Thermotropic Liquid Crystals, Fundamentals

325 Pages·1988·6.455 MB·English

by  Professor Dr. Ger Vertogen, Professor Dr. Wim H. de Jeu (auth.)

45
Springer Series in Chemical Physics
Edited by Fritz P. Schafer
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Springer Series in Chemical Physics
Editors: Vitalii I. Goldanskii Fritz P. Schafer J. Peter Toennies
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Volume 45 Thermotropic Liquid Crystals, Fundamentals
By G. Vertogen and W.H. de Jeu
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G. Vertogen W. H. de Jeu
Thermotropic
Liquid Crystals,
Fundamentals
With 93 Figures
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo
Professor Dr. Ger Vertogen
Institute for Theoretical Physics, Catholic University, Toernooiveld
NL-6525 ED Nijmegen, The Netherlands
Professor Dr. Wim H. de Jeu
Open University, P.O. Box 2960, NL-6401 DL Heerlen and
FOM-Institute for Atomic and Molecular Physics, Kruislaan 407
NL-1098 SJ Amsterdam, The Netherlands
Series Editors Professor Dr. Fritz Peter Schafer
Max-Planck-Institut fiir
Biophysikalische Chemie
0-3400 Gottingen-Nikolausberg, FRG
Professor Vitalii I. Goldanskii Professor Dr. J. Peter Toennies
Institute of Chemical Physics Max-Planck-Institut fiir Stromungsforschung
Academy of Sciences, Kosygin Street 3 BottingerstraBe 6-8
Moscow V-334, USSR 0-3400 Gottingen, FRG
ISBN-13: 978-3-642-83135-5 e-ISBN-13: 978-3-642-83133-1
001: 10.1007/978-3-642-83133-1
Library of Congress Cataloging-in-Publication Data. Vertogen, G. (Gerrit), 1940-Thermotropic liquid crystals,
fundamentals. (Springer series in chemical physics; v. 45) Bibliography: p. Includes index. 1. Liquid crystals.
I. Jeu, W.H. de (Wilhelmus Hendrikus), 1943-. I. Title. II. Series. QD923.V47 1987 548'.9 87-14673
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© Springer-Verlag Berlin Heidelberg 1988
Softcover reprint ofthe hardcover I st edition 1988
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2153/3150-543210
I libri non sono tatti per crederci,
rna per essere sottoposti a indagine
(Guglielmo da Baskervilla)
Preface
The motto of this book is quoted from "II Nome della Rosa" by U mberto
Eco. The English translation reads "Books are not made to be believed,
but to be subjected to inquiry". The veracity of this statement, which not
only holds for books but also for scientific papers in general, seems trivial.
Unfortunately, however, the reality often turns out differently. We hope
that our book will be subjected to a serious inquiry and that it may lead to
many fruitful discussions. We would certainly appreciate receiving readers'
reactions on possible faults or mistaken starting points.
In writing the book we aimed at a unified and critical account of the
fundamental aspects of liquid crystals. Instead of attempting to compile the
latest results and cover the field of liquid crystals in the widest possible
sense, we concentrate on and discuss the assumptions made in developing
theories - and hence in analyzing experimental data - bearing in mind Ein
stein's dictum "Er8t die Theone entscheidet daruber, was beobachtet werden
kann" (Only the theory decides on what can be observed). In order to facil
itate the study of the book we have avoided intimidating mathematics. The
only unfamiliar mathematical tool may be tensor analysis, which we felt was
essential for a clear presentation. For the reader's convenience, however, we
have incorporated a simple introduction to this subject.
The book has been divided into four parts. Part I about liquid crystals
in general is quite descriptive in character. Part II deals with the macro
scopic continuum theory of liquid crystals. In particular we present a sys
tematic development of the theory starting from a tensorial point of view,
thus emphasizing the symmetry of the various phases. Part III is mainly de
voted to a discussion of those experimental techniques that provide relevant
microscopic information on the orientational behaviour of liquid crystals.
Much attention is paid to the interpretation of experimental data. Part IV
discusses the theory of the various phases and their attendant phase tran
sitions, both from a Landau and from a molecular-statistical point of view.
The merits of the molecular approach are critically examined. For the sake
of clarity we have simplified the existing models as far as possible, thus
hoping to facilitate a better understanding of the theory.
Finally we wish to express our sincere appreciation to M.J.R. Straat
man for her invaluable support in typing and organizing this text. We also
VII
wish to thank J.F.M. Wieland for making the drawings. We greatly ben
efited from the comments of S.J. Picken, who read the entire manuscript
and improved on our English. Finally our thanks go to C.A.M. Govers, E.F.
Gramsbergen, B.C.H. Krutzen and 1. Longa for valuable discussions and
comments on parts of the book. It is clear, however, that we remain entirely
responsible for the final contents.
October 1987 G. Veriogen, W.H. de leu
VIII
Contents
Part I MESOMORPHIC BEHAVIOUR
1. Introduction................................................. 3
1.1 Mesomorphic Behaviour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Mesogenic Compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Classification of the Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2. Nematic Liquid Crystals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1 Nematics Proper. . ....... .... .... ... .... ... .. ... .... .. . . . 20
2.2 Chiral Nematics.. ... .. .. .. ... ........ ... .... ... .. . . . ..... 25
3. Smectic Liquid Crystals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Broken Symmetry and the Organization of Smectics .. .. .. 29
3.2 Smectics with Liquid Layers..... ....... ....... . .. . ... . ... 33
3.2.1 Smectics A. ....... ........ .. .. .. . .... .. .. . . ... .. .. 35
3.2.2 Smectics C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Smectics with Bond-Orientational Order. . . . . . . . . . . . . . . . . . 41
3.4 Smectics with Ordered Layers........ .. ..... .. .... . . . .. .. 44
4. Other Liquid Crystalline Systems... . . . . . . . . . . . . . . . . . . . . . . 48
4.1 Cubic Thermotropic Mesophases. . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Mesophases of Disc-Like Molecules. . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Liquid Crystalline Polymers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3.1 Liquid Crystalline Main-Chain Polymers.. .... .. .. . 53
4.3.2 Liquid Crystalline Side-Chain Polymers... ... ...... 55
4.4 Lyotropic Liquid Crystals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Part II CONTINUUM THEORY
5. Static Continuum Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1 Cartesian Tensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
IX
5.2 Macroscopic Order Parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3 The Frank Free Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.4 General Properties of the Director Field. . . . . . . . . . . . . . . . . . 82
5.5 Appendix................................................ 86
6. Effects of External Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.1 Interaction Between Applied Fields and Director Fields. .. 89
6.2 Frederiks Transitions... ... . ...... .. .. ..... .. ... .. . ... .... 92
6.3 The Cholesteric-Nematic Transition....................... 101
6.4 Elastic Constants and Molecular Structure. . . . . . . . . . . . . . . . 103
7. Applications of Continuum Theory....................... 106
7.1 Disclinations............................................. 106
7.1.1 The Axial Disclination Line................ ........ 108
7.1.2 The Perpendicular Disclination Line. .. . .. . ... .. .. . 112
7.2 Fluctuations in the Nematic Phase... ....... ........ ..... . 114
7.3 Light Scattering by Nematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.4 Optical Properties of Chiral Nematics . . . . . . . . . . . . . . . . . . . . 125
7.4.1 Introduction....................................... 125
7.4.2 General Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.5 Correlations in the Smectic A Phase. ... .. ... .... . .. ... .. . 134
8. Fluid Dynamics of Nematics............................... 137
8.1 Fluid Dynamics of Isotropic Liquids. . . . . . . . . . . . . . . . . . . . . . 137
8.2 Nematodynamics......................................... 140
8.3 Viscosity Measurements..... ....... .. ...... ... .. . . .. ..... 147
8.4 Electrohydrodynamic Instabilities. . . . . . . . . . . . . . . . . . . . . . . . . 153
Part III ORIENTATIONAL ORDER
AND ANISOTROPIC PROPERTIES
9. Orientational Order... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
9.1 Microscopic Order Parameters... ..... ... .. .. . .. . ... . ... .. 167
9.2 Magnetic Anisotropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
9.3 Nuclear Magnetic Resonance. ....... ... .. .. . .. ... .. . ..... 176
9.4 Polarized Raman Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
9.5 X-Ray Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
10. Anisotropic Physical Properties.. .... .. .. .. . .. .. . .. . .. .. . . 190
10.1 The Refractive Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
x
10.2 The Dielectric Permittivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
10.3 Transport Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
10.3.1 Mass Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
10.3.2 Electrical Conduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 204
11. Dynamic Behaviour of the Molecules.................... . 207
11.1 Neutron Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
11.2 Nuclear Magnetic Resonance and Relaxation..... ........ 209
11.3 Dielectric Relaxation..... ....................... ..... .. . 214
Part IV LIQUID CRYSTALLINE PHASES
AND PHASE TRANSITIONS
12. Landau Theory of Liquid Crystalline Phases............. 221
12.1 The Basic Ideas of Landau Theory...................... 221
12.2 The Nematic-Isotropic Transition........ ....... ........ . 224
12.3 Fluctuations in the Isotropic Phase. . . . . . . . . . . . . . . . . . . . . . 231
12.4 The Smectic-Nematic Transition. . . . . . . . . . . . . . . . . . . . . . . . . 238
13. Molecular Statistical Theory of the Nematic Phase... . . 245
13.1 Introduction to the Theory of Simple Liquids..... ....... 245
13.2 The Equation of State of Nematics ...................... 251
13.3 The Onsager Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
13.4 The Maier-Saupe Approach............................. 271
13.5 Theory of the Chiral Nematic Phase..................... 276
13.6 On the Relevance of Molecular Models. . . . . . . . . . . . . . . . . . . 280
14. Molecular Statistical Theory of the Smectic Phases..... 283
14.1 Theory of the Smectic A-Nematic Transition.. ........ ... 283
14.1.1 The Meyer-Lubensky Model. . . . . . . . . . . . . . . . . . . . . 284
14.1.2 The Kobayashi-McMillan Model................. 292
14.2 Theory of the Smectic C Phase.......................... 298
14.3 Theory of the Chiral Smectic C Phase................... 304
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Index of Compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
XI