalline at low temperatures, showing a diffraction pattern with numerous diffraction lines [4]. Xray studies reveal two phase transitions: solid crystalline to liquid crystalline at ⬃346 K and liquid crystalline to isotropic at ⬃395 K. This compound exhibits a very interesting chain structure change within the lamellar phase when it is heated. The coefﬁcient of expansion is greater in some directions than in others. Another interesting feature is the increase of the crystal long spacing in passing from the crystal line phase to the liquid crystalline phase, but as temperature increases the thickness of the bilayer shrinks. The appearance of the long dspacing line of the lamellar phase in the isotropic liquid phase indicates the persistence of the lamellar structural elements within the liquid phase. The unit cell of dioctadecyldimethylammonium bromide (DODAB) is triclinic, with two molecules in the unit cell [87]. An interdigitated packing in which {001} plane polar headgroups alternate with terminal methyl groups is proposed. In pure DODAB, the polar layer melts at ⬃360 K, producing a narrow domain of the ﬂuid liquid with the texture of an inverse hexagonal mesophase. The transition point at ⬃373 K corresponds to the isotropic phase formation. On cooling, an unusual texture appears. On a slightly cloudy, scarcely birefringent background, many strongly birefringent golden structures with the shape of twin needles are obtained. Interaction of long-chain n-alkylammonium halides with a halide of a divalent metal leads to the formation of salts of the general formula (RNH3) 2MX4 with peculiar phase changes in the solid state [65]. Bis(n-alkylammonium)bromo zincates with n ⫽ 10–16 display two reversible high entropy solid crystalline–solid crystalline phase transitions and a solid crystalline–liquid crystalline (smectic phase) transition up to at least 450 K. In general, changes in the length and structure of the long chain inﬂuence the

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thermal behavior. Long-chain potassium dialkylphosphate salts are solid crystals at room temperature, but when heated above their melting temperature a cubic mesophase followed by a columnar mesophase of hexagonal symmetry is observed [91]. The stability range of the cubic mesophase decreases signiﬁcantly when the length of the alkyl chains increases. Introduction of a double bond lowers the temperature of phase transition [35]. The replacement of hydrogen by ﬂuorine atoms generally results in a decrease in the enthalpy changes, while the effect on the temperature of transition is rather complicated [92]. The nature of the headgroup plays a crucial role in determining the phase transition, for two main reasons. One is the electrostatic interaction among headgroups at the bilayer surface, which may differently affect the stability of the bilayer structure. The other is the inﬂuence of the headgroup on the alignment of the hydrocarbon chains. For example, protonated pyridinium salts show a simple single phase transition from the solid crystalline state to an isotropic liquid, while methylated pyridinium salts exhibit solid crystalline–solid crystalline, solid crystalline–liquid crystalline, and liquid crystalline–isotropic liquid transitions [77]. An excellent example of counterion inﬂuence is the quite different thermal behavior of double-chain 1-methyl-3,5-bis(n-hexadecyloxycarbonyl)pyridinium ion in crystals with iodide or chloride as counterion [4]. The iodide salt revealed three phase transitions: solid crystalline–solid crystalline at ⬃326 K, solid crystalline–liquid crystalline at ⬃358 K, and liquid crystalline–isotropic liquid at ⬃378 K. The X-ray diffraction pattern of the liquid crystalline phase could be best rationalized in terms of a smectic-H phase. The chloride anion could be unfavorable for liquid crystalline behavior because of its smaller ionic radius relative to the iodide anion. Less shielding of the positive charges of the pyridinium rings by the chloride counterion leads to increased electrostatic repulsion between headgroups. Alkali metal salts of dihexadecylphosphoric acid heated above the melting temperature display columnar mesophases with lithium and sodium as counterions, whereas potassium, rubidium, and cesium as counterions show a cubic phase between the solid crystalline phase and the columnar mesophase [93]. Thermal behavior of double-chain surfactants shows complex phase transitions from the solid state to the isotropic liquid. The correlation between thermal behavior and molecular structure of synthetic double-chain surfactants can be generalized as follows: 1. The entropy change of the phase transitions falling within the range of 60– 220 J/K mol indicates that all phase transition processes are closely related (chain melting). 2. The temperature of transition and enthalpy and entropy changes mainly increase with increasing lengths of tails.

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3.

Headgroup interactions (electrostatic and/or hydrogen bonding) raise the temperature of transition.

REFERENCES 1. D Myers. Surfactant Science and Technology, 2nd ed., VCH, New York, 1992. 2. H Ringsdorf, B Schlarb, J Venzmer. Angew Chem Int Ed Engl 27:113–158 (1988). 3. K Larsson. In: Food Emulsions (S Friberg, ed.), Marcel Dekker, New York, 1976, pp. 39–36. 4. RG Laughlin. The Aqueous Phase Behavior of Surfactants. Academic Press, New York, 1994, pp. 181–237. 5. DM Small. The Physical Chemistry of Lipids: From Alkanes to Phospholipids, Plenum Press, New York, 1986, pp. 25–32. 6. L Hernqvist. In: Crystallization and Polymorphism of Fats and Fatty Acids (Surfact Sci Ser Vol. 3) (N Garti, K Sato, eds.), Marcel Dekker, New York, 1988, pp. 97– 137. 7. GA Jeffrey, H Maluszynka. Acta Cryst B 45:447–452 (1989). 8. A Mueller-Fahrnow, V Zabel, M Steifa, R Hilgenfeld. J Chem Soc Chem Commun 1986:1573–1574 (1986). 9. AI Kitaigorodsky. Molecular Crystals and Molecules, Academic Press, London, 1973. 10. S Abrahamsson, B Dahle´n, H Lo¨fgren, I Pasher. Prog Chem Fats Other Lipids 16: 125–133 (1978). 11. MG Broadhurst. J Res Natl Bur Stand A. Phys and Chem 66A:241–249 (1962). 12. R Haase, H Schoenert. In: Solid–Liquid Equilibrium (ES Halberstadt, ed.), Pergamon Press, Oxford, 1969, pp. 81–87. 13. V Busico, A Ferraro, M Vacatello. Mol Cryst Liq Cryst 128:243–261 (1985). 14. RG Laughlin, RL Munyon, Y-C Fu, AJ Fehl. J Phys Chem 94:2546–2552 (1990). 15. L Mandelkren, A Prasad, RG Alamo, GM Stack. Macromolecules 23:2595–3700 (1990). 16. GW Gray. Molecular Structure and Properties of Liquid Crystals, Academic Press, New York, 1962. 17. JC Dubois, J Billard. Liq Cryst Ordered Fluids 4:1043–1051 (1984). 18. TL Threlfall. Analyst 120:2435–2460 (1995). 19. BD Ladbrooke, D Chapman. Chem Phys Lipids 3:304–367 (1969). 20. ML Klein. J Chem Soc Faraday Trans 88:1701–1705 (1992). 21. M Kodama, S Seki, Adv Colloid Interface Sci 35:31–138 (1991). 22. A Skoulios, V Luzzati. Nature 183:1310–1312 (1959). 23. V Busico, A Ferraro, M Vacatello. J Phys Chem 88:4055–4058 (1984). 24. J Bonekamp, B Hegemann, J Jonas. Mol Cryst Liq Cryst 87:13–28 (1982). 25. DM Glover, TR Lomer. Mol Cryst Liq Crys 53:181–188 (1979). 26. RD Vold, JD Grandine, MJ Vold. J Colloid Sci 3:339–361 (1948). 27. AR Ubbelohde, HJ Michels, JJ Duruz. Nature 228:50–52 (1970). 28. NJ Krog. In: Food Emulsions, 2nd ed. (S Frieberg, ed.), Marcel Dekker, New York, 1990, pp. 127–180. 29. V Busico, P Cernicchiaro, P Corradini, M Vacatello. J Phys Chem 87:1631–1635 (1983).

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13 Thermal Behavior of Foods and Food Constituents ALOIS RAEMY and PIERRE LAMBELET Nestle´ Research Center, Nestec Ltd., Lausanne, Switzerland NISSIM GARTI Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

I. Introduction II.

What Are Foods?

478 478

III. Thermal Analysis and Calorimetric Techniques of Interest

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IV.

480 480 481 485 489 490

Thermal Behavior of Food Constituents A. Water B. Lipids C. Carbohydrates (glucides) D. Proteins E. Minor constituents

V. Thermal Behavior of Raw and Reconstituted Foods A. Phenomena related to food composition B. Interaction between food constituents C. Biological processes VI.

VII.

492 492 493 494

Self-Heating, Self-Ignition, and Safety Aspects A. Self-heating, self-ignition, and rise in pressure B. Simulation of process conditions

494 494 495

Other Thermodynamic Parameters A. Speciﬁc heat B. Heats of combustion C. Heat conductivity and thermal diffusivity D. Heats of solution

496 496 497 497 497 477

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VIII. Related Techniques IX.

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Conclusion

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References

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I. INTRODUCTION Chocolate bars should melt in the mouth and not in the hand, and the heating of oil should not lead to a kitchen ﬁre. Based on such common examples, we may understand the interest in studying the thermal behavior and properties of foods. In the investigation of foods by thermal analysis and calorimetric techniques, many effects can be observed in the temperature range between ⫺50°C and 300°C. These thermal phenomena may be either endothermic processes (such as melting, denaturation, gelatinization; and evaporation) or exothermic processes (such as crystallization and oxidation). Through precise knowledge of such effects, optimal conditions for safe storage or processing of foods can be deﬁned. The main operations concerned are summarized in the following table.

Below 0°C Around 70°C Around 100° Around 140°C Above 140°C

Freezing and freeze-drying Pasteurization, solid–liquid extraction Drying, cooking Ultrahigh temperature sterilization (of milk products) Frying, roasting (of coffee and coffee surrogates)

Thus, the thermal and also, more generally, the physicochemical properties of foods are of particular interest to the food technologist. To introduce the subject, we ﬁrst present some general aspects of food constitution and of the most useful calorimetric techniques in this context. Because the thermal behavior of foods depends strongly on their composition, we concentrate at ﬁrst on the thermal characteristics of food constituents—of water, lipids, glucides, proteins, and minor constituents—and then consider composite and reconstituted foods. Aspects of process safety are also considered.

II.

WHAT ARE FOODS?

Foods are materials in a raw, processed, or reconstituted form that are consumed by humans or animals for their growth, health, and satisfaction (or even pleasure). Enteral and parenteral solutions are also foods, as are fruits, fruit juices, milk, milk powders, meat, and animal (pet) food.

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Chemically, foods are mainly composed of water, lipids, glucides, and proteins. In addition, they contain comparatively small proportions of some minerals and various organic substances. Minerals are often analyzed globally as ash. The organic substances can be vitamins, emulsiﬁers, acids, antioxidants, pigments, polyphenols, or ﬂavors. In some cases, foods contain physiologically active substances, such as caffeine or theobromine, and even toxic substances, such as natural toxins in mushrooms or, toxins produced by microorganisms. The main constituents just referred to are responsible for the physical properties (structure, texture, and color) as well as the ﬂavor of foods. Sometimes, speciﬁc natural or synthetic ingredients (such as salt or antioxidants) are added to improve the food properties [1–3].

III. THERMAL ANALYSIS AND CALORIMETRIC TECHNIQUES OF INTEREST Differential scanning calorimetry (DSC) is the main approach used today for studying thermal properties of foods (phase transitions, reactions, and speciﬁc heats). Older systems, such as containers ﬁtted with sensors that follow the rising temperature of a heating bench, autoclaves with additional pressure sensors, or (high pressure) differential thermal analysis (DTA) instruments, are still useful. Modulated DSC is also applied today to food studies [4–9]. However, the trend is toward the use of microcalorimeters (in the isothermal or scanning mode) with high sensitivities, especially for a more sensitive observation of the weak thermal phenomena that occur between 0°C and 100°C [10– 13]. Parameters such as the heat of solution may also be of interest, so the use of solution calorimeters or of heat ﬂux calorimeters with stirring devices is also recommended for studying certain food systems [14]. Instruments such as power compensation DSC, heat ﬂux DSC, or intermediate systems have proved their worth in the study of foods and food constituents. The most important criteria for selecting the appropriate instrument for a speciﬁc problem are temperature range, sample size, and the sensitivity and resolution of the instrumentation. When studying food constituents, analysis of small samples gives a better resolution of thermal effects; this can be important for studying the polymorphism of fats and is a necessity for purity determinations. In contrast, large samples represent better the bulk material for composite foods; heat ﬂux calorimeters with large crucibles (sometimes ﬁtted with pressure sensors or pH-meters) are therefore often preferred [14]. This criterion is particularly important in the ﬁeld of process safety, especially for adiabatic calorimeters [15]. Moreover, experiments with large samples must be performed at low heating rates.

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Complementary data on food and food constituents are obtained by other thermal analysis techniques, such as thermomanometry, thermogravimetry (TG), thermomicroscopy or hot stage microscopy (HSM), differential mechanical (thermal) analysis (DMA or DMTA), titration calorimetry, and microwave dielectric measurements during temperature scan. Adiabatic bomb calorimeters or isoperibolic calorimeters are used to determine the heat of combustion of foodstuffs. Although the values may be important in the context of process safety, they are mainly used to calculate caloric values of food for human nutrition or when foods (usually oils) are used as energy sources for engines.

IV.

THERMAL BEHAVIOR OF FOOD CONSTITUENTS

A. Water Water is present in most natural foods, at levels up to 90–95% w/w in some fruits (oranges) and vegetables (tomatoes). Most beverages contain high proportions of water. Water exists in foods in various forms: free water, water droplets, water adsorbed on a surface, chemically bound water, crystal water, and composition water. Often water is removed from processed foods to improve their keeping quality or to reduce their weight and volume. In most cases, however, part of this water is extremely difﬁcult to remove, so even dehydrated foods may contain 2–3% residual water. The physics of water, as a pure substance and as part of biological systems, has been studied by many workers [16–18]; the basic phenomena are described in a volume edited by Franks [19]. As shown in Fig. 1, water has three phase transitions in the temperature range of interest: crystallization on cooling (or ice melting on heating), vaporization (or vapor liquefaction), and sublimation. Relatively high enthalpy values accompany melting and vaporization (334 J/g at 0°C and 2250 J/g at 100°C, respectively, under atmospheric pressure). Thus, these two endothermic phenomena are easily observed when studying foods by calorimetric techniques. Sublimation (freezedrying) takes place only under high vacuum, so this phenomenon is more difﬁcult to detect [18]. A large number of studies have dealt with the behavior of water below 0°C (e.g., supercooling of water-in-oil emulsions) and determinations of free and bound water, around 0°C [20–25]. The crystallization enthalpy of water depends on temperature (see Ref. 19), which may be important in supercooled emulsions. Moreover, the difference in the speciﬁc heats of ice [2.05 J/(g ⋅ K)] and water [4.18 J/(g ⋅ K)] may introduce some error. Around 100°C, thermal analysis measurements with open crucibles distinguish among adsorbed, absorbed, and crystal water. Thus, DSC curves, TG curves, or microwave dielectric measurements give information on water content or on the

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FIG. 1 Phase diagram of water indicating the course of two different drying processes. Tp, triple point; Cp, critical point; a, air-drying; f, freeze-drying.

state of drying of foods [26–29]. The peak due to water vaporization in calorimetric curves often masks other phenomena of interest, such as the crystallization or decomposition of carbohydrates. To observe such effects, analyses have to be performed on samples in sealed crucibles (or under pressure). In such cases, however, it is important, for reasons of safety, to remember that the water vapor pressure increases rapidly with temperature, especially above 150°C. At 300°C, the water vapor pressure already amounts to 85 bars!

B. Lipids The physical properties of edible fats and oils are closely related to those of triglycerides, which constitute the major part of lipids (molar ratio higher than 90%). The occurrence of more than one crystalline form (polymorphism) is a general characteristic of lipids or triglycerides in the solid state. A fat’s ability to undergo polymorphic changes is important, mainly because of its effect on food texture and appearance. It has been proved that DSC, in combination with X-ray diffraction, is one of the most efﬁcient techniques for the study of the phase changes of lipids, including solid–liquid (melting), liquid–solid (crystallization), and solid–solid transitions [30–36]. The temperature range between

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FIG. 2 (A) Heating curves of dl-α,β-distearin, showing the melting of the stable polymorphic form (at 70°C) during the ﬁrst run (——) and the melting (at 60°C) of a less stable polymorphic form during the second (— - - —) and third (- --) runs (superimposed). (B) Cooling curve (— ⋅ —) of dl-α,β-distearin, showing crystallization at 55°C. Instrument: DSC 7. (Courtesy of Perkin-Elmer Corp.)

⫺50°C and 80°C is of special interest; melting enthalpies are between 100 and 200 J/g. In the context of quality control, such calorimetric curves can be used as ﬁngerprints for the considered fats. As examples, Figs. 2 and 3 present the thermal polymorphism of two glycerides, distearin and tristearin, as displayed by a power compensation DSC instrument. The inﬂuence of composition, processing parameters, thermal history, and aging can be clearly described by means of DSC investigations on lipid polymorphism. Contamination (adulteration) of fats can also be detected in calorimetric curves recorded during the crystallization [37] or melting [38] of lipid mixtures. In the same way, the solid fat index (SFI) representing the ratio of solid to liquid in a partially crystallized lipid at a given temperature can be obtained from the calorimetric melting curve by sequential peak integration [31,39,40]. SFI values are currently used in the fat industry for quality control and for monitoring processes such as interesteriﬁcation, fractionation, hydrogenation, and tempering.

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FIG. 3 Calorimetric curves of tristearin showing, during the ﬁrst heating (solid curve), the melting of the stable polymorphic form around 75°C and, during the second heating, (— -- —), the melting of two less stable forms around 55°C and 70°C, with partial crystallization around 65°C. Instrument: DSC 7. (Courtesy of Perkin-Elmer Corp.)

They are determined from the equation

SFI (T ) ⫽ 1 ⫺

冮冮

T

H(T ) dT

T0

(1)

T 1

H(T ) dT

T0

where T0 is the onset temperature of melting, T1 is the end temperature of melting, and H(T ) is the enthalpy at the selected temperature. Lipid oxidation is an exothermic phenomenon that can be followed, at least at elevated temperatures, by DSC or (preferably) by isothermal calorimetry [41– 44]. Measurements can be performed under a static air atmosphere or, better, under oxygen ﬂow or oxygen pressure. In the isothermal mode, induction times can be deﬁned according to published procedures using other techniques (see Fig. 4). Figure 5 compares the oxidative stability at 130°C of three very different oils (safﬂower, blackcurrant seed, and Nujol). Induction time values can be used

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FIG. 4 Determination of induction times A and B. A is the time lag between the start of oxidation and the start (extrapolated onset) of exothermic heat ﬂow. B is the time lag between the start of oxidation and the maximum of exothermic heat ﬂow. (Adapted from Ref. 41.)

FIG. 5 Calorimetric curves of three oils with different stabilities, oxidized at 130°C under oxygen ﬂow. (⋅ ⋅ ⋅) Safﬂower oil; (——) blackcurrant seed oil; (- --) Nujol. Instrument: Setaram DSC 111, isothermal mode. (From Ref. 41.)

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to determine the oxidative stability of lipids [41,42] or the efﬁciency of food antioxidants [41,43]. Thermal data on most triglycerides and lipids are compiled in handbooks [45]. In addition, DSC and microcalorimetry are very often used to study transitions in biological membranes, because lipids are major constituents of living cells.

C. Carbohydrates (Glucides) During heating of (crystalline) carbohydrates, one generally observes ﬁrst fusion and then exothermic decomposition (pyrolysis), which often immediately follows melting [46–48]. Other effects may also be detected: vaporization of water in hydrated carbohydrates, glass transitions and crystallization of amorphous sugars. Figure 6 presents the calorimetric curves of amorphous sucrose and amorphous cellobiose (both heated in sealed crucibles) between 70°C and 270°C. The onset temperatures of the exothermic decomposition observed on heating these carbohydrates in sealed vessels varied between 100°C and 230°C [46]; the corresponding enthalpies ranged from 300 to 800 J/g. The onset temperatures of fusion were found to be between 60°C and 220°C, with enthalpies from about 40 to 330 J/g. All values given here should be considered as approximate. With open containers the temperature range of thermal effects is much higher, probably because various hot gases are released during the decomposition [47,48]. It has long been known that amorphous carbohydrates have a glass transition around 50°C [49]. Glass transitions and crystallization studies by thermal analysis techniques are very

FIG. 6 Calorimetric curves of amorphous sucrose and cellobiose (both heated in sealed crucibles); c, Crystallization; f, fusion; d, decomposition. Instrument: Setaram C80. (From Ref. 46.)

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current [50–54], and even subzero temperature glass transitions have been detected for aqueous solutions [55]. In most food powders obtained by industrial (fast) drying techniques such as freeze-drying or spray-drying, the carbohydrates (sucrose, lactose, etc.) are not crystalline but amorphous. At ambient temperature and low water activity, they are in the amorphous glassy state. If temperature and/or water activity increases, they change to an amorphous rubbery state. The temperature at which this happens is called the glass transition temperature, Tg . However, this phenomenon is observed over a temperature range, and, depending on the measuring conditions (annealing, thermal history), an overshoot called relaxation is observed as shown in Fig. 7. Glass transition as well as the following crystallization phenomena depend strongly on water activity and moisture content, as shown in the calorimetric curves of Fig. 8, and on the molecular weight of the carbohydrates, as shown in the graph presented in Fig. 9. Even if the food products are not perfectly stable below the glass transition, for storage it is very important in most cases to stay below this critical tempera-

FIG. 7 DSC curves of galactose (a) at ﬁrst rewarming and (b, c) after annealing at 14°C for (b) 1 h and (c) 24 h. Cooling and heating scanning rates: 10°C/min. (From Ref. 51 with permission from Technomic Publishing Company, Inc.)

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FIG. 8 Calorimetric curves of amorphous sucrose showing the variation of the glass transition and crystallization temperatures at different water activities Aw . Instrument: Setaram Micro-DSC. (From Ref. 52 with permission from the editors of J Thermal Anal.)

FIG. 9 Effect of water activity on glass transition temperatures of disaccharides and maltodextrins with various molecular weights (M values in daltons). (From Ref. 54 with permission from Elsevier Science.)

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ture. Glass transition is also a basic concept for the understanding of processing, especially drying, agglomeration, and encapsulation. Glass transition is also observed for proteins in powder form. For extrusion or similar cooking and texturization processes, many workers study in particular the endothermic gelatinization of starches and other carbohydrates (e.g., carrageenans) in the presence of water as well as the retrogradation of the gelatinized products [56–67]. Starch gelatinization is deﬁned as the collapse (disruption) of molecular order within the starch granule, as shown by irreversible changes in its properties such as granular swelling, native crystalline melting, loss of birefringence, and starch solubilization [68]. In a calorimetric curve (see Fig. 10), gelatinization is observed as a peak around 60°C (depending in particular on the salt content), together with a change in the speciﬁc heat. Enthalpies of about 10–20 J/g dry matter (DM) are measured when the moisture content is about 50%. Starch retrogradation is deﬁned as a process that occurs when gelatinized starch molecules begin to reassociate in an ordered structure; under favorable conditions, a crystalline order appears [68]. The heat slowly released by the recrystallization of the gel can be detected by means of a microcalorimeter [69] (see Fig. 11). However, most workers follow the retrogradation indirectly by observing the melting of the microcrystals formed after a given storage period. The corresponding broad melting peak is found in the calorimetric curves between 40°C and 80°C; the measured enthalpies are generally lower than 10 J/g DM and are often called retrogradation enthalpies. Retrogradation studies are of great importance to the understanding of such phenomena as the staling of bread.

FIG. 10 Gelatinization and speciﬁc heat change of native wheat starch (water solution of 40% dry matter). Instrument: Setaram Micro-DSC. (Adapted from Ref. 69.)

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FIG. 11 Retrogradation at 4°C of gels obtained from native wheat and potato starches (water solutions of 50% DM). Instrument: Setaram Micro-DSC, isothermal mode. (Adapted from Ref. 69.)

D. Proteins The functional properties (solubility, antigenicity, viscosity, capacity to form a gel or to emulsify lipids) of foods such as dairy products are essentially determined by their proteins. Heat treatments of proteins in water induce damage (denaturation) to the molecular structure [70,71]. Calorimetric techniques allow measurement of the energy changes that accompany conformational transitions in proteins. The methods of investigation as well as many results were ﬁrst presented by Privalov [72,73]. The denaturation of proteins in aqueous solutions is seen as one or two endothermic phenomena encountered in the temperature range between 40°C and 160°C. The corresponding enthalpies are very weak; values between 1 and 20 J/g DM are generally observed. Calorimetric techniques have been used extensively to determine the conditions (pH, buffer, temperature, ionic strength, salt or carbohydrate content of the solution) that best maintain the physicochemical properties of proteins or promote ﬂavor binding or release capacity [74–77] and to study whey proteins, especially β-lactoglobulin (see Fig. 12) and α-lactalbumin, as well as soy proteins [78]. Similarly, the thermal denaturation of legume proteins such as legumin and vicilin [79], of egg white [80,81], and of meat [82], ﬁsh [83], and cereal proteins [84] has been studied with the help of DSC. DSC curves demonstrate the stabilizing effect of the binding of iron (or other metal ions) on protein (Fig. 13) [85]. The thermal denaturation of enzymes also gives information on their inactivation [86]. The loss of gel structure can be observed for meat gelatin by DSC around 30°C [87]. Although calorimetry of proteins is rarely performed on dry samples, this kind of analysis at least allows investigation of the glass transition and protein oxidation.

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FIG. 12 Calorimetric curves showing the heat denaturation of β-lactoglobulin in solution as a function of temperature at pH 3.5 (dashed line) and in the pH range 6.0 ⬍ pH ⬍ 8.0. Instrument: DuPont thermal analyzer 990. (From Ref. 75.)

E. Minor Constituents Physiologically active substances that are present in minor quantities in foodstuffs can be studied in their pure forms or in aqueous solutions. Crystalline caffeine has been studied extensively in the anhydrous or monohydrate form and in solution, particularly by calorimetric techniques [88–90]. Caffeine shows a solid–solid transformation around 140°C and melts at around 235°C, as shown in the calorimetric curve of Fig. 14.

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FIG. 13 Calorimetric curves showing the heat denaturation of ovotransferrin (conalbumin) in solution. (a) Apo-ovotransferrin; (b, c) ovotransferrin 39% saturated with iron; (d) ovotransferrin fully saturated with iron. The bar represents a heat ﬂow of 500 µJ/s. Instrument: DuPont thermal analyzer 990. (From Ref. 85.)

FIG. 14 Calorimetric curve of pure β-caffeine. Instrument: DuPont thermal analyzer 990. (From Ref. 88.)

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V. THERMAL BEHAVIOR OF RAW AND RECONSTITUTED FOODS A. Phenomena Related to Food Composition Depending on the food composition, most of the main phenomena mentioned for the major constituents (carbohydrate melting excepted) are observed also with raw and reconstituted foods; however, the corresponding peaks in the calorimetric curves are broader. The effects due to minor constituents can be detected only in special cases. Around 0°C, the melting curves of water in high moisture foods such as ice creams introduce the differentiation between ‘‘bound’’ and ‘‘free’’ water. The amount of free water relative to the total amount of water (R) is given by the equation R⫽

∆Hm (1 ⫺ S)∆Hw

(2)

where S is the percentage of solute (or of dry matter), 1 ⫺ S is the percentage of water, ∆Hm is the measured fusion enthalpy (J/g) and ∆Hw is the fusion enthalpy of pure water (J/g). Figure 15 presents calorimetric curves with ice melting peaks for various foods [91]. A detailed description of the low temperature behavior of many foods has been given by Riedel [92,93]. The enthalpy differences, with the zero enthalpy value at ⫺60°C, have been compiled in tables or nomographs, which are very useful for chemical engineering calculations. Calorimetric cooling curves generally show freezing and supercooling very clearly; the temperature range of freezing is of particular interest in relation to freezing or cold storage. Around ambient temperature, the melting of fat can be observed in reconstituted foods and even in some raw foods such as cocoa beans. In the context of lipid research, modern instrumentation (DSC, microcalorimetry) allows the study of phase transitions, even in complex biological membranes [94–96]. Around 70°C, the gelatinization of ﬁnely divided ﬂours (starches) mixed with water can be observed. Retrogradation, for instance bread staling, can also be studied [97]. Crystallization of amorphous sugars (e.g., crystallization of amorphous lactose in milk powders [98]) can be detected in reconstituted foods. However, protein denaturation is no longer detected clearly when studying liquid whole milk products containing lipids, lactose, calcium, etc. Around and above 100°C, the boiling of water is generally prevented by using sealed containers; this allows the detection of other phenomena such as carbohydrate decomposition. This is observed in the calorimetric curves of reconstituted foods such as milk powders and in the curves of raw foods such as coffee beans, chicory roots, and cereal grains [98–101].

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FIG. 15 Low-temperature calorimetric curves of carrots, reindeer meat, and white bread, showing ice melting. Instrument: Mettler DSC 30. (From Ref. 91.)

Lipid oxidation can be observed if the lipids are on the food surface and thus in contact with oxygen. This condition can be fulﬁlled for some processed foods and some reconstituted foods. The oxidation of minor constituents such as polyphenols is a possible cause of self-heating in hay, to temperatures above those normally reached during fermentation. To measure the heat released by these phenomena, speciﬁc calorimetric experiments have to be performed.

B. Interaction Between Food Constituents In addition to the caloric phenomena due to each constituent alone, there are also interactions between food constituents. The corresponding thermal effects can be detected in model binary mixtures and sometimes, with more difﬁculty, in raw or reconstituted foods.

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Maillard reactions, the browning reactions between proteins and reducing sugars, are observed in the calorimetric curves of lactose–casein mixtures or in those of milk powders [98]. Maillard reactions are exothermic, take place above ambient temperature, and depend on the moisture content of the product. The corresponding enthalpies are not so important (less than 100 J/g DM). Phase transitions of starch–lipid complexes are also seen in calorimetric curves. These weak endothermic phenomena occur around 100°C and have enthalpies of less than 30 J/g DM [57]. Sometimes interactions between water and the foods or food constituents (dissolution, absorption, or desorption) in addition to interactions of cations and sugars in water are studied [102–104].

C. Biological Processes Many foods are obtained by fermentation. In this context, measuring the heat released during the fermentation process gives information relevant for dimensioning fermentors or for safety [105,106]. On the other hand, microorganisms can lead to spoilage of wet foods during storage. Calorimetric techniques are therefore also used to obtain a basic knowledge of the metabolic activities of bacteria, yeasts, and fungi [107]. A calorimetric method has been proposed to determine bacterial thermal death times [108].

VI.

SELF-HEATING, SELF-IGNITION, AND SAFETY ASPECTS

A. Self-Heating, Self-Ignition, and Rise in Pressure Fires and dust explosions are known hazards in many industries, including the food industry. Self-heating and self-ignition studies are thus often of interest to develop better deﬁned safety conditions for high temperature processing operations when sufﬁcient oxygen is available. Studies of spontaneous combustion of powders very often consider sample deposition on a heating plate or in a furnace heated to a known temperature. The data obtained by these tests are generally compiled as minimum ignition temperatures for dust layers [109]. Similar measurements of self-ignition temperatures can be performed by using differential thermal analysis (DTA) techniques with air or oxygen atmosphere. The sample can be heated under oxygen ﬂow or oxygen pressure. The well-deﬁned measuring conditions are an advantage, particularly the precise heating rates possible with thermal analysis instruments and the stepwise temperature increase of adiabatic calorimeters [110,111]. Figure 16 presents the DTA curves of cellulose heated and burned under 25 bars of oxygen.

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FIG. 16 DTA curves of cellulose heated and burned under 25 bars of oxygen. Highpressure DTA 404 H instrument from Netzsch. (From Ref. 112.)

Self-heating can lead to self-ignition of the food if sufﬁcient oxygen is available. The main phenomena involved in thermal runaway of food products are fermentation, carbohydrate decomposition, lipid oxidation, and probably polyphenol and protein oxidation. However, other weaker exothermic effects such as Maillard reactions could participate in the initial temperature increase. If oxygen is in low concentrations, it is often the elevated pressure resulting from the rise in temperature in a closed medium that presents a risk (of bursting the autoclave, for example). Further dangers can come from degassing associated with fermentation or decomposition reactions; the gas emitted could lead to a rise in pressure (or be inﬂammable).

B. Simulation of Process Conditions Sometimes thermal analysis techniques must be applied unconventionally if we are to be able to carry out the measurements under conditions close to those of the process being studied. Thus, for example, the calorimetric study of a sample in a sealed cell simulates what happens in a homogeneously heated autoclave. DTA or DSC measurements can also be carried out under a constant pressure of an inert gas or even under supercritical CO2 [112]. Figure 17 presents a scheme for a DTA experiment under supercritical CO2.

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FIG. 17 Scheme of a DTA experiment under supercritical CO2. High-pressure DTA 404 H instrument from Netzsch. (From Ref. 112.)

VII. OTHER THERMODYNAMIC PARAMETERS A. Speciﬁc Heat It is evident that calorimetric techniques are often used to determine the speciﬁc heats of foods. The methods, and a synthesis of the results, are presented in the literature [113]. The use of a standard such as synthetic sapphire simpliﬁes the determination of speciﬁc heats. By measuring the standard, an empty cell, and the substance, the speciﬁc heat value C2 of the sample can be obtained directly by comparison. For a given temperature, C2 ⫽ C1

m1 (Q2 ⫺ Q0 ) m2 (Q1 ⫺ Q0 )

(3)

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where m1 is the mass of the standard substance, m2 is the sample mass, C1 is the speciﬁc heat of the standard substance, and Q0, Q1, and Q2 are the required heat quantities for the empty cell, the standard substance, and the sample, respectively. The values obtained vary between 0.9 J/(g ⋅ K) for very dry food products to 4.18 J/(g ⋅ K) for water. It is therefore evident that the moisture content of a food has a strong inﬂuence on its speciﬁc heat value.

B. Heats of Combustion During the combustion of a food product, a large amount of energy is liberated. Values determined with calorimetric bombs or isoperibolic calorimeters correspond to about 39 kJ/g for fat, 23 kJ/g for protein, and 17 kJ/g for carbohydrate.

C. Heat Conductivity and Thermal Diffusivity Other parameters such as heat conductivity or thermal diffusivity can be of interest to the food technologist and can, in some cases, be determined by calorimetry, by conducting special experiments.

D. Heats of Solution The dissolution of ingredients, minerals, food constituents, or even foods in water or in other solvents can be observed by calorimetry. The data are determined in the isothermal mode.

VIII.

RELATED TECHNIQUES

Some related thermal analysis techniques give mechanical and rheological rather than thermal information. These techniques include thermodilatometry (which is no longer of great interest for food studies), dynamic mechanical analysis (DMA), and dynamic mechanical thermal analysis (DMTA) [114]. Other techniques, such as X-ray diffraction, near-infrared (NIR) reﬂectance, low and high resolution nuclear magnetic resonance (NMR), microscopy, and light scattering, give information that characterizes a food before or after a thermal treatment. Low resolution NMR, for instance, is well known for rapidly giving SFI values of fats that correspond to those obtained by DSC [40]. X-ray diffraction can also be adapted, by temperature control of the sample, to follow the lipid phase transitions by recording the diffraction patterns versus temperature [115,116]. If the (lipid) sample is placed in a temperature-controlled cell, even microscopic techniques can be used to follow crystal growth or melting [117]. It is also worth noting that for caffeine solutions a thermodynamic parameter such as the enthalpy of dimerization of caffeine in water can be determined comparatively by dissolution calorimetry and by high resolution NMR [118,119].

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Thermal analysis techniques can also be coupled with the use of other instruments such as mass spectrometers or gas chromatographs to analyze the gases evolved during decomposition. Finally, mathematical models help in applying thermodynamic data to engineering problems.

IX.

CONCLUSION

Other reviews of this type exist, and books have been published on the thermophysical properties of foods [120–126]. It should become clear from this review that calorimetry, (high pressure) DTA, and DSC give relevant, reproducible data that are of great importance in many ﬁelds of food technology, because this information characterizes the food globally. From the basics of food technology it is easy to understand that calorimetric techniques help in quality control, improvement of food characteristics, development of new operations, and process safety [127–134]. Many thermal effects that have been neglected until now, mainly because of experimental difﬁculties, remain to be studied. New technologies such as high hydrostatic pressure have recently promoted new DSC studies of proteins, lipids, and starches. Finally, food is sometimes used as a symbol, like the cheese in a fable of La Fontaine, to express things that are true in other ﬁelds. It is also true that many other ﬁelds, such as pharmaceuticals analysis, polymer physics or chemistry, materials and safety sciences, and semiconductor physics, have helped us to understand the thermal and more generally the physicochemical behavior of foods [135–140].

ACKNOWLEDGMENT We thank Dr. Ian Horman for reviewing the manuscript. This chapter is based on an earlier version published by A. Raemy and P. Lambelet [Thermal behaviour of foods. Thermochimica Acta 193: 417–439 (1991)] with permission from Elsevier Science.

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Raemy et al. processing. Thermochim Acta 95:441–446 (1985); A Raemy, M Gardiol. Parame`tres thermodynamiques et se´curite´ des ope´rations industrielles, ASIC, 12th Colloque, Montreux, 1987, pp. 320–330. NN Mohsenin. Thermal Properties of Foods and Agricultural Materials, Gordon and Breach, New York, 1980. WM MacInnes, Ph Roulet. Dynamic-mechanical properties of starch gels. Rheol Acta 26:431–434 (1988). IT Norton, CD Lee-Tuffnell, S Ablett, SM Bociek. A calorimetric, NMR and Xray diffraction study of the melting behavior of tripalmitin and tristearin and their mixing behavior with triolein. J Am Oil Chem Soc 62:1237–1244 (1985). L Hernqvist, B Herslo¨f, K Larsson, O Podlaha. Polymorphism of rapeseed oil with a low content of erucic acid and possibilities to stabilize the β′-crystal form in fats. J Sci Food Agric 32:1197–1202 (1981). K Kawamura. The DSC thermal analysis of crystallization behavior in palm oil. J Am Oil Chem Soc 56:753–758 (1979). A Cesaro, E Russo, V Crescenzi. Thermodynamics of caffeine aqueous solutions. J Phys Chem 80:335–339 (1976). I Horman, B Dreux. Estimation of dimerisation constants from complexationinduced displacements of 1H-NMR chemical shifts: Dimerisation of caffeine. Helv Chim Acta 67:754–764 (1984); 68:72–75 (1985). A John, PN Shastri. Studies on food macromolecules by differential scanning calorimetry: A critical appraisal. J Food Sci Technol 35:1–14 (1998). A Schiraldi. Calorimetry, thermal analysis and chemical thermodynamics in food science. Thermochim Acta 162:253–264 (1990). M Peleg, EB Bagley. Physical Properties of Foods, Avi, Westport, CT, 1983. R Jowitt, F Escher, M Kent, B McKenna, M Rogues. Physical Properties of Foods, Elsevier Applied Science, London, 1987. S Rahman. Food Properties Handbook, CRC Press, Boca Raton, FL, 1995. TW Schenz, EA Davis. Thermal analysis. In: Food Analysis, 2nd ed. (SS Nielsen, ed.), Aspen Publishers, Gaithersburg, MD, 1998, pp. 587–598. VR Harwalkar, CY Ma, eds. Thermal Analysis of Foods, Elsevier, London, 1991. MJ Lewis. Physical Properties of Foods and Food Processing Systems, VCH, Weinheim, 1987. P Zeuthen, JC Cheftel, eds. Thermal Processing and Quality of Foods, Elsevier, London, 1984. S Friberg. Food Emulsions, Marcel Dekker, New York, 1976. L Rey, JC May, eds. Freeze-Drying/Lyophilization of Pharmaceutical and Biological Products, Marcel Dekker, New York, 1999. ST Beckett, ed. Physico-Chemical Aspects of Food Processing, Blackie, London, 1995. DR Heldmann, DB Lund, eds. Handbook of Food Engineering, Marcel Dekker, New York, 1992. M Rao, RW Hartel, eds. Phase/State Transitions in Foods, Marcel Dekker, New York, 1998. MS Rahman, ed. Handbook of Food Preservation, Marcel Dekker, New York, 1999.

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Index

Absorption, 494 Acridine, 139 Activation energy, 417 Active carbon, 169 Adhesion, 358 Adhesive interactions, 397 Adiabatic bomb calorimeters, 480 Adsorbate-adsorbent interactions, 163 Adsorbent, 365, 370, 375 Adsorption, 337, 398 capacity, 363, 365, 366, 375, 384 excess, 367–374, 384, 393 excess isotherms, 365, 377, 381 forces, 365 isotherms, 336, 349, 401, 433 layer, 363, 365–367, 372, 398 measurements, 401 of aerosil dispersions, 398 of binary liquid mixtures, 362 of surfactant, 335, 336 phenomena on ﬁne powders, 343 volume, 365 Agglomeration, 488 Aggregate formation, 354 Aggregation, 155, 300 number, 2, 298, 305, 320 Aging, 415, 418, 434

α-lactalbumin, 489 Alcohol interactions, 94 Alkanephosphonic acid, 168 Alkyl chains, 392 Alkyl glucosides, 320, 321 Alkyl polyoxyethylenes, 353 Alkylammonium chain lengths, 385 Alkylbenzene polyoxyethylenes, 353 Alkylbenzyldimethylammonium bromides, 353 Alkyl-N-acetylamino saccharides, 216 Alumina oxide, 169 Alkylpyridinium chlorides, 353 Alkylsulﬁnylalkanols, 353 Alkyltrimethylammonium bromide, 138, 316 Alkyltrimethylammonium halides, 353 Amino acid, 440 Amorphous, 163 silica gel, 377 Antigenicity, 489 Antioxidants, 479 AOT, 3, 5, 8, 65, 91, 111, 141, 160, 161, 163, 166, 353, 432, 433, 438–440, 442, 444 Apolar solvents, 2, 3 Apo-ovotransferrin, 491 507

508 Aspartame, 438, 441–444 Asymmetrical catanionic surfactants, 466 Atomic force microscopy, 336 Attractive interactions, 305 Azobenzene, 457 Azoxybenzene, 457 Batch sorption microcalorimetry, 343 β-caffeine, 491 Bentonite, 353 Benzyldimethylhexadecylammonium chloride, 3 Bicontinuous structure, 6, 7 Bilayer, 284, 312, 321–324, 327, 330, 394, 452, 453, 460, 471 orientation of vermiculite, 394 stability, 470 structure, 453, 468 surface, 261 thickness, 465 Binary liquid mixtures, 359, 397 mixtures, 364 Bingham equation, 399 Biocatalysis, 12 Biochemical reactions, 17 Biological, 444 cells, 444 gels, 161 membranes, 8, 159, 321, 471, 485 mineralization, 444 process, 159 Biomembrane, 12, 256, 471 Biomineralization, 421, 429 Biphase transition, 136 Biphenyl, 457 Birefringence, 452 β-lactoglobulin, 489, 490 Block coploymer, 154, 156, 157 Bound crystal water, 443 water, 60, 93, 163, 249, 252, 420, 480 Bovine corneas, 161 serum albumin, 169 Bridging orientation of vermiculite, 394 Bulk water, 161, 1661, 72, 270 Butanol, 79, 80, 96, 392–395, 397

Index Caffeine, 490 Calcium carbonates, 438 ﬂuoride, 438 Calorimetric thermograms, 140 Calorimetry, 8, 86, 121, 131, 196, 201, 336–338, 497 Calorimetry of proteins, 489 Capacity to form a gel, 489 Carbohydrate decomposition, 495 Carrageenan, 488 Carrots, 493 Cascade nucleation, 26, 47 Cataionic surfactants, 459 Cationic surfactants, 136 Cellobiose, 485 Cellulose, 494, 495 Cereal proteins denaturation, 489 Cetyltrimethylammonium methacrylate (CTAM), 138 Chain ramiﬁcation, 133 Characterization of inorganic compounds, 414 of organic compounds, 414 of the solid phase, 420 Chemical process, 159 Chocolate bars, 478 Cholesterol, 10, 137, 146, 325 Cholesteric liquid crystalline state, 455 Chromium nitrate, 103 Classiﬁcation of calorimeters, 336 Classiﬁcation of enthalpy isotherms, 375 Clausius-Clapeyron equation, 350 Clay minerals, 380 nonswelling mineral, 380 Cluster formation, 416 Clusters, 160 Coagel, 139 Coalescence, 184 Cocoa beans, 492 Coffee, 478 Coffee surrogates, 478 Colligative effects, 166 Colloidal dispersions, 409 particles, 377 Color, 479

Index Compact crystals, 415, 425 Complex, 214 liquid, 203 Composition of mixed liposomes, 152 Conalbumin, 491 Conductance, 6 Conductivity, 452 Conﬁned regions, 159 Conformational rearrangements, 146 Control of crystal morphology, 428 crystallization, 429 by additives, 426 polymorphism, 438, 440 Cooking, 488 Copolymer, 154 Cosmetics, 24 Cosurfactant, 107, 223, 227 Coulomb attraction, 350 Critical micellar concentration, 430, 433 Critical supersaturation, 417, 434 Cross-linker, 104 Cryo-TEM, 94 Cryothermal electron microscopy, 94 Crystal growth, 415, 417, 419, 420, 422, 434 structure, 434, 454 water, 480 -crystal transition, 139 Crystalline dispersions, 413, 415, 418 hydrates, 142, 418 phase, 462 Crystallization, 134, 193, 195, 418, 423, 429–431, 434, 435, 437, 439, 442, 443, 481, 482, 483, 485, 487, 488, 492 of water, 161 enthalpy, 165, 480 in conﬁned spaces, 434 in microemulsions, 437 of amorphous lactose, 492 of amorphous sugars, 485 of solutes, 439 of triglycerides, 435 phenomena, 486

509 [Crystallization] process, 445 rate, 134, 429 Crystalluria, 430 Crystal-mesophase, 140 D2O, 65, 234, 242, 442 DDACl, 431, 432 DDADDS, 464 DeADeS, 464 Decaglycerol dioleate, 3 Decane, 235, 242 Decanephosphonic acid, 134, 136 Decomposition, 142, 485 reaction, 495 Decylammonium decyl sulfate, 460, 462 Decylmethylsulfoxide, 353 Degree of super saturation, 420 Degree of supercooling, 435 Dehydrated foods, 480 Dehydration, 322, 417, 420, 421, 424, 443, 444 of alcohols, 322 of Na⫹ ions, 422 Demicellization, 296, 303–307, 309, 316, 317, 319 Denaturation, 478, 489, 490 Dendrites, 425 Dendritic crystals, 415, 417, 424 Depletion of solution concentration, 420 Deposition of solute ions, 422 Desorption, 494 Detergent, 312–315, 324, 326, 329, 330, 332 Diacylphosphatidylethanolamine, 256 Diacylphosphatidylglycerol, 256 Diacylphosphatidylcholine, 256 Didodecyldimethylammonium bromide, 3, 91, 98, 135, 136, 161 Dielectric spectroscopy, 215 Different modes of crystallization, 424 Differential interferometry, 342 molar enthalpies, 352 refractometer, 347 refractometry, 342

510 Dihexadecylphosphoric acid, 473 Diketopiperazine, 443 Dilatometry, 435 Dilinoleylphosphatidylethanolamine, 324 Dimerization of caffeine, 497 Dimethylaminoethanol, 89 Dimethyldecylphosphine oxide, 127–129 Dimethyldihexadecylammonium, 386 Dimyristoylphosphtidylcholine, 143, 151, 257 Dimyristoylphosphtidylethanolamine, 256 Dioctadecyldimethylammonium, 389, 390 Dioctadecyldimethylammonium bromide, 91, 98, 161, 472 Dioctadecyldimethylammonium chloride, 472 Dioctadecylmethylammonium chloride, 472 Dioleylphosphatidylcholine, 324 Dioleylphosphatidylglycerol, 324 Dipalmitoylphosphatidyl choline Dipalmitoylphosphatidylcholine, 132, 256 Dipalmitoylphosphatidylethaolamine, 256 Dipalmitoylphosphatidylglycerol, 256 Dipalmitoylphosphatidylcholine, 324 Diphenylamine, 139 Diphenylazomethine, 457 Dipole-dipole number, 2 Disodium n-decanephosphonate, 98, 103, 136 Dispersed solid particles, 362 Dissacharides, 487 Dissolution, 127, 494 calorimetry, 497 Distearin, 482 DMA, 497 DMPC, 257, 321, 322, 325 DMPE, 267, 268–271, 274–276, 281– 286, 288, 289, 291, 292 Dodecane, 61, 66, 96, 217, 227, 233, 236 Dodecanol, 78 Dodecylammonium dodecylsulfate, 460 Dodecylammonium propionate, 2 Dodecylammonium vermiculite, 392–397

Index Dodecyldiammonium vermiculite, 393, 395, 396 Dodecylpyridinium bromide, 139 Dodecylpyridinium iodide, 3 Double-chain surfactants, 471 DPPC, 258–267, 271, 275–281, 288, 289, 292, 324, 330 DPPE, 257 DPPG, 270, 272, 273, 291, 292 Droplet-droplet distance, 48 Drying process, 481, 488 Dynamic mechanical analysis, 497 Effect of hydrophobization, 375 Egg white denaturation, 489 Electrical conductivity, 70, 110, 111, 215, 241 double layer, 418 Electrolyte, 8, 419 Electron spin resonance, 62 Electrostatic interactions, 4, 470 Ellipsometry, 336 Emulsiﬁcation boundary, 51 Emulsiﬁed microdroplets, 163 Emulsion, 157, 183, 194, 201, 415, 434– 437, 443, 480 crystallization, 439 polymerization, 24 Encapsulation, 488 Endothermic transition, 156, 468 Energy barrier, 43, 45 of formation, 185 Enthalpic interaction, 343 Enthalpies of solidiﬁcation, 192 Enthalpy, 154, 156, 162, 224, 252–254, 264, 228, 229, 231, 304, 325, 354, 385, 488, 268, 270, 274, 275, 296, 300, 314, 322, 324, 327, 328, 331, 336, 342, 345, 347, 359, 363, 364, 375, 376, 389, 414, 473 changes, 468 of freezing, 435 functions, 377 isotherms, 367, 372, 373, 376, 384 isotherms of diplacement, 350, 351

Index [Enthalpy] of crystallization, 200 of demicellization, 320 of displacement, 339, 340, 342, 349, 360–362, 368–373, 392 of immersion, 342 isotherms, 376 of melting, 217 of micelle formation, 303, 332 of micellization, 296, 299, 316 of octadecane, 136 of solution, 8 of water, 161, 162 of wetting, 379, 389 Entropy, 163, 165, 223, 239, 300, 392, 397, 414, 473 change, 154 Enzymatic activity, 438 ESR, 62 Ethanol, 96 Ethoxylated 20-sorbitan monolaurate, 436 alcohols, 76, 93 siloxanes, 77, 88 Eutectic composition, 139 melting, 139 point, 131 Evaporation, 128 Everett-Schay function, 363 Exothermic decomposition, 485 process, 478 Experimental observation, 45 Extraction processes, 12 Extreme viscosity, 160 Fermentation, 494, 495 Ferritin, 444 First hydration layer of bromide ion, 161 Fish denaturation, 489 Fish cut, 27 Flavor, 479 of food, 479 Flocculation, 415, 417, 418, 420, 434, 440

511 Flow sorption microcalorimetry, 346, 349, 393 Food antioxidants, 483 composition, 492 constituents, 477, 480, 497 industry, 494 properties, 479 Force balance technique, 336 Formation, 413, 419 and transformation of crystalline dispersions, 413, 415 and transformation of precursor phases, 420 of CTAM, 138 of diketopiperazine, 443 Fourier transform infrared spectroscopy, 414, 134, 167, 168 Fractionation, 482 Free energy, 32, 300, 416, 418, 419, 471 Free enthalpy of adsorption, 382, 395 of wetting, 363 Free water, 61, 87, 161, 162, 167, 480 Freeze-drying, 478, 480, 486 Freezing, 159, 478 Frying, 478 Functional properties, 489 Fusion, 128 temperature, 167 Galactose, 486 Gel, 148, 275, 281, 287, 288, 290, 488, 489 ﬁltration, 86 mesophase, 145 transition, 148 phase, 137, 139, 262–264, 267, 268, 270–274, 277–280, 282, 283, 285-287, 290–292, 330 phase of lipid-water systems, 261 structure, 489 systems, 422 Gelatinization, 478, 488, 492 Gel-like structures, 420 Gel-liquid crystal transition, 132, 135

512 Gel-liquid crystalline phase transition, 137, 142, 147, 256 Gel-micellar solution transition, 139 Geophysical process, 159 Gibbs energy, 222, 239 equation, 403, 404 phase, 27, 42 Gibbs-Thompson relation, 416 Glass transition, 239, 240, 485–489 Glass-liquid transition, 240 Globular aggregates, 3 Glucitol, 317 Glucose, 317 Glycerides, 482 Glycerol esters, 87 Gradual decomposition, 138 Guar, 103 Hamaker constants, 398, 399, 401 HDP-illite, 382, 383 HDP-kaolinite, 384 HDP-montmorillonite, 386, 389 Headgroup area, 4 effect, 336 -headgroup interactions, 321 interactions, 474 network, 141 Heat capacity, 121, 127, 128, 129, 131, 163, 187, 207, 209, 210, 326, 336 conductivity, 497 denaturation, 491 evolution, 295 of bilayer-micelle phase transformation in mixtures of phospholipids and detergents, 312 evolution of micellization, 300 evolution of the self-assembly, 305 extraction, 396 ﬂux, 338, 339 of combustion, 497 of demicellization, 305, 307 of evaporation, 302 of fusion, 162 of immersion, 359, 377, 401, 404, 407 of micelle formation, 154, 320 of micellization, 316, 328

Index [Heat capacity] of mixing, 162 of solution, 497 of transition, 316 of a triblock copolymer, 156 of wetting, 359, 377, 378, 386, 388 partitioning of amphipiles, 321 Heptane, 379, 398–401, 403–405, 407, 408 Heterogeneous nucleation, 418, 435 Hexadecane, 66, 79, 138, 158, 200, 201, 218, 221, 223, 224, 228, 229, 231, 232, 234, 235, 238, 436, 437 Hexadecylpyridinium, 388, 390, 386, 389 illites, 381 vermiculite, 392 cation, 387 Hexadecyltrimethylammonium alkyl sulfate, 468, 469 Hexadecyltrimethylammonium bromide, 466 Hexadecyltrimethylammonium decyl sulfate, 466, 467 Hexadecyltrimethylammonium dodecyl sulfate, 466, 467 Hexadecyltrimethylammonium tetradecyl sulfate, 466, 467 Hexagonal, 107 lattice, 453 mesophase, 136, 161, 472 symmetry, 473 Hexanol, 61, 66, 82, 96, 222, 224 High resolution NMR, 497 HLB number, 336 Homogeneous nucleation, 417, 418, 420, 423, 425, 435 phospholipid, 144 HPLC, 349 Hydrated decanephosphonic acid, 140 gel, 291 ion, 160 Hydration, 4, 251, 424 bonds, 13 layer, 171

Index [Hydration] number, 160 of DPPG bilayers, 271 of the gel phase, 274 of the nonionic surfactants, 172 of the solid phase, 350 of the surfactant molecule, 168, 350 shell, 163 water, 163, 443, 160 Hydrocarbon tail, 135 Hydrodynamic methods, 86 techniques, 86 Hydrogel, 103 membranes, 132 Hydrogen bonding, 153, 160, 257, 261, 350, 474 bonds, 134, 141, 142, 171, 257, 266, 300, 301, 303 Hydrogenation, 482 Hydrophilic enzymes, 438 headgroups, 3, 160 macromolecules, 8 Hydrophilicity of surfactant, 318 Hydrophobized motmorillonite, 387 Hydrosols, 378 Hydroxyapatite, 420, 421 Ice formation, 160 Ideal solution behavior, 163 Ill-deﬁned in natural phospholipids, 132 Illite, 385 Immersion, 398 microcalorimetry, 341, 343, 359 Immersional wetting, 364 enthalpies, 385, 386 enthalpy isotherms, 376, 383 on nonswelling clay, 380 Impurity, 426, 435, 436, 439 Inclusion of cholesterol, 137, 324 Incorporation of hydrocortisone-21-palmitate, 150 Indole, 139

513 Induced crystallization, 434 Industrial process, 159 Infrared spectroscopy, 62, 419, 456 Inhibition of dissolution, 434 Interaction with polyelectrolyte, 153 Interdigitated palisades, 137 Interesteriﬁcation, 482 Interface-induced nucleation, 435 Interfacial area, 55 energy, 416, 425 energy of the germ, 185 layer, 365, 390–392 properties, 183 water, 165, 166, 169, 172 Interlamellar sorption, 386 space, 391 water, 270, 273, 280, 283, 285, 289, 292, 248, 253, 254, 257, 260, 261, 263, 264, 269 Interlayer composition, 392 Intermicellar interactions, 5, 7, 12 Interparticle attraction, 404 interactions, 358, 405, 407, 409 Interphasal water, 61, 80, 226, 228 Inverse microemulsions, 162 Ionic strength, 419, 489 surfactants, 4 Irreversible process, 240 Isooctane, 73, 87, 111, 223, 237, 242, 437, 444 Isoperiblolic calorimeters, 480, 497 Isothermal, 121 calorimetry, 483 titration calorimetry, 296, 313 Isotropic, 129 liquid, 127, 129, 452, 454, 473 liquid transition, 136, 461 ITC, 296, 297, 300, 305, 308, 310, 311, 332 Kalonite, 353, 385 Kidney stones, 423, 430

514 Kinetic of crystallization, 435 of diffusion, 201 of reactions, 445 of ripening, 197 of solution mediated phase transformation, 432 parameters, 456 transformation, 432 Kirchhoff’s law, 135, 136 K-oleate, 222, 224 Krafft boundary, 123 eutectic point, 139 temperature, 139 L2 transition, 40 Lactitol, 317 Lactose, 317, 486, 492 Lactose-casein mixtures, 494 Lamellar, 107 crystal, 455 interface, 470 liquid crystal, 455 mesophase, 129 morphology, 37 phase, 29, 35, 111, 471 structure, 456 thickness, 462, 464, 468 Laminar mesophase, 129, 136 Large unilamellar vesicles, 331 Laser Raman spectroscopic range, 137 Latent heat, 39, 42 Lecithin, 3, 5, 10 Legume protein denaturation, 489 Legumin, 489 Level of drug incorporation, 151 Light scattering, 497 Lipid -lipid interactions, 322 oxidation, 493, 495 transitions, 290 Liposomes, 143, 148, 150 Liquid crystal, 255, 281, 288, 290, 292, 452, 455 transitions, 140, 460, 470

Index Liquid crystalline behavior, 456 formation, 459 organization, 454, 466 phases, 107, 134, 137, 159, 167, 277, 287, 457, 458, 465, 470, 471 state, 455 Liquid -liquid separation system, 184 -solid transitions, 184 sorption, 357 sorption equilibrium, 390 Lithium ions, 160 Living cells, 485 Lowering of the melting point, 166 Lubricants, 24 Lyomesophases, 127 Lyospheres, 362 Lyotropic liquid crystals, 167 mesophases, 158, 232, 452 Maillard reactions, 494, 495 Maltodextrines, 487 Mass balance of surfactant, 156 Mass fraction of water, 158 Measurements of wetting, 408 Meat denaturation, 489 Mechanism of adsorption, 335 of crystallization, 444 of nucleation, 420 Melting enthalpy, 163, 250, 251 enthalpy of pure water, 162 of blends, 136 point, 161, 162, 163 Mesomorphism, 457, 458 Mesophase, 129, 140 Mesophase-isotropic liquid transition, 141 Meta-chloronitrobenzene, 436 Metastable ice, 163 Methyldodecanoic acid, 149 Methyl-3,5-bis(n-hexadecyloxcarbonyl) pyridinium ion, 473 Micellar catalysis, 163

Index Micellar solutions, 135, 136 Micellar swelling, 4 Micelle formation, 321 Micelles, 214, 300, 305, 312, 314, 315, 325, 326, 330, 332, 345 Micellization, 155, 300, 303, 316–320, 332 of block copolymer, 153 phenomena, 155 process, 155 Microcalorimetric measurements, 54, 342 Microcalorimetry, 54, 340, 386, 485, 492 Microemulsions, 5, 27, 158, 159, 214, 217–219, 220, 221, 223, 227, 233–237, 239, 240–243, 415, 434, 437–440, 442–444 as microreactor, 440 Microstructure, 121, 459 Microstructure surface, 132 Microstructure surface, 163 Microstructured ﬂuids, 159 Microwave dielectric measurements, 480 Milk powders, 494 Milk products, 478 Mimetic systems, 12 Mineralization, 444 Mineralization of bone, 421 teeth, 421 Mixed bilayers, 331 Mixed emulsions, 183 Mixed micelles, 314, 316, 325, 326, 328, 459 Mixed vesicles, 148 Mixing-dimixing phenomena, 128 Mixtures of small copolymers, 155 Modiﬁed silicate surfaces, 392 Molar adsorption enthalpies, 383 Molar enthalpy, 314, 349, 350 Molar heat capacity, 156 Molar mass distribution, 155 Molecular diffusion, 47 Molecular motion, 239 Molecular structure, 438, 489 Monodisperse droplets, 44

515 Monolayer adsorption, 433 orientation of vermiculite, 394 structures, 453 Monosodium n-decanephosphonate, 98, 103, 136 Montmorillonite, 384, 386, 388 Mucopolysaccharides, 80 Multilamellar aqueous dispersions of phospholipid, 143 dispersions, 151, 248 structures, 151 vesicles, 292 Multiple emulsions, 183, 197 N,N-Dimethyldecylamine N-oxide, 352, 353 Na-kaolinite, 384 n-alkanophosphonic acid, 134, 136, 161 Na-montmorillonite, 384 Nanocontainers, 1 Nanoparticles 7, 12, 440 Nanoreactors 1, 17 Nanosized particles, 438 Nanosolvents, 1 Naphthylamine, 139 Natural toxins in mushrooms, 479 Near infrared spectroscopy, 456, 497 Nematic liquid crystalline state, 455 Neutron reﬂection, 336 Neutron scattering, 171 NMR, 62, 86, 90, 111, 172, 234, 248, 435, 442, 443, 458, 497 N-octylribonamide, 88 Nonaqueous dispersions, 357, 401 Nonfreezable interlamellar, 248 Nonfreezable water, 60, 86, 89 Nonfreezing water, 160 N-propionyl amine, 318 Nuclear magnetic resonance, 62 Nucleation, 26, 47, 186, 276, 415, 416, 422, 434–436 of molecular crystals, 434 of zeolites, 422 process, 43 Number of oscillations, 53

516 Octadecylammonium, 388, 389 Octadecyldimethylchlorosilane, 372 Octadecylpyridinium, 386 Octaethylene glycol mono n-dodecyl ether, 76, 168, 328 Octanol, 324 Octyl β-d-monoglucoside, 353 Octylglucoside, 319, 320, 325–328 Optical density of suspensions, 399 Organogels, 12 Organophilized hexadecylpyridinium, 380 Organosols, 357 Osmometry, 2 Ostwald ripening, 415, 418 Ostwald-de Izaguirre equation, 362, 365 Oxidation, 478, 484, 493 Oxidative stability, 483 Oxidative stability of lipids, 483 Palisade layer, 14 Parental solutions, 478 Particle formation, 440 size, 204 Particle-liquid interactions, 397, 398 Particle-particle interactions, 398 Pasteurization, 478 Pentane, 212 Peptides, 440 Percolation, 6, 12, 69, 241, 242, 244 transitions, 222 Perﬂuoropolyether, 216, 219, 239 pH, 346 Pharmaceuticals, 24 Phase diagram, 27, 129, 131, 214, 215, 313, 439, 481 separation, 43, 47, 107, 153, 155 transformation, 135, 415, 419 transition, 129, 201, 204, 221, 222, 236, 239, 275, 281, 332, 452, 456, 457, 472, 473, 480 of lipids, 287 of pyridinium salts, 458 Phenylalanine, 438, 441

Index Phosphate groups, 161 Phosphatidylcholine, 80, 111, 326, 327 Phosphatidylethanolamine, 145, 256 Phospholipid bilayer, 63, 247 Phospholipid vesicles, 321 Phospholipids, 146, 161, 256, 312, 324, 330 Physical adsorption, 367 process, 159 properties, 171 of edible fats, 481 Physicochemical behavior of foods, 498 properties, 161 of foods, 478 Pigments, 479 Planar bilayers, 166, 471 Platelets, 148 Polar headgroup, 132, 136, 146 interactions, 444 molecules, 8 Poloxamer, 157 Poly(4-hydroxystyrene) Poly(2-hydroxyethyl methacrylate), 103 Poly(ethylene glycol), 162, 169 Poly(methyl methacrylate), 132 Polyacrylic acid as a function of pH, 152 Polydimethylsiloxane, 83 Polyelectrolyte, 153 Polymerization of single-phase microemulsions, 438 solubilizates, 438 Polymethylsiloxanes, 103 Polymorphic transitions, 414, 454 Polymorphism, 452, 457, 458, 464, 468, 481 Polymorphism of fats, 479 Polymorphs, 418, 427, 428, 442, 465 of phenylalanine, 441 Polyoxyethylene, 66, 84 chains, 168 oleyl alcohol, 76 Polypeptide gramicidin, 151 Polyphenol, 479, 495 POPC, 325, 328, 330

Index Portion of the lipid molecule, 147 Potassium oleate, 61 Potato starch, 489 Precipitation kinetics, 420 Premicelles, 307 Presence of impurities, 419 Principles of biomineralization, 444 Properties of biominerals, 429 of emulsions, 183 of foods, 478 of precipitates, 419 of self assembling, 204 of the adsorption layer, 397 of water, 164 Propylene oxide, 154 Protein denaturation, 489 oxidation, 489, 495 surfaces, 169 Pyrolysis, 485 Quasi elastic light scattering, 215 Quenching, 163, 236 Radiotracer technique, 86 Rate of gas diffusion, 414 of heat transport, 414 of nucleation, 418 of precipitations, 419 Reconstituted foods Recrystallization, 415, 441 of diketopiperazine, 443 Redlich–Kister equations, 363, 381 Refractive index measurements, 398 Reindeer meat, 493 Retrogradation, 488, 489, 492 Reversed micelles, 1, 4, 5 Rewarming, 486 Rheological analysis, 399 data, 402 ﬂow curves, 400, 401, 408 parameters, 405, 406 properties, 397, 407 of the suspension, 346, 409

517 Ripening, 201 Roasting, 478 Role of impurities, 436 Rotation of the head group, 146 Safety aspects, 494 Salinity, 346 Saturated phospholipid, 144 Scattering peaks, 107 Scattering vector, 108 Schay–Nagy classiﬁcation, 375 SDS, 319, 320, 432 Secondary aggregation, 305, 306 Secondary hydration shell, 171 Second-order transition, 239 Self assembly, 2, 203, 295–297, 314, 331, 445 Self-aggregation, 296 Self-heating, 494, 495 Self-ignition, 494, 495 Semiconductor clusters, 438 Silica gel, 163, 169 Silver halides, 438 Single chain surfactant, 456 Single crystal diffraction, 456 Sludge dewatering, 159 Sludges, 159, 166 Small angle neutron scattering, 94, 160, 215, 359 Small angle X-ray scattering, 94, 359, 397, 407–409 Small unilamellar vesicles, 331 Smectic, 455, 457 Sodium, 4-(1-heptylnoyl)benzenesulphate, 168 Sodium alkylbenzene sulfonates, 354 Sodium alkylsulfates, 354 Sodium alkylxylenesulfonates, 354 betaines, 354 Sodium bis(2-ethylhexyl)sulfosuccinate, 3 Sodium cellulose sulfate, 103 Sodium cholate, 319, 431 Sodium deoxycholate, 319 Sodium dioctylphosphinate, 91, 103, 133, 161, 167 Sodium hexanoate, 354

518 Sodium-illite, 381–384 Sodium oleate, 354 Solid fat index, 482, 497 Solid state NMR, 456 Solid state transitions of surfactant crystals, 451 Solid/liquid adsorption layer, 361 Solid/liquid interactions, 383, 397 Solid/liquid interfaces, 359, 363, 380 Solid/liquid interfacial interactions, 362 Solid/liquid transformation, 436 Solid/solution interfaces, 335 Solidiﬁcation processes, 190 Solidiﬁcation transition, 189 Solid-liquid extraction, 478 cooking, 478 Solid-liquid interfacial interactions, 359, 362, 377 Solids in binary liquids, 367 Solid-solid transitions, 184 Solubility, 489 Solubilization, 331, 439 Solution-mediated phase transformation, 418, 422, 426, 427, 431 Solvates, 418 Solvation, 392 Solvent shell, 163 Sound absorption, 6 Soy proteins, 489 Speciﬁc heat, 31, 41, 46, 121, 189, 456, 488, 496 of foods, 496 Spectrophotometer, 347 Spectroscopic properties, 163 Spherulites, 444 Spongelike structures, 24 Spray drying, 486 S-Shaped excess isotherms, 372 Stability of aerosol dispersions, 397 Stability of disperse systems, 358, 397 Stability of emulsions, 183 Stable bilayers, 457 Stable sol, 415 Stable structures, 420 Starch, 488 Starch gelatinization, 488

Index Starch solubilization, 488 State of water in surfactant based systems, 159 Static permittivity, 6 Static viscosity, 12 Stearoylarachidonylphosphatidylcholine, 324 Stereochemistry, 336 Steroid content, 150 Stilbene, 140 Stoichiometric displacement, 340 Stokes-Einstein law, 47 Stretched water, 160, 171 Structural transitions, 67, 169 Structure, 479 Subgel phase, 275 Sublimation, 128, 480 Subzero temperature behavior, 59 Sucrose esters, 77 Sucrose monostearate, 87 Supercooled emulsion, 480 Supercooling, 435, 480 Supercritical CO2, 495, 496 Supermolecules, 3 Supersaturation, 47, 416–420, 422, 428 Surface coverage, 387 diffusion, 422 layer composition, 391 structures of montmorillonite, 380 Surfactant adsorption, 353 Surfactant based microstructures, 163, 171 systems, 159 Surfactant crystals, 452 Surfactant monomer concentration, 155 Surfactant-surfactant interactions, 4, 5 Suspension, 7, 358, 400–407 SUV, 328 Swelling, 386, 389–391 clays, 343 of bentonites, 390 of hydrophobic Symmetrical catanionic surfactants, 460, 470 Synthetic phospholipid, 143

Index TDATDS, 464 Teﬂon powder, 349 Temperature, 121 Temperature dependence, 48, 52, 127 Tempering, 482 Tertiary oil recovery, 24 Tetrabutylammonium nitrate, 353 Tetradecane, 200 Tetradecylammonium tetradecylsulfate, 460 Tetradecylpyridinium, 386, 389 Tetraethylene glycol monododecylether, 3 Texture, 479 Texturization process, 488 Theoretical considerations, 297 Thermal behavior, 478 of different types of zeolites, 422 of food constituents, 480 of foods, 477 of raw foods, 492 of reconstituted foods, 492 of surfactant crystal, 453 Thermal characteristics of food constituents, 478 Thermal conductivity, 208, 212 denaturation of enzymes, 489 diffusivity, 497 microscopy, 414 properties of foods, 479 transitions, 132 Thermochemistry of organic, organometallic and inorganic compounds, 414 Thermodilatometry, 497 Thermodynamic properties, 124, 163 of crystallization, 439 Thermodynamic stability, 204, 241 Thermogravimetric analysis, 430 Thermogravimetry, 480 Thermomanometry, 480 Thermotropic liquid crystalline states, 455 Thickness of adsorption layer, 363, 407, 409 Titration sorption microcalorimetry, 344 Toxins produced by microorganisms, 479

519 Transformation of crystalline dispersions, 413, 415 Transformation temperature, 143 Transition temperature, 145, 162, 223 Transitions, 121 Transport phenomena, 452 Triblock copolymer, 155 Tricaprylin, 80, 87 Triglycerides, 485 Trimethylammonium bromide, 317 Trimethylammonium methacrylate, 138 Triphenylmethane, 140 Tristearin, 482, 483 Turbidity of suspension, 399 Tween-20, 436 Twin arrangement, 339 Two-dimensional nucleation, 417 Ultracentrifugation, 86 Ultrahigh temperature sterilization, 478 Ultrasonic velocity measurements, 435 Ultrasound velocity, 437 Unilamellar vesicles van der Waals forces, 350 van der Waals interactions, 301, 304, 398 van’t Hoff model, 151 Vapor liquiﬁcation, 480 Vapor pressure, 161, 165 Vaporization, 142, 480 Vermiculite, 380, 390, 391 Vesicles, 143, 312, 314, 315, 325, 326, 331, 332, 444, 459 Vesicular assemblies, 289 Vicilin, 489 Vicinal water, 163 Vincent model, 398 Viscosity, 6, 86, 452, 489 Vitamins, 479 Wastewater treatment, 159 Water adsorbed, 480 behavior, 159, 247 distribution diagrams, 255 droplets, 480

520 [Water] penetration into the interfacial region of the bilayers, 145 solubilization, 4 transport, 47 vaporization, 481 Water-in-oil emulsions, 200 Water-surfactant interactions, 61 Weaker hydration structure, 160 Wetting, 358 characteristics, 409 enthalpy, 385 properties, 398

Index Wheat, 489 Wheat starch, 488 White bread, 493 X-ray diffraction, 86, 92, 110, 248, 256, 386, 392, 414, 419, 425, 426, 430, 436, 442, 456, 458, 460, 462, 468, 470, 473, 481, 497 Zeolites, 169, 377, 378, 422, 423 Zwitterionic headgroups, 9 Zwitterionic surfactants, 80, 85, 157, 354