Physical Properties of Liquid Crystals...studied chemistry at the University of Frankfurt/Main,...

D. Demus, J. Goodby, G.W. Gray, H.-W. Spiess, V Vill

Physical Properties of Liquid Crystals

6B WILEY-VCH Weinheim - New York Chichester Brisbane - Singapore - Toronto

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D. Demus, J . Goodby, G. W. Gray, Physical Properties of Liquid Crystals

H.-W. Spiess, V. Vill

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D. Demus, J. Goodby, G.W. Gray, H.-W. Spiess, V Vill (Eds.)

Handbook of Liquid Crystals ISBN 3-527-29502-X (4-Volume Set)

J. L. Serrano (Ed.) Metallomesogens ISBN 3-527-29296-9

D. Demus, J. Goodby, G.W. Gray, H.-W. Spiess, V Vill

Physical Properties of Liquid Crystals

6B WILEY-VCH Weinheim - New York Chichester Brisbane - Singapore - Toronto

Prof. Dietrich Demus Veilchenweg 23 06 1 18 Halle Germany

Prof. John W. Goodby School of Chemistry University of Hull Hull, HU6 7RX U.K.

Prof. George W. Gray Merck Ltd. Liquid Crystals Merck House Poole BH IS 1 TD U.K.

Prof. Hans-Wolfgang Spiess Max-Planck-Institut fur Polymerforschung Ackermannweg 10 55 128 Mainz Germany

Dr. Volkmar Vill Institut fur Organische Chemie Universitat Hamburg Martin-Luther-King-Platz 6 20 146 Hamburg Germany

This book was carefully produced. Nevertheless, authors, editors and publisher do not warrant the informa- tion contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illus- trations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No. applied for.

A catalogue record for this book is available from the British Library.

Deutsche Bibliothek Cataloguing-in-Publication Data:

Physical properties of liquid crystals I ed. by Dietrich Deinus . . . - 1 Aufl. - Weinheim ; New York ; Chichester ; Brisbane ; Singapore ; Toronto : Wiley-VCH, 1999

ISBN 3-527-29747-2

0 WILEY-VCH Vcrlag GmbH. D-60469 Weinheim (Federal Republic of Germany), 1999

Printed on acid-free and chlorine-free paper.

All rights reserved (including those of translation in other languages). No part of this book may be reproduced i n any form - by photoprinting, microfilm, or any other means - nor transmitted or translated into machine lan- guage without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Composition, Printing and Bookbinding: Fa. Konrad Triltsch Druck- und Verlagsanstalt GmbH, D-97070 Wiirzburg. Printed in the Federal Republic of Germany.

The Editors

’ D.Dernus studied chemistry at the Martin-Luther-University, Halle, Germany, where he was also awarded his Ph. D. In 1981 he became Professor, and in 1991 Deputy Vice-Chancellor of Halle University. From 1992-1994 he worked as a Special Technical Advisor for the Chisso Petrochemical Corporation in Japan. Throughout the period 1984-1 99 I he was a member of the International Planning and Steering Commi- tee of the International Liquid Crystal Conferences, and was a non-ex- ecutive director of the International Liquid Crystal Society. Since 1994 he is active as a Scientific Consultant in Halle. He has published over 3 10 scientific papers and 7 books and he holds 170 patents.

J. W. Goodby studied for his Ph. D. in chemistry under the guidance of G. W. Gray at the University of Hull, UK. After his post-doctoral research he became supervisor of the Liquid Crystal Device Materials Research Group at AT&T Bell Laboratories. In 1988 he returned to the UK to become the Thorn-EMI/STC Reader in Industrial Chemistry and in 1990 he was appointed Professor of Organic Chemistry and Head of the Liquid Crystal Group at the University of Hull. In 1996 he was the first winner of the G. W. Gray Medal of the British Liquid Crystal So- ciety.

G. W. Gray studied chemistry at the University of Glasgow, UK, and received his Ph. D. from the University of London before moving to the University of Hull. His contributions have been recognised by many awards and distinctions, including the Leverhulme Gold Medal of the Royal Soci- ety (l987), Commander of the Most Excellent Order of the British Em- pire (1991), and Gold Medallist and Kyoto Prize Laureate in Advanced Technology (1995). His work on structure/property relationships has had far reaching influences on the understanding of liquid crystals and on their commercial applications in the field of electro-optical displays. In 1990 he became Research Coordinator for Merck (UK) Ltd, the com- pany which, as BDH Ltd, did so much to commercialise and market the electro-optic materials which he invented at Hull University. He is now active as a Consultant, as Editor of the journal “Liquid Crystals” and as author/editor for a number of texts on Liquid Crystals.

VI The Editors

H. W. Spiess studied chemistry at the University of Frankfurt/Main, Germany, and obtained his Ph. D. in physical chemistry for work on transition metal complexes in the group of H. Hartmann. After professorships at the University of Mainz, Munster and Bayreuth he was appointed Direc- tor of the newly founded Max-Planck-Institute for Polymer Research in Mainz in 1984. His main research focuses on the structure and dynamics of synthetic polymers and liquid crystalline polymers by advanced NMR and other spectroscopic techniques.

V. Vill studied chemistry and physics at the University of Munster, Germany, and acquired his Ph. D. in carbohydrate chemistry in the group of J. Thiem in 1990. He is currently appointed at the University of Ham- burg, where he focuses his research on the synthesis of chiral liquid crystals from carbohydrates and the phase behavior of glycolipids. He is the founder of the LiqCryst database and author of the Landolt- Bornstein series Liquid crystal.^.

List of Contributors

Barois, P. (IV:6.1) Centre de Recherche P. Pascal Ave. A. Schweitzer 33600 Pessac Cedex France

Blinov, L. M. (IV:9) Institute of Crystallography Russian Academy of Sciences Leninsky prosp. 59 117333 Moscow Russia

Bouligand, Y. (IV:7) Histophysique et Cytophysique Ecole Pratique des Hautes Etudes 10, rue A. Bocquel 49 100 Angers France

Cladis, P. E. (IV:6.3 and IV:6.4) Advanced Liquid Crystal Technologies, Inc. P.O. Box 1314 Summit, NJ 07902 USA

Dunmur, D. A.; Toriyama, K. (IV: 1-5) Department of Chemistry University of Southampton Southampton SO 17 1 BJ U.K.

Goodby, J. W. (11) School of Chemistry University of Hull Hull, HU6 7RX U.K.

Gray, G. W. (I and 11) Merck Ltd. Liquid Crystals Merck House Poole BH15 1TD U.K.

JkrGme, B. (IV: 10) FOM-Institute for Atomic and Molecular Physics Kruislaan 407 1098 SJ Amsterdam The Netherlands

Kapustina, 0. (IV: 1 1) Shvernik St. 4 117036 Moscow Russia

Leslie, F. M. (111: I ) University of Strathclyde Dept. of Mathematics Livingstone Tower 26 Richmond Street Glasgow GI 1XH U.K.

VIII List of Contributors

Noack, F.' (IV:13) IV. Physikalisches Institut Universitat Stuttgart Pfaffenwaldring 57 70550 Stuttgart Germany

Osipov, M. (III:2) Institute of Crystallography Academy of Science of Russia Leninski pr. 59 Moscow 117333 Russia

Palffy-Muhoray, P. (IV: 12) Kent State University Liquid Crystal Institute Kent, OH 44242 USA

Pollmann, P. (IV:6.2.4) Universitat GH Paderborn FB 13, Chemie u. Chemietechnik FG Physikal. Chemie 33095 Paderborn Germany

Schneider, F.; Kneppe, H. (IV:8) Universitat GH Siegen Physikal. Chemie 57068 Siegen Germany

Thoen, J. (IV:6.2.1) Katholieke Universiteit Leuven Departement Natuurkunde Laboratorium voor Akoestiek en Thermische Fysica Celstijnenlaan 200 D 3001 Leuven (Heverlee) Belgium

Wedler, W. (IV:6.2.2 and IV:6.2.3) Tektronix, Inc.; CPID

26600 SW Parkway Wilsonville, OR 97070-1000 USA

MIS 63-424

Wilson, M. R. (III:3) Department of Chemistry University of Durham South Road Durham, DHI 3LE U.K.

Contents

Chapter I: Introduction and Historical Development George W Gray 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 The Early Years up to About 1925 . . . . . . . . . . . . . . . . . . . . . . . 2

3 The Second Phase from 1925 to 1959 . . . . . . . . . . . . . . . . . . . . . 5

Lyotropic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 4.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Polymer Dispersed Liquid Crystals (PDLCs) and Anchoring . . . . . . . . . 12 4.4 Materials and New Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

. . . . . . . . . . . . . . . . 1

4 4.1

4.3

The Third Phase from 1960 to the Present Time . . . . . . . . . . . . . . . . 8

Chapter 11: Guide to the Nomenclature and Classification of Liquid Crystals . . . 17 John W Goodby and George W Gruy 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 General Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 Structural Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Polymeric Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5 Notation of Thermotropic Liquid Crystalline Properties . . . . . . . . . . . . 20 5 . I Description of the Solid State . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.1.1 Description of Soft Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.2 Description of the Liquid Crystalline Phases . . . . . . . . . . . . . . . . . . 21 5.2.1 Nematic and Chiral Nematic Phases . . . . . . . . . . . . . . . . . . . . . . 21 5.2.2 Smectic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.2.3 Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.2.4 Columnar Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2.5 Plastic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

X Contents

5.2.6 Condis Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Description of the Clearing Parameters . . . . . . . . . . . . . . . . . . . . . 23

6 Stereochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.2.7 Cubic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.2.8 Re-entrants 23 5.3

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

Chapter 111: Theory of the Liquid Crystalline State . . . . . . . . . . . . . . . . . 25

1

1.1 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.3 1.3.1 1.3.2 1.4 1.4.1 1.4.2 1.4.3 1.4.4 1.5

2

2.1 2.2

2.2.1 2.2.2 2.2.3 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 2.4.2

Continuum Theory €or Liquid Crystals . . . . . . . . . . . . . . . . . . . . . 25

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Equilibrium Theory for Nematics . . . . . . . . . . . . . . . . . . . . . . . . 26 The Frank-Oseen Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Body Forces and Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 The Equilibrium Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Proposed Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Equilibrium Theory for Smectic Liquid Crystals . . . . . . . . . . . . . . . . 32 An Energy Function for SmC Liquid Crystals . . . . . . . . . . . . . . . . . 32 Equilibrium Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Dynamic Theory for Nematics . . . . . . . . . . . . . . . . . . . . . . . . . 35 Balance Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A Rate of Work Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 The Viscous Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Molecular Theories of Liquid Crystals . . . . . . . . . . . . . . . . . . . . . 40 M . A . Osipov Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Microscopic Definition of the Order Parameters for Nematic and Smectic Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Uniaxial Nematic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Biaxial Nematic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Smectic A and C Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Anisotropic Intermolecular Interactions in Liquid Crystals . . . . . . . . . . 44 Hard-core Repulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Electrostatic and Dispersion Interactions . . . . . . . . . . . . . . . . . . . . 44 Model Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Molecular Theory of the Nematic Phase . . . . . . . . . . . . . . . . . . . . 47 Mean-field Approximation and the Maier-Saupe Theory . . . . . . . . . . . 47 Short-range Orientational Correlations . . . . . . . . . . . . . . . . . . . . . 51

Frank M . Leslie

A Virtual Work Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Contents XI

2.4.3 2.4.4 2.4.5 2.4.6 2.5 2.5.1 2.5.2 2.5.3 2.5.4 2.6 2.7

3

3.1 3.1.1 3.1.2 3.1.3 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3

Excluded Volume Effects and the Onsager Theory . . . . . . . . . . . . . . Packing Effects in Thermotropic Nematics . . . . . . . . . . . . . . . . . . The Role of Molecular Biaxiality . . . . . . . . . . . . . . . . . . . . . . .

Molecular Models for Simple Smectic Phases . . . . . . . . . . . . . . . . 60 Mean-field Theory of the Nematic-Smectic A Transition . . . . . . . . . . 60 Phase Diagram of a Hard-rod Fluid . . . . . . . . . . . . . . . . . . . . . . 63 The Role of Intermolecular Attraction . . . . . . . . . . . . . . . . . . . . 65 Smectic A-Smectic C Transition . . . . . . . . . . . . . . . . . . . . . . . 65 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Molecular Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Techniques of Molecular Modelling . . . . . . . . . . . . . . . . . . . . . . Molecular Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Molecular Dynamics and Monte Carlo Simulation . . . . . . . . . . . . . . Quantum Mechanical Techniques . . . . . . . . . . . . . . . . . . . . . . . 78 Applications of Molecular Modelling . . . . . . . . . . . . . . . . . . . . . Determination of Molecular Structure . . . . . . . . . . . . . . . . . . . . . Determination of Molecular Properties . . . . . . . . . . . . . . . . . . . . Determination of Intermolecular Potentials . . . . . . . . . . . . . . . . . . Large-Scale Simulation of Liquid Crystals . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

52 54 56 58 Density Functional Approach to the Statistical Theory of Liquid Crystals . .

Mark R . Wilson 72

74

78 78 80 81 82

Chapter I V Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

1 Tensor Properties of Anisotropic Materials . . . . . . . . . . . . . . . . . . 87

1.1 Macroscopic and Microscopic Properties . . . . . . . . . . . . . . . . . . . 92 David Dunmur and Kazuhisa Toriyama

1.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

2

2.1 2.2 2.2.1 2.2.2 2.2.3 2.3 2.4 2.5 2.6 2.7

Magnetic Properties of Liquid Crystals . . . . . . . . . . . . . . . . . . . . 102

Magnetic Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Types of Magnetic Polarization . . . . . . . . . . . . . . . . . . . . . . . . 104 Diamagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Paramagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Diamagnetic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . 106 Paramagnetic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . 108 Ferromagnetic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . 110 Applications of Magnetic Properties . . . . . . . . . . . . . . . . . . . . . 110 References 112

David Dunmur and Kazuhisa Toriyama

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

XI1 Contents

3 Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Symmetry of Liquid Crystal Phases and the Optical Indicatrix . . . . . . . . 115 Molecular Theory of Refractive Indices . . . . . . . . . . . . . . . . . . . . 115 Optical Absorption and Linear Dichroism . . . . . . . . . . . . . . . . . . . 119 Refractive Indices and Liquid Crystal Phase Structure . . . . . . . . . . . . 121 Optics of Helicoidal Liquid Crystal Structures . . . . . . . . . . . . . . . . 124

4 Dielectric Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Dielectric Response of Isotropic Fluids . . . . . . . . . . . . . . . . . . . . 129 Dielectric Properties of Anisotropic Fluids . . . . . . . . . . . . . . . . . . 133 The Electric Permittivity at Low Frequencies: The Static Case . . . . . . . . 133

4.2. I . 1 Nematic Phase 133 4.2.1.2 The Smectic Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

5 Elastic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5 . I Introduction to Torsional Elasticity . . . . . . . . . . . . . . . . . . . . . . 151 5.2 Director Distribution Defects and Fluctuations . . . . . . . . . . . . . . . . 157

Defects in Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 5.2.2 Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Curvature Elasticity of Liquid Crystals in Three Dimensions . . . . . . . . . 161 Electric and Magnetic Field-induced Deformations . . . . . . . . . . . . . . 163 Director Distribution in Magnetic Fields . . . . . . . . . . . . . . . . . . . 164

5.4.2 Director Distribution in Electric Fields . . . . . . . . . . . . . . . . . . . . 167

5.4.3.1 Capacitance Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 5.4.3.2 Birefringence Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 5.4.4 Frkedericksz Transition for Chiral Nematics . . . . . . . . . . . . . . . . . 170 5.4.5 FrCedericksz Transitions for Smectic Phases . . . . . . . . . . . . . . . . . 171 5.5 Molecular Aspects of Torsional Elasticity . . . . . . . . . . . . . . . . . . . 172 5.5.1 van der Waals Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 5.5.2 Results from Lattice Models . . . . . . . . . . . . . . . . . . . . . . . . . . 175 5.5.3 Mean Field and Hard Particle Theories . . . . . . . . . . . . . . . . . . . . 175 5.5.4 Computer Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

David Dunmur and Kazuhisa Toriyama 3.1 3.2 3.3 3.4 3.5 3.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

David Dunmur and Kazuhisa Toriyama 4.1 4.2 4.2.1

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

4.2.2 Frequency Dependence of the Electric Permittivity: Dielectric Relaxation . . 143 4.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

David Dunmur and Kazuhisa Toriyama

5.2.1

5.3 5.4 5.4.1

5.4.3 FrCedericksz Transitions as a Method for Measuring Elastic Constants . . . 168

5.6

5.7 References 178

Experimental Aspects of Elastic Constants and Comparison with Theoretical Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . 177

6 Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 6.1 Phase Transitions Theories . . . . . . . . . . . . . . . . . . . . . . . . . . 179

6.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

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

Philippe Barois

Contents XI11

6.1.2 The Isotropic-Nematic Transition . . . . . . . . . . . . . . . . . . . . . . . 179 6.1.2. I Mean Field Approach (Landau-de Gennes) . . . . . . . . . . . . . . . . . . 179 6.1.2.2 Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 6.1.2.3 Isotropic-Nematic Transition in Restricted Geometries . . . . . . . . . . . . 182 6.1.3 The Nematic-Smectic A Transition . . . . . . . . . . . . . . . . . . . . . . 183 6.1.3.1 Definition of an Order Parameter . . . . . . . . . . . . . . . . . . . . . . . 183 6.1.3.2 Mean Field Description (McMillan, de Gennes) . . . . . . . . . . . . . . . 184

Analogy with Superconductors . . . . . . . . . . . . . . . . . . . . . . . . 184 6.1.3.4 Critical Exponents and Scaling . . . . . . . . . . . . . . . . . . . . . . . . 187 6.1.3.5 Renormalization Group Procedures . . . . . . . . . . . . . . . . . . . . . . 188 6.1.3.6 Dislocation Loops Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 6.1.4 The Smectic A-Smectic C Transition . . . . . . . . . . . . . . . . . . . . . 189 6.1.4.1 The Superfluid Helium Analogy . . . . . . . . . . . . . . . . . . . . . . . . 189 6.1.4.2 The N-SmA-SmC Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 6.1.5 The Smectic A-Hexatic Smectic B Transition . . . . . . . . . . . . . . . . 191 6.1.6 Phase Transitions in Chiral Liquid Crystals . . . . . . . . . . . . . . . . . . 192 6.1.6.1 Chirality in Nematic and Smectic Liquid Crystals . . . . . . . . . . . . . . 192 6.1.6.2 Mean Field Chiral N-SmA-SmC model . . . . . . . . . . . . . . . . . . . 193 6.1.6.3 Twist Grain Boundary Phases . . . . . . . . . . . . . . . . . . . . . . . . . 194 6.1.7 Frustrated Smectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 6.1.7.1 Polar Smectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 6.1.7.2 The Model of Frustrated Smectics (Prost) . . . . . . . . . . . . . . . . . . . 197 6.1.7.3 The Mean Field Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 6.1.7.4 Critical Properties of the Isolated SmA-SmA Critical Point . . . . . . . . . 202 6.1.7.5 The Re-entrant Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . 204 6.1.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 6.1.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

Experimental Methods and Typical Results . . . . . . . . . . . . . . . . . . 208 6.2.1 Thermal Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

6.2. I . 1 Introduction 208 6.2.1.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 6.2.1.3 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 6.2.1.4 Calorimetric Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Photoacoustic and Photopyroelectric Results . . . . . . . . . . . . . . . . . 229 6.2.1.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 6.2.1.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 6.2.2 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

6.2.2.1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 General Conclusions from Density Studies on Liquid Crystals . . . . . . . . 232 Studies of Calamitic Compounds . . . . . . . . . . . . . . . . . . . . . . . 236

6.2.2.4 Discotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 Lyotropics and Anhydrous Soaps . . . . . . . . . . . . . . . . . . . . . . . 241 Polymeric Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

6.1.3.3

6.2

Jun Thoen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.1.5

Wolfgang Wedler

6.2.2.2 6.2.2.3

6.2.2.5 6.2.2.6

XIV Contents

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

6.2.2.7 Further Studies 241 6.2.2.8 References 242 6.2.3 Metabolemeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

Wolfgang Wedler 6.2.3.1 Thermobarograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

High Pressure Investigations . . . . . . . . . . . . . . . . . . . . . . . . . 253

Phase transitions at High Pressures . . . . . . . . . . . . . . . . . . . . . . 254 Critical Phase Transitions Under Pressure . . . . . . . . . . . . . . . . . . . 266

6.2.4.4 Pressure-Volume-Temperature Behavior . . . . . . . . . . . . . . . . . . . 269 6.2.4.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Fluctuations and Liquid Crystal Phase Transitions . . . . . . . . . . . . . . 277

The Nematic-Isotropic Transition . . . . . . . . . . . . . . . . . . . . . . . 278 The Uniaxial-Biaxial Nematic Transition . . . . . . . . . . . . . . . . . . . 279

6.3.4 Type I Smectic A's: Nematic-Smectic A Transition . . . . . . . . . . . . . 279 6.3.5 Type I1 Smectic A's: Cholesteric-Smectic A Transition . . . . . . . . . . . 281 6.3.6 Transitions between Tilted and Orthogonal Smectic Phases . . . . . . . . . 282 6.3.7 B-SmB-SmA Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 6.3.8 Fluctuations at Critical Points . . . . . . . . . . . . . . . . . . . . . . . . . 284 6.3.8.1 BPI,,- Isotropic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 6.3.8.2 SmA, and SmA, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 6.3.8.3 NAC Multicritical Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 6.3.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 6.3.10 References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 6.4 Re-entrant Phase Transitions in Liquid Crystals . . . . . . . . . . . . . . . 289

6.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 6.4.2 R 1 : Re-entrance from Frustration . . . . . . . . . . . . . . . . . . . . . . . 291 6.4.3 Re-entrance from Geometric Complexity . . . . . . . . . . . . . . . . . . . 298 6.4.4 R3: Re-entrance from Competing Fluctuations . . . . . . . . . . . . . . . . 300 6.4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 6.4.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3.2 References 253 6.2.4

6.2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 6.2.4.2 6.2.4.3

P. Pollmann

6.2.4.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 6.3

6.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 6.3.2 6.3.3

P. E . Cladis

P. E . Cladis

7

7.1 7.1 . 1 7.1.2

Defects and Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

Definitions. Conventions and Methods . . . . . . . . . . . . . . . . . . . . 304 Local Molecular Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . 304 Microscopic Preparations of Liquid Crystals . . . . . . . . . . . . . . . . . 304

7.1.2.1 Thermotropic Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 7.1.2.2 Lyotropic Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

Yves Bouligand

Contents XV

7.1.2.3 7.1.3 7.1.4 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 7.3 7.3.1 7.3.2 7.3.3 7.3.4 7.3.5 7.3.6 7.3.7 7.4 7.4.1 7.4.2 7.4.3 7.4.4 7.4.4. I 7.4.4.2 7.4.4.3 7.4.4.4 7.4.4.5 7.4.4.6 7.4.5 7.4.6 7.4.7 7.4.7.1 7.4.7.2 7.4.7.3 7.4.7.4 7.4.7.5 7.4.7.6 7.4.7.7 7.4.7.8 7.5

Liquid Monocrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

Other Microscopic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 311

Singular Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Singular Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 Interface Defects (Points and Lines) . . . . . . . . . . . . . . . . . . . . . 313 The Nature of Thick and Thin Threads . . . . . . . . . . . . . . . . . . . . 316 Topological Structure of Defects . . . . . . . . . . . . . . . . . . . . . . . 316 The Volterra Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 The Volterra Process in Nematic. Smectic A and Cholesteric Phases . . . . . 316 A Different Version of the Volterra Process . . . . . . . . . . . . . . . . . . 318 Continuous and Discontinuous Defects in Cholesteric Phases . . . . . . . . 321 Core Disjunction into Pairs of Disclinations . . . . . . . . . . . . . . . . . 325 Optical Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 Classification of Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Geometrical Constraints and Textures . . . . . . . . . . . . . . . . . . . . . 328 Parallel Surfaces and Caustics in Liquid Crystals . . . . . . . . . . . . . . . 328

Images of Liquid Crystals in Polarizing Microscopy . . . . . . . . . . . . . 308

Strong Deformations Resulting in Defects . . . . . . . . . . . . . . . . . . 311

Dupin’s Cyclides and Focal Conics . . . . . . . . . . . . . . . . . . . . . . 328 Slight Deformations of Dupin’s Cyclides . . . . . . . . . . . . . . . . . . . 331 Textures Produced by Parallel Fluid Layers . . . . . . . . . . . . . . . . . . 332 Planar Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 Focal Conics and Polygonal Textures . . . . . . . . . . . . . . . . . . . . . 333 Fan Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 Texture Distribution in Lamellar Mesophases . . . . . . . . . . . . . . . . . 335 Illusory Conics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 Walls, Pseudowalls and Broken Aspects . . . . . . . . . . . . . . . . . . . 337 Origin of Spirals in Chiral Liquid Crystals . . . . . . . . . . . . . . . . . . 340 Defects and Mesophase Growth . . . . . . . . . . . . . . . . . . . . . . . . 341 Defect Energies and Texture Transformations . . . . . . . . . . . . . . . . . 342 Disclination Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Disclination Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Focal Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 Translation Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 Simulations of Defects and Textures . . . . . . . . . . . . . . . . . . . . . 345 Defect Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Textures and Defect Associations . . . . . . . . . . . . . . . . . . . . . . . 347 Crystals of Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

8

8.1 8.1.1

Flow Phenomena and Viscosity . . . . . . . . . . . . . . . . . . . . . . . . 352

Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 Shear Viscosity Coefficients q,. q2. q3. and q I 2

E Schneider and H . Kneppe

. . . . . . . . . . . . . . . 353

XVI Contents

8.1.2 8.1.3 8.1.4 8.1.5 8.1.6 8.1.7 8.1.8 8.1.9 8.2 8.2.1 8.2.2 8.2.3 8.2.4 8.3 8.3.1 8.3.2 8.3.3 8.4 8.4.1 8.4.2 8.4.3 8.4.4 8.5 8.6

Rotational Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 Flow Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 Viscous Flow under the Influence of Elastic Torques . . . . . . . . . . . . . 358 Transverse Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 Backflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Discotic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Cholesteric Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . 364 Helical Axis Parallel to the Shear Gradient (Case I) . . . . . . . . . . . . . 364 Helical Axis Parallel to the Flow Direction (Case 11) . . . . . . . . . . . . . 365 Helical Axis Normal to v and grad v (Case 111) . . . . . . . . . . . . . . . . 365 Torque Generation Under Flow . . . . . . . . . . . . . . . . . . . . . . . . 366 Biaxial Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . 366 Shear Viscosity Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Rotational Viscosity Coefficients . . . . . . . . . . . . . . . . . . . . . . . 368 Flow Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 SmCPhase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 Shear Flow with a Fixed Director Orientation . . . . . . . . . . . . . . . . 369 Rotational Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 Flow Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 SmC* Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 SmAPhase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

Influence of Temperature and Order Parameter on the Viscosity Coefficients 362

9 Behavior of Liquid Crystals in Electric and Magnetic Fields . . . . . . . . . 375

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 9.2 9.2.1 Shift of Phase Transition Temperatures . . . . . . . . . . . . . . . . . . . . 376 9.2.1.1 Second-Order Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 9.2.1.2 Strong First-Order Transitions . . . . . . . . . . . . . . . . . . . . . . . . . 377 9.2.1.3 Weak First-Order Transitions . . . . . . . . . . . . . . . . . . . . . . . . . 379 9.2.2 Influence of the Field on Order Parameters . . . . . . . . . . . . . . . . . . 380 9.2.3 Changes in Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 9.2.3.1 Induced Biaxiality in Nematics . . . . . . . . . . . . . . . . . . . . . . . . 381 9.2.3.2 The Kerr Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 9.2.4 Specific Features of Twisted Phases and Polymers . . . . . . . . . . . . . . 383 9.2.4.1 Bluephases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 9.2.4.2 Twist Grain Boundary Phases . . . . . . . . . . . . . . . . . . . . . . . . . 385 9.2.4.3 Comment on Polymer Liquid Crystals . . . . . . . . . . . . . . . . . . . . 386 9.3 Distortions due to Direct Interaction of a Field with the Director . . . . . . . 386 9.3.1 Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 9.3.1.1 Classical Frederiks Transition . . . . . . . . . . . . . . . . . . . . . . . . . 386 9.3.1.2 Field-Induced Periodic Structures . . . . . . . . . . . . . . . . . . . . . . . 390

Lev M . Blinov

Direct Influence of an Electric or Magnetic Field on Liquid Crystal Structure . 376

Contents XVII

9.3.1.3 Flexo-Electric Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 9.3.2 Twisted Nematics and Cholesterics . . . . . . . . . . . . . . . . . . . . . . 395 9.3.2.1 Twist and Supertwist Structures . . . . . . . . . . . . . . . . . . . . . . . . 395 9.3.2.2 Instability of the Planar Cholesteric Texture . . . . . . . . . . . . . . . . . 397 9.3.2.3 Field Untwisting of the Cholesteric Helix . . . . . . . . . . . . . . . . . . . 399 9.3.2.4 Flexoelectric Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 9.3.3 Smectics and Discotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 9.3.3.1 Field Behavior of Achiral Smectics . . . . . . . . . . . . . . . . . . . . . . 403 9.3.3.2 Chiral Ferroelectrics and Antiferroelectrics . . . . . . . . . . . . . . . . . . 406 9.4 Eiectrohydrodynamic Instabilities . . . . . . . . . . . . . . . . . . . . . . . 413 9.4.1 Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 9.4.1.1 Classification of Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . 413 9.4.1.2 Isotropic Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 9.4.1.3 Anisotropic Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 9.4.2 Cholesterics and Smectics . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 9.4.2.1 Cholesterics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 9.4.2.2 Smectics A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 9.4.2.3 Smectics C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 9.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 9.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427

10

10.1 10.2 10.2.1 10.2.2 10.2.3 10.3 10.3.1 10.3.2 10.3.3 10.4 10.4.1 10.4.2 10.4.3 10.5

Surface Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 Macroscopic Alignment of Nematic Liquid Crystals . . . . . . . . . . . . . 434 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Anchoring Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Anchoring Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436 Microscopic Surface Order of Nematic Liquid Crystals . . . . . . . . . . . 438 Surface Orientational Order . . . . . . . . . . . . . . . . . . . . . . . . . . 438 Microscopic Anchoring Mechanisms at Solid Substrates . . . . . . . . . . . 439 The Nematic/Isotropic and NematicNapor Interfaces . . . . . . . . . . . . . 441 Orientation of Other Liquid Crystals . . . . . . . . . . . . . . . . . . . . . 442 Smectic and Chiral Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . 442 Polymer Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 Lyotropic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

Blandine JkrBme

11 Ultrasonic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447

Structural Transformation in Liquid Crystals . . . . . . . . . . . . . . . . . 447

11.1.1.1 Homogeneous Distortion Stage . . . . . . . . . . . . . . . . . . . . . . . . 448 1 1.1.1.2 Spatially Periodic Distortion Stage . . . . . . . . . . . . . . . . . . . . . . 452 11.1 . 1 . 3 Inhomogeneous Distortion Stage . . . . . . . . . . . . . . . . . . . . . . . 453

Olga A . Kapustina

Orientation Phenomena in Nematics 1 1.1 1 I . I . 1 . . . . . . . . . . . . . . . . . . . . . 448

XVIII Contents

11.1.2 Cholesterics in an Ultrasonic Field . . . . . . . . . . . . . . . . . . . . . . 455 1 1.1.2.1 Periodic Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 11.1.2.2 Storage Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 1 1.1.2.3 Focal-Conic to Planar Texture Transition . . . . . . . . . . . . . . . . . . . 456 1 1.1.2.4 Bubble Domain Texture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 1 1.1.2.5 Fingerprint Texture Transition . . . . . . . . . . . . . . . . . . . . . . . . . 457

Smectic Phase in an Ultrasound Field . . . . . . . . . . . . . . . . . . . . . 457 11.2 Wave Interactions in Nematics . . . . . . . . . . . . . . . . . . . . . . - . . 457

Acousto-electrical Interactions in Nematics . . . . . . . . . . . . . . . . . . 460 Ultrasound Studies of Liquid Crystals . . . . . . . . . . . . . . . . . . . . . 461 Ultrasonic Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

11.4.3 Acoustic Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 Monitoring Boundary Effects . . . . . . . . . . . . . . . . . . . . . . . . . 463

11.4.5 Acoustic Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464 11.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464

1 1.1.3

1 1.3 1 I . 4 1 1.4.1 I I . 4.2 Photoacoustic Spectroscopy 463

11.4.4

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

12

12.1 12.2 12.2.1 12.2.2 12.3 12.3.1 12.4 12.5 12.5.1 12.5.2 12.5.3 12.5.4 12.6 12.6.1 12.6.2 12.6.3 12.7 12.8

Nonlinear Optical Properties of Liquid Crystals . . . . . . . . . . . . . . . 467

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 Interaction between Electromagnetic Radiation and Liquid Crystals . . . . . 467 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 Nonlinear Susceptibility and Hyperpolarizability . . . . . . . . . . . . . . . 468 Nonlinearities Originating in Director Reorientation . . . . . . . . . . . . . 469 D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Kerr Effect 469 Optical Field-Induced Reorientation . . . . . . . . . . . . . . . . . . . . . 470 Nonlinearities without Director Reorientation . . . . . . . . . . . . . . . . 472 Optical-Field-Induced Orientational Order . . . . . . . . . . . . . . . . . . 472 Thermal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Conformational Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Electronic Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 Optical Harmonic Generation . . . . . . . . . . . . . . . . . . . . . . . . . 475 Bulk Second Harmonic Generation . . . . . . . . . . . . . . . . . . . . . . 475 Surface Second Harmonic Generation . . . . . . . . . . . . . . . . . . . . . 476 Third Harmonic Generation . . . . . . . . . . . . . . . . . . . . . . . . . . 476 Materials and Potential Applications . . . . . . . . . . . . . . . . . . . . . 476 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477

P. Pa l&-Mu ho ru y

13 Diffusion in Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . 480

13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 13.2 Theoretical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 13.2.1 The Diffusion Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 13.2.2 Basic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 13.2.3 Model Refinements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

F: Nouck f

Contents XIX

13.3 13.3.1 13.3.2 13.3.3 13.4 13.4.1 13.4.2 13.4.3 13.4.4 13.4.5 13.4.6 13.4.7 13.5

Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 Tracer Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 Quasielastic Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . 484 Magnetic Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 Selected Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 The Experimental Dilemma . . . . . . . . . . . . . . . . . . . . . . . . . . 486 Nematic Mesophase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 Nematic Homologues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 Smectic Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 Solute Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 Lyotropic Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 Selected Diffusion Constants . . . . . . . . . . . . . . . . . . . . . . . . . 490 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490

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Chapter I Introduction and Historical Development

George W Gray

1 Introduction

It is with a sense of responsibility that I be- gin this summary of the historical development of liquid crystals, because one of the two authors of the original Handbook of Liquid Crystals of 1980 [ 11 was Professor Hans Kelker, a friend and a very well in- formed authority on the history of the subject and the personalities involved in the earlier stages of its emergence. Those who attended the Twelfth International Liquid Crystal Conference in Freiburg in 1988, which marked the centenary of the discovery of liquid crystals, and heard Professor Kelker’s plenary lecture - Some Pictures of the History of Liquid Crystals [2] - which was part of a conference session devoted to a historical review of the field, will know this. Here he demonstrated that he was in possession of a very wonderful collection of manuscripts and photographs relating to the scientists who, in the latter part of the nineteenth century and the early part of the twen- tieth century, laid the foundations of our present-day knowledge of liquid crystals.

I am not in that privileged situation, but I have worked in the field for 50 years, beginning my first experiments on aromatic carboxylic acids in October 1947. I have therefore worked through approaching half of the historical span of the subject, including the most recent years during which the subject has expanded and deepened so markedly. I hope this first-hand experience will counterbalance my lack of detailed his-

torical knowledge of the earlier years, as possessed by Professor Kelker. Were he alive today, I hope he would not disapprove of what I write in this chapter.

The history of the development of liquid crystals may be divided into three phases: 1. The period from their discovery in the lat-

ter part of the nineteenth century through to about 1925, the years during which the initial scepticism by some that a state of matter was possible in which the properties of anisotropy and fluidity were com- bined, through to a general acceptance that this was indeed true, and publication of a first classification of liquid crystals into different types.

2. The period from 1925 to about 1960, during which general interest in liquid crystals was at a fairly low level. It was a niche area of academic research, and only relatively few, but very active, scientists were devoted to extending knowledge of liquid crystals. Two world wars and their aftermaths of course contributed greatly to the retardation of this field during this period. Taking the aftermaths of the wars into account, probably at least 15 years were effectively lost to progress during this second phase.

3 . The period from 1960 until today is by contrast marked by a very rapid development in activity in the field, triggered of course by the first indications that tech- nological applications could be found for liquid crystals. These early indications

I Introduction and Historical Development 2

2

were justified, and led to today’s strong electro-optical display industry. The quest for new applications stimulated research and the flow of financial support into the involved areas of chemistry, physics, electrical and electronic engi- neering, biology, etc. As a marker of this activity, the numbers of papers and patents published in 1968 was about 2000 and this had risen to 6500 in 1995.

The Early Years up to About 1925

The question as to when liquid crystals were discovered must now be addressed. In pin- pointing a discovery, it is necessary to distinguish simple observations of an unusual phenomenon or effect from observations that develop into an understanding of the meaning and significance of that phenomenon or effect. If we accept that the latter cri- teria must be met to justify the word discovery, then the credit for the discovery of liquid crystals must go to Friederich Reinitzer, a botanist of the Institute for Plant Physiol- ogy of the German University of Prague, who in a paper submitted on May 3, 1888 [3], described his observations of the colored phenomena occurring in melts of cholesteryl acetate and cholesteryl benzoate. In addition, he noted the “double melting” behavior in the case of cholesteryl benzoate, whereby the crystals transformed at 145.5 “C into a cloudy fluid, which sud- denly clarified only on heating to 178.5 “C. Subsequent cooling gave similar color effects (but see later) to those observed on cooling the melt of cholesteryl acetate. To- day of course we know that the colored phenomena reported by Reinitzer are character- istic of many cholesteric or chiral nematic (N*) liquid crystal phases.

In his article [ 3 ] , Reinitzer acknowl- edges that other workers before him had observed curious color behavior in melts of cholesteryl systems. He mentions that Pla- nar in Russia and Raymann in Paris had noted violet colors reflected from cholesteryl chloride and that Lobisch in Germany had observed a bluish-violet flourescence in the case of cholesteryl amine and cholesteryl chloride. Two things distinguish these earlier observations from those of Reinitzer. These are Reinitzer’s recording of the “double melting” property of cholesteryl benzoate, and the fact that Reinitzer carried out preliminary studies on thin films of cholesteryl benzoate and noted the range of spec- tral colors reflected as the temperature de- creased until crystallization occurred and the complementary nature of the colored light when the sample was viewed in trans- mission. Moreover, Reinitzer knew of the excellent work of the German physicist Pro- fessor Otto Lehmann, then at the Polytech- nical School at Aachen, in designing and developing polarization microscopes, and recognized that Lehmann could advise on the optical behavior of his cholesteryl esters.

The approach to Lehmann was made in March 1888 and the correspondence is ex- cellently documented in Kelker and Knoll’s article [2]. This interaction led to agreement that Reinitzer’s materials were homogeneous systems of which Lehmann wrote in Au- gust 1889: “It is of high interest for the physicist that crystals can exist with a softness, being so considerable that one could call them nearly liquid.” This led quickly to the submission by Lehmann, by then at the University of Karlsruhe, of his paper Uber fliessende Kristalle to the Zeitschrift fu r Physikalische Chemie [4].

Significantly, this uses for the first time the term liquid crystal. As a consequence of the above events and the development of our understanding of liquid crystals which

2 The Early Years up to About 1925 3

stemmed from them, we must clearly ac- knowledge Reinitzer as the true discoverer of liquid crystals and the date of the event as March 14, 1888.

It should be noted that the discovery related exclusively to materials we now class as thermotropic liquid crystals, wherein the liquid crystal phases form either on heating crystals or on cooling isotropic liquids, that is, as a consequence of thermal effects. In addition to thermotropic liquid crystals, a second class of fluid anisotropic materials is known, namely, lyotropic liquid crystals where the disruptive effect on the crystal lattice involves a solvent (often water), coupled where necessary with thermal change. Here, the order of the crystal is broken down by the solvent and the molecules form mi- celles which then arrange themselves in an ordered way, while allowing fluidity. Ex- cess of solvent completes the decrease in order and an isotropic solution is formed. Ob- servations of anisotropy and optical birefringence in such systems were indeed made well before Reinitzer’s discovery, but like the observations of Planar, Raymann, and Lobisch, there was no followthrough to a re- alization of the full significance of what was being seen. These observations were made by Mettenheimer [ 5 ] , Valentin [6], and Vir- chow [7] in the period 1834-1861, and involved studies of biological samples derived from nerve tissue, for example, myelin, a complex lipoprotein which can be separated into fractions and which forms a sheath round nerve cells. In water-containing sodium oleate, these sheaths develop what have been called myelinic forms vis- ible microscopically, especially in polarized light, as fluid, birefringent entities. Progress on these anisotropic systems was however impeded by the complexity and lack of re- producibility of the biological systems involved, and whilst predating the studies of Reinitzer and Lehmann are not generally re-

garded as marking the discovery of liquid crystals.

Following publication of his paper in 1 889 [4], Lehmann continued work with liquid crystals and indeed dominated the scene in the late 1800s and the early part of the twen- tieth century, continuing to publish on liquid crystals until the year of his death in 1922.

Turning to purely synthetic materials, un- like the cholesteryl esters which were of nat- ural origin, examples of liquid crystal behavior were found in these by Lehmann in 1890. The materials were azoxy ethers pre- pared by Gattermann and Ritschke [8]. The next ten years or so saw studies of p-meth- oxycinnamic acid and in 1902 the synthesis by Meyer and Dahlem [9] of the first smectogen, ethyl p-azoxybenzoate, although not recognized structurally for what it was at that time. Through studying such materials, Lehmann did however recognize that all liquid crystals are not the same, and indeed in 1907 he examined the first liquid crystal material exhibiting two liquid crystal phases. This material had what was later shown to be a smectic A (SmA) and a cholesteric (N*) phase. Significantly in the context of much later work in the field of applications, he also reported on the aligning effects of surfaces on liquid crystals.

Despite the growing number of compounds shown to exhibit liquid crystal phases (and in a short number of years Vorlander contributed about 250), the acceptance of liquid crystals as a novel state of matter was not universal. Tammann in particular [ 101 persisted in the view that liquid crystals were colloidal suspensions, and was in bit- ter argument with Lehmann and Schenk who upheld the view that they were homogeneous systems existing in a new state dis- tinct from the crystalline solid and isotropic liquid states. Nernst [ 1 I] too did not sub- scribe to the latter view and believed that liquid crystals were mixtures of tautomers.

4 I Introduction and Historical Development

There was however a steadily growing body of evidence supporting the view that liquid crystals represent a true state of matter and acceptance of this slowly grew, aided by the excellent reviews of 1905 by Schenk (Kristalline Fliissigkeiten und f lus- sige Kristalle) [ 121 and Vorlander (Kristal- Zinisch-fliissige Substanzen) [ 131. There then followed the important review of optical effects by Stumpf [14] and, much later, an important paper was that by Oseen [15] on a kinetic theory of liquid crystals. The real seal of acceptance of liquid crystals for what they are, i.e., a fascinating and dis- tinct state of matter, was however given in 1922 in the famous publication by G. Frie- del [16] in the Annales de Physique, entit- led Les Etats Mesomorphes de la Matidre.

Here, in connection with Friedel’s article and on a personal note, I well remember my research supervisor, Professor and later Sir Brynmor Jones, sending me to the library to find the appropriate journal, requiring that I produce a complete translation from French of all 273 pages in order to be “ful- ly familiar with all that had been written”. This I dutifully did in the fullness of time, and on taking my translation to show my supervisor, he then reached up to a shelf and withdrew a black notebook saying “now you can compare the quality of your translation with mine!” I learned much from that exer- cise, as will anyone who repeats it today.

In addition to containing a wealth of in- formation on microscopic techniques and materials, Friedel’s article represented in 1922 the first classification of liquid crystals into types, i.e., nematic, smectic and cholesteric. Today, of course, cholesterics are known simply as chiral nematics with no need that they be derived from cholesterol, and we recognize the existence of several polymorphic smectic forms, whereas Frie- del allowed for only one (today’s smectic A; S m A).

Friedel did however understand the layered nature of smectics, firstly through the stepped edges possessed by smectic droplets with a free surface, and secondly through his detailed studies of the optical microscopic textures of thin films of smectic phases. He understood the optical dis- continuities, i.e., the defects, of the smectic focal-conic texture and saw the relationship of the black lines delineating ellipses of different eccentricities and their associated hy- perbolae in terms of focal-conic “domains” which may be divided into a series of parallel, curved surfaces known as Dupin cyclides. He also understood that the optically extinct homeotropic textures of smectics of the type he studied gave positive uniaxial interference figures consistent with systems of layers lying flat to the surface. His microscopic studies demonstrated the im- mense value of the optical microscope as a precise scientific instrument in studies of all types of liquid crystal phases.

Friedel’s article, coupled with the publications on synthesis and studies of new liquid crystal materials by organic chemists in Germany, notably Vorlander (see, for example, his monograph Chemische Kristallo- graphie der Flussigkeiten of 1924 [17]), firmly cemented in place all the earlier observations, providing a firm basis on which to build the future structure of the subject.

Before moving on to phase two of the history, we might just return to Reinitzer, the discoverer of liquid crystals, and recognize the quality of his powers of observation, for not only did he focus on the color effects and double melting, but also he noted the blue color appearing in the isotropic melt just before the sample turned into the cloudy cholesteric phase. About this, he said the following: “there appeared (in the clear melt) at a certain point a deep blue colour which spread rapidly through the whole mass and almost as quickly disappeared,

3 The Second Phase from 1925 to 1959 5

again leaving in its place a uniform turbid- ity. On further cooling, a similar colour effect appeared for the second time to be followed by crystallisation of the mass and a simultaneous disappearance of the colour effect.” The turbid state and the second col- or effect were of course due to the cholesteric phase, but the first transient blue color we now know was associated with the optically isotropic ‘blue phases’ we are familiar with today. Although Lehmann believed that this transient effect represented a different state, the full significance of Reinitzer’s observations had to wait until the 1980s when these isotropic cubic phases became a focus of attention in condensed matter physics.

A further point concerning the first phase of our history of liquid crystals is about nomenclature, a matter about which scientists of today still love to argue. In the early years, however, the debate was sparked by Friedel who strongly objected to Lehmann’s term liquid crystal, on the basis that liquid crystals were neither true liquids nor true crystals. The term does of course remain in wide- spread use today, simply because the juxta- position of two contradictory terms carries an element of mystery and attraction. Frie- del preferred the term mesomorphic to describe the liquid crystal state, and the associated term mesophase, reflecting the inter- mediate nature of these phases between the crystalline and isotropic liquid states. These terms are again widely used today and co- exist happily with the Lehmann terminolo- gy. A useful term springing from Friedel’s nomenclature is the word mesogen (and also nematogen and smectogen), used to describe a material that is able to produce mesophases. The associated term mesogenic is used by some to indicate that a material does form liquid crystal phases and by others to indicate that a compound is structurally suit- ed to give mesophases, but may not, if, for

example, the melting point of the crystalline state is too high. Then the isotropic liquid is produced directly from the crystal, and, on cooling, crystallization may occur too quickly for even a monotropic liquid crystal phase to form. Yet this compound may show strong tendencies to be mesomorphic if binary phase diagrams of state are examined using a standard material as the second component. My view is that the term mesogenic should be used to describe a structural compatibility with mesophase formation, without the requirement that a phase is actually formed. After all, if the compound does really form a mesophase, the description of it as mesomorphic is perfectly ade- quate.

Finally, on the subject of nomenclature, Friedel of course gave us today’s terms smectic and nematic with their well-known Greek derivations.

3 The Second Phase from 1925 to 1959

In the first part of this period, Vorlander and his group in Halle contributed strongly to the growing number of compounds known to form liquid crystal phases, some showing up to three different mesophases. Based upon his work came the recognition that elongated molecular structures (lath- or rod-like molecules) were particularly suit- ed to mesophase formation. His work also showed that if the major axis of a molecule were long enough, protrusions could be tol- erated without sacrifice of the liquid crystal properties. Thus 1,4-disubstituted naphtha- lenes with a strong extension of the major axis through the I ,4-substituents were liquid crystalline, despite the protruding second ring of the naphthalene core. It is inter- esting that Vorlander records that the mate-


rials behaved as liquid crystallline resins or lacquers (an early thought perhaps about the potential of liquid crystals for applications).

In his book Nature’s Delicate Phase of Matter, Collings [ 181 remarks that over 80 doctoral theses stemmed from Vorlander ’s group in the period 1901-1934. Further evidence of Vorlander’s productivity is found in the fact that five of the 24 papers presented at the very important and first ever sym- posium on liquid crystals held in 1933 under the auspices of the Faraday Society in Lon- don, Liquid Crystals and Anisotropic Fluids - A General Discussion [ 191, were his. Per- haps the most important consequence of Vorlander’s studies was that in laying down the foundations of the relationship between molecular structure and liquid crystal properties, attention was focused upon the molecules as the fundamental structural units of the partially ordered phases. Up to then, even Lehmann had been uncertain about the units involved in the ordering and what occurred at the actual transitions.

The Faraday Meeting of 1933 was of great importance in bringing together the small number of active, but often isolated, scientists involved at that time in liquid crystal research. This propagated knowledge and understanding, but, as we shall see, it also generated some dispute.

As early as 1923, de Broglie and E. Frie- del (the son of G. Friedel) had shown [20] that X-ray reflections could be obtained from a system of sodium oleate containing water, and that the results were consistent with a lamellar or layered structure. This X- ray work was extended [21] in 1925 to Vorlander’s thermotropic ethyl p-azoxybenzoate, confirming G. Friedel’s conclusions of a layered structure stemming from his microscopic studies of smectic defect structures. Further, in the period 1932- 1935, Herrmann [22], who also contributed to the 1933 Faraday Discussion, was deci-

sive in confirming the lamellar nature of smectics by X-ray studies which included Vorlander’s material exhibiting more than one smectic phase. The latter work substan- tiated a change from a statistical order in the layers of one srnectic to a hexagonal ordering in the lower temperature phase. A tilted lamellar structure was also found by Herr- mann for some thallium soaps [23].

Amongst other names of historical interest featured on the Faraday Discussion pro- gram were, for example, Frkedericksz and Zolina (forces causing orientation of an anisotropic liquid), Zocher (magnetic field effects on nematics), Ostwald, Lawrence (lyotropic liquid crystals), Bernal, Sir W. H. Bragg (developing the concept of Dupin cyclides in relation to Friedel’s earlier studies of focal-conics), and also Ornstein and Kast who presented new arguments in favor of the swarm theory, which was first put for- ward in 1907-1909 by Bose [24]. This theory had proposed that the nematic phase consisted of elongated swarms of some 1 Oh molecules, and in the 1930s much effort was given to proving the existence of these swarms, which were used to explain some, but not all, of the physical properties of nematics. However, at the 1933 Faraday Meet- ing, the presentation of Oseen [25] and the strong reservations expressed by Zocher during the discussions were already casting shadows of doubt on the swarm theory. To- day of course we accept that definitive proof of the existence of swarms was never obtained, and by 1938 Zocher was expressing further strong reservations about the theory [26], proposing alternatively that the nematic phase is a continuum, such that the molecular orientation changes in a continuous manner throughout the bulk of the mesophase. This was called the distortion hypothesis and together with Oseen’s work marked the beginning of the modern continuum theory of liquid crystals. However, de-

3 The Second Phase from 1925 to 1959 7

velopments here had to wait until after the second world war when Frank [27], at a further Faraday discussion in 1958, and conse- quent upon his re-examination of Oseen’s treatment, presented it as a theory of curvature elasticity, to be advanced in the next historical phase by names such as Ericksen, Leslie, de Gennes, and the Orsay Group in France.

The period following the war up until the 1950s is also significant for the work of Chatelain [28], in collaboration with Fal- gueirettes. Using surface alignment techniques, they measured the refractive indices of different nematics, and Chatelain produced his theoretical treatment of the val- ues of the ordinary and extraordinary indices of refraction of an oriented nematic melt.

Following Vorlander, other chemists were now becoming interested in new liquid crystal materials, and in the early 1940s we find publications on structure/property relations by Weygand and Gabler [29]. Lat- er, in the 1950s, Wiegand [30] in Germany and the author in the UK were also making systematic changes in the structures of me- sogens to establish the effects on liquid crystal behavior. The author’s work included not only systematic modifications to aromatic core structures, but also studies of many ho- mologous series, establishing clearly that within series systematic changes in transition temperature always occur, within the framework of a limited number of patterns of behavior. In the period 1951-1959, the author published some 20 papers on structure/property relations in liquid crystals. These are rather numerous to reference here, but in the account of the third historical phase from 1960 until today, reference to relevant reviews and books is given.

Lyotropic liquid crystals also progressed during this second phase. Lawrence’s paper at the 1933 Faraday meeting discussed the pb,ase diagrams for different compositions

of fatty acid salts, recognizing the different phase types involved and the transitions undergone with change of temperature and/or water content. Examples of aromatic materials, including dyes, giving lyotropic phases were also found, and solvents other than water as the lyophase were ex- plored.

The early work of Robinson et al. [31] was also done in this period. This involved solutions of poly-y-benzyl-L-glutamate in organic solvents. These solutions exhibited the selective light reflecting properties of thermotropic cholesteric liquid crystals.

This period of history also saw the publication of work by Eaborn and Hartshorne [32] on di-isobutylsilandiol, which generated a mesophase. This was a puzzling result at the time, as the molecular shape was in- consistent with views of the time that liquid crystal formation required rod-shaped molecules. Light would be shed on this only after the discovery of liquid crystal phases formed by disc-shaped molecules in the early 1970s.

Finally, it should be noted that in this period, in 1957, a very important review on liquid crystals was published by Brown and Shaw [33]. This did much to focus the attention of other scientists on the subject and certainly contributed to the increase in liquid crystal research, which was to herald the strong developments in the early 1970s.

The period 1925-1959 may be usefully summarized now. Although the level of activity in the field was limited, important developments did occur in relation to:

- the influence of external fields (electric and magnetic) on liquid crystals;

- the orienting influences of surfaces; - measurements of the anisotropic physical

properties of aligned liquid crystals; - the range of new liquid crystal materials

and structure/property relationships;


- the development of theories of the liquid crystal state ranging from the swarm theory to the emerging continuum theory;

- increased awareness of the value of polarizing optical microscopy for the iden- tification of mesophases, the determination of transition temperatures, and reaching a fuller understanding of defect textures.

4 The Third Phase from 1960 to the Present Time

The first ten years of this period saw several important developments which escalated interest and research in liquid crystals. Among these, there was the publication by Maier and Saupe [34] of their papers on a mean field theory of the nematic state, focusing attention on London dispersion forces as the attractive interaction amongst molecules and upon the order parameter. This theory must be regarded as the essen- tial starting point for the advances in theoretical treatments of the liquid crystal state which followed over the years.

There was also much activity in the field of new liquid crystal materials, notably by Demus et al. [35] in Germany and by the author who, in 1962, produced his monograph Molecular Structure and the Properties of Liquid Crystals [36], published by Academ- ic Press,

Also, further X-ray studies began to ad- vance knowledge of the structure of liquid crystal phases, particularly smectics. The work of de Vries and Diele should be men- tioned, and later on, notably that by Leve- lut and co-workers in France and Leadbet- ter in England (see, for example, [37, 38]), work which culminated in the 1980s in a clear structural elucidation and classification of smetic liquid crystals. This distin-

guished the true lamellar smectics with lit- tle or no correlation between layers from lamellar systems, previously regarded as smectics, which possess three-dimensional order and are really soft crystals. Today, the true smectics are labeled SmA, for example, and the crystal phases are referred to simply by a letter such as K, or by CrK. The phase once known as SmD and first observed by the author and co-workers in lat- erally nitro substituted biphenyl carboxylic acids [39] is now recognized [40] as a cubic liquid crystal phase. Several other examples of cubic thermotropic liquid crystal phases are now known [4 1, 421.

Such studies focused attention on the microscopic textures of liquid crystal phases. The defects characterizing these textures are now well understood through rather beauti- ful studies by workers such as Klkman [43], and from textures it is now possible to go a long way towards characterizing the phase behavior of new materials. A great deal of work on phase characterization has been done, and two reference sources are important [44,45]. Through such detailed studies of phase behavior, new phenomena were often recognized and explained, for example, the re-entrance phenomenon through the work of Cladis [46], and the existence of the blue phases (BPI, BPII, and BPIII) through the work of several groups [47]. We should remember of course that Reinitzer did ob- serve blue phases many years earlier and knew, without understanding the situation, that something occurred between the isotropic liquid and the N* phase on cooling many chiral materials. Reflectance microscopy played a big part in the eventual elucidation of these phases as cubic phases in- volving double twist cylinders.

The widened interest in liquid crystals exemplified above had its origins in a number of events, such as the publication of the Brown and Shaw review [ 3 3 ] and the

Physical Properties of Liquid Crystals...studied chemistry at the University of Frankfurt/Main,...

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