Handbook of Liquid Crystals, Volume 2A: Low Molecular Weight Liquid Crystals I

D. Demus, J. Goodby, G. W. Gray, H.-W. SDiess. V. Vill I Handbook of Liquid Crystals 8WILEY-VCH Handbook of Liquid ...

Author: Dietrich Demus | John W. Goodby | George W. Gray | Hans-Wolfgang Spiess | Volkmar Vill

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

Handbook of Liquid Crystals

8WILEY-VCH

Handbook of Liquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill

VOl. 1: Fundamentals Vol. 2 A: Low Molecular Weight Liquid Crystals I Vol. 2 B: Low Molecular Weight Liquid Crystals I1 VOl. 3 : High Molecular Weight Liquid Crystals

Further title of interest:

J. L. Serrano: Metallomesogens ISBN 3-527-29296-9

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

Handbook of Liquid Crystals Vol. 2 A: Low Molecular Weight Liquid Crystals I

6BWILEY-VCH

Weinheim New York Chichester Brisbane Singapore Toronto

Prof. Dietrich Demus Veilchenweg 23 061 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 BH15 1TD 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 20146 Hamburg Germany

This book was carefully produced. Nevertheless, authors, editors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, 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:

Handbook of liquid crystals / D. Demus .. . - Weinheim ; New York ; Chichester ; Brisbane ; Singapore ; Toronto : Wiley-VCH ISBN 3-527-29502-X Vol. 2A. Low molecular weight liquid crystals. - 1. - (1998) ISBN 3-527-2927 1-3

0 WILEY-VCH Verlag GmbH. D-60469 Weinheim (Federal Republic of Germany), 1998 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 in any form - by photoprinting, microfilm, or any other means - nor transmitted or translated into machine language 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 and Printing: Fa. Konrad Triltsch Druck- und Verlagsanstalt GmbH, D-97070 Wurzburg. Bookbinding: Wilhelm Osswald & Co., D-67433 Neustadt Printed in the Federal Republic of Germany.

The Editors D. Demus

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 1 he was a member of the International Planning and Steering Commitee of the International Liquid Crystal Conferences, and was a non-executive director of the International Liquid Crystal Society. Since 1994 he i s active as an Scientific Consultant in Halle. He has published over 310 scientific papers and 7 hooks and he holds 170 patients.

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 Society.

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 Society (1987), Commander of the Most Excellent Order ofthe British Empire (199l), and Gold Medallist and Kyoto Prize Laureate in Advanced Technology (1 995). 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 company 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 Frankfurmain, 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, Miinster and Bayreuth he was appointed Director 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 gorup of J. Thiem in 1990. He is currently appointed at the University of Hamburg, 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 LandoltBornstein series Liquid Crystals.

List of Contributors Volume 2A, Low Molecular Weight Crystals I

Bahadur, B. (IJI:3.3-3.4) Displays Center Rockwell Collins Inc. 400 Collins Road NE Ceder Rapids, IA 52498 USA Blinc, R.; Musevic, I. (111:2.6) J. Stefan Institute University of Ljubljana Jamova 39 61 11 1 Ljubljana Slovenia Booth, C. J. (IV: 1) Sharp Labs. of Europe Ltd. Edmund Halley Road Oxford Science Park Oxford OX4 4GA U.K. Coates, D. (V:3) Merck Ltd. West Quay Road Poole, BH15 1HX U.K. Coles, H. J. (IV:2) University of Southampton Dept. of Physics and Astronomy Liquid Crystal Group Highfield, Southampton SO17 IBJ U.K.

Goodby, J. W. (I and V:l) School of Chemistry University of Hull Hull, HU6 7RX U.K. Guillon, D. (11) IPCMS MatCriaux Organiques 23, rue de Loess 67037 Strasbourg Cedex France Hirschmann, H.; Reiffenrath, V. (111:3.1) Merck KGaA LC FO/P Frankfurter StraBe 250 6427 1 Darmstadt Germany Huang, C. C. (V:2) University of Minnesota Dept. of Physics Minneapolis, MN 55455 USA Kaneko, E. (111:3.2) Hitachi Research Laboratory Hitachi Ltd. 1-1, Ohmika, 7-chome Hitachi-shi Ibaraki-ken, 3 19- 12 Japan

VIII

List of Contributors

Kneppe, H.; Schneider, F. (111:2.5) Institut f. Physikal. Chemie Universitat Siegen 57068 Siegen Germany Kresse, H. (111:2.2) Martin-Luther-Universitat Halle-Wittenberg Fachbereich Chemie Institut f. Physikalische Chemie Muhlpforte 1 06108 Halle (Saale) Germany

Pelzl, G. (111:2.4) Fachbereich Chemie Institut f. Physikalische Chemie Muhlpforte 1 06108 Halle (Saale) Germany Stannarius, R. (III:2.1 und 111:2.3) Universitat Leipzig LinnCstraBe 5 04 103 Leipzig Germany Toyne, K. J. (111: 1) The University of Hull Liquid Crystals & Advanced Organic Materials Research Group Hull HU6 7RX U.K.

Outline Volume 1

Chapter I: Introduction and Historical Development . . . . . . . . . . . . . . . . . . . 1 George W Gray Chapter 11: Guide to the Nomenclature and Classification of Liquid Crystals . . . . . 17 John W Goodby and George W Gray Chapter 111: Theory of the Liquid Crystalline State . . . . . . . . . . . . . . . . . . . 25 1 25 Continuum Theory for Liquid Crystals . . . . . . . . . . . . . . . . . . . . Frank M . Leslie Molecular Theories of Liquid Crystals . . . . . . . . . . . . . . . . . . . . 40 2 M . A. Osipov 3 Molecular Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Mark R. Wilson Chapter I V General Synthetic Strategies . . . . . . . . . . . . . . . . . . . . . . . . Thies Thiemann and Volkmar Vill

87

Chapter V: Symmetry and Chirality in Liquid Crystals. . . . . . . . . . . . . . . . . 1 15 John W Goodby Chapter VI: Chemical Structure and Mesogenic Properties . . . . . . . . . . . . . . 133 Dietrich Demus Chapter VII: Physical Properties . . . . . . . . . . . . . Tensor Properties of Anisotropic Materials . 1 David Dunmur and Kazuhisa Toriyama Magnetic Properties of Liquid Crystals . . . 2 David Dunmur and Kazuhisa Toriyamu Optical Properties . . . . . . . . . . . . . . . 3 David Dunmur and Kazuhisa Toriyama Dielectric Properties . . . . . . . . . . . . . . 4 David Dunmur and Kazuhisa Toriyumu 5 Elastic Properties. . . . . . . . . . . . . . . . David Dunmur and Kazuhisa Toriyama 6 Phase Transitions. . . . . . . . . . . . . . . .

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

189 . . . . . . . . . . . . . . . . 189

. . . . . . . . . . . . . . . . 204 . . . . . . . . . . . . . . .

2 15

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

23 1

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

253

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

28 1

X

Outline

6.1 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.3 6.4 7

8 9

10 11 12 13

Phase Transitions Theories . . . . . . . . . . . . . . . . . . . . . . . . . . Philippe Barois Experimental Methods and Typical Results . . . . . . . . . . . . . . . . Thermal Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jan Thoen Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wolfgang Wedler Metabolemeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wolfgang Wedler High Pressure Investigations . . . . . . . . . . . . . . . . . . . . . . . . . P. Pollmann Fluctuations and Liquid Crystal Phase Transitions . . . . . . . . . . . . F! E . Cladis Re-entrant Phase Transitions in Liquid Crystals . . . . . . . . . . . . . . F! E . Cladis Defects and Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y Bouligand Flow Phenomena and Viscosity . . . . . . . . . . . . . . . . . . . . . . . Frank Schneider and Herbert Kneppe Behavior of Liquid Crystals in Electric and Magnetic Fields . . . . . . . Lev M. Blinov Surface Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Blandine Je'rdme Ultrasonic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Olga A . Kapustina Nonlinear Optical Properties of Liquid Crystals . . . . . . . . . . . . . . P. Palm-Mu hora y Diffusion in Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . i? Noack

281

. 310 310 334 350 355

. 379 . 391 406 454

. 477 535 549

. 569 582

Chapter VIII: Characterization Methods . . . . . . . . . . . . . . . . . . . . . . . . 595 1 Magnetic Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 Claudia Schmidt and Hans Wolfgang Spiess X-Ray Characterization of Liquid Crystals: Instrumentation . . . . . . . . 619 2 Richard H . Templer Structural Studies of Liquid Crystals by X-ray Diffraction . . . . . . . . . 635 3 John M . Seddon 4 Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680 Robert M . Richardson 699 Light Scattering from Liquid Crystals . . . . . . . . . . . . . . . . . . . . 5 Helen E Gleeson Brillouin Scattering from Liquid Crystals . . . . . . . . . . . . . . . . . . 719 6 Helen i? Gleeson 727 Mossbauer Studies of Liquid Crystals . . . . . . . . . . . . . . . . . . . . 7 Helen E Gleeson

Outline

XI

Chapter IX: Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 1 Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 Ian C. Sage 2 Nondisplay Applications of Liquid Crystals . . . . . . . . . . . . . . . . . 763 WilliamA . Crossland and Timothy D . Wilkinson 823 3 Thermography Using Liquid Crystals . . . . . . . . . . . . . . . . . . . . Helen E Gleeson 4 Liquid Crystals as Solvents for Spectroscopic, Chemical Reaction. and Gas Chromatographic Applications . . . . . . . . . . . . . 839 William J . Leigh and Mark S. Workentin Index Volume 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

897

Volume 2 A Part I: Calamitic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

Chapter I: Phase Structures of Calamitic Liquid Crystals . . . . . . . . . . . . . . . . . 3 John W Goodby Chapter 11: Phase Transitions in Rod-Like Liquid Crystals . . . . . . . . . . . . . . . 23 Daniel Guillon Chapter 111: Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . 47 1 Synthesis of Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . 47 Kenneth J . Toyne 2 Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Elastic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . . 60 2.1 Ralf Stannarius Dielectric Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . 91 2.2 Horst Kresse Diamagnetic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . 113 2.3 Ralf Stannarius Optical Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . 128 2.4 Gerhard Pelzl 2.5 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Herbert Kneppe and Frank Schneider 2.6 Dynamic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . 170 R. Blinc and I . MuSevic' Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 199 TN, STN Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 3.1 Harald Hirschmann and Volker Reiffenrath Active Matrix Addressed Displays . . . . . . . . . . . . . . . . . . . . . . 230 3.2 Eiji Kaneko

XI1 3.3 3.4

Outline

Dynamic Scattering . . . . . . . . Birendra Bahadur Guest-Host Effect . . . . . . . . . Birendra Bahadur

. . . . . . . . . . . . . . . . . . . . . 243 . . . . . . . . . . . . . . . . . . . . . 257

Chapter IV. Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . 303 1 The Synthesis of Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . 303 Christopher J. Booth 2 Chiral Nematics: Physical Properties and Applications . . . . . . . . . . . 335 Harry Coles Chapter V: Non-Chiral Smectic Liquid Crystals . . . . . . . . . . , . . . . . . . . . 41 1 1 Synthesis of Non-Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . 41 1 John W: Goodby 2 Physical Properties of Non-Chiral Smectic Liquid Crystals. . . . . . . . . 441 C. C. Huang Nonchiral Smectic Liquid Crystals - Applications . . . . . . . . . . . . . 470 3 David Coates

Volume 2B Part 2: Discotic Liquid Crystals. . .

. . . . . . . . . . . . . . . . . , . . . . . . . . 491

Chapter VI: Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . 493 1 Synthesis of Chiral Smectic Liquid Crystals. . . . . . . . . . . . . . . . . 493 Stephen M. Kelly 2 Ferroelectric Liquid Crystals. . . . . . . . . . . . . . . . . . . . . . . . . 515 Sven 7: Lagenvall 3 Antiferroelectric Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . 665 Kouichi Miyachi and Atsuo Fukuda Chapter VII: Synthesis and Structural Features. . . . . . . . Andrew N. Cammidge and Richard J. Bushby

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

Chapter VIII: Discotic Liquid Crystals: Their Structures and Physical Properties

S. Chandrasekhar

693

. . . 749

Chapter IX: Applicable Properties of Columnar Discotic Liquid Crystals . . . . . Neville Boden and Bijou Movaghar

. . 781

Outline

XI11

Part 3: Non-Conventional Liquid-Crystalline Materials . . . . . . . . . . . . . . . . 799 Chapter X: Liquid Crystal Dimers and Oligomers . . . . . . . . . . . . . . . . . . .801 Corrie 7: Imrie and Geoflrey R. Luckhurst Chapter XI: Laterally Substituted and Swallow-Tailed Liquid Crystals . . . . . . . . 835 Wolfgang Weissjlog Chapter XII: Phasmids and Polycatenar Mesogens . . . . . . . . . . . . . . . . . . . 865 Huu-Tinh Nguyen. Christian Destrade. and Jacques Malthite Chapter XIII: Thermotropic Cubic Phases . . . . . . . . . . . . . . . . . . . . . . . Siegmar Diele and Petra Goring

887

Chapter XIV: Metal-containing Liquid Crystals . . . . . . . . . . . . . . . . . . . . Anne Marie Giroud-Godquin

901

Chapter X V Biaxial Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . B. K. Sadashiva

933

Chapter XVI: Charge-Transfer Systems . . . . . . . . . . . . . . . . . . . . . . . . Klaus Praefcke and D . Singer

945

Chapter XVII: Hydrogen-Bonded Systems . . . . . . . . . . . . . . . . . . . . . . . Takashi Kato

969

Chapter XVIII: Chromonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . John Lydon

981

Index Volumes 2 A and 2 B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1009

Volume 3 Part 1: Main-Chain Therrnotropic Liquid-Crystalline Polymers . . . . . . . . . . . . . 1 Chapter I: Synthesis. Structure and Properties . . . . . . . . . . . . . . . . . . . . . 1 Aromatic Main Chain Liquid Crystalline Polymers . . . . . . . . . . . Andreas Greiner and Hans- Werner Schmidt Main Chain Liquid Crystalline Semiflexible Polymers . . . . . . . . . . 2 Emo Chiellini and Michele Laus Combined Liquid Crystalline Main-ChaidSide-Chain Polymers . . . . . 3 Rudo2f Zentel Block Copolymers Containing Liquid Crystalline Segments . . . . . . . 4 Guoping Ma0 and Christopher K. Ober

. 3 . . .3 . . 26

. . 52 . . 66

XIV

Outline

Chapter 11: Defects and Textures in Nematic Main-Chain Liquid Crystalline Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Claudine Noel

93

Part 2: Side-Group Thermotropic Liquid-Crystalline Polymers . . . . . . . . . . . . 121 Chapter 111: Molecular Engineering of Side Chain Liquid Crystalline Polymers by Living Polymerizations . . . . . . . . . . . . . . . . . . . . . . . . . . Coleen Pugh and Alan L. Kiste

123

Chapter I V Behavior and Properties of Side Group Thermotropic Liquid Crystal Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jean-Claude Dubois, Pierre Le Barny, Monique Mauzac, and Claudine Noel

207

Chapter V Physical Properties of Liquid Crystalline Elastomers . . . . . . . . . . . 277 Helmut R. Brand and Heino Finkelmann Part 3: Amphiphilic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . .

303

Chapter VI: Amphotropic Liquid Crystals . . . Dieter Blunk, Klaus Praefcke and Volkmar Ell

305

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

Chapter VII: Lyotropic Surfactant Liquid Crystals . . . . . . . . . . . . . . . . . . . 341 C. Fairhurst, S. Fuller, J. Gray, M. C. Holmes, G. J. 7: Eddy Chapter VIII: Living Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Siegfried Hoffmann

393

Chapter IX: Cellulosic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . Peter Zugenmaier

45 1

Index Volumes 1 - 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

483

Contents Volume 2 A

Part I: Calamitic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . .

1

Chapter I: Phase Structures of Calamitic Liquid Crystals . . . . . . . . . . . . . . 3 John W Goodby 1

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

3

2

Melting Processes of Calamitic Thermotropic Liquid Crystals . . . . . . . . .

4

3 3.1 3.2 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5

Structures of Calamitic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . 6 The Nematic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Structures of Smectic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . 7 The Structures of the Orthogonal Smectic Phases . . . . . . . . . . . . . . . 7 Structure of the Smectic A Phase . . . . . . . . . . . . . . . . . . . . . . . . 7 Structure in the Hexatic B Phase . . . . . . . . . . . . . . . . . . . . . . . . 10 Structure of the Crystal B Phase . . . . . . . . . . . . . . . . . . . . . . . . 10 Structure of Crystal E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Structures of the Tilted Smectic Phases . . . . . . . . . . . . . . . . . . . . . 13 Structure of the Smectic C Phase . . . . . . . . . . . . . . . . . . . . . . . . 13 Structure of the Smectic I Phase . . . . . . . . . . . . . . . . . . . . . . . . 16 Structure of the Smectic F Phase . . . . . . . . . . . . . . . . . . . . . . . . 16 Structures of the Crystal J and G Phases . . . . . . . . . . . . . . . . . . . . 17 Structures of the Crystal H and K Phases . . . . . . . . . . . . . . . . . . . . 18

4

Long- and Short-Range Order . . . . . . . . . . . . . . . . . . . . . . . . . .

18

5

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

20

Chapter 11: Phase Transitions in Rod-Like Liquid Crystals . . . . . . . . . . . . . 23 Daniel Guillon 1

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

2 2.1 2.2 2.3 2.4

Isotropic-Nematic (Iso-N) Transition . . . . . . . . . . . . . . . . . . . . . 23 Brief Summary of the Landau-de Gennes Model . . . . . . . . . . . . . . . . 23 Magnetic Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Deviations from the Landau-de Gennes Model . . . . . . . . . . . . . . . . . 25

23

XVI

Contents

3 3.1 3.2

Nematic-Smectic A (N-SmA) Transition . . . . . . . . . . . . . . . . . . . . 26 The McMillan-de Gennes Approach . . . . . . . . . . . . . . . . . . . . . . 26 Critical Phenomena: Experimental Situation . . . . . . . . . . . . . . . . . . 26

4 4.1 4.2 4.3 4.4 4.5 4.6

Smectic A-Smectic C (SmA-SmC) Transition . . . . . . . . . . . . . . . . . General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Critical Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Smectic A-Smectic C* (SmA-SmC*) Transition . . . . . . . . . . . . . . . . The Nematic-Smectic A-Smectic C (NAC) Multicritical Point . . . . . . . . SmA-SmC Transition in Thin Films . . . . . . . . . . . . . . . . . . . . . .

5 5.1 5.2

Hexatic B to Smectic A (SmBhex-SmA) transition . . . . . . . . . . . . . . 36 General Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 SmBhex-SmA Transition in Thin Films . . . . . . . . . . . . . . . . . . . . 37

6 6.1 6.2 6.3

Induced Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Mechanically Induced SmA-SmC Transition . . . . . . . . . . . . . . . . . . 38 Electrically Induced Transitions . . . . . . . . . . . . . . . . . . . . . . . . 39 Photochemically Induced Transitions . . . . . . . . . . . . . . . . . . . . . . 39

7 7.1 7.2 7.3 7.4

Other Transitions . . . . . . . . . . . . . . . . . Smectic C to Smectic I (SmC-SmI) Transition . Smectic C to Smectic F (SmC-SmF) Transition Smectic F to Smectic I (SmF-SmI) Transition . Smectic F to Smectic Crystalline G (SmF-SmG)

8

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

43

Chapter 111: Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . .

47

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12

. . . .

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29 29 30 30 32 33 35

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. . . . . . . . . . . . 41 . . . . . . . . . . . . . 41 . . . . . . . . . . . . . 41 . . . . . . . . . . . . . 42 Transition . . . . . . . . . . 42

Synthesis of Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . 47 Kenneth J . Toyne 47 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benzene. Biphenyl and Terphenyl Systems . . . . . . . . . . . . . . . . . . . 48 Cyclohexane Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 1,4-Disubstituted-bicyclo[2.2.2]octanes . . . . . . . . . . . . . . . . . . . . 50 2,5.Disubstituted.l. 3.dioxanes . . . . . . . . . . . . . . . . . . . . . . . . . 51 2,5.Disubstitute d.pyridines . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2,5.Disubstituted.pyrimidines . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3,6.Disubstituted.pyridazines . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Naphthalene systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Unusual Core Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Ester Linkages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Lateral Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Contents

1.13 1.14 1.15

XVII

4-c-(trans-4-Alkylcyclohexyl)-l-alkyl-r- 1.cyanocyclohexanes . . . . . . . . . 55 Terminal Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Elastic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . . . 60 Ralf Stannarius 2.1.1 Introduction to Elastic Theory . . . . . . . . . . . . . . . . . . . . . . . . . 60 63 2.1.2 Measurement of Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . 2.1.2.1 Frkedericksz Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.1.2.2 Light Scattering Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.1.2.3 Other Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.1.3 Experimental Elastic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.1.4 MBBA and n-CB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.1.5 ‘Surface-like’ Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.1.6 Theory of Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 2.1.7 Biaxial Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 84 2.1.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1

2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.3 2.3.1 2.3.2 2.3.2.1 2.3.2.2 2.3.2.3 2.3.2.4 2.3.2.5 2.3.3 2.3.4 2.3.5 2.3.6 2.4 2.4.1 2.4.2

Dielectric Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . Horst Kresse Rod-like Molecules in the Isotopic State . . . . . . . . . . . . . . . . . . . . Static Dielectric Constants of Nematic Samples . . . . . . . . . . . . . . . The Nre Phenomenon and the Dipolar Correlation . . . . . . . . . . . . . . Dielectric Relaxation in Nematic Phases . . . . . . . . . . . . . . . . . . . . Dielectric Behavior of Nematic Mixtures . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diamagnetic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . Ralf Stannarius Magnetic Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement of Diamagnetic Properties . . . . . . . . . . . . . . . . . . Faraday-Curie Balance Method . . . . . . . . . . . . . . . . . . . . . . . . Supraconducting Quantum Interference Devices Measurements . . . . . . NMR Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magneto-electric Method . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanical Torque Measurements . . . . . . . . . . . . . . . . . . . . . . . Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Increment System for Diamagnetic Anisotropies . . . . . . . . . . . . . . Application of Diamagnetic Properties . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 91 91

. 92 . 98 99 102 109

. 113 113

. 116 116

. 116 117 117 118 118 . 124 125 126

Optical Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . . 128 Gerhurd Pelzl Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

XVIII 2.4.3 2.4.4 2.4.5 2.4.6 2.4.7 2.4.8 2.4.9 2.5 2.5.1 2.5.2 2.5.2.1 2.5.2.2 2.5.2.3 2.5.2.4 2.5.2.5 2.5.3 2.5.3.1 2.5.3.2 2.5.3.3 2.5.3.4 2.5.4 2.5.4.1 2.5.4.2 2.5.4.3 2.5.5 2.6 2.6.1 2.6.2 2.6.3 2.6.4 2.6.5 2.6.6 2.6.7 2.6.8 2.6.9 2.6.10 2.6.11 2.6.12 2.6.13 2.6.14

Contents

Temperature Dependence of Birefringence and Refractive Indices . . . . . . 132 Dispersion of ne. no and An . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Refractive Indices of Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . 135 Birefringence in Homologous Series . . . . . . . . . . . . . . . . . . . . . 136 Determination of Molecular Polarizability Anisotropy and Orientational Order from Birefringence Data . . . . . . . . . . . . . . . . . . . . . . . . 136 Relationships between Birefringence and Molecular Structure . . . . . . . . 137 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Herbert Kneppe and Frank Schneider Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determination of Shear Viscosity Coefficients . . . . . . . . . . . . . . . . General Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determination of Rotational Viscosity . . . . . . . . . . . . . . . . . . . . . General Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Methods with Permanent Director Rotation . . . . . . . . . . Relaxation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Leslie Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determination from Shear and Rotational Viscosity Coefficients . . . . . . . Determination by Means of Light Scattering . . . . . . . . . . . . . . . . . Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dynamic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . R. Blinc and Z. MuSevic' Quasielastic Light Scattering in Nematics . . . . . . . . . . . . . . . . . . . Nuclear Magnetic Resonance in Nematics . . . . . . . . . . . . . . . . . . . Quasielectric Light Scattering and Order Fluctuations in the Isotropic Phase Nuclear Magnetic Resonance and Order Fluctuations in the Isotropic Phase . Quasielastic Light Scattering and Orientational Fluctuations below Tc . . . Nuclear Magnetic Resonance and Orientational Fluctuations below Tc . . . . Optical Ken Effect and Transient Laser-Induced Molecular Reorientation . . Dielectric Relaxation in Nematics . . . . . . . . . . . . . . . . . . . . . . . Pretransitional Dynamics Near the Nematic-Smectic A Transition . . . . . . Dynamics of Nematics in Micro-Droplets and Micro-Cylinders . . . . . . . Pretransitional Effects in Confined Geometry . . . . . . . . . . . . . . . . . Dynamics of Randomly Constrained Nematics . . . . . . . . . . . . . . . . Other Observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

142 142 142 142 143 147 150 150 155 155 156 157 160 165 165 166 167 167 170 170 173 174 175 177 177 181 182 183 184 188 189 190 191

Contents

3 3.1 3.1.1 3.1.2 3.1.2.1 3.1.2.2 3.1.2.3 3.1.3 3.1.3.1 3 .1.3.2 3.1.3.3 3.1.3.4 3.1.4 3.1.4.1 3.1.4.2 3.1.4.3 3.1.4.4 3.1.4.5 3.1.4.6 3.1.4.7 3.1.4.8 3.1 .5 3.1 .5. 1 3.1.5.2 3.1.5.3 3.1.5.4 3.1.6 3.2 3.2.1 3.2.1.1 3.2.1.2 3.2.1.3 3.2.1.4 3.2.1.5 3.2.2 3.2.3 3.2.4 3.2.4.1 3.2.4.2 3.2.5 3.2.6

XIX

Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i99 TN. STN Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Harald Hirschmunn and Volker Reiffenruth Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Twisted Nematic Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 Configuration and Operation Principles of Twisted Nematic Displays . . . . 200 Optical Properties of the Unactivated State . . . . . . . . . . . . . . . . . . 200 Optical Properties of the Activated State . . . . . . . . . . . . . . . . . . . 202 204 Addressing of Liquid Crystal Displays . . . . . . . . . . . . . . . . . . . . Direct Addressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Passive Matrix Addressing . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 The Improved Alt-Pleshko Addressing Technique . . . . . . . . . . . . . . 207 Generation of Gray Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Supertwisted Nematic Displays . . . . . . . . . . . . . . . . . . . . . . . . 208 Influence of Device and Material Parameters . . . . . . . . . . . . . . . . . 208 Configuration and Transmission of a Supertwisted Nematic Display . . . . . 211 Electro-optical Performance of Supertwisted Nematic Displays . . . . . . . 213 Dynamical Behavior of Twisted Nematic and Supertwisted Nematic Displays 2 13 Color Compensation of STN Displays . . . . . . . . . . . . . . . . . . . . . 215 Viewing Angle and Brightness Enhancement . . . . . . . . . . . . . . . . . 218 218 Color Supertwisted Nematic Displays . . . . . . . . . . . . . . . . . . . . . Fast Responding Supertwisted Nematic Liquid Crystal Displays . . . . . . . 219 Liquid Crystal Materials for Twisted Nematic and Supertwisted Nematic 220 Display Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials with High Optimal Anisotropy . . . . . . . . . . . . . . . . . . . 221 Materials with Positive Dielectric Anisotropy . . . . . . . . . . . . . . . . . 221 Materials for the Adjustment of the Elastic Constant Ratio K33/Kll . . . . 225 226 Dielectric Neutral Basic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References 227 Active Matrix Addressed Displays . . . . . . . . . . . . . . . . . . . . . . 230 Eiji Kuneko Thin Film Diode and Metal-Insulator-Metal Matrix Address . . . . . . . . . 230 230 Diode Ring Matrix Address . . . . . . . . . . . . . . . . . . . . . . . . . . Back-to-back Diode Matrix Address . . . . . . . . . . . . . . . . . . . . . . 230 Two Branch Diode Matrix Address . . . . . . . . . . . . . . . . . . . . . . 231 SiNx Thin Film Diode Matrix Address . . . . . . . . . . . . . . . . . . . . 231 232 Metal-lnsulator-Metal Matrix Address . . . . . . . . . . . . . . . . . . . . CdSe Thin Film Transistor Switch Matrix Address . . . . . . . . . . . . . . 233 a-Si Thin Film Transistor Switch Matrix Address . . . . . . . . . . . . . . . 234 p-Si Thin Film Transistor Switch Matrix Address . . . . . . . . . . . . . . . 237 Solid Phase Crystallization Method . . . . . . . . . . . . . . . . . . . . . . 238 Laser Recrystallization Method . . . . . . . . . . . . . . . . . . . . . . . . 238 Metal-oxide Semiconductor Transistor Switch Matrix Address . . . . . . . . 239 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

xx 3.3 3.3.1 3.3.2 3.3.2.1 3.3.2.2 3.3.2.3 3.3.3 3.3.4 3.3.4.1 3.3.4.2 3.3.5 3.3.6 3.3.6.1 3.3.6.2 3.3.6.3 3.3.6.4 3.3.6.5 3.3.6.6 3.3.7 3.4 3.4.1 3.4.2 3.4.2.1 3.4.3 3.4.4 3.4.4.1 3.4.4.2 3.4.5 3.4.6 3.4.6.1 3.4.6.2 3.4.6.3 3.4.6.4 3.4.7 3.4.7.1 3.4.7.2 3.4.8 3.4.8.1

Contents

Dynamic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Birendra Bahadur Introduction and Cell Designing . . . . . . . . . . . . . . . . . . . . . . . . Experimental Observations at DC (Direct Current) and Low Frequency AC (Alternating Current) Fields . . . . . . . . . . . . . . . . . . . . . . . . . . Homogeneously Aligned Nematic Regime . . . . . . . . . . . . . . . . . . Williams Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dynamic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observations at High Frequency AC Field . . . . . . . . . . . . . . . . . . Theoretical Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . Carr-Helfrich Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dubois-Violette, de Gennes, and Parodi Model . . . . . . . . . . . . . . . . Dynamic Scattering in Smectic A and Cholesteric Phases . . . . . . . . . . Electrooptical Characteristics and Limitations . . . . . . . . . . . . . . . . Contrast Ratio Versus Voltage, Viewing Angle, Cell Gap, Wavelength, and Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Display Current Versus Voltage, Cell Gap, and Temperature . . . . . . . . . Switching Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of Conductivity, Temperature and Frequency . . . . . . . . . . . . . Addressing of DSM (Dynamic Scattering Mode) LCDs (Liquid Crystal Displays) . . . . . . . . . . . . . . . . . . . . . . . . . . . Limitations of DSM LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

243

Guest-Host Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Birendra Bahadur Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dichroic Dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemical Structure. Photostability. and Molecular Engineering . . . . . . . Cell Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dichroic Parameters and Their Measurement . . . . . . . . . . . . . . . . . Order Parameter and Dichroic Ratio of Dyes . . . . . . . . . . . . . . . . . Absorbance. Order Parameter. and Dichroic Ratio Measurement . . . . . . . Impact of Dye Structure and Liquid Crystal Host on the Physical Properties of a Dichroic Mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical. Electro.Optica1. and Life Parameters . . . . . . . . . . . . . . . . . Luminance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contrast and Contrast Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . Switching Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Life Parameters and Failure Modes . . . . . . . . . . . . . . . . . . . . . . Dichroic Mixture Formulation . . . . . . . . . . . . . . . . . . . . . . . . . Monochrome Mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Black Mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heilmeier Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Threshold Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . .

257

243 244 244 244 246 247 247 248 249 250 251 251 252 253 253 254 254 254

257 259 260 266 268 268 269 271 271 272 272 273 273 274 274 274 275 276

Contents

XXI

3.4.8.2 Effects of Dye Concentration on Electro-optical Parameters . . . . . . . . . 276 3.4.8.3 Effect of Cholesteric Doping . . . . . . . . . . . . . . . . . . . . . . . . . . 278 3.4.8.4 Effect of Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 3.4.8.5 Effect of Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 3.4.8.6 Impact of the Order Parameter . . . . . . . . . . . . . . . . . . . . . . . . . 279 3.4.8.7 Impact of the Host . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 3.4.8.8 Impact of the Polarizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 3.4.8.9 Color Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 3.4.8.10 Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 282 3.4.9 Quarter Wave Plate Dichroic Displays . . . . . . . . . . . . . . . . . . . . . 283 3.4.10 Dye-doped TN Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.11 Phase Change Effect Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . 284 3.4.1 1.1 Threshold Characteristic and Operating Voltage . . . . . . . . . . . . . . . . 286 3.4.1 1.2 Contrast Ratio, Transmission Brightness, and Switching Speed . . . . . . . . 287 289 3.4.1 1.3 Memory or Reminiscent Contrast . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 1.4 Electro-optical Performance vs Temperature . . . . . . . . . . . . . . . . . 291 3.4.1 1.5 Multiplexing Phase Change Dichroic LCDs . . . . . . . . . . . . . . . . . . 291 291 3.4.12 Double Cell Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . 291 3.4.12.1 Double Cell Nematic Dichroic LCD . . . . . . . . . . . . . . . . . . . . . . 3.4.12.2 Double Cell One Pitch Cholesteric LCD . . . . . . . . . . . . . . . . . . . 292 3.4.12.3 Double Cell Phase Change Dichroic LCD . . . . . . . . . . . . . . . . . . . 292 292 3.4.13 Positive Mode Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . . . . 292 3.4.13.1 Positive Mode Heilmeier Cells . . . . . . . . . . . . . . . . . . . . . . . . 3.4.13.2 Positive Mode Dichroic LCDs Using a X 4 Plate . . . . . . . . . . . . . . . 295 3.4.13.3 Positive Mode Double Cell Dichroic LCD . . . . . . . . . . . . . . . . . . 295 3.4.13.4 Positive Mode Dichroic LCDs Using Special Electrode Patterns . . . . . . . 295 3.4.13.5 Positive Mode Phase Change Dichroic LCDs . . . . . . . . . . . . . . . . . 295 3.4.13.6 Dichroic LCDs Using an Admixture of Pleochroic 296 and Negative Dichroic Dyes . . . . . . . . . . . . . . . . . . . . . . . . . . 296 3.4.14 Supertwist Dichroic Effect Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 Ferroelectric Dichroic LCDs 3.4.15 297 3.4.15.1 Devices Using A Single Polarizer . . . . . . . . . . . . . . . . . . . . . . . 297 3.4.15.2 Devices Using No Polarizers . . . . . . . . . . . . . . . . . . . . . . . . . 297 3.4.16 Polymer Dispersed Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . 298 3.4.17 Dichroic Polymer LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 3.4.18 Smectic A Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.19 Fluorescence Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . . . . 299 299 3.4.20 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter I V Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . 1 1.1

303

The Synthesis of Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . 303 Christopher J . Booth Introduction to the Chiral Nematic Phase and its Properties . . . . . . . . . 303

XXII 1.2 1.3 1.3.1 1.4 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5 1.6 1.6.1 1.6.2 1.6.3 1.7 1.7.1 1.7.2 1.7.3 1.74 1.8 1.9 2 2.1 2.2 2.2.1 2.2.1.1 2.2.1.2 2.2.1.3 2.2.1.4 2.2.2 2.2.2.1 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 2.4.2 2.4.3 2.4.4 2.5 2.5.1

Contents

Formulation and Applications of Thermochromic Mixtures . . . . . . . . . . 305 Classification of Chiral Nematic Liquid Crystalline Compounds . . . . . . . 307 Aspects of Molecular Symmetry for Chiral Nematic Phases . . . . . . . . . 308 Cholesteryl and Related Esters . . . . . . . . . . . . . . . . . . . . . . . . . 310 Type I Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . 311 Azobenzenes and Related Mesogens . . . . . . . . . . . . . . . . . . . . . 312 Azomethine (Schiff’s Base) Mesogens . . . . . . . . . . . . . . . . . . . . 313 Stable Phenyl. Biphenyl. Terphenyl and Phenylethylbiphenyl Mesogens . . . 314 (R)-2-(4-Hydroxyphenoxy)-propanoic Acid Derivatives . . . . . . . . . . . 319 Miscellaneous Type I Chiral Nematic Liquid Crystals . . . . . . . . . . . . 323 Type I1 Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . 325 Azomethine Ester Derivatives of (R)-3-Methyladipic Acid . . . . . . . . . . 325 Novel Highly Twisting Phenyl and 2-Pyrimidinylphenyl Esters of (R)-3-Methyladipic Acid . . . . . . . . . . . . . . . . . . . . . . . . . . 326 Chiral Dimeric Mesogens Derived from Lactic Acid or 1.2-Diols . . . . . . 327 Type I11 Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . 327 Tricyclo[4.4.0.03,8]decaneor Twistane Derived Mesogens . . . . . . . . . . 328 Axially Chiral Cyclohexylidene-ethanones . . . . . . . . . . . . . . . . . . 328 Chiral Heterocyclic Mesogens . . . . . . . . . . . . . . . . . . . . . . . . . 330 Chiral Mesogens Derived from Cyclohexane . . . . . . . . . . . . . . . . . 331 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 Chiral Nematics: Physical Properties and Applications . . . . . . . . . . . . Harry Coles Introduction to Chiral Nematics: General Properties . . . . . . . . . . . . . Static Properties of Chiral Nematics . . . . . . . . . . . . . . . . . . . . . . Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Textures and Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical Propagation (Wave Equation Approach) . . . . . . . . . . . . . . . Optical Propagation (‘Bragg’ Reflection Approach) . . . . . . . . . . . . . Pitch Behavior as a Function of Temperature, Pressure, and Composition . . Elastic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuum Theory and Free Energy . . . . . . . . . . . . . . . . . . . . . . Dynamic Properties of Chiral Nematics . . . . . . . . . . . . . . . . . . . . Viscosity Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lehmann Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Macroscopic Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Field-Induced Distortions in Chiral Nematics . . . . . . . . . . . . . . . . . Magnetic Fields Parallel to the Helix Axis . . . . . . . . . . . . . . . . . . Magnetic Fields Normal to the Helix Axis . . . . . . . . . . . . . . . . . . Electric Fields Parallel to the Helix Axis . . . . . . . . . . . . . . . . . . . Electric Fields Normal to the Helix Axis . . . . . . . . . . . . . . . . . . . Applications of Chiral Nematics . . . . . . . . . . . . . . . . . . . . . . . . Optical: Linear and Nonlinear . . . . . . . . . . . . . . . . . . . . . . . . .

335 335 342 342 350 356 362 365 368 369 374 374 377 379 382 382 386 388 391 394 394

Contents

2.5.2 2.5.3 2.5.3.1 2.5.3.2 2.5.3.3 2.6 2.7

XXIII

Thermal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 External Electric Field Effects . . . . . . . . . . . . . . . . . . . . . . . . . 399 400 Long Pitch Systems (p>>A) . . . . . . . . . . . . . . . . . . . . . . . . . . Intermediate Pitch Length Systems (p = A). . . . . . . . . . . . . . . . . . . 401 403 Short Pitch Systems ( p e a ) . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions and the Future . . . . . . . . . . . . . . . . . . . . . . . . . . 404 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

Chapter V. Non-Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . . . . 411 Synthesis of Non-Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . 411 John W Goodby Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 1.1 Template Structures for the Synthesis of Smectogens . . . . . . . . . . . . . 411 1.2 414 1.2.1 Terminal Aliphatic Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . at the End of the Core . . . . . . . . . . . . . . . . . 415 Polar Groups Situated 1.2.2 Functional Groups that Terminate the Core Structure . . . . . . . . . . . . . 417 1.2.3 418 1.2.4 Core Ring Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 1.2.5 Liking Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 1.2.6 Lateral Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Syntheses of Standard Smectic Liquid Crystals . . . . . . . . . . . . . . . . 426 1.3 1.3.1 Synthesis of 4-Alkyl- and 4-alkoxy-4’-cyanophenyls: Interdigitated Smectic A Materials (e.g., 8CB and (80CB) . . . . . . . . . . . . . . . . . 426 1.3.2 Synthesis of 4-Alkyl-4-alkoxybiphenyl-4’-carboxylates: Hexatic 427 Smectic B Materials (e.g., 650BC) . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Synthesis of 4-Alkyloxy-benzylidene-4-alkylanilines: Crystal B and G Materials (e.g., nOms) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 1.3.4 Synthesis of Terephthalylidene-bis-4-alkylanilines: Smectic I. Smectic F. Crystal G and Crystal H Materials (e.g., TBnAs) . . . . . . . . . . . . . . . 428 1.3.5 Synthesis of 4-Alkoxy-phenyl-4-alkoxybenzoates:Smectic C Materials . . . 429 1.3.6 Synthesis of 4-Alkylphenyl-4-alkylbiphenyl-4’-carboxylates:Smectic C. Smectic I. Hexatic Smectic B Materials . . . . . . . . . . . . . . . . . . . . 430 1.3.7 Synthesis of 4-(2-Methylutyl)phenyl-4-alkoxybiphenyl-4’-carboxylates: Smectic C. Smectic I. Smectic F. Crystal J. Crystal K and Crystal G 430 Materials (nOmls. e.g., 80SI) . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.8 Synthesis of 2-(4-n-Alkylphenyl)-5-(4-n-alkoxyoxyphenyl)pyrimidines: Smectic F and Crystal G Materials . . . . . . . . . . . . . . . . . . . . . . 431 1.3.9 Synthesis of 3-Nitro- and 3-Cyano-4-n-alkoxybiphenyl-4‘-carboxylic Acids: Cubic and Smectic C Materials . . . . . . . . . . . . . . . . . . . . 433 1.3.10 Synthesis of bis-[ 1-(4’-Alkylbiphenyl-4-y1) -3-(4-alkylphenyl)propane-l.3-dionato]copper(Il). Smectic Metallomesogens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 Synthesis of Smectic Materials for Applications . . . . . . . . . . . . . . . 435 1.4 1.4.1 Synthesis of Ferroelectric Host Materials . . . . . . . . . . . . . . . . . . . 435 1

XXIV 1.4.2 1.5 1.6

Contents

Synthesis of Antiferroelectric Host Materials . . . . . . . . . . . . . . . . . 437 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

Physical Properties of Non-Chiral Smectic Liquid Crystals . . . . . . . . . C. C. Huang 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Smectic A Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 2.2.1 Macroscopic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 X-ray Characterization of Free-Standing Smectic Films . . . . . . . . . . 2.3 Hexatic Smectic B Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Macroscopic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Thin Hexatic B Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Smectic C Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 2.4.1 Physical Properties near the Smectic A-Smectic C Transition . . . . . . . 2.4.1.1 Bulk Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Macroscopic Behavior of the Smectic C Phase . . . . . . . . . . . . . . . 2.4.2.1 Bulk Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Tilted Hexatic Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Identification of Hexatic Order in Thin Films . . . . . . . . . . . . . . . . 2.5.2 Characterization of Hexatic Order in Thick Films . . . . . . . . . . . . . . 2.5.3 Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 3.1 3.2 3.3 3.3.1 3.3.1.1 3.3.1.2 3.3.2 3.3.2.1 3.3.2.2 3.3.2.3 3.3.3 3.3.3.1 3.3.3.2 3.3.3.3 3.3.3.4 3.3.3.5 3.4 3.5 3.5.1

. 441

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. . .

Nonchiral Smectic Liquid Crystals - Applications . . . . . . . . . . . . . . David Coates Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Smectic Mesogens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laser-Addressed Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reverse Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lasers and Dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Characteristics and Applications . . . . . . . . . . . . . . . . . . . Line Width and Write Speed. . . . . . . . . . . . . . . . . . . . . . . . . . Contrast Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Projection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Color Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Commercial Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermally and Electrically Addressed Displays . . . . . . . . . . . . . . . . Dielectric Reorientation of SmA Phases . . . . . . . . . . . . . . . . . . . . Materials of Negative Dielectric Anisotropy . . . . . . . . . . . . . . . . .

441 443 443 446 447 448 450 452 452 452 457 457 461 461 462 464 464 467 470 470 471 473 473 473 475 476 476 476 477 478 478 478 478 478 478 481 482 482

Contents

3.5.2 3.5.3 3.6 3.6.1 3.6.2 3.6.3 3.7 3.8 3.9 3.10

xxv

Materials of Positive Dielectric Anisotropy . . . . . . . . . . . . . . . . . . 482 A Variable Tilt SmA Device . . . . . . . . . . . . . . . . . . . . . . . . . . 482 Dynamic Scattering in SmA Liquid Crystal Phases . . . . . . . . . . . . . . 483 485 Theoretical Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 Response Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Displays Based on Dynamic Scattering . . . . . . . . . . . . . . . . . . . . 486 Two Frequency Addressed SmA Devices . . . . . . . . . . . . . . . . . . . 486 487 Polymer-Dispersed Smectic Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions 489 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489

XXVI

Contents

Volume 2 B

Part 11: Discotic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . Chapter VI: Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . 1 Synthesis of Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . . Stephen M . Kelly 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Long Pitch Chiral Smectic Liquid Crystals or Dopants . . . . . . . . . . . 1.2 1.2.1 Schiff’s bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Aromatic Esters with Alkyl Branched Alkyl Chains . . . . . . . . . . . . 1.2.3 Aromatic Heterocycles with Alkyl-Branched Alkyl Chains . . . . . . . . . 1.2.4 Esters and Ethers in the Terminal Chain . . . . . . . . . . . . . . . . . . . . 1.2.5 Halogens at the Chiral Center . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.6 Cyclohexyl a-Fluorohexanoates . . . . . . . . . . . . . . . . . . . . . . . . 1.2.7 Gyano Groups at the Chiral Center . . . . . . . . . . . . . . . . . . . . . . 1.2.8 Optically Active Oxiranes and Thiiranes . . . . . . . . . . . . . . . . . . 1.2.9 Optically Active y-Lactones . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.10 Optically Active &Lactones . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.11 Miscellaneous Optically Active Heterocycles . . . . . . . . . . . . . . . . 1.3 Short Pitch Chiral Smectic Liquid Crystals or Dopants . . . . . . . . . . . 1.3.1 Optically Active Terphenyl Diesters . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Optically Active Methyl-Substituted Dioxanes . . . . . . . . . . . . . . . 1.4 Antiferroelectric Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . 1.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7 2.3 2.3.1 2.3.2 2.3.3

491 493

. 493 493

. 495

496

. 497 . 500

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Ferroelectric Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . Sven T Lagerwall Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polar Materials and Effects . . . . . . . . . . . . . . . . . . . . . . . . . . Polar and Nonpolar Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . The Nonpolarity of Liquid Crystals in General . . . . . . . . . . . . . . . . Behavior of Dielectrics in Electric Fields: Classification of Polar Materials . Developments in the Understanding of Polar Effects . . . . . . . . . . . . . The Simplest Description of a Ferroelectric . . . . . . . . . . . . . . . . . . Improper Ferroelectric s . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Piezoelectric Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Necessary Conditions for Macroscopic Polarization in a Material . . . . The Neumann and Curie Principles . . . . . . . . . . . . . . . . . . . . . . Neumann’s Principle Applied to Liquid Crystals . . . . . . . . . . . . . . . The Surface-Stabilized State . . . . . . . . . . . . . . . . . . . . . . . . . .

501 503 503 506 506 508 508 508 509 509 510 510 512 515 515 520 520 522 523 527 531 536 539 541 541 542 544

Contents

2.3.4 2.3.5 2.3.6 2.3.7 2.4 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.4.6 2.4.7 2.4.8 2.4.9 2.5 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 2.5.6 2.5.7 2.5.8 2.5.9 2.5.10 2.5.11 2.6 2.6.1 2.6.2 2.6.3 2.6.4 2.6.5 2.6.6 2.6.7 2.6.8 2.6.9 2.7 2.7.1 2.7.2 2.7.3 2.7.4 2.7.5 2.7.6 2.7.7 2.7.8

XXVII

Chirality and its Consequences . . . . . . . . . . . . . . . . . . . . . . . . 548 The Curie Principle and Piezoelectricity . . . . . . . . . . . . . . . . . . . . 550 Hermann's Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552 The Importance of Additional Symmetries . . . . . . . . . . . . . . . . . . 553 The Flexoelectric Polarization . . . . . . . . . . . . . . . . . . . . . . . . . 555 Deformations from the Ground State of a Nematic . . . . . . . . . . . . . . 555 The Flexoelectric Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 556 The Molecular Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 Analogies and Contrasts to the Piezoelectric Effect . . . . . . . . . . . . . . 558 The Importance of Rational Sign Conventions . . . . . . . . . . . . . . . . 559 The Flexoelectrooptic Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 560 Why Can a Cholesteric Phase not be Biaxial? . . . . . . . . . . . . . . . . . 563 Flexoelectric Effects in Smectic A Phases . . . . . . . . . . . . . . . . . . . 564 Flexoelectric Effects in Smectic C Phases . . . . . . . . . . . . . . . . . . . 564 The SmA*-SmC* Transition and the Helical C* State . . . . . . . . . . . . 568 The Smectic C Order Parameter . . . . . . . . . . . . . . . . . . . . . . . . 568 The SmA*-SmC* Transition . . . . . . . . . . . . . . . . . . . . . . . . . 571 The Smectic C* Order Parameters . . . . . . . . . . . . . . . . . . . . . . . 573 The Helical Smectic C* State . . . . . . . . . . . . . . . . . . . . . . . . . 574 The Flexoelectric Contribution in the Helical State . . . . . . . . . . . . . . 576 Nonchiral Helielectrics and Antiferroelectrics . . . . . . . . . . . . . . . . . 577 Simple Landau Expansions . . . . . . . . . . . . . . . . . . . . . . . . . . 578 The Electroclinic Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 The Deformed Helix Mode in Short Pitch Materials . . . . . . . . . . . . . 587 The Landau Expansion for the Helical C* State . . . . . . . . . . . . . . . . 588 The Pikin-Indenbom Order Parameter . . . . . . . . . . . . . . . . . . . . . 592 Electrooptics in the Surface-Stabilized State . . . . . . . . . . . . . . . . . 596 The Linear Electrooptic Effect . . . . . . . . . . . . . . . . . . . . . . . . . 596 The Quadratic Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 Switching Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600 The Scaling Law for the Cone Mode Viscosity . . . . . . . . . . . . . . . . 602 Simple Solutions of the Director Equation of Motion . . . . . . . . . . . . . 603 Electrooptic Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 604 Optical Anisotropy and Biaxiality . . . . . . . . . . . . . . . . . . . . . . . 608 The Effects of Dielectric Biaxiality . . . . . . . . . . . . . . . . . . . . . . 610 The Viscosity of the Rotational Modes in the Smectic C Phase . . . . . . . . 613 Dielectric Spectroscopy: To Find the yand &TensorComponents . . . . . . 617 Viscosities of Rotational Modes . . . . . . . . . . . . . . . . . . . . . . . . 617 The Viscosity of the Collective Modes . . . . . . . . . . . . . . . . . . . . 618 The Viscosity of the Noncollective Modes . . . . . . . . . . . . . . . . . . 620 The Viscosity yp from Electrooptic Measurements . . . . . . . . . . . . . . 622 The Dielectric Permittivity Tensor . . . . . . . . . . . . . . . . . . . . . . . 622 The Case of Chiral Smectic C* Compounds . . . . . . . . . . . . . . . . . . 623 Three Sample Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . 625 Tilted Smectic Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626

XXVIII

Contents

2.7.9 2.7.10 2.8 2.8.1 2.8.2 2.8.3 2.8.4 2.8.5 2.8.6 2.8.7 2.8.8 2.8.9 2.8.10 2.8.1 1 2.9 2.10

Nonchiral Smectics C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Limitations in the Measurement Methods . . . . . . . . . . . . . . . . . . . FLC Device Structures and Local-Layer Geometry . . . . . . . . . . . . . . The Application Potential of FLC . . . . . . . . . . . . . . . . . . . . . . . Surface-Stabilized States . . . . . . . . . . . . . . . . . . . . . . . . . . . . FLC with Chevron Structures . . . . . . . . . . . . . . . . . . . . . . . . . Analog Gray Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thin Walls and Thick Walls . . . . . . . . . . . . . . . . . . . . . . . . . . C1 and C2 Chevrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The FLC Technology Developed by Canon . . . . . . . . . . . . . . . . . . The Microdisplays of Displaytech . . . . . . . . . . . . . . . . . . . . . . . Idemitsu’s Polymer FLC . . . . . . . . . . . . . . . . . . . . . . . . . . . . Material Problems in FLC Technology . . . . . . . . . . . . . . . . . . . . Nonchevron Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Is There a Future for Smectic Materials? . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

Antiferroelectric Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . 665 Kouichi Miyachi and Atsuo Fukuda Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 Origin of Antiferroelectricity in Liquid Crystals . . . . . . . . . . . . . . . 665 Biased or Hindered Rotational Motion in SmC* Phases . . . . . . . . . . . 665 Biased or Hindered Rotational Motion in SmCA* Phases . . . . . . . . . . . 669 Spontaneous Polarization Parallel to the Tilt Plane . . . . . . . . . . . . . . 671 Obliquely Projecting Chiral Alkyl Chains in SmAPhases . . . . . . . . . . 673 Thresholdless Antiferroelectricity and V-Shaped Switching . . . . . . . . . 675 Tristable Switching and the Pretransitional Effect . . . . . . . . . . . . . . . 675 Pretransitional Effect in Antifenoelectric Liquid Crystal Displays . . . . . . 679 Langevin-type Alignment in SmCR* Phases . . . . . . . . . . . . . . . . . 682 Antiferroelectric Liquid Crystal Materials . . . . . . . . . . . . . . . . . . . 684 Ordinary Antiferroelectric Liquid Crystal Compounds . . . . . . . . . . . . 684 Antiferroelectric Liquid Crystal Compounds with Unusual Chemical Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 688 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689

3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3 3.3.1 3.3.2 3.3.3 3.4 3.4.1 3.4.2 3.5

627 628 629 629 630 634 637 639 644 648 650 651 653 655 658 660

Chapter VII: Synthesis and Structural Features . . . . . . . . . . . . . . . . . . 693 Andrew N . Cammidge and Richard J . Bushby 1

General Structural Features . . . . . . . . . . . . . . . . . . . . . . . . . .

693

2 2.1 2.1.1

Aromatic Hydrocarbon Cores . . . . . . . . . . . . . . . . . . . . . . . . . Benzene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Esters and Amides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

694 694 694

Contents

XXTX

2.1.2 2.1.3 2.1.4 2.2 2.3 2.4 2.5 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13

Multiynes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697 Hexakis(alkoxyphenoxymethy1) Derivatives . . . . . . . . . . . . . . . . . 698 Hexakis(a1kylsulfone) Derivatives . . . . . . . . . . . . . . . . . . . . . . . 698 Naphthalene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 Anthracene (Rufigallol) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700 Phenanthrene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701 Triphenylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702 Ethers. Thioethers and Selenoethers . . . . . . . . . . . . . . . . . . . . . . 702 Esters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 Multiynes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 Unsymmetrically Substituted Derivatives . . . . . . . . . . . . . . . . . . . 705 Modifications of the Number and Nature of Ring Substituents . . . . . . . . 708 Dibenzopyrene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 Perylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 Truxene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Decacyclene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714 Tribenzocyclononatriene . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715 Tetrabenzocyclododecatetraene . . . . . . . . . . . . . . . . . . . . . . . . 717 Metacyclophane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 Phenylacetylene Macrocycles . . . . . . . . . . . . . . . . . . . . . . . . . 719

3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.8.1 3.8.2 3.8.3 3.9 3.9.1 3.9.2 3.9.3 3.9.4 3.9.5 3.9.6 3.9.7 3.9.8 3.9.9 3.9.10 3.9.1 1

Heterocyclic Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720 Pyrillium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720 Bispyran . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722 Condensed Benzpyrones (Flavellagic and Coruleoellagic Acid) . . . . . . . 723 Benzotrisfuran . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723 Oxatruxene and Thiatruxene . . . . . . . . . . . . . . . . . . . . . . . . . . 724 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dithiolium 725 Tricycloquinazoline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726 Porphyrin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 Octa-Substituted Porphyrin . . . . . . . . . . . . . . . . . . . . . . . . . . 727 meso.Tetra(p.alkyl.phenyl).porphyrin ..................... 729 Tetraazaporphyrin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729 Phthalocyanine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 730 Peripherally Substituted Octa(alkoxymethy1)phthalocyanine . . . . . . . . . 730 Peripherally Substituted 0cta.alkoxyphthalocyanines . . . . . . . . . . . . . 731 Peripherally Substituted Octa-alkylphthalocyanine . . . . . . . . . . . . . . 733 Tetrapyrazinoporphyrazine . . . . . . . . . . . . . . . . . . . . . . . . . . . 734 Peripherally Substituted Octa(alkoxycarbony1)phthalocyanines . . . . . . . 734 Peripherally Substituted Octa-(p-alkoxylpheny1)phthalocyanine . . . . . . . 735 Peripherally Substituted Tetrabenzotriazaporphyrin . . . . . . . . . . . . . . 735 Tetrakis[oligo(ethyleneoxy]phthalocyanine . . . . . . . . . . . . . . . . . . 736 Non-Peripherally Substituted Octa(alkoxymethy1)-phthalocyanines . . . . . 736 Non-Peripherally Substituted Octa-alkylphthalocyanine . . . . . . . . . . . 737 Unsymmetrically Substituted Phthalocyanines . . . . . . . . . . . . . . . . 739

xxx

Contents

Saturated Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cyclohexane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tetrahydropyran (Pyranose Sugars) . . . . . . . . . . . . . . . . . . . . . . Hexacyclens and Azamacrocyles . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

739 739 741 742 743

Chapter VIII: Discotic Liquid Crystals: Their Structures and Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S . Chandrasekhar

749

1

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

749

2 2.1 2.1.1 2.1.2 2.2 2.3 2.4 2.5 2.6

Crystalline Structures . . . . . . . . . . . . . . 750 Description of the Liquid . The Columnar Liquid Crystal . . . . . . . . . . . . . . . . . . . . . . . . . 750 752 NMR Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High Resolution X-Ray Studies . . . . . . . . . . . . . . . . . . . . . . . . 753 Columnar Phases of ‘Non-discotic’ Molecules . . . . . . . . . . . . . . . . 755 The Nematic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757 757 The Columnar Nematic Phase . . . . . . . . . . . . . . . . . . . . . . . . . The Chiral Nematic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . 758 The Lamellar Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759

3

Extension of McMillan’s Model of Smectic A Phases to Discotic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

760

4

Pressure-Temperature Phase Diagrams . . . . . . . . . . . . . . . . . . . .

762

5

Techniques of Preparing Aligned Samples . . . . . . . . . . . . . . . . . . 764

6

Ferroelectricity in the Columnar Phase . . . . . . . . . . . . . . . . . . . .

7

The Columnar Structure as a One-Dimensional Antiferromagnet . . . . . . . 766

8

Electrical Conductivity in Columnar Phases . . . . . . . . . . . . . . . . . . 766

9

Photoconduction in Columnar Phases . . . . . . . . . . . . . . . . . . . . .

10 10.1 10.2 10.3 10.4 11 11.1 11.2 12 13 14

Continuum Theory of Columnar Liquid Crystals . . . . . . . . . . . . . . . 769 The Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769 770 Acoustic Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . 771 Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanical Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772 Defects in the Columnar Phase . . . . . . . . . . . . . . . . . . . . . . . . 773 Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774 Disclinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774 The Properties of Discotic Nematic Phases . . . . . . . . . . . . . . . . . . 775 Discotic Polymer Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . 776 777 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 4.1 4.2 4.3 5

765

768

Contents

XXXI

Chapter IX: Applicable Properties of Columnar Discotic Liquid Crystals . . . . 781 Neville Boden and Bijou Movaghar 1

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

2 2.1 2.2

Molecular Structure-Property Relationships . . . . . . . . . . . . . . . . . . 782 782 HATn Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783 The Phthalocyanines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 3.1 3.2

Electrical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HATn Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemically Doped Materials . . . . . . . . . . . . . . . . . . . . . . . . . .

784 784 787

4

Dielectric Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

788

5

Fluorescence Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .

790

6

Gaussian Transit Characteristics . . . . . . . . . . . . . . . . . . . . . . . .

791

7 7.1 7.2

Anisotropy of Charge Mobility and Inertness to Oxygen . . . . . . . . . . . 792 792 Xerography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 792 Phthalocyanine Based Gas Sensors . . . . . . . . . . . . . . . . . . . . . .

8

Selforganizing Periodicity, High Resistivity. and Dielectric Tunability . . . . 792

9 9.1 9.2

Ferroelectrics and Dielectric Switches . . . . . . . . . . . . . . . . . . . . . Nematic Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ferro- and Antiferroelectric Phases . . . . . . . . . . . . . . . . . . . . . .

10

Novel Absorption Properties. Fluorescence, and Fast Exciton Migration . . . 795

11

Applications of Doped Columnar Conductors . . . . . . . . . . . . . . . . . 795

12

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

795

13

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

796

Part 3: Non-Conventional Liquid-Crystalline Materials . . . . . . . .

781

794 794 794

799

Chapter X: Liquid Crystal Dimers and Oligomers . . . . . . . . . . . . . . . . . 801 Corrie 7: Imrie and Geoffrey R . Luckhurst 1

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

2

Structure-Property Relationships in Liquid Crystal Dimers . . . . . . . . . . 801

3 3.1 3.2 3.3

Smectic Polymorphism Conventional Smectics . Intercalated Smectics . Modulated Smectics . .

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

801 804 804 807 812

XXXII

Contents

4

Chiral Dimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

Oligomeric Systems and Relation to Dimers . . . . . . . . . . . . . . . . . 813

6 6.1 6.2

Molecular Theories for Liquid Crystal Dimers . . . . . . . . . . . . . . . . 814 The Generic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815 A More Complete Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 822

7

Molecular Shapes of Liquid Crystal Dimers . . . . . . . . . . . . . . . . . . 829

8

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

813

832

Chapter XI: Laterally Substituted and Swallow-Tailed Liquid Crystals . . . . . 835 Wolfgang Weissjlog 1

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

835

2 2.1 2.2 2.3

Laterally Alkyl Substituted Rod-Like Mesogens . . . . . . . . Long-Chain 2-Substituted 1.4.Phenylene bis(Benzoates) . . . . Further mesogens bearing one Long-Chain Group in the Lateral Two Long-Chain Substituents in Lateral Positions . . . . . . .

835 835 837 841

3 3.1 3.2

Mesogens incorporating Phenyl Rings within the Lateral Segments . . . . . 843 Mesogens with One Lateral Segment containing a Phenyl Group . . . . . . . 843 Mesogens with Two Lateral Segments each containing a Phenyl Ring . . . . 850

4

Swallow-Tailed Mesogens . . . . . . . . . . . . . . . . . . . . . . . . . . .

850

5

Double-Swallow-Tailed Mesogens

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

855

6

Further Aspects and Concluding Remarks . . . . . . . . . . . . . . . . . . . 857

7

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

....... ....... Position . . .......

860

Chapter XII: Plasmids and Polycatenar Mesogens . . . . . . . . . . . . . . . . . 865 Huu-Tinh Nguyen. Christian Destrade. and Jacques Malthzte 1

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

865

2

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

865

3

Synthesis Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

866

4 4.1 4.1.1 4.1.2 4.1.3

Mesomorphic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866 Polycatenars with Only Aliphatic Chains . . . . . . . . . . . . . . . . . . . 867 Phasmids or Hexacatenar Mesogens 3mpm-3mpm . . . . . . . . . . . . . . 867 Pentacatenars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869 Tetracatenars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869

Contents

XXXIII

4.2 4.2.1 4.2.2

Polycatenars with Polar Substituents . . . . . . . . . . . . . . . . . . . . . 875 Polycatenars with Hydrogenated and Fluorinated Chains . . . . . . . . . . . 875 Polycatenars with Other Polar Substituents . . . . . . . . . . . . . . . . . . 877

5 5.1 5.2

The Core. Paraffinic Chains. and Mesomorphic Properties . . . . . . . . . . 879 879 Core Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Number and Position of Chains . . . . . . . . . . . . . . . . . . . . . . . . 880

6 6.1 6.1.1 6.1.2 6.1.3 6.1.4 6.2

Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structures of Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . . Nematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lamellar Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Columnar Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystalline Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

882 882 882 882 882 883 883

7

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

884

8

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

884

Chapter XIII: Thermotropic Cubic Phases . . . . . . . . . . . . . . . . . . . . . Siegmar Diele and Petra Goring 1 Historical Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

887 887

2

Chemical Structures and Phase Sequences . . . . . . . . . . . . . . . . . . 888

3

On the Structure of the Cubic Phases . . . . . . . . . . . . . . . . . . . . .

895

4

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

899

5

899

Chapter X I V Metal-containing Liquid Crystals . . . . . . . . . . . . . . . . . . 901 Anne Marie Giroud-Godquin 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901 2 Early Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901 3 3.1 3.2 3.2.1 3.2.1.1 3.2.1.2 3.2.1.3 3.2.2 3.2.2.1

Metallomesogens with Monodentate Ligands . . . . . . . . . . . . . . . . Organonitrile Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . n-Alkoxystilbazole Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . Distilbazole Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Palladium and Platinum . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Iridium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monostilbazole Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . Platinum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 902

902 902 903 903 903 903 903 904

XXXlV

Contents

3.2.2.2 Rhodium and Iridium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.2.3 Tungsten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Pyridine Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 3.3.1 Rhodium and Iridium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Acetylide Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Isonitrile Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.3 4.4 4.4.1 4.4.2 4.4.2.1 4.2.2.2 4.4.2.3 4.4.3 4.5 4.5.1 4.5.2 4.5.3 4.5.4 4.6 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5 4.7 4.7.1 4.7.1.1 4.7.1.2 4.7.1.3

Metallomesogens with Bidentate Ligands . . . . . . . . . . . . . . . . . . . Carboxylate Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alkali and Alkaline Earth Carboxylates . . . . . . . . . . . . . . . . . . . . Lead, Thallium. and Mercury Carboxylates . . . . . . . . . . . . . . . . . . Dinuclear Copper Carboxylates . . . . . . . . . . . . . . . . . . . . . . . . Dinuclear Rhodium. Ruthenium. and Molybdenum Carboxylates . . . . . . PDiketonate Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Copper Complexes with Two or Four Peripheral Chains . . . . . . . . . . . Copper Complexes with Eight Peripheral Chains . . . . . . . . . . . . . . . Malondialdehyde Complexes . . . . . . . . . . . . . . . . . . . . . . . . . Dicopper Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Metal Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glycoximate Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sulfur Containing Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . Dithiolene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dithiobenzoate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nickel and Palladium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Dithio Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N-0 Donor Sets: Salicylaldimine Ligands . . . . . . . . . . . . . . . . . . Copper. Nickel, and Palladium . . . . . . . . . . . . . . . . . . . . . . . . . Platinum, Vanadyl, and Iron . . . . . . . . . . . . . . . . . . . . . . . . . . Rhodium and Iridium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polymeric Liquid Crystals Based on Salcylaldimine Ligands . . . . . . . . . Cyclometalated Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . Azobenzene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arylimines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthopalladated Diarylazines . . . . . . . . . . . . . . . . . . . . . . . . . Aroylhydrazine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthopalladated Pyrimidine Complexes . . . . . . . . . . . . . . . . . . . . Metallocen Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ferrocene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monosubstituted Ferrocene . . . . . . . . . . . . . . . . . . . . . . . . . . 1,1’ Disubstituted Ferrocene . . . . . . . . . . . . . . . . . . . . . . . . . . 1,3 Disubstituted Ferrocene . . . . . . . . . . . . . . . . . . . . . . . . . .

904 904 904 904 904 905 906 906 906 906 906 907 908 909 909 910 911 911 911 911 913 913 913 913 914 914 914 914 915 915 917 917 917 918 918 919 920 921 921 921 921 921 922 922

Contents

xxxv

4.7.2 4.7.3

Ruthenocene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Iron Tricarbonyl Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . .

5 5.1 5.1.1 5.1.2 5.1.3 5.1.4 5.2 5.3

Metallomesogens with Polydentate Ligands . . . . . . . . . . . . . . . . . . 923 Phthalocyanine Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923 Copper Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923 Manganese. Copper. Nickel. and Zinc Complexes . . . . . . . . . . . . . . 924 924 Lutetium Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon. Tin. and Lead Complexes . . . . . . . . . . . . . . . . . . . . . . . 924 925 Porphyrin Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Amine Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926

6

Lyotropic Metal-Containing Liquid Crystals . . . . . . . . . . . . . . . . . 926

7

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

927

8

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

928

Chapter X V Biaxiai Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . B. K . Sadashiva

933

1

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

933

2

Theoretical Prediction of the Biaxial Nematic Phase . . . . . . . . . . . . . 933

3

Structural Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

934

4

Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

935

5 5.1 5.2

Characterization Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Diffraction Studies . . . . . . . . . . . . . . . . . . . . . . . . . . .

937 937 938

6

Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

941

7

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

942

Chapter XVI: Charge-Transfer Systems . . . . . . . . . . . . . . . . . . . . . . . K. Praefcke and D . Singer 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

945 945

2

Calamitic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

946

3

Noncalamitic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

952

4

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

964

923 923

XXXVI

Contents

Chapter XVII: Hydrogen-Bonded Systems . . . . . . . . . . . . . . . . . . . . . Takashi Kato

969

2 2.1 2.1.1 2.1.2 2.1.3 2.1.4 2.2 2.2.1 2.2.2 2.2.3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pyridine/Carboxylic Acid System . . . . . . . . . . . . . . . . . . . . . . . Self-Assembly of Low Molecular Weight Complexes . . . . . . . . . . . . . Structures and Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability of Hydrogen Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . Electrooptic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Self-Assembly of Polymeric Complexes . . . . . . . . . . . . . . . . . . . Side-Chain Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Main-Chain Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

969 969 969 969 972 973 973 973 973 974 974

3 3.1 3.2

Uracil/Diamino-p yridine System . . . . . . . . . . . . . . . . . . . . . . . Low Molecular Weight Complexes . . . . . . . . . . . . . . . . . . . . . . Polymeric Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

975 975 975

4

Miscellaneous Thermotropic H-Bonded Compounds by Intermolecular Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

976

5

Lyotropic Hydrogen-Bonded Complexes . . . . . . . . . . . . . . . . . . .

977

6

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

978

1

Chapter XVIII: Chromonics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . John Lydon 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 A Well-Defined Family Distinct from Conventional Amphiphiles . . . . . . 1.2 The Chromonic N and M Phases . . . . . . . . . . . . . . . . . . . . . . . 1.3 Drug and Dye Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Molecular Structure of Chromonic Species . . . . . . . . . . . . . . . . .

981

2 2.1 2.2 2.3 3 3.1 3.2

The History of Chromonic Systems . . . . . . . . . . . . . . . . . . . . . The Early History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Disodium Cromoglycate and Later Studies . . . . . . . . . . . . . . . . . . The 3-Way Link Between Drugs, Dyes, and Nucleic Acids . . . . . . . . .

983 983 984 985

The Forces that Stabilize Chromonic Systems . . . . . . . . . . . . . . . . Hydrophobic Interactions or Specific Stacking Forces? . . . . . . . . . . . The Aggregation of Chromonic Molecules in Dilute Solution and on Substrat Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . .

986 986

4

Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

988

5

Optical Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

989

981 981 982 982 983

987

Contents

XXXVII

6

X-Ray Diffraction Studies . . . . . . . . . . . . . . . . . . . . . . . . . .

7 7.1 7.2 7.3 7.4 7.5 7.6

The Extended Range of Chromonic Phase Structures . . . . . . . . . . . . 993 The P Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993 Chromonic M Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 998 Chiral Chromonic Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . 998 More Ordered Chromonic Phases . . . . . . . . . . . . . . . . . . . . . . 998 Chromonic Layered Structures . . . . . . . . . . . . . . . . . . . . . . . . 999 Corkscrew and Hollow Column Structures . . . . . . . . . . . . . . . . . . 999

8

The Effect of Additives on Chromonic Systems: Miscibility and Intercalation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

The Biological Roles of Chromonic Phases . . . . . . . . . . . . . . . . . 1001

10

Technological and Commercial Potential of Chromonic Systems . . . . . . 1005

11

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1005

12

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

1006

Index Volumes 2 A and 2B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1009

991

1000

General Introduction

Liquid crystals are now well established in basic research as well as in development for applications and commercial use. Because they represent a state intermediate between ordinary liquids and three-dimensional solids, the investigation of their physical properties is very complex and makes use of many different tools and techniques. Liquid crystals play an important role in materials science, they are model materials for the organic chemist in order to investigate the connection between chemical structure and physical properties, and they provide insight into certain phenomena of biological systems. Since their main application is in displays, some knowledge of the particulars of display technology is necessary for a complete understanding of the matter. In 1980 VCH published the Handbook of Liquid Ctystals, written by H. Kelker and R. Hatz, with a contribution by C. Schumann, which had a total of about 900 pages. Even in 1980 it was no easy task for this small number of authors to put together the Handbook, which comprised so many specialities; the Handbook took about 12 years to complete. In the meantime the amount of information about liquid crystals has grown nearly exponentially. This is reflected in the number of known liquid-crystalline compounds: in 1974 about 5000 (D. Demus, H. Demus, H. Zaschke, Fliissige Kristalle in Tabellen) and in 1997 about 70000 (V. Vill, electronic data base LIQCRYST). According to a recent estimate by V. Vill, the cur-

rent number of publications is about 65000 papers and patents. This development shows that, for a single author or a small group of authors, it may be impossible to produce a representative review of all the topics that are relevant to liquid crystals on the one hand because of the necessarily high degree of specialization, and on the other because of the factor of time. Owing to the regrettable early decease of H. Kelker and the poor health of R. Hatz, neither of the former main authors was able to continue their work and to participate in a new edition of the Handbook. Therefore, it was decided to appoint five new editors to be responsible for the structure of the book and for the selection of specialized authors for the individual chapters. We are now happy to be able to present the result of the work of more than 80 experienced authors from the international scientific community. The idea behind the structure of the Handbook is to provide in Volume 1 a basic overview of the fundamentals of the science and applications of the entire field of liquid crystals. This volume should be suitable as an introduction to liquid crystals for the nonspecialist, as well as a source of current knowledge about the state-of-the-art for the specialist. It contains chapters about the historical development, theory, synthesis and chemical structure, physical properties, characterization methods, and applications of all kinds of liquid crystals. Two subse-

XL

General Introduction

quent volumes provide more specialized information. The two volumes on Low Molecular Weight Liquid Crystals are divided into parts dealing with calamitic liquid crystals (containing chapters about phase structures, nematics, cholesterics, and smectics), discotic liquid cry stah, and non-conventional liquid crystals. The last volume is devoted to polymeric liquid crystals (with chapters about main-chain and side-group thermotropic liquid crystal polymers), amphiphilic liquid crystals, and natural polymers with liquid-crystalline properties. The various chapters of the Handbook have been written by single authors, sometimes with one or more coauthors. This provides the advantage that most of the chapters can be read alone, without necessarily having read the preceding chapters. On the other hand, despite great efforts on the part of the editors, the chapters are different in style, and some overlap of several chapters could not be avoided. This sometimes results in the discussion of the same topic from

quite different viewpoints by authors who use quite different methods in their research . The editors express their gratitude to the authors for their efforts to produce, in a relatively short time, overviews of the topics, limited in the number of pages, but representative in the selection of the material and up to date in the cited references. The editors are indebted to the editorial and production staff of WILEY-VCH for their constantly good and fruitful cooperation, beginning with the idea of producing a completely new edition of the Handbook of Liquid Crystals continuing with support for the editors in collecting the manuscripts of so many authors, and finally in transforming a large number of individual chapters into well-presented volumes. In particular we thank Dr. P. Gregory, Dr. U. Anton, and Dr. J. Ritterbusch of the Materials Science Editorial Department of WILEY-VCH for their advice and support in overcoming all difficulties arising in the partnership between the authors, the editors, and the publishers. The Editors

Part I: Calamitic Liquid Crystals

Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998

Chapter I Phase Structures of Calamitic Liquid Crystals John W Goodby

1 Introduction In a discussion concerning the structures of liquid crystal phases formed by rod-like molecules, a point is often reached where the arguments centre on which structural features actually define the liquid-crystalline state. For example, when a conventional solid melts to a liquid, the strongly organized molecular array of the solid collapses to yield a disordered liquid where the molecules translate, tumble, and rotate freely. Thus, at the melting point the molecules undergo large and rapid simultaneous changes in rotational, positional, and orientational order. However, when the melting process is mediated by liquid-crystalline behaviour there is usually a stepwise breakdown in this order. The incremental steps of this decay occur with changing temperature, thus producing a variety of thermodynamically stable intermediary states between the solid and the liquid. This collection of structurally unique phases essentially constitutes the thermotropic liquid crystalline mesomorphic state [ 1, 21. Liquid crystals, therefore, are classically defined as those orientationally ordered phases that occur between the breakdown of positional/translational order on melting a solid, and the breakdown of orientational order on melting to a liquid [ 3 ] . However, for the purposes of discussing mesophase structures, all of the ordered states that occur between the increase in molecular rotational freedom on heating of the solid

and the breakdown of orientational order on melting to the liquid will be described in the following sections of this chapter. Thus, in these terms the melting process can be characterized in the following way: first, an initial breakdown in order with the molecules oscillating or rotating rapidly about one or more axes; second, a collapse of the long-range positional ordering of the molecules to give a state where the molecules have short-range positional order (1.5-70 nm), but yet they still have longrange orientational order; and third, a disruption in the short-range and long-range order to produce a completely disordered liquid. Consequently, for a scenario involving materials where the constitutent molecules have rod-like shapes, the first step in the breakdown of order is for the relatively static lath-like molecules of the solid to oscillate, or rotate rapidly, about a given axis (usually the long axes of the molecules) to give a ‘smectic-like’ crystal phase. Next, the long-range positional order is then lost to produce a smectic liquid crystal mesophase. Third, the local packing order is destroyed, but the orientational order still remains with the molecules reorganizing so that their long axes lie roughly in the same direction (known as the director of the phase) to give the nematic phase. Finally, this order breaks down to give the amorphous liquid. This description (after Gray and Goodby [4]) of the

4

I Phase Structures of Calamitic Liquid Crystals

Figure 1. The melting process of a calamitic (rod-like) liquid-crystalline material.

melting process for rod-like molecules is shown schematically in Fig. 1. As with other states of matter, the mesophases are indefinitely stable at defined temperatures and pressures. Mesophases observed above the melt point during the heating process are stable and termed enantiotropic [5],whereas those phases that oc-

cur below the melt point on supercooling of the crystal are metastable and called monotropic. Transitions between the various liquid crystal mesophases invariabIy occur at defined temperatures and with little hysteresis observed between heating and cooling cycles.

2 Melting Processes of Calamitic Thermotropic Liquid Crystals The loss of order in the melting of the smectic state can be broken down further into smaller increments via the changes in the packing order of the molecules. These incremental changes correspond to the formation of 13 structurally distinct layered modifications classified by miscibility stud-

ies and given the code letters A, Bhex,B, C , Calt,E, F, 6, H, I, J, and K (note that the D phase has a cubic structure [4, 51 even though the constituent molecules are rodlike in nature, and therefore because it does not have a truly layered structure it is omitted from the list of smectic phases).

2

Melting Processes of Calamitic Thermotropic Liquid Crystals

It is interesting to note at this point that the original classification of the smectic modifications was not made through structural investigations of the phases, but rather by miscibility studies using phase diagrams [6]. Phases that were found to be miscible over the entire concentration range of the phase diagram for binary systems were said to belong to the same miscibility group, irrespective of whether or not they were actually known to have the same structures. Consequently, the classification of the unidentified phases of a novel material become a test of miscibility rather than immiscibility [6]. Phase sequencing with respect to temperature, and priority sequencing in pure materials and in phase diagrams has led to a thermodynamic ordering of the phases in the smectic state [7]. For example, current knowledge gives the sequence as

5

Isotropic Liquid, N, SmA, D, SmC, SmC,,t, [SmBh,,, SmIl, B, SmF, J, G, E, K, H, crystal

+ increasing order -+ where N is the nematic phase, D is a cubic phase, SmA, SmB,,,, SmC, SmC,,,, SmI, and SmF are smectic liquid crystals, and B, J, G, E, K, and H are ‘smectic-like’ soft crystal phases. Over the last twenty years, however, Xray diffraction techniques have been used to investigate the structures of the smectic modifications [8-131. This has led to combining miscibility classification with structural observations. Thus, certain structural features, such as the extent of the positional ordering, tilt orientational ordering, packing structure, and bond orientational ordering can be associated with each individual

Figure 2. The plan and elevation structures of the smectic phases.

6

I

Phase Structures of Calamitic Liquid Crystals

miscibility group. The structural properties of each miscibility class are depicted in Fig. 2. No material has yet been found that exhibits all of these phases, but many com-

3

pounds exhibit complex polymorphism as in, for example, 4-(2-methylbutyl)phenyl4n-octylbiphenyl-4'-carboxylate [SSI, CES, E. Merck (BDH)], which has an N, SmA, SmC, SmI, J, G phase sequence [14].

Structures of Calamitic Liquid Crystals

3.1 The Nematic Phase The nematic phase is essentially a one-dimensionally ordered elastic fluid in which the molecules are orientationally ordered, but where there is no long range positional ordering of the molecules. In this phase the rod-like molecules tend to align parallel to each other with their long axes all pointing roughly in the same direction [ 151. The average direction along which the molecules point is called the director of the phase, and is usually given the symbol n. The rod-like molecules in the nematic phase are free to rotate about their long axes and to some degree about their short axes, concomitantly, the relaxation times for rotations about their short axes are much longer (=lo5 to lo6 times per second) than those about their long

Figure 3. The structure of the nematic phase.

axes (=lo" to 10l2 times per second). For discussions concerning molecular dynamics in liquid-crystalline media see references [ 16-20]. The structure of the nematic phase is depicted in Fig. 3. In the bulk nematic phase, there are as many molecules pointing in one direction relative to the director as there are pointing in the opposite direction (a rotation of 1SO'), that is the molecules have a disordered headto-tail arrangement in the phase. Thus the phase has rotational symmetry relative to the director. The degree to which the molecules are aligned along the director is termed the order parameter of the phase, which is defined by the equation

s = -(3c0s2 1 e-1) 2

(1)

where Ois the angle made between the long axis of each individual rod-like molecule and the director. The brackets in the equation imply that this is an average taken over a very large number of molecules. An order parameter of zero implies that the phase has no order at all (it is liquidlike), whereas a value of one indicates that the phase is perfectly ordered: all the long axes of the molecules are parallel to one another and to the director. For a typical nematic phase the order parameter has a value in the region of 0.4-0.7 indicating that the molecules are considerably disordered. The order parameter has the same symmetry properties as the nematic phase, in that

3

the order parameter is unchanged by rotating any molecule through an angle of 180". The nematic phase is birefringent owing to the anisotropic nature of its optical properties. The extraordinary ray travels at a slower velocity than the ordinary ray, thereby indicating that the phase has a positive birefringence. Moreover, in most nematic phases the molecules are rotationally and orientationally disordered with respect to their short axes, and consequently, the phase is optically uniaxial. However, in some cases, particularly for molecules with broad molecular shapes, the degree of rotational freedom of the molecules about their long axes is restricted. This could lead to a preferred macroscopic ordering of the board shaped molecules to give a nematic phase that is biaxial, see Fig. 4 [21, 221.

3.2 Structures of Smectic Liquid Crystals The lamellar smectic state is readily divided into four subgroups by considering first, the extent of the in-plane positional or-


7

dering of the constituent molecules, and second, the tilt orientational ordering of the long axes of the molecules relative to the layer planes, see Fig. 2 [4]. Two groups can be defined where the molecules have their long axes on average normal to the layers. These two groups are distinguished from each other by the extent of the positional ordering of the constituent molecules. For example, the smectic A and hexatic B phases are smectic liquid crystals in which the molecules have only short-range positional order [23], whereas the crystal B and crystal E phases are 'smectic-like' soft crystal modification [ 10, 241 where the molecules have long-range positional ordering in three dimensions [3]. Two other classes can be distinguished where the molecules are tilted with respect to the layer planes. In the smectic C, smectic I, and smectic F phases the molecules have short-range orientationa1 ordering [14, 251, whereas in the crystal G. crystal H, crystal J and crystal K phases the molecules have long-range three-dimensional ordering [lo, 251. Thus, smectics A, C, Calt,Bhex,I, and F are essentially smectic liquid crystals, whereas B, E, G, H, J, and K are crystal phases. These latter phases, however, have somewhat different properties from normal crystals, for example, their constituent molecules are reorienting rapidly about their long axes ( 1 0' times per second) [ 19, 261.

3.3 The Structures of the Orthogonal Smectic Phases 3.3.1 Structure of the Smectic A Phase In the smectic A phase the molecules are arranged in layers so that their long axes are

8

I


Figure5 Structure of the orthogonal smectic A phase.

on average perpendicular to the layer planes, see Fig. 5. The molecules are undergoing rapid reorientational motion about their long axes on a time scale of 10" times per second. They are also undergoing relaxations about their short axes on a time scale of lo6times per second. The molecules are arranged so that there is no translational periodicity in the planes of the layers or between the layers. Therefore, there is only short range ordering extending over a few molecular centres at most (~1.5-2.5 nm), with the ordering falling off in an algebraic fashion [27,28j. Perpendicular to the layers the molecules are essentially arranged in a one dimensional density wave [3], therefore, the layers themselves must be considered as being diffuse. As a consequence, the concept of a lamellar mesophase is somewhat misleading because the layers are so diffuse that on a macroscopic scale they are almost non-existent. In actual fact, the molecules are arranged within the lamellae in such a way that they are often randomly tilted at slight angles with respect to the layer normal. This makes the layer spacing on average slightly shorter than the molecular length. Typically, the molecules have time dependent tilts anywhere up to about 14-15' from the layer normal [29-311. However, as the tilting is random across the

bulk of the phase, the mesophase is optically uniaxial with the optic axis perpendicular to the lamellae, and hence the phase has overall D, symmetry. The smectic A phase can also have other variations in which the molecules are not arranged in singular molecular layers but are organized in semi-bilayer and bilayer structures. Semi-bilayer ordering is typically caused either by intesdigitation or partial pairing of the molecules 132, 331. Smectic A phases that have these structures invariably occur for materials where the molecules carry terminal polar groups, such as cyano moieties. In a typical example, the molecules overlap so that the polar terminal groups interact with the ends of the central cores of adjacent molecules. In doing so the molecules overlap to give a bilayer structure that has a bilayer spacing which is approximately 1.4 times the molecular length of a single molecule. This phase is often given the symbol SmA, where the d stands for a dimeric system. A closely related sub-class of the smectic A phase also exists where the molecules form a bilayer structure, where the bilayer spacing this time is equal to approximately twice the molecular length [34]. In this case, the polar terminal groups of the molecules overlap with each other to form dimers where the length of the paired system is equal to approximately twice the individual molecular length. This phase is called the srnectic SmA, phase. This phase could also be considered as having a monolayer structuring where the molecules in each individual layer point in the same direction, but directions alternate from layer to layer giving an antiferroelectric ordering. Figure 6 depicts this layer ordering using ovoid shaped molecules to demonstrate the directional ordering of the molecules. As with the other smectic A phases, the molecules in the SmA, phase are in dynamic motion, and

3

consequently the pairing of the molecules should be considered to be in constant flux. Alternatively, it is also possible to have polar molecular systems where the molecules do not overlap with each other to form a bilayer structure, but instead the molecules form lamellae where they are arranged in a disordered head-to-tail way so that a monolayer structure results (see Fig. 6). This phase has been given the symbol SmA,, and transitions can be found from monolayer SmA, to bilayer SmA, and SmA, phases. It is also possible to have other variants of the smectic A phase, for instance it is feasible to have a structure composed of SmA, layers where the layers have a periodic in-


9

plane correlation extending over approximately 15 nm. This correlation, which extends over a large number of molecules, is produced by a half layer shift in the lamellae structuring. By periodic shifting of the bilayers into an adjacent layers above and below an undulating structure is formed [35]. At the point where there is a shift in the layer ordering a region of the SmA, phase is produced within the SmA, phase. Alternatively, the structure of this phase can be viewed as being composed of layers where the molecules point in the same direction, and where this direction flips or inverts on a scale of approximately 15 nm. This structure has been called the ‘ribbon’

Figure 6. Bilayer and monolayer structures of the smectic A phase.

10

I


or antiphase phase, and has been given the symbol Sml?. When this phase is formed, it is thought to be due to incommensurabilities between the lengths of the monomeric and the dimeric species [36, 371. In addition, a case has been reported for the coexistence of two colinear incommensurate density waves of types SmA, and SmA, [38]. The sub-phases of smectic A can therefore be described in the following way [3]: SmA, is a conventional smectic A phase where the molecules have random head-totail orientations; - SmA, is a bilayer phase with antiferroelectric ordering of the constituent molecules; - SmA, is a semi-bilayer phase with partial molecular overlapping due to associations; and - SmA is a phase with a modulated antiferroelectric ordering of the molecules within the layers giving a ribbon-like structure. -

Thus, it can be seen, that the smectic A phase is rather more complicated than the simple picture often presented of molecules arranged in orthogonal layers. It is very important to remember that the layer structure is only weak and that dimeric interactions can play an important part in the structuring of the phase.

3.3.2 Structure in the Hexatic B Phase The structure [3,4,23,39,40] of the hexatic B phase is relatively close to that of the smectic A phase, in that the molecules are arranged in layers so that their long axes are orthogonal to the layered planes. Locally, the molecules are essentially hexagonally close packed and are undergoing rapid reorientational motion about their long axes on a similar time scale to the smectic A phase.

In the planes of the layers the molecules have only short range periodic order extending over a distance of 15 to 70 nm. Although, the positional ordering is short range, the hexagonal close packing array extends over a long distance. The hexagonal packing matrix has the same orientation both in the plane and between the planes of the layers, thereby extending in three dimensions. For a well-aligned system, the orientation of the hexagonal packing array extends to infinity in three dimensions. This ordering is referred to as long range bond orientational order [41-431. Long range bond orientational order simply means that when we consider molecules which are arranged in a hexagonal close packed domain in one part of a bulk sample, and then move a long distance away from that particular area of the specimen, we will find a similar hexagonally close packed domain that has the same orientation, however, there will be no relationship between the positional ordering of the two domains (see Fig. 7). Between the layers there is no correlation of the molecules, thus, out of the plane the order is only short range. The hexatic B phase is, therefore, easily distinguished from the crystal B phase, where the molecules have long range periodic order in three dimensions. When the hexatic B phase is formed from the smectic A phase on cooling it does so via a first order phase transition. This phase transition however is relatively weak and sometimes approaches becoming second order.

3.3.3 Structure of the Crystal B phase In the crystal B phase [3, 4, 8, 241, like the hexatic B and the smectic A, the mole-

3

Structures of Calarnitic Liquid Crystals

11

Figure 7. Structure of the hexatic smectic B phase.

cules are arranged in layers with their long axes orthogonal to the layer planes. Again, as with the other phases, the molecules are undergoing rapid reorientational motion about their long axes on a time scale of 10' times per second. However, there is one big difference between this phase and the hexatic B phase, this is that the molecules have long range translational order in three dimensions (see Fig. 8). This makes the phase akin to a plastic crystal, and therefore, the crystal B phase could be called an anisotropic plastic crystal. As with the hexatic B phase, the molecules are hexagonally close-packed, with the hexagonal packing array extending to infinity in three dimensions. However, the crystal B phase can show some variations in the inter-layer stacking, and mono-, bi-, and tri-layer unit cells can be obtained [441 (see Fig. 8). For example, as the layers are hexagonally close-packed, the layer structuring of the crystal B phase can either:

'

have molecules that lie directly on top of one another to give AAAA layer packing, - have alternate layers shifted in such a way so that the molecules in adjacent layers to an object layer lie in positions between the molecules of the object layer, this gives ABABAB packing,

have the adjacent layers to the object layer shifted in opposite directions so as to give ABCABCABC packing, and - have layers B and C that are not necessarily in the trigonal positions relative to layer A, resulting in a layer symmetry that is lower than hexagonal [45]. -

Examples of AAAA, ABABAB and ABCABC stacking structures are shown in Fig. 9. In addition, transitions between different packing structures can occur with respect to temperature. In a real sample, however, no enthalpy effects can be detected despite the fact that there are symmetry changes occurring with such transitions.

-

Figure 8. Structure of the crystal B phase showing ABC packing.

12

I Phase Structures of Calamitic Liquid Crystals

Figure 9. Interlayer stacking structures of the crystal B phase.

Again, as with the hexatic B phase, the mesophase has long range bond orientationa1 order [3]. The bond orientational order takes the form of a hexagonal packing net that has the same orientation on passing from layer to layer and extends to infinity within the layer. Therefore, the crystal packing structure and the bond orientational order are identical (Fig. 8). The crystal B phase can be easily distinguished from the hexatic B phase by comparison of their respective X-ray diffraction patterns. The X-ray diffraction pattern for the hexatic B phase shows diffuse scattering, whereas in a well-aligned crystal B phase the scattering profile is sharpened into resolution limited diffraction spots [3]. Interestingly, the results obtained from X-ray studies of crystal B phases suggest that the molecules

are not lateraIly separated enough to allow for free rotation of the molecules about their long axes to occur [46]. This indicates that the rotational motion of the molecules for the most part must be cooperative [47].

3.3.4 Structure of Crystal E In the structure of the crystal E phase the molecules are also arranged so that their long axes are perpendicular to the layer planes. Locally the molecules are packed in an orthorhombic array [48], and therefore the phase is biaxial [49]. The distance between molecules is such that they cannot undergo free rotation about their long axes [50], and thus the molecules are packed in a herringbone array. The molecules are

3


13

Figure 10. Structure of the crystal E phase.

undergoing rapid reorientational motion about their long axes [40, 511, again on a time scale of 10" times per second, see Fig. 10, however, this motion is not full, free rotation, but of an oscillatory nature, thus, the lath-like molecules are flapping cooperatively about their long axes. The layers in this phase are much more better defined than they are in the smectic A phase, and the molecules have long range in-plane and outof-plane periodic order. In some cases, the E phase is also found to have bilayer structuring as in the crystal B phase [26] and, like the crystal B phase, the E phase can be considered as being a 'soft' crystal.

3.4 Structures of the Tilted Smectic Phases 3.4.1 Structure of the Smectic C Phase In the smectic C phase the constituent molecules are arranged in diffuse layers

where the molecules are tilted at a temperature-dependent angle with respect to the layer planes [3, 41. When the smectic C phase is formed from the smectic A phase upon cooling, the temperature dependence of the tilt angle approximately takes the form ( @ T = (@O(TA-C-

(2)

where ( O ) , is the tilt angle at temperature T "C, (O), is a constant, TA-C is the smectic A to smectic C transition temperature, T is the temperature and a i s an exponent which is usually set equal to 0.5 [52] (typically the experimental value of the exponent is found to be less than 0.5) [53, 541. The molecules within the layers are locally hexagonally close-packed with respect to the director of the phase; however, this ordering is only short range, extending over distances of approximately 1.5 nm. Over large distances, therefore, the molecules are randomly packed, and in any one domain the molecules are tilted roughly in the same direction in and between the layers (see Fig. 11). Thus, the tilt orientational ordering between successive layers is preserved

14

I


Figure 11. Structure of the tilted smectic C phase.

over long distances. Consequently the smectic C phase has C,,, symmetry and is weakly optically biaxial. A sub-phase of the smectic C phase also exists which is called (for the moment) the alternating smectic C (SmC,,,) phase [55-571. This phase was originally discovered by Levelut et al. [55]and given the code letter smectic 0. However, the chiral version of this phase was labelled as being an antiferroelectric smectic C phase by Fukuda [58], and it is this descriptor that is in current, general use. Consequently, the achiral modification of the antiferroelectric phase requires a matching code letter, and therefore, for the present we have opted to use smectic Calt as this term best describes the structure of the phase in relation to the antiferroelectric label. The in-plane ordering of the molecules is thought to be identical to that of the smectic C phase. The major difference between the alternating C and normal smectic C phases resides in the relationship between the tilt directions in successive layers. In the alternating tilt phase the tilt direction is rotated by 180" on passing from one layer to the next [56]. Thus the tilt direction appears to flip from one layer to the next, thereby producing a zig zag layered structuring. Consequently, the director of the phase is effectively normal to the layer planes, as shown in Fig. 12. However, there appear to

be no long range positional correlations of the molecules between layers, even though the orientational ordering appears to be long range. So far, the alternating C phase has always been found to occur below the smectic C phase on cooling for compounds that exhibit both phases. In addition to the alternating smectic C sub-phase, other sub-phases of the smectic C phase can be found for systems where the molecules carry terminal polar groups (e.g. cyano) [3]. These sub-phases are identical to those of the smectic A phase, except for the fact that the molecules are tilted with respect to the layer planes. Thus, the smectic C1,C2, Cd and phases are the direct analogues of the A , , A,, A, and A phases respectively [59, 601. The sub-phases of smectic C can therefore be described in exactly the same way:

c

SmC, is a conventional smectic C phase where the molecules have random head-totail orientations. - SmC, is a bilayer phase with antiferroelectric ordering of the constituent molecules. - SmC, is a semi-bilayer phase with partially formed molecular associations. - SmC is a phase with a modulated antiferroelectric ordering of the molecules within the layers giving a ribbon-like structure. -

The structures of these phases are shown together in Fig. 13.

3


15

Figure 12. Structure of the alternating tilt smectic C,,, phase.

Figure 13. Bilayer structures of the tilted smectic C phase.

16

I


3.4.2 Structure of the Smectic I Phase In the smectic I phase the molecules are arranged in a similar fashion to the way they are organized in the C phase, see Fig. 14. In the I phase, however, the in-plane ordering is much more extensive, with the molecules being hexagonally close packed with respect to the director of the phase [12, 14, 61-63]. The positional ordering of the molecules extends over distances oE 15 to 60 nm within the layers, and is therefore short range in nature [ 121.There are some indications that the positional order, in fact, decays in an algebraic fashion unlike that thought to occur for the smectic F phase [25]. Out-of-plane correlations of the molecular positions are, however, very weak [3]. The phase, however, possesses long-range bond orientational order in that the hexagonal packing of the molecules remains in the same orientation over long distances in three dimensions even though the positional order is only short range. Thus, the tilt orientation between layers, as in the C phase, is preserved over many layers. Another feature associated with the tilt in the I phase is that it is directed towards an apex of the hexagonal packing net: a structural parameter that distinguishes the phase from smectic F. Thus, the smectic I phase is essentially atilt-

ed equivalent of the hexatic smectic B phase, that is, it is a three-dimensionally stacked hexatic phase. The molecules in the smectic I phase, like the smectic C and hexatic B phases, are expected to be in dynamic motion about their long axes, presumably on a similar time scale. The rotation is expected to be of a cooperative nature as the molecular centres are separated by only 0.4-0.5 nm.

3.4.3 Structure of the Smectic F Phase The structure of the smectic F phase [63] is almost identical to that of the smectic I phase, in as much as the molecules are hexagonally close packed with respect to the director of the phase, and they have shortrange positional ordering within the layers. Like the I phase, the F phase also has longrange bond orientational order in three dimensions (see Fig. 15). The primary difference between the two phases, however, is one of tilt direction, which in the I phase is directed towards the apex of the hexagonal net, whereas in the F phase it is directed toward an edge of the net, compare Figs. 14 and 15 [61]. There is also some evidence that suggests that the I and F phases differ somewhat in the extent of in-plane ordering,

Figure 14. Structure of the smectic I phase.

3

Structures of Calarnitic Liquid Crystals

17

Figure 15. Structure of the smectic F phase.

with the F phase having a slightly longer correlation length than smectic I [64, 651. The molecular dynamics, however, are presumed to be similar to those of the smectic I and C phases. The positional correlations between the layers are weak, thus the mesophase could almost be considered as a weakly coupled two-dimensionally ordered system.

3.4.4 Structures of the Crystal J and G Phases The crystal J and G modifications [66,67] are the crystalline analogues of the smectic I and F phases, respectively [3, 41. For example, in the J phase the molecules are arranged in layers where their long axes are

tilted with respect to the layer planes. Looking down the tilt direction of the phase, the molecules are arranged in a pseudohexagonal packing structure, with the tilt being directed towards the apex of this array. The molecules have long-range periodic ordering within the layers and between the layers [68]. Packing of one layer on top of another tends to be of the AAA type [SO, 611, as shown in Fig. 16. The primary difference between the crystal J and G phases is the same as the difference between the smectic I and F phases that is, for the G modification the tilt is directed towards the edge of the hexagonal packing array, whereas in J it is towards the apex, compare Figs. 16 and 17. Essentially, as far as the extent of positional ordering is concerned, these modifications are crystallinic. However, the mo-

Figure 16. Structure of the crystal J phase.

18

I


/TNA1p"2>. Experimentally, the scaling relationships seem valid and it is found unusually that tI1 2 5 [33, 341 directly from X-ray scattering. For all the compounds studied to date, vIIis found to be larger than v,, but the values seem to depend significantly on the nematic range. Basically, vII~0.57-0.83, v,=0.39-0.68, and y=l.10-1.53 (see Table 1). It is worth pointing out that all the materials cited in Table 1 satisfy the anisotropic scaling relation (to within experimental limits)

x

v,\+ 2v, + a = 2

(9)

However, the data recorded for different materials do not seem to correspond to a universal behavior of the transition. For example, in the case of compounds with large nematic ranges, the critical exponents are close to an x y , helium-like behavior with a=-0.007, vll=vi=0.67, and y= 1.32 [40], but the question of the anisotropy is not explained [35,41]. Other proposals have been made to consider that the transition belongs to an anisotropic class with vIl=2V, [42], or vl,=3/2v, [431. Another suggestion is to consider that for some compounds the N-SmA transition is close to a critical point when the values of T N A I T N I are high [44]. But in all these cases, the question of anisotropy is not solved. A very recent and more complete compilation [45] of the effective exponents a, vII,and v, for the N-SmA transition shows that they exhibit a complicated behavior, but more or less systematic as a function of the McMillan ratio T N A I T N r ;

29

the latter can be considered therefore as a useful tool, but rather imprecise, to measure the strength of two important couplings: on the one hand, the coupling between the smectic and the nematic order parameters (crossover towards a critical point), on the other, the coupling between the director fluctuations and the smectic order parameter (anisotropic behavior of the correlation lengths). Indeed, there is no complete theory that predicts correctly the values of the exponents. Recent theoretical predictions of Patton and Anderek provide new interest concerning this transition [46, 471; their model predicts a very gradual crossover from isotropic to anisotropic critical behavior and also a broad, weakly anisotropic region. However, the N-SmA transition still remains a theoretical challenge, and in spite of the large number of experimental studies already reported, many others are needed to find out the universal class of this transition.

4 Smectic A-Smectic C (SmA-SmC) Transition 4.1

General Description

In the smectic C phases, the molecules are disordered within the layers as in the smectic A phases, but tilted with respect to the layer normal. The tilt angle 0 is directly coupled with the layer thickness, whereas the azimuthal angle @ is not (Fig. 6). The smectic C phase is often followed by a smectic A phase at higher temperatures, and in such a case, the tilt angle decreases to zero with increasing temperature. If the SmA-SmC transition is of second order, the tilt angle 0 decreases regularly and continuously to zero; when it is of first order, the tilt angle 8 jumps abruptly from a

I1 Phase Transitions in Rod-Like Liquid Crystals

30

A

Z

axis

J

X

Figure 6. Geometry of the smectic C phase: z is the normal to the layer, 8 is the tilt angle, and (b the azimuthal angle, d is the direction of the long molecular axis projection onto the plane of the layers.

finite value to zero at the transition temperature. The smectic C order is characterized by the two parameters 8 and 4, and therefore the order parameter can be written as

w= 8ei@

For example, it was argued that the bare cor213 l l q,l ) of the tilt anrelation length ( { o = ~ o113 gle fluctuations is so large that the critical domain, as defined by the Ginzburg criterion [5 11, should be very small, and therefore only a mean field behavior can be observed [521. From a microscopic point of view, the tilt of the molecule in a smectic layer is influenced by the tilt of many other molecules simultaneously, and as a consequence corresponds to large values of the correlation and Other experimental lengths studies have been interpreted in the same way; the SmA-SmC transition thus being well described by a mean field expression, but using a large sixth order term in the free energy [53, 541

tol, top

F = F,

+ a t e 2 + be4 +ce6 + etc.

(12)

After minimization, 8 =0 for T > TCA and

1'2-1]

112

for Tto, e varies as l t ~ ' ' ~ .

6C, z K + A*'ltl-"

4.3 Experimental Situation

(11)

where Kis a constant, t=(T-TcA)ITc,, and a -0.007; below the transition, the tilt angle is predicted to vary according to the law 8=K'I t i p with p 0.35 and K' a constant.

=

=

4.2

Critical Behavior

Evidence of helium-like critical behavior has been reported by means of light scattering [49] and optical interferometry [50] experiments. However, other experiments have shown that the transition is mean-field.

Specific heat measurements show mainly a mean-field behavior with a sixth order term included in the free energy expression [53-571 (Fig. 7); however, the agreement between the model and the measurements of C, in the neighborhood of the transition has been a controversial question in the milliKelvin temperature range, and especially in the smectic A phase [58]. For the tilt angle temperature dependence, mean-field [52, 591 and helium-like behavior [58] are reported. Helium-like behavior has been reported in one compound (Fig. 8), and the

4

Smectic A-Smectic C (SmA-SmC) Transition

31

I38

I34 %

G

x.

I30

I76

corresponding interferometric study indicates that the critical behavior extends over a few tenths of a degree from the SmA-SmC transition. Finally, sound attenuation measurements show the existence of heliumlike fluctuations [60], whereas the variation of the specific heat for the same compound seems to indicate a mean-field behavior [61]. A more recent study indicates that ultrasound damping measurements reveal important pretransitional effects in the vicinity of the SmA-SmC transition [62]. These effects show that the transition is not of a Landau mean-field type for this compound, even though specific heat [63], Xray [52], and dilatometric [64] measurements performed on the same sample are in favor of a mean-field behavior. To take into account these contradictory results, it has been suggested that the value of T g ,corresponding to the Ginzburg criterion, should depend on the variable under study [65].

Figure 7. (a) Tilt angle variation as a function of temperature for compound 40.7 (see Table 1) (open and filled circles). The triangles are the reciprocal of the susceptibility (b) Heat capacity data near the SmC-SmA transition in compound 40.7, R is the gas constant (after [54]).

0.6

I .o

It is important to point out that the contradiction about the behavior of the tilt angle, 8, in the immediate neighborhood of the transition can be related to the way 8 is determined, either through the ratio dcld, (d, and d, being the layer thickness in the smectic C and smectic A phase, respectively), or measured directly on oriented samples. Indeed, the critical model considers that, in a very small temperature range close to the SmA-SmC transition, the 8 variation is mainly due to fluctuations, implying a very small variation of the layer spacing. Within this critical domain, extrapolation of the smectic A layering d, into the smectic C phase as a function of temperature could no longer be correct. As a result, the measurements performed on oriented samples can reveal a variation of 8 as a function of temperature, globally compatible with the critical behavior in the vicinity of the transition, whereas this main critical contribution is not

I1 Phase Transitions in Rod-Like Liquid Crystals >

1

. .

. ,

. ..

/

bad)

,

,

, 10-h

,

,

,

,

,

IC

, , ,

0.05 O,'

0.01

0.1

0.355 0.35

Figure 8. (a) Interferometric measurements of tilt angle as a function of temperature fitted to the power law v=volzlp [z=(T,-T)IT,] for AMCll (azoxy4,4'(di-undecyl a-methylcinnamate)). The lengths of the arrows display the difference (multiplied by 100) between the experimental data and the fitted law. (b) Fitted p values and their standard deviations on reducing the fitted range (T,- i",) (test of stability for the asymptotic law). (c) Idem for AT, (T,is the temperature limit, up to which data have been taken into account for the fits; after [%I).

taken into account when 8 is determined through the ratio d,ld,. All the previous studies concern second order SmA-SmC transitions, which are generally the case for nonchiral systems [66, 671. In fact, an increase of the tricritical character (i.e., of the weight of the sixth order term in the development of the free energy) has been found when the width of the smectic A phase decreases for the compound exhibiting the N-SmA-SmC and

I-SmA-SmC sequences [28,68-711. In the mean field approximation, this indicates that the variation of 8 is all the more steep as the temperature domain of the smectic A phase is narrower, in agreement with some studies made on mixtures and on pure compounds exhibiting the N-SmA-SmC sequence [72-761. These experimental results suggest a change in the order of the transition when approaching N-SmA-SmC and I-SmA-SmC triple points. Within experimental accuracy, this has been verified for only one homologous series [75] among several series and binary systems studied so far. Moreover, a systematic study has shown that the narrowness of the SmA domain is less important than, for example, the existence of strong transverse dipole moment in the molecule. Indeed, all the compounds exhibiting a first order SmA-SmC (or SmA-SmC*) transition possess this molecular feature and can also exhibit a wide SmA temperature domain [77-791. The existence of tricritical points between the first and second order SmA-SmC domains has been demonstrated in the case of binary systems [80, 811. When studying the variation of 6 on approaching such a triple point, a crossover between the mean-field and the tricritical behavior has been found in a temperature domain varying from a few hundredths to a few tenths of a degree from the transition [82]. Some cases of first order smectic C to smectic A transition are reported; the first order behavior seems to be related to the coupling between the tilt angle and the biaxiality [68, 821.

4.4 Smectic A-Smectic C* (SmA-SmC*) Transition The smectic C* phase is obtained with chiral optically active molecules. Each layer is

4

Smec)tic A-Smectic C (SmA-SmC) Transition

p\

Figure9. Schematic diagram of the stacking of smectic C* layers ( P stands for the polarization).

Figure 10. Electroclinic effect: the induced tilt angle as a function of the applied electric field in the smectic A phase of a ferroelectric liquid crystal of compound 1 at 0.6"C above the SmC*-SmA transition (after L1.591).

spontaneously polarized. The structure is characterized by a twist about the layer normal, such that the tilt, 8, and the polarization direction, P , rotate from one layer to the

33

next one (Fig. 9). There is an evident coupling between P and 8 which manifests itself above the SmC*-SmA transition, where an applied electric field induces a tilt angle even in the smectic A phase (electroclinic effect, see Fig. 10). The smectic C*smectic A transition may be of first or second order [78, 821. .4first phenomenological model to describe the SmA-SmC* transition was proposed by Meyer [83]. The transition was supposed to be second order, and the effect of the helical torsion occurring below the transition was neglected. Despite its first order approximation, this model was able to describe some physical phenomena observed with these ferroelectric phases (polarization induced by shear stress or piezoelectric effect, field induced tilt or electroclinic effect). In order to get a better agreement with the experimental results, the approach was then developed and complicated by introducing phenomenological coefficients in the general expansion of the free energy, including a sixth order term in 8 and a term in 82P 2 [84, 851. Indeed, the agreement with the various properties of the ferroelectric phases seems more satisfactory [84, 861.

4.5 The NematicSmectic A-Smectic C (NAC) Multicritical Point The NAC point represents the intersection of the N-SmA, SmA-SmC, and N-SmC phase boundaries in a thermodynamic diagram (transition temperatures as a function of concentration (x) or pressure ( P ) ) . Close to this point, all the transitions become continuous, and at the transition the three phases cannot be distinguished [87]. The existence of such a multicritical point was first found in the temperature/concentration


34

27s

29s 305 Pressure (bar)

285

I

Figure 11. Pressure-temperature diagram for a single component liquid crystal showing the existence of the NAC point (after [90]). (1 bar= lx105 N m-*.) 315

+

P '

I

0

P+ d O+

d

325

the N-SmC transition resulting from tilt fluctuations in the nematic phase [91]; the latent heat of the N-SmC transition was predicted to disappear at the NAC point, and this has been verified experimentally [28, 67, 70, 921. X-ray diffraction experiments were also in agreement with this model [93, 941 and show that there is a universal NAC topology (Fig. 12). The NAC phase diagram can thus be described by the following equations TNA- TNAC = ANAI x - WAC

-2

-1

0

X-X,,,

1 a-u

2

TNC- TNAC =ANc

I0 1 + ~

IX - xNAC I 0 2 + ~

(- xNAC x

1 1

l-x ~ m c

Figure 12. Universal topology of the NlSmAlSmC phase diagram as a function of the concentration (after [160]).

=AAc

diagram of binary mixtures [88,89], and later in the temperature/pressure diagram of a single component liquid crystal system (Fig. 11) [90]. The NAC point was described as a Lifschitz point, with the first order character of

The experiments seem consistent [90, 93-96] with @ lz @2=0.5-0.6 and @3 z 1.4-1.7. In a more recent development of the model, the role of pretransitional fluctuations has been taken into account [97]. This model predicts the existence of a biaxial nemat-

TAC- TNAC

IX

- xNAC

1 0 3 + B / X- xNAC I

(14)

4

Smectic A-Smectic C (SmA-SmC) Transition

ic phase (N,) between the nematic and the smectic C phase, in the vicinity of the triple point. Thus four phases, N, N,, SmA, and SmC are predicted to meet at a point giving rise to a multicritical point topology. This description is connected with the model first proposed by Grinstein and Toner [98], but no experimental study has been able to prove the existence of such a biaxial nematic phase so far. Other models assume that a tricritical point should exist on the SmA-SmC line in a domain where it would be undetectable due to the experimental accuracy [99, 1001. This assumption is based on the large tricritical character of ACp as a function of the width of the smectic A phase, and also the discovery of new compounds with a first order SmA-SmC transition. But these models are in contradiction with the universal topology of the phase diagrams around the NAC point. To conclude, it now seems accepted that the NAC point has a universal topology. The biaxial nematic phase has not been found experimentally, and there is still a need for theoretical analysis of fluctuations in the vicinity of the NAC point.

4.6 SmA-SmC Transition in Thin Films The behavior of a system close to a critical point or to a second order phase transition depends on the spatial dimensionality. Smectic liquid crystals can easily be formed into thin films freely suspended on a frame, and are thus good candidates for investigating the thermodynamic behavior in a reduced dimensionality. As for the phase transitions concerned, on the one hand, the role of fluctuations is expected to become more and more important and to lead, therefore, to a destabilization of the more ordered

35

phase in thin films; on the other hand, surface interactions should lead to a stabilization of the same phase [101-1031. Moreover, Kosterlitz and Thoulesss have proposed a theory for the melting of two-dimensional systems, consisting mainly of a binding-unbinding transition of defects [ 1041. Thus very thin films (only a few smectic layers thick) of liquid crystals exhibiting the SmA-SmC transition are good physical examples for studying in that context. The first studies of thin liquid crystal films exhibiting the SmA-SmC transition were done in the late 1970s by the Harvard group [l05-1081. However, they were not able to discuss in detail the critical behavior of the SmA-SmC transition in such films. Then Heinekamp et al. [ 1091showed, by ellipsometry measurements, that the SmA-SmC transition temperature is strongly dependent on the film thickness, the transition temperature increasing with decreasing film thickness. They described their films as a stack of (N-2) interior layers possessing bulk critical parameters, whereas the two surface layers were described by critical parameters different from the bulk parameters. Also, from studies on very thin films (3-11 smectic layers), Amador and Pershan concluded that, when decreasing the temperature from the smectic A phase, the tilt appears first only in the two surface layers, the interior layers remaining smectic A in nature, until the transition to the smectic C phase [ 1 101. More recently, Bahr and Fliegner studied the behavior of a first order SmA-SmC transition in free-standing liquid crystal films [ 111 3. For films thicker than 1 5 layers, a first order transition is observed at the same temperature as in the bulk, but the surface layers are always tilted in the whole temperature range, regardless of the film thickness. In films thinner than 15 layers, surface interactions become predominant, and the first


36

n

a

30

W

20

?5

10

Figure 13. Temperature dependence of the tilt angle, 6, in various free standing films, the thickness of which varies from 190 layers (bottom line) to two layers (top line) (after [I 1 I]).

order transition is transformed into a continuous transition on decreasing the film thickness, and then vanishes completely for films thinner than six layers (Fig. 13). The same behavior has been observed optically by Kraus et al. for films thinner than 90 layers [ 1121.Finally, it is interesting to highlight the case of one recent study, where a layer by layer SmA-SmC transition is found in a film four layers thick [ 1131.

5 HexaticB to Smectic A (SmB,,,-SmA) transition

order). This phase has been proved, by Xray studies, to exist in some liquid crystals compounds [ 1141; it has been described also as a stack of two-dimensional hexatic layers resulting in three-dimensional long range hexatic order [115]. Upon heating, this phase transforms into the smectic A phase, which can be considered as a stack of two-dimensional liquid layers. In the same way, Halperin and Nelson [ 1161 extended the theory of Kosterlitz and Thouless [lo41 to describe the process through which a two-dimensional solid melts into the isotropic phase via an intermediate hexatic phase. The typical hexatic in-plane order is characterized by a sixfold modulation of the Xray diffuse scattering ring corresponding to the molecular correlations. The angular dependence of the X-ray scattering intensity in the plane of the smectic layers can be written as I

(x)= 10 + 16 cos [6 (x- 41

(15)

where Z6=0 in,the smectic A phase but not is the angle in the hexatic phase, and between the in-plane component of the wavevector transfer q and one reference axis x (see the schematic diagram of a typical X-ray scattering pattern of the SmB,,, phase shown in Fig. 14). The order parameter can thus be chosen as Y=I, e6@. In that respect, the SmB,,,-SmA transition could be interpreted as belonging to the superfluid helium universality class [114],

x

5.1 General Presentation In the hexatic phase, the molecules are distributed on a hexagonal lattice, but the positional order does not extend over distances larger than a few hundred angstroms, whereas the bond orientational order extends over very large distances (long range

Figure 14. Schematic diagram showing a typical Xray scattering pattern of the SmB,,, phase.

5

1

0'

66 5

I

650BC

I

I

67.0

Hexatic B to SmecticA (SmBl,,,-SmA) transition

I

I

67.5

I

I

68.0 TEMPERATURE ("C)

L

68.5

Figure 15. Temperature dependence of the heat capacity at the SmB,,,-SmA transition for compound 2 (after [ I 171).

2

with the exponent of the specific heat, a, equal to -0.007. In experimental studies, a was found to be close to 0.6 [117, 1181 (Fig. 15), and the transition appeared to be continuous [I 191. One possible explanation for the large heat capacity critical exponent ( a z 0 . 6 ) of the SmB,,,-SmA transition is the proximity of a critical point, resulting from the coupling of bond orientational order with some herringbone order [ 1 181. Another explanation may be related to the difficulty in fitting the experimental data. Other calorimetric studies have been performed on a different sample [ 1201, but the heat capacity data could not be fitted with a power law expression, and the transition was confirmed as having an asymmetric first order nature. On the same sample, sound damping measurements have shown the importance of the fluctuations of the hexatic order parameter around the SmB,,,-SmA transition [ I2 I 1. Recent results on new compounds ( a zO.l-0.20) are still not consistent with theoretical predictions [ 1221.

37

5.2 SmB,,,-SmA Transition in Thin Films The free-standing film is a very interesting physical system, in which the sample thickness can very easily be varied from two to a few hundred molecular layers. It can be used to test the theories of two-dimensional melting, the evolution of phase transitions as a function of the dimensionality of the system, and to investigate substrate-free, two-dimensional transitions and the effect of free surfaces [ 1191. In order to analyze the small heat capacity anomalies associated with phase transitions in very thin films, a new AC calorimeter technique has been set up [123]. Thus detailed calorimetric studies of free-standing liquid crystal films have been performed near the SmB,,,-SmA transition of several compounds [ 124- 1261. Let us consider in detail the results for a ten layer film, as illustrated in Fig. 16. It is interesting to see the three distinct heat capacity peaks and one heat capacity jump. Near 7 1 "C, the layers standing on the outer surfaces undergo a transition to the hexatic phase. Then the two layers adjacent to the former ones undergo a transition to the hexatic phase at 65 "C. Finally, the six interior layers transform into the hexatic phase at 64.5"C, corresponding to the largest peak. This behavior, typical of thin free-standing films, shows that the StnBh,,-SmA transition is a layer-by-layer transition, occurring in three steps, with first a surface ordering developed at high temperature (hexatic order on a liquid-like substrate). For films thicker than 300 layers, the data indicate that the SmB,,,-SmA transition is continuous. Further experiments on two layer films clearly show a sharp anomaly in the heat capacity behavior, suggesting that the SmB,,,-SmA transition is not well described by the theory of defect-mediated


38

4.5

t

-."

I

t

mz4.0 g

750BC

1

8

:

1

v 5.

)i

$ 3.5.

u"

Surface CryE 3,0 Transition L

Interior HexB Transition

Adjacent HexB Transition

L

/. .

.

I

.

.

I

.

.

.

*

Surface Transition

.

Figure 16. Temperature dependence of

.

the heat capacity of a ten-layer freestanding film of compound 3 (after

,

.

i .

.

.

,

phase transitions [ 1011. Moreover, the critical exponent a (=0.28+0.05) found in these systems indicates that some additional long range order (which contributes to the divergent nature of the heat capacity anomaly) should also exist at this transition. Indeed, in a very recent study on a compound that does not exhibit herringbone order, the pretransitional divergence in the heat capacity is still present in thin films [127], indicating that the two-dimensional melting theory in its present form is not able to describe completely the SmB,,,-SmA transition in liquid crystal thin films. In conclusion, the physical origin of the surface order in free-standing films is not fully understood. It seems that the smectic C (see Sec. 4.6) as well as the hexatic B smectic phases are stabilized by a free surface with respect to the smectic A phase (see data reported above). X-ray measurements have shown that the layer fluctuations become very small close to the surface of the films [ 1281,and some theoretical arguments [129] are in favor of a quenching of the layer fluctuations, resulting in an enhancement of the hexatic surface order.

.

.

.

[1191). H

l

,

c

5

0

I

~ o 0-C7H15

6 Induced Phase Transitions A large variety of external fields can be applied to a liquid crystal (magnetic field, surface field, etc.). Here, we report only on the phase transitions induced by applying a mechanical and an electrical field, and phase transitions induced photochemically.

6.1 Mechanically Induced SmA-SmC Transition Ribotta and co-workers were the first to observe that a uniaxial pressure applied normal to the smectic A layers induces a transition to the smectic C phase when the stress exceeds a threshold value [ 1301. The behavior is much more pronounced when the stress is applied at a temperature close the SmA-SmB transition. The finite tilt angle induced can be directly related to B, the elastic constant of compression. Further studies have shown that the temperature dependence of the critical stress and strain re-

6 Induced Phase Transitions

39

6.2 Electrically Induced Transitions

Ternper'irurc

(

C)

Figure 17. Pressure-temperature diagram of p-ethoxybenzoic acid showing the occurrence of nematic and smectic phases at high pressure (after [1341). (1 bar= 1 x lo5 N rn-'.)

quired to mechanically induce one phase from the other allows the Landau parameters of the transition to be determined [ 1311. More recently, it has also been shown that the first order phase transition between the smectic A and smectic C* phases in freely suspended films can be induced by changes in the tension of these films [ 1321. High isotropic pressure has also been proved to induce mesomorphism [ 1331, and in particular to induce a liquid crystalline behavior in compounds that do not form liquid crystalline phases at atmospheric pressure (Fig. 17) [134]. The case of the reentrant nematic phase, discovered by applying high pressure, is also now famous ([ 1351and Sec. 6.4 of Chap. VII of Vol. 1 of this handbook).

Concerning the same transition, an induced SmA-SmC* transition was observed when an electric field was applied in a chiral compound at a temperature near the transition [ 136, 1371, the SmA-SmC* transition temperature increasing under an electric field (Fig. 18). This field-induced transition was attributed to the large spontaneous polarization and to the first order behavior of the transition. Further studies have shown that the first order transition between the polarized smectic A phase and the ferroelectric smectic C* phase terminates at a critical point in the temperature-electric field plane [1.38, 1391. In a recent work, isotropic-nematicsmectic A phase transitions in thermotropic liquid crystals were also induced by applying an electric field [140]. The liquid crystal investigated (a mixture of 8CB and lOCB) showed a first order isotropic to smectic A transition. When in the isotropic phase and near the spontaneous transition temperature, a field-induced first order transition was observed from a paranematic to a nonspontaneous nematic phase. For higher values of the applied electric field, another first order transition occurred from the nonspontaneous nematic to a phase exhibiting the same order as a smectic A phase. A phenomenological Landau-de Gennes model has been developed to describe these transitions [ 1411.

6.3 Photochemically Induced Transitions The photochemically induced nematic/ isotropic phase transition was first described by Pelzl [ 1421. More recently, pho-

Fi


40 76 74 72 70 68

64

0

2

4

6

8

10

0

2

4

6

8

10

27

0

2

4

6

8

10

168 14

0

2

4

6

8

1

0

170

166

164 1620

2

0

4

6

8

10

2

4

6

8

1

0

Figure 18. SmA-SmC* transition temperature ("C) as a function of the applied electric field for different compounds [(a)-(f)] (the abscissa is the field strength in V/pm) (after [1371).

Applied electric field (V/ym) Trans

Cis 366nm

-

N=N

A

>420nm or thermal

\-

- 0.56nm

Figure 19. The isomerization of azobenzene (after [1451).

toisomerizing azo-molecules dissolved in host liquid crystals in the nematic phase were demonstrated to induce a reversible isothermal transition to the isotropic phase upon conversion of the azo-molecules from their trans-isomeric state to the cis state

(Fig. 19) [143, 1441. The assumption is that the bent cis-isomer is less easily packed into the nematic matrix than the linear transform, and tends to disrupt the packing of neighboring liquid crystal molecules. An increase in the cis-isomer population produces a corresponding reduction in the order of the system, eventually giving rise to complete isotropy. More recently, mesomorphic azo-dyes incorporated into ferroelectric liquid crystals were shown to induce a reversible isothermal phase transition from a smectic phase to a second smectic phase of higher symmetry, or simply to reduce the level of order of a given smectic phase, without causing a complete transition to a higher symmetry phase [145]. Both effects are achieved by the UV (ultraviolet)

7

excitation of the mesomorphic azo-molecules dissolved at low concentrations in the host.

7

Other Transitions I

41 I

Other Transitions

7.1 Smectic C to Smectic I (SmC-SmI) Transition In both smectic C and I phases, the molecules are tilted within the smectic layers. On decreasing the temperature, the SmC-SmI transition corresponds to the establishment of a hexatic order in the smectic I phase, characterized by a three-dimensional long range bond orientational order combined with a short range positional order within the smectic layers. This has been shown in general to be a strong first order transition by dilatometric experiments (Fig. 20) [ 1461. In the case of a TBDA (terephthal-his-4,ndecylaniline) compound, the SmC-SmI transition is accompanied by a sudden jump of the tilt angle from 15" in the SmI phase to almost 30" in the smectic C phase. It has been proposed [ 1461 that this phenomenon is related to the fact that the positional order in the SmI phase is efficient enough to lock the molecules in well defined relative positions and to fix the tilt angle with respect to the layers at a given constant value. At the transition, the molecular interactions lose their efficiency and molecules tilt more drastically in order to relax the elastic constraints imposed upon the paraffinic chains of the molecules. Heat capacity measurements performed on several compounds around the SmCSmI transition seem to confirm its first order nature, but they are only able to provide a qualitative description [ 147, 1481. These results are consistent with X-ray results, indicating the existence of a small but finite

555

t I

long range bond orientational order in the smectic C phase [ 1491. Finally, the first observation of a smectic C-smectic I critical point was reported very recently [ 1501. The experimental data obtained by X-ray diffraction indicate that the molecular tilt induces hexatic order even in the smectic C phase, and therefore both smectic C and I phases should be considered to have the same symmetry.

7.2 Smectic C to Smectic F (SmC-SmF) Transition The smectic F phase can also be considered as a tilted hexatic phase similar to the smectic I phase, the difference between the two phases lying in the direction of the long molecular axes with respect to the two-dimensional arrangement within the smectic layers [151]. Calorimetric and X-ray diffraction studies of several compounds of the homologous TBnA series carried out around the SmC-SmF transition clearly indicate the first order nature of the corresponding transition, with, in particular, a jump in the


42

bond orientational order [152, 1531. In a very recent work, a synchrotron X-ray diffraction study of the transition in thin, freely suspending films was reported [ 1541. The SmC-SmF transition was found to be strongly first order even in films as thin as 60 layers, in contrast with the Kosterlitz-Thouless theory of melting of two-dimensional systems (hexatic to isotropic phase transition) [ 1041.

7.3 Smectic F to Smectic I (SmF-SmI) Transition In the smectic F phase, all the long molecular axes are tilted towards the longest side of a rectangular cell, whereas in the smectic I phase, the long molecular axes are tilted along the shortest side of a rectangular cell (Fig. 21) [155]. The SmF-SmI transition has been seen to be continuous [ 1461 or weakly first order [151], with no discontinuity in the variation of the molar volume nor in that of the layer spacing. Two processes have been proposed to explain the transition. In the first one, the lattice remains fixed and all the long molecular axes perform a collective rotation around the layer normal with no change of the tilt angle; in the second case, the molecular axes remain unchanged but there is a rotation of the spatial arrangement. Other experimen-

tal studies are still needed to distinguish between the collective molecular rotation and the lattice rotation.

7.4 Smectic F to Smectic Crystalline G (SmF-SmG) Transition Dilatometric measurements have shown that the SmF-SmG transition is continuous (Fig. 22) [ 1461or exhibits a very small jump of volume [ 1561. This is surprising since the transition corresponds to large structural changes. First, the three-dimensional correlations between layers present in the SmG phase no longer exist in the SmF phase. Second, the positional order within the layers, which is long range in the SmG phase, only extends over a few hundreds angstroms in the SmF phase. Moreover, the layer thickness does not show any discontinuity at the transition, and the diffuse peaks in the SmF phase are observed in the same region as the Bragg peaks in the SmG phase. Recent deu-

U tilt to side of hexagonal net

(SF)

tilt to apex of

hexagonal net (S,)

Figure 21. Different tilt directions in SmF and SmI phases (after [155]).

5 90 105

T (OC)

125

Figure 22. Molar volume of TBDA in the vicinity of the SmG-SmF transition (after [146]).

8

terium NMR (nuclear magnetic resonance) studies [ 1571show that the SmF-SmG transition is characterized by the absence of any variation of the molecular orientational order across the transition, implying local herringbone order in the SmF phase. Therefore, the orientational order does not seem to play a significant role in the transition. All these results seem to indicate that the SmF-SmG transition does not change the short range structure, and that the aliphatic chains, by melting, play a predominant role [ 1581. In the case of another compound [ 1561, strong hysteresis effects have been observed concerning this transition. These effects have been interpretated as being due to the significant role played by dislocations and defects at the transition. Acknowledgements: The author thanks Prof. Y. Galerne for helpful discussions.

8 References [I] P. G. de Gennes. Mol. Cryst. Liq. Cryst. 1971, 12, 193. [2] M. A. Anisimov, Mol. Cryst. Liq. Cryst. 1988, 162A, I . [ 3 ] E. F. Gramsbergen, L. Longa, W. H. de Jeu, Phys. Rep. 1986, 135, 195. [4] T. W. Stinson, J. D. Litster, Phys. Rev. Lett. 1970, 25, 503. [S] C. Chu, C. S. Bak, F. L. Fin, Phys. Rev. Lett. 1972,28, 1111. [6] T. W. Stinson, J. D. Litster, Phys. Rev. Lett. 1973, 30, 688. [7] E. Gulary, B. Chu, J. Chem. Phys. 1975, 62, 798. [8] T. W. Stinson, J. D. Litster, N. A. Clark, J. Phys. Paris 1979, 33, 69. [9] B. Pouligni, J. P. Marcerou, J. R. Lalanne, H. Coles, Mol. Phys. 1983,49, 583. [lo] C. Strazielle, H. J. Coles, J. Phys. Paris 1979, 408, 95. [I I ] B. Malraison, Y. Poggi, C. Filippini, Solid State Commun. 1979,31,843. [ 121 J. Thoen, H. Marynissen, W. Van Dael, Phys. Rev. A 1982,26, 2886. [13] P. H. Keyes, Phys. Lett. 1978, 67A, 132.

References

43

[I41 A. Gohin, C. Destrade, H. Gasparoux, J. Prost, J . Phys. Paris 1983, 44, 427. [IS] L. V. AdLhemyan, L. T. Adzhemyan, A. Y. Volkov, L. A. Zubkov, I. V. Melnik, V. P. Romanov, Sov. Phys. JETP 1984,60,712. [ I 6 1 H. Zink, W. H. de Jeu, Mol. Cryst. Liq. Cryst. 1985,124, 287. [ 171 W. L. McMillan, Phys. Rev. A 1971, 4, 1238. [ IC;] P. G. deGennes,SolidState Commun. 1972,107, 53. P. G. de Gennes, Mol. Cryst. Liq. Cryst. 1973, 21,49. W. L. McMillan, Phys. Rev. A 1972, 6, 936. W. Wagner, Mol. Cryst. Liq. Cryst. 1983,98,247. C. W. Garland, M. Meichle, B. M. Ocko, A. R. Kortan, C. R. Safinya, J. L. Yu, J. D. Litster, R. J. Birgeneau, Phys. Rev. A 1983, 27, 3234. J. Thoen, H. Marynissen, W. Van Dael, Phys. Rev. Lett. 1984,52,204. J. H. Marynissen, J. Thoen, W. Van Dael, Mol. Cryst. Liq. Cryst. 1985, 124, 195. E. F. Gransbergen, W. H. de Jeu, J. Chem. Soc., Furaday Trans. I1 1980, 84 (8), 1015. V. G. K. Pisipati, N. V. S. Rao, D. M. Potukuchi, P. R. Alapati, P. B. Rao, Mol. Cryst. Liq. Cryst. 1989, 167, 167. K. J. Stine, C. W. Garland, Phys. Rev. A 1989, 39, 3148. J. Thoen, R. Parret, Liq. Cryst. 1989, 5, 479. L. Cheung, R. B. Meyer, H. Gruler, Phys. Rev. Lett. 1973, 31, 349. M. Delaye, R. Ribotta, G. Durand, Phjs. Rev. Lett. 1973, 31,443. R. Mohmood, D. Brisbin, 1. Kahn, C. Gooden, A. Baldwin, D. Johnson, Phys. Rev. Lett. 1985, 54, 1031. A. de Vries, Mol. Cryst. Liq. Cryst. 1970,10,3 I; 1970, 10, 219. J. D. Litster, R. J. Birgeneau, M. Kaplan, C. R. Safinya, J. Als-Nielsen in Ordering in Strongly Fluctuating Condensed Matter Systems (Ed.; T. Riste), Plenum, New York 1980. J. D. Litster, J. Als-Nielsen, R. J. Birgeneau, S . S. Dana, D. Davidov, F. Garcia-Golding, M. Kaplan, C. R. Safinya, R. J. Schaetzing, J. Phys. Paris (Suppl. C3) 1979,40, 339. K. W. Evans-Lutterodt, J. W. Chung, B. M. Ocko, R. J. Birgeneau, C. Chiang, C. W. Garland, J. W. Goodby, Nguyen Huu Tinh, Phys. Rev. A 1987, 36, 1387. C. R. Safinya, R. J. Birgeneau, T. D. Litster, M. E. Neubert, Phys. Rev. Lett. 1979, 43. 1171. R. J . Birgeneau, C. W. Garland, G. B. Kasting, B. M. Ocko, Phys. Rev. A 1981,24, 2624. B. M. Ocko, R. J . Birgeneau, J. D. Litster, M. E. Neubert, Phys. Rev. Lett. 1981, 52, 208. D. Davidov, C. R. Safinya, M. Kaplan, S. S . Dana, R. Schaetzing, R. J. Birgeneau, J. D. Litster, Phys. Rev. B 1979, 19, 1657.

44


[40] C. Dasgupta, B. I. Halperin, Phys. Rev. Lett. 1981,47, 1556. [41] C. W. Garland, G. Nounesis, K. J. Stines, Phys. Rev. A 1989,39,4919. 1421 D. R. Nelson, J. Toner, Phys. Rev. B 1981,24,363. [43] J. Toner, Phys. Rev. B 1982, 26,462. [44] D. Brisbin, R. de Hoff, T. E. Lokhart, D. L. Johnson, Phys. Rev. Lett. 1979,43, 1171. [45] C. W. Garland, G. Nounesis, Phys. Rev. E 1994, 49, 2964. [46] B. R. Patton, B. S. Anderek, Phys. Rev. Lett. 1992,69, 1556. [47] B. S. Anderek, B. R. Patton, Phys. Rev. E 1994, 49, 1393. [48] P. G. de Gennes, C. R. Acad. Sci. Paris 1972, B274, 758. [49] M. Delaye, J. Physique Paris 1979,40, C3-350. [SO] Y.Galerne, Phys. Rev. 1981, A24, 2284. [51] V. L. Ginzburg, Sov. Phys. Solid State 1960, 2, 1824; L. P. Kadanoff, W. Goetze, D. Hamblen, R. Hecht, E. A. Lewis, D. Davidov, V. V. Palciaukas, M. Rayl, J. Swift, D. Aspnes, J. Kane, Rev. Mod. Phys. 1967,39,365. [52] C. R. Safinya, M. Kaplan, J. Als-Nielsen, R. J. Birgeneau, D. Davidov, J. D. Litster, D. L. Johnson, M. E. Neubert,J. Phys. Rev. B 1980,21,4149. [53] C. C. Huang, J. M. Viner, Phys. Rev. A 1982,25, 3385. [S4] R. J. Birgeneau, C. W. Garland, A. R. Kortan, J. D. Litster, M. Meichle, B. M. Ocko, C. Rosenblatt, L. J. Yu, J. W. Goodby, Phys. Rev. A 1983, 27, 1251. [55] J. Thoen, G. Seynhaeve, Mol. Cryst. Liq. Cryst. 1985,127,229. [56] M. Meichle, G. W. Garland, Phys. Rev. A 1983, 27,2624. [57] S. Dumrograttana, G. Nounesis, C. C. Huang, Phys. Rev. A 1986, 33,2 181. [58] Y. Galerne, J. Physique Paris 1985,46, 733. [S9] D. Guillon, A. Skoulios, J. PhysiqueParis 1977, 38,79. [60] D. Collin, J. L. Gallani, P. Martinoty, Phys. Rev. Lett. 1988, 61, 102. [61] P. Das, K. Ema, C. W. Garland, Liq. Cryst. 1989, 4,205. [62] D. Collin, S. Moyses, M. E. Neubert, P. Martinoty, Phys. Rev. Lett. 1994, 73, 983. [63] C. A. Schantz,D. L. Johnson,Phys. Rev. A 1978, 17, 1.504. [64] A. Zywocinski, S . A. Wieczorek, Phys. Rev. A 1985,31,479. [65] L. Benguigui, P. Martinoty, Phys. Rev. Lett. 1989,63, 774. [66] M. Petrov, L. Komitov, P. Simova, G. Hauck, Phys. Status SolidiA 1985,89,451. [67] R. de Hoff, R. Biggers, D. Brisbin, D. L. Johnson, Phys. Rev. A 1982, 25,472. [68] S. C. Lien, C. C. Huang, Phys. Rev. A 1984,30, 624.

[69] R. de Hoff, R. Biggers, D. Brisbin, R. Mahmood, C. Gooden, D. L. Johnson, Phys. Rev. Lett. 1988, 61, 664. [70] C. C. Huang, S. C. Lien, Phys. Rev. Lett. 1981, 47, 1917. [71] J. Boerio-Goates, C. W. Garland, R. Shashidar, Phys. Rev. A 1990,41,3192. [72] R. Dabrowski, J. Szulc, B. Sosnowska, Mol. Cryst. Liq. Cryst. 1992,215, 13. [73] M. Koden, T. Anabuki, K. Nakagawa, K. Awane, Jpn. J. Appl. Phys. 1991,30, 1129. [74] S. Kumar, Phys. Rev. A 1981, 23, 3207. [75] S. Prasad Krishna, V. N. Raja, D. S. Rao, G. G. Nair, M. E. Neubert, Phys. Rev. A 1990, 42, 2479. [76] M. Koden, T. Anabuki, Ferroelectrics 1991, 121,295. [77] H. Y. Liu, C. C. Huang, T. Min, M. D. Wand, D. M. Walba, N. A. Clark, C. Bahr, G. Heppke, Phys. Rev. A 1989,40,6759. [78] C. Bahr, G. Heppke, Mol. Cryst. Liq. Cryst. Lett. 1986,4, 31. [79] B. R. Ratna, R. Shashidar, G. G. Nair, S. Prasad Krishna, C. Bahr,G. Heppke, Phys. Rev. A 1988, 37, 1824. [80] G. Heppke, D. Loetzsch, R. Shashidar, Liq. Cryst. 1989, 5,489. [81] H. Y. Liu, C. C. Huang, C. Bahr, G. Heppke, Phys. Rev. Lett. 1988, 61, 345. [82] R. Shashidar,B. R. Ratna, G. G. Nair,S. Prasad, C. Bahr, G. Heppke, Phys. Rev. Lett. 1988, 61, 547; J. Zubia, M. Castro, J. A. Puertolas, J. Etxebarria, M. A. Perez Jubindo, M. R. de la Fuente, Phys. Rev. E 1993,48, 1970. [83] R. B. Meyer,Mol. Cryst. Liq. Cryst. 1977,40,33. [84] S. Dumrongrattana, C. C. Huang, Phys. Rev. Lett. 1986, 56, 464; C. C. Huang, S . Dumrongrattana, Phys. Rev. A 1986,34, 5020. [85] B. Zeks, Mol. Cryst. Liq. Cryst. 1984,114,259; T. Carlsson, B. Zeks, A. Levstik, C. Filipic, I. Levstik, R. Blinc, Phys. Rev. A 1987,36,1484. [86] R. Blinc, B. Zeks, M. Copic, A. Levstik, I. Musevic, I. Drevensek, Ferroelectrics 1990, 104, 159. [87] D. L. Johnson, J. Chim. Physique 1983,80,4S. [88] G. Sigaud, F. Hardouin, M. F. Achard, Solid State Commun. 1977, 23, 35. [89] D. L. Johnson, D. Allender, R. de Hoff, C. Maze, E. Oppenheim, R. Reynolds, Phys. Rev. B 1977, 16, 470. [90] R. Shashidar, B. R. Ratna, S. Krishna Prasad, Phys. Rev. Lett. 1984,53, 2141. [91] J. H. Chen, T. C. Lubensky, Phys. Rev. A 1976, 14, 1202. [92] M. A. Anisimov, V. P. Voronov, A. 0. Kulkov, F. J. Kholmurodov, J. Physique Paris 1985, 46, 2137. [93] L. J. Martinez-Miranda, A. R. Kortan, R. J. Birgeneau, Phys. Rev. Lett. 1986, 56, 2264.

8

[94] L. J. Martinez-Miranda, A. R. Kortan, R. J. Birgeneau, Phys. Rev. A 1987,36,2372. 1951 D. Brisbin, D. L. Johnson, H. Fellnert, M. E. Neubert, Phys. Rev. Lett. 1983, 50, 178. [96] M. A. Anisimov, V. P. Voronov, Liq. Cryst. 1988,3,403. [97] T. C. Lubensky, Mol. Cryst. Liq. Cryst. 1987, 146, 55. [98] G. Grinstein, J. Toner, Phys. Rev. Lett. 1983, 51, 2386. [99] R. de Hoff, R. Biggers, D. Brisbin, R. Mahmood, C. Gooden, D. L. Johnson, Phys. Rev. Lett. 1981,47, 664. [IOO] A. Kallel, Y. Mlyk, Phase Trans. 1991, 33, 261. [ l o l l C. Bahr, lnt. J . Mod. Phys. 1994, B8, 3051. [lo21 B. M. Ocko, A. Braslau, P. S . Pershan, J. AlsNielsen, M. Deutsch, Phys. Rev. Lett. 1986,57, 94. [lo31 P. S . Pershan, J . Phys. Paris 1989, 50, 1; P. S . Pershan, A. Braslau, A. H. Weiss, J. Als-Nielsen, Phys. Rev. A 1987, 35, 4800. [lo41 J. M. Kosterlitz, D. J. Thouless, J. Phys. Paris 1972, C5, 124; 1973, C6, 1181. [lOS] C. Y. Young, R. Pindak, N. A . Clark, R. B. Meyer, Phys. Rev. Lett. 1978, 40, 773. [lo61 C. Rosenblatt, R. Pindak, N. A. Clark, R. B. Meyer, Phys. Rev. Lett. 1979, 42, 1220. 11071 C. Rosenblatt, R. B. Meyer, R. Pindak, N. A. Clark, Phys. Rev. A 1980, 21, 140. [I081 R. Pindak, C. Y. Young, R. B. Meyer, N. A. Clark, Phys. Rev. Lett. 1980, 45, 1193. [ 1091 S. Heinekamp, A. Pelcovits, E. Fontes, E. Y. Chen, R. Pindak, R. B. Meyer, Phys. Rev. Lett. 1984,52, 1017. [I101 S. M. Amador, P. S . Pershan, Phys. Rev. A 1990,41,4326. [111] C. Bahr, D. Fliegner, Phys. Rev. A 1992, 46, 7657. [112] I. Kraus, P. Pieranski, E. Demikhov, H. Stegerneyer, J. W. Goodby, Phys. Rev. E 1993, 48, 1916; I. Kraus, P. Pieranski, E. Demikhov, H. Stegerneyer, J. W. Goodby, A. Slaney, M. Osipov, Ber. Bunsenges. Phys. Chem. 1993, 97, 1376. [ 1131 C. Bahr, D. Fliegner, Phys. Rev. Lett. 1993, 70, 1842. [I141 R. Pindak, D. E. Moncton, S . C. Davey, J. W. Goodby, Phys. Rev. Lett. 1981, 46, 1135. [115] R. J. Birgeneau, J. D. Litster, J. Phys. Paris Lett. 1978, 39, 399. [ 1161 B. I. Halperin, D. R. Nelson, Phys. Rev. Lett. 1978, 41, 121; D. R. Nelson, B. I. Halperin, Phys. Rev. B 1979, 19, 2457. [117] C. C. Huang, J. M. Viner, R. Pindak, J. W. Goodby, Phys. Rev. Lett. 1981, 46, 1289. [ 1 181 T. Pitchford, G . Nounesis, S. Dumrograttana, J. M. Viner, C. C. Huang, J. W. Goodby, Phys. Rev. A 1985,32, 1938.

References

45

[ 1 191 C. C. Huang, T. Stoebe, Adv.Phys. 1993,42,343. (1201 C. C. Huang, G. Nounesis, D. Guillon, Phys. Rev. A 1986, 33, 2602. [I211 J. L. Gallani, P. Martinoty, D. Guillon, G. Poeti, Phys. Rev. A 1988, 37, 3638. 11221 G. Iannacchione, E. Gorecka, W. Pyzuk, S . Kumar, D. Finotello, Phys. Rev. E 1995.51, 3346. [I231 R. Geer, C. C. Huang, R. Pindak, J. W. Goodby, Phys. Rev. Lett. 1989, 63, 540; R. Geer, T. Stoebe, T. Pitchford, C. C. Huang, Rev. Sci. Instrum. 1991, 62, 415. [I241 R. Geer, T. Stoebe, C. C. Huang, J. W. Goodby,M. Cheng, J. T. Ho, s. W. Hui, Nature 1992, 355, 152. [I251 C. C. Huang, R. Geer, T. Stoebe, Mol. Cryst. Liq. Cryst. 1992, 212,9. [I261 T. Stoebe, C. C. Huang, J. W. Goodby, Phys. Rev. Lett. 1992, 68, 2944. [127] A. J. Jin, M. Veurn, T. Stoebe, C. F. Chou, J. T. Ho, S. W. Hui, V. Surendranath, C. C. Huang, Phys. Rev. Lett. 1995, 74, 4863. 1281 D. J. Tweet, R. Holyst, B. D. Swanson, H. Stragier, L. B. Sorensen, Phys. Rev. Lett. 1990, 65, 2157. 1291 R. Holyst, Phys. Rev. B 1992, 46, 15542. 1301 R. Ribotta, R. B. Meyer, G. Durand, J. Physique Lett. 1974,35, 161; R. Bartolino, G. Durand, Phys. Rev. Lett. 1977, 39, 1346. 1311 R. Bartolino, G. Durand, J . Physique Paris 1984, 45, 889. [132] I. Kraus, P. Pieranski, E. Demikhov, J . Phys. Condens. Matter 1994, 6, A415. 11331 J. Robberecht, Bull. Soc. Chim. Belg. 1938,47, 537. [13,4] S . Chandrasekhar, S . Ramaseshan, A. S . Presham Wala, B. K. Sadashiva, V. Surendranah, Prumana Supplement I 1973, 117; R. Shashidar, S. Chandrasekhar, J. Physique Coll. 1985, 36, C1-48. 11351 P. E. Cladis, Phys. Rev. Lett. 1975, 35,48. 11361 C. Bahr, G. Heppke, Mol. Cryst. Liq. Cryst. 1987, 150b, 313. (1371 S. Kobayashi, S . Ishibashi, Mol. Cryst. Liq. Cryst. 1994, 2.57, 18 1. [138] C.Bahr, G.Heppke, Phys. R e v . A 1989, 39, 5459. 11391 C. Bahr,G. Heppke,Phys. Rev. A 1991,44,3669. 11401 1. Lelidis, G. Durand, Phys. Rev. Lett. 1994, 73, 672. [ 14 I1 I. Lelidis, Thesis, University of Orsay, 1995. [ 1421 G. Pelzl, Z. Chem. 1977, 17, 294. [ 1431 T. Ikeda, T. Miyamoto, S. Kurihara, S. Tazuke, Mol. Cryst. Liq. Cryst. 1990, 188, 207. [144] C. H. Legge, G. R. Mitchell, J . Phys. D 1992, 25, 492. [ 1451 H. J. Coles, H. G. Walton, D. Guillon, G. Poeti, Liq. Cryst. 1993, 15, 551; 1994, 17, 333. [I461 D. Guillon, A. Skoulios, J. J. Benattar, J. Physique Paris 1986, 47, 133.

46


[I471 J. M. Viner, C. C. Huang, Phys. Rev. A 1983, 27, 2763. [I481 C. W. Garland, J. D. Litster, K. J. Stine, Mol. Cryst. Liq. Cryst. 1989, 170, 71. [I491 J . D. Brock, R. J. Birgeneau, J. D. Litster, A. Aharony, Contemp. Phys. 1989,30,321. [I501 S. KrishnaPrasad,D. S . ShankarRao,S. Chandrasekhar, M. E. Neubert, J. W. Goodby, Phys. Rev. Lett. 1995, 74, 270. [I511 J. J. Benattar, F. Moussa, M. Lambert, J. Chim. Physique 1983, 86,99. [152] K. J. Stine, C. W. Garland, Phys. Rev. A 1989, 39, 3148. [I531 D.Y. Noh, J. D. Brock, J. D. Litster, R. J. Birgeneau, J. W. Goodby, Phys. Rev. B 1989,40,4920. [I541 Q . J. Harris, D. Y. Noh, D. A. Turnbull, R. J. Birgeneau, Phys. Rev. E 1995,51,5797. [I551 G. W. Gray, J. W. Goodby, Smectic Liquid Crystals, Leonard Hill, London 1984. [I561 Y. Thiriet, J. A. Schulz, P. Martinoty, D. Guillon, J. Physique Paris 1984, 45, 323. [I571 J. L. Figueirinhas, J. W. Doane, Mol. Cryst. Liq. Cryst. 1994,238, 61. [I581 F. Moussa, J. J. Benattar, C. Williams, Mol. Cryst. Liq. Cryst. 1983, 99, 145.

[I591 M. Z. Cherkaoui, J. F. Nicoud, Y. Galerne, D. Guillon, J. Physique Paris 1995,5, 1263. [I601 P. G. de Gennes, J. Prost, The Physics of Liquid Crystals, Clarendon, Oxford 1993. [I611 S. Chandrasekhar, Liquid Crystals, Cambridge University Press, Cambridge 1992. [ I621 M. A. Anisinov, Critical Phenomena in Liquids and Liquid Crystals, Gordon and Breach, London 1991. [I631 J. D. Litster, Critical Phenomena, McGrawHill, New York 1971. [ 1641 Phase Transitions in Liquid Crystals (Eds.: S. Martelluci, A. N. Chester), NATO AS1 Series Series B: Physics, Plenum, New York 1992,290. [I651 J. D. Litster, Phil. Trans. Roy. SOC., London 1983, A309, 145. [166] P. S. Pershan, Structure of Liquid Crystals, World Scientific, Singapore 1988. [ 1671 G. Vertogen, W. H. de Heu, Thermotropic Liquid Crystals, Fundamentals, Springer, Berlin 1988. [I681 Advances in Liquid Crystals, Vols. 1-6 (Ed.: G. H. Brown).


Chapter I11 Nematic Liquid Crystals

Synthesis of Nematic Liquid Crystals Kenneth J. Toyne

1.1 Introduction This brief account of methods for the synthesis of nematic liquid crystals concentrates on the most frequently encountered core systems, linking and terminal groups: the synthetic methods presented are often applicable to more unusual nematogens and to compounds showing other mesophases (see V. Vill in Volume 1, Chapter IV on General Synthetic Strategies). In general, but not exclusively [ 11, calamitic nematic liquid crystals are characterized by their elongated, lath-like shape which can be achieved in a variety of ways, including the following: by appropriate substitution in certain types of ring system which are used to provide some rigidity for the molecule: by using selected linking groups to connect the rings, broadly to preserve the linearity of the molecule: and by choosing terminal substituents which provide a necessary fluidity or give increased intermolecular associations. A general representation which summarizes the typical features required is

R'-A-[L]-B-[L]-C-[L]-D-R2 where R ' and R2 are terminal groups; A, B, C, D are the same or different ring systems,

and usually two to four of these units are present, L represents specific linking groups or the direct attachment of rings by a single bond. Large numbers of examples of terminal groups [2-41 have been considered and compared, and some of the most common of these, along with typical rings and linking groups, are listed below. Kings:

Linking groups:

single bond, -CH=CH-, -C 0) is the anisotropy of the dielectric constant. Note that in electrically driven cells the cell thickness plays no role in the critical voltage, as both the electrical and the elastic free energy terms are scaled in an equal manner. Only the dielectric anisotropy enters the equations as an additional parameter. Like in the magneto-optical method, optical detection may be applied in the electrically driven case as well. As an alternative, the cell capacitance C is a convenient measure of the transition threshold and the tilt deformation of the director field. The capacitance versus voltage curves can be used to determine the dielectric and elastic constants and the surface tilt angles [ 191. K , is given by the critical field and K,, is obtained from the slope of the C(u> curve. In the

,

66

2.1

Elastic Properties of Nematic Liquid Crystals

electric experiment, the steepness of the deformation versus voltage characteristics is not determined by the elastic splayhend ratio alone, but also by the dielectric ratio E~,IE which ~ , has to be measured independently. The twist transition can neither be evoked straightforwardly with electric fields nor detected easily with capacitive measurements, although this is possible, in principle, with lateral electrodes (e.g. Pashkovsky et al. [20]), but the director deformation is then complex and two-dimensional. Instead of using a pure twist cell, one can measure K2, from a 90" twisted nematic (TN) planar cell [21-231. The threshold voltage is given by

Koyama et al. [24] have shown that in the planar cell geometry it is possible to determine all three bulk elastic constants as well , as the dielectric coefficients E~~and E ~ and the magnetic anisotropy A x in one cell under simultaneous application of an electric field and a magnetic field and using different orientations of the cell. Before giving analytical expressions for the director deformations in FrCedericksz cells, we will summarize the magnetic and electrical methods. The advantage of electro-optical measurements is that the cell thickness does not enter the equations and is therefore ruled out as an error source. Furthermore, the electric field can always be considered strictly perpendicular to the sample plane. On the other hand, in the electric method conductivity effects can influence the measurements and exact knowledge of E , , and is required to extract the second elastic constant from the birefringence or capacitance characteristics. Moreover, the electric measurement is restricted

to the splay geometry unless one deals with more complex director deformations. A problem with capacitive measurements is that the observable is averaged over the whole electrode plane, and this requires very homogeneously switching cells with no disclinations or defects. When optical detection is used, one can pick a cell region free of disclination lines (which may appear due to the degeneracy of the FrCedericksz transition), and homogeneity of the transition can easily be verified. In magnetic measurements, homogeneity of the driving field has to be guaranteed. The adjustment of the angle between the sample and the field is critical. Small deflections of the magnetic field from the cell normal in splay geometry can lower considerably the apparent threshold field. The exact measurement of the magnetic induction in the sample is not trivial. On the other hand, the advantage of the magnetic method is that one sample cell is sufficient for the determination of all three bulk elastic constants, by applying the magnetic field first in splay and subsequently rotated by 90" in twist geometry. In order to relate the cell capacitance or optical transmission curves in splay or bend geometry to the elastic ratios, exact analytical equations for the director field in the cell are used. The one-dimensional deformation of the director field rz = [cos O(z), 0, sinO(z)] induced by electric or magnetic fields in splay geometry is found by minimizing the free energy d

F = J'f(z>dz= 0

d

I f , (z>+ h (z)dz 0

where f , is the bulk elastic energy density introduced above and ffis the field term

- - 1H B = - p O ( 1 + x l ) H 2 2 +pOAX H~ sin2 8

2.1.2 Measurement of Elastic Constants

in the magnetic case, or

with the effective refraction index neff determined by the director profile,

in the electric case for the electrically isolated cell (constant charge), E is the electric field strength and D the electric displacement. (Gruler and co-workers [ 171 have shown that the Euler-Lagrange equations for a contacted cell (constant voltage) are equivalent.) The Euler-Lagrange variational principle leads to the relations ~

-

~~~-

67

-

X B Isin26, -sin26 do=-I dz dBc 1+qsin28

1

=n, 1 J [1+vsin26(z)]-112 dz d

do where is the optical wavelength, n, and no are the extraordinary and ordinary refractive indices of the nematic respectively, and v=n:/ni- 1. Substitution of Eqs. ( 5 )and (6) gives

for magnetic and and ~~

~

~

~

sin26___ , - sin26 dz 1 (1+q sin2@)(I+< sin26)(l+c sin26,) for electric deflections, which can be integrated to yield the director field. The parameters are the elastic ratio q = K,,/K, - 1 and the dielectric ratio 1. The maximum tilt angle 6, in the cell midplane is related to the electric or magnetic field, respectively, by the self-consistency conditions for electric stimulation

and magnetic stimulation

q is introduced by sin 8 = sin 6 , = sinq, and FA= \ l+Asin 2 6,sin 2 q,(A={q,O just after the phase transition is /N. From the dielectric data on the well oriented sample, only the decrease of the effective dipole moment in the parallel direction can be seen. was deA nearly stepwise change of tected in 4-nitrobenzyl 2,5-bis-(4-n-hexyloxybenzoy1oxy)-benzoate with a molecular shape like a 'h' [136] (see Fig. 13). In all the cases mentioned before, the tendency to form antiparallel oriented aggregates is very high but it can be destroyed by adding of

7

t

$6

0 ' 0.5

I

I

1

5

-

10 fl kHz

1

50

100

Figure 11. The dielectric loss of the sample of Fig. 10 measured parallel to the nematic director [ 1341. The numbers are the temperatures, TIK.

3 70

-

390 TIK

410

Figure 12. Static dielectric constants of the given oxazole derivative 11351.

98

2.2

Dielectric Properties of Nematic Liquid Crystals

anobiphenyl in benzene by Kedziora and Jadzyn [141] and shown in Fig. 14, confirm this idea. But dielectric measurements on reentrant phases give an entirely different picture. The expected big change of the dipolar correlation [ 142- 1441 cannot be found because there is no big difference in the data between the N and the N,., phases in Fig. 15 which can support the model. There 41 3 80

I

I

I

400

TIK-

4 20

J

25 I

440

Figure 13. Static and quasistatic dielectric constants of a laterally branched molecule with a 'h' like shape [136].

T=303K Q

1

10 0

high concentrations of rod-like molecules [137, 1381. By fitting the molecular shapes to each other the antiparallel correlation can easily be changed in a statistical one in a binary system (Sec. 2.2.5 of this Chapter). In the light of these results, the antiparallel orientation of the dipoles in the strong polar derivatives of cyanobiphenyl is not so strong and does not result in a change of sign of the dielectric anisotropy [25] (see Fig. 5).

-

2 3 c/mo[ 1-1

1

4

Figure 14. The apparent dipole moment of 4-n-pentyl-4'-cyanobiphenyl. The line is related to a model of association [141].

2.2.3 The N,, Phenomenon and the Dipolar Correlation The re-entrant phenomenon was discovered on strong polar compounds [139]. Therefore, it was assumed that an equilibrium between monomers and associates is responsible for the return of the nematic phase below a smectic [140]. Without any doubt in strong polar compounds, a reduction of the effective dipole moment ,u to an apcan be observed by dilution of parent paPp the sample in an unpolar solvent. Experimental data, measured on 4-n-pentyl-4'-cy-

,

I

300

,

, , ,,

-

330 TIK

, 360

I

Figure 15. Experimental values of the static dielectric constants, the mean dielectric constant and the static dielectric anisotropy of a mixture with a N,, phase [ 1441.

2.2.4

are only different activation energies for the reorientation around the short molecular axis (EA(N)<EA(N,,) and in a second caseEA(Nr,l)'EA(N) andEA(Ni-e,)<EA(N) were found [ 1431. Also it was found experimentally that the N,, phase appears in relatively unpolar compounds [ 1451. This leads to the conclusion that the existence of reentrant phases is connected with small changes of the dipolar and steric interactions. A detailed discussion of these problems is given by Chandrasekhar [ 1461.

2.2.4 Dielectric Relaxation in Nematic Phases As shown in Fig. 1 the two main relaxation mechanisms (reorientation around the short and long molecular axis) are influenced in different way by the phase transitions. Thereby the reorientation around the short molecular axis characterized by zI1or fRll (zll = (2nfRIl)-' changes stepwise at this transition. From this step the change in the degree of order can be calculated [23], but one has to use the same mechanism in the isotropic state as reference. The last condition is not always fulfilled because of a superposition of different mechanisms [147]. If the sample exhibits a dipole moment only in the direction of the long molecular axis, the theoretical prediction for the step of zll is in a good agreement with the experimental data [36 b]. The absolute value of zll can vary over many decades. At higher temperatures and in samples s with a low viscosity zll can be about [ 1481 and can go to infinity at the glass transition. If the last case is excluded one can try to make an universal model. Starting point is the idea that in general, the relaxation times z,,give a straight line in an Arrhenius plot: In ~ l l =(E,/R) T-'

+ C.

(2)

Dielectric Relaxation in Nematic Phases

99

Eq. (2) can be also used for the clearing temperature T(N/I). By subtracting the same equation at the clearing temperature one can obtain (31

= &R(% - I ) 2, = &R

'Tll/T~l(N/I)

= E,/RT(N/I)

4 = T(N/is)/T

It is shown in Fig. 16 that Eq. (3) is well fulfilled in the homologous series of 4-n-alkyloxyphenyl 4-n-methoxybenzoates. But if one considers samples of different chemical classes [36 c] there are much higher deviations from such a corresponding behavior. Differences in the activation energies can be observed if there is only a short nematic phase range. zll(N/I)can be related to the viscosity of the isotropic phase [36 c]. Equation (3) and the correlation between the viscosity in the isotropic state and zl,(N/I) can be used for estimating approximated values of zllfor a sample with a given clearing temperature. A second result is interesting from theoretical point of view. The question is: are there different relaxation times of mole-

v

0

0.02

004

0.06

0.08

IQR-ll-Figure 16. Dielectric relaxation times of 4-n-alkyloxyphenyl4-methoxybenzoates in a reduced description [148c].

100

2.2

I'l 7


cules with different molecular shapes? The answer is directly related to the problem of different degrees of order in a mixture and the approximation of the mean field model. At first one has to say that there is a strong interaction between the different compounds in a mixture which can be seen in common phase transition temperatures. From the dynamic behavior there are big differences between the sum of the relaxation curves of the single components and the measured absorption of a mixture as demonstrated for four substituted derivatives of phenyl benzoates in Fig. 17 [36 d]. This situation, dominated by the mean field interaction, can be considerably changed if there is a stronger variation of the length-to-width relation of the respective molecules. To investigate this, measurements on small concentrations of a strong polar compound in a nematic mixture have to be carried out. First systematic measurements in this direction were done by Heppke and his coworkers [ 1491. Experimental results [150, 1511 of the four component basic mixture shown in Fig. 17 A

0

E;

Figure 18. Cole-Cole presentation of the mixture from Fig. 17 with 5 mol% of A at T=298 K [150].

are presented in Fig. 18. The separation in two different reorientation ranges in the parallel direction is evident from the two Cole-Cole plots. Furthermore, the following molecules were added to the basic mixture.

C

D For comparison Cole-Cole plots of the basic mixture with D are given in Fig. 19. In contrast to Fig. 18, the added compound D reorients faster than the mixture. By plotting the experimentally obtained relaxation frequencies versus the reciprocal temperature, the following activation energies could be calculated for the solute [150, 1511. compound E,lkJmol-l

0.1

1 flMHz

-

-

A 113

B 89

10

Figure 17. Dielectric loss of the four component mixture Mi, of the single compounds a-d and of the sum of the components at T=325.6 K [36d].

E,

C 64

-

D 55

Figure 19. Cole-Cole plots of the mixture containing 5 mol% of D at T=279.5 K [151].

2.2.4

They indicate the systematic increase of the with elongation of the molecule. In order to make this relation more quantitative, the length-to-width ratio Y was estimated from models of the molecules. Thereby the flexible alkyl chains were neglected. A plot of the relaxation frequencies of the added compounds in the mixture versus Y at 3 13 K in Fig. 20 gives a good correlation. By comparing the relaxation frequencies with the activation energies of the respective samples, it can be seen: the lower thefR the higher the E A values [ 1491. The presented correlations give rise to the possibility of designing mixtures with very low relaxation frequencies useful for a two frequency addressing display [152- 1541. The principle of such display is that, it is driven in the ‘off’ and ‘on’ state by an external electrical voltage. This is possible if a sample exhibits at low frequencies a positive and at high a negative dielectric anisotropy. This can be achieved by a very intensive dielectric ahsorption in the parallel direction which changes the sign of A&’ at the cross-over frequencyfo. One serious problem of this tech-

Dielectric Relaxation in Nematic Phases

101

nique is the temperature dependence of

EA

fo given in the first approximation by that

Figure 20. Dielectric relaxation frequencies of the solute A-D as function of the length-to-width relation r (thereby the flexible alkyl chain was neglected), T=313 K [ l S l ] .

of fR. The former remark also contains the limitations of this method: by lowering the cross-over frequency the temperature range is reduced in which such a display works. Let us remember the question at the beginning! One can say that in a mixture, there is a tendency of a mean field interaction but molecules with stronger deviation in the molecular shape show their individual relaxation frequencies in a mixture. If one considers the different moments of inertia for the molecules A-D, one cannot expect such a big change infRn.Furthermore, one can dilute these compounds in the mixture to infinity and the change in fR should be relatively small [ 1501. The last argument means that all mixtures have nearly the same clearing temperature. This can only support the idea that the soluted molecules should be differ in their degree of order from that of the solvent. In the discussion about the clearing temperature as reference point for the dielectric relaxation frequencies, the influence of the glass transition was neglected. Therefore, at first some general remarks are necessary. If a liquid is cooled down very fast the crystallization can be avoided. It is obvious that the mean distance between the molecules is reduced by cooling. Therefore, at a certain temperature one molecule cannot rotate if the neighbors do not give enough space. This results in a coupling of motions of the molecules with decreasing temperature. This mechanistic model explains the increasing cooperativity and at least the freezing process of motions. To verify this model for low molecular weight liquid crystals, it is important to increase the viscosity of the respective liquids. To avoid crystallization it is also useful to make mixtures [ 12, 14, 151. In this way one is able to reduce the relaxation frequencies

r-

102

2.2 Dielectric Properties of Nematic Liquid Crystals

for the two main processes to very low values. Experimental data are shown for E! and &‘in Figs. 2 1 and 22. It is evident from these data that the absorption intensity does not decrease at low temperatures. This means from theoretical point of view that the probability for the molecules to reorient about the main axis is the same as it is at higher temperatures. There is only the increasing activation energy (increasing cooperativity) as demonstrated in Fig. 23. It could also be shown that the absorption intensity decreases overtime due to the crystallization of the sample [ 1501. Coming back to the model discussed above, one should expect some local reorientation processes which need a rela-

2.8

3.2

-

3.6

4.0

4.4

1 m TI K

Figure 23. Arrhenius plot of all measured relaxation frequencies of the mixture with a high glass temperature. Curve 3 was obtained without orientation [14].

t

w

9s

OA

0.2

n -

0.01

0.1

1

10

100

flkHz-

Figure 21. Dielectric relaxation frequencies of a mixture with high glass temperature for the parallel direction. The conductivity was only given for 2, the second high frequency relaxation only for 1. 1:315.6K, 2:331.1K, 3:339.2K, 4:346.5K, 5 : 351.6 K, 6 : 359.6 K [14].

tively small free volume. Indeed, such a local motion could be separated at low temperatures on the high frequency side of the reorientation around the long molecular axis. This mechanism denoted with 3 in Fig. 23 has a lower activation energy. It seems to be a split up of mechanism 3 from a common reorientation around the short molecular axis. This is just the effect of increasing cooperativity that influences only such reorientation’s which need a relatively big free volume.

2.2.5 Dielectric Behavior of Nematic Mixtures 0.01

0.1

1 flkHz-

10

100

Figure 22. Dielectric loss of the mixture form Fig. 21 measured in the perpendicular direction. 1 :287.6 K, 2 :289.3 K, 3 :296.7 K, 4 : 301.4 K, 5 :308.8 K [14].

As mentioned in Section 2.2.2 of this chapter, connecting molecular data with the dielectric constant is a general problem. Therefore, it is difficult to calculate the behavior of an ‘ideal mixture’ as can be done in thermodynamics. Nevertheless one can

2.2.5

Dielectric Behavior of Nematic Mixtures

try to approximate the experimental data by some ‘mixing rules’ which are useful for technical application. If one starts with the Onsager model applied by Maier and Meier on nematic liquid crystals (Eq. (l)),one can write for a two component mixture, consisting of the molecules A and B:

103

360f.-

1 A&O,AB (x, T )= ; F ~ N A S(x, A TI . [AaA - F ( p 2 /2kT) ( 1 - 3 cos2pA)]

+ NB SB (X, T ) [AaB - F ( p i /2 k T ) (1 - 3 cos2P B ) ] ’

(4)

In this case it was assumed that the factors of the internal field F and h are the same for both compounds. The former discussed problem of different degrees of order for the two components was considered. N means the number of particles per unit volume. Equation (4) can be simplified if component B is not oriented in the nematic matrix or exhibit a very small degree of order S, (x,T ) .By this approximation one should expect a change of AE(x, T ) with the molar fraction x and with the temperature. An experimental verification was done on the binary system of 4-n-octyloxyphenyl 4-n-pentyloxybenzoate (A) and 2-methylphenylbenzoate (B) [ 15.51. The phase diagram in Fig. 24 shows that the nematic phase is destroyed by adding the liquid B. This behavior is typical for this kind of phase diagram: the order is destroyed by addition of the isotropic compound as well as with increasing temperature. In the last case the clearing temperature can be used as a reference point [22]. The dielectric anisotropy measured at constant concentration is plotted in Fig. 25 versus the temperature difference T - Tb. Tbmeans the beginning of the clearing process by heating indicated as big line in the phase diagram in Fig. 24. It is obvious from this picture, that there are no big differences in the values, in other words S,(T) behaves similarly with

(A1 0

0.4

0.2 XB

0.6

Figure 24. Phase diagram of the nematic compound A and a nonliquid crystalline B. The bold line indicates Tb [155].

-0.4

1

-0.3

I

0

-0.2

w

4

- 0.1 0 -30 -20

-10

O

IO

(T-TbllK-

Figure 25. Dielectric anisotropies at different concentrations indicated in the phase diagram Fig. 23 [155].

respect to the temperature Tb and seems to be independent of the concentration. On the other hand A% was plotted as a function of xB at a constant temperature (Fig. 26). This picture is quite similar to that of Fig. 25. Near to a critical concentration A&()strongly decreases. The slope of should reflect the change of ST(x), a ‘lyotropic degree of order’. The addition of the isotropic compound with a lower viscosity causes an in-

104


-0.4r-----l 0

xB

35 0

-

0.10

0.20

1

290 A

Figure 26. Dielectric anisotropies at different temperatures as indicated in the phase diagram Fig. 23 [155].

crease offRll[ 1551.With respect to the phase diagram and the results obtained, it makes no sense to apply a simple mixing rule of the general formula A%, AB (x, T ) = XA AEA + XB A E .~

c-----l I

(5)

Equation (5) can be derived from Eq. (4) by neglecting of the differences between the degrees of order of A and B and replacing of the volume fraction by the molar fraction. To test the validity of such a simple rule, experiments on mixtures of two liquid crystalline components are necessary. A mixing rule similar to Eq. (5) was established for samples without a permanent dipole moment by Bottcher (see [156]). Experimental data of such a binary system with 4-nhexyloxyphenyl 4-methoxybenzoate (A) and ethylhydrochinone 1,4-bi-(4-n-hexylbenzoate) (B) are presented in the Figs. 26 and 27 [ 1271. There are no big differences between the clearing temperatures of both compounds, but in order to eliminate the effect of the degree of order a temperature T=0.98 Tb (Tb see bold line in the phase diagram) was chosen. There is a positive deviation from the simple mixing rule for A& ,, and a negative with respect to E ~ , ~ ~

B

0.5 XB-

Figure 27. Phase diagram of two nematic compounds [127].

For technical application A& is an important quality. Therefore, for the calculation according to the mixing rule, often between 5 and 10 mol% of compound B are added to the basic mixture A. In this way the beginning of the slope shown as a dotted line in Fig. 28 is estimated. In our case these data ,, at xB< 0.4. This are better for calculating A& method is also used for the estimation of an approximated value of A&,,(B) which is in about +0.90. The experimental value of A&,,(B) =0.68 makes it clear that the approx-

A

B'

-

0.5

B

Figure 28. Static dielectric values of the mixture . shown in Fig. 27 [127].

2.2.5

imation Eq. ( 5 ) is only useful for a calculation of AE, for small concentrations of B (see also [154, 771). All the problems discussed can be neglected if the interactions in the mixtures are strong. A classical example for this is substituted acids which form dimeric associates by hydrogen bonding. With increasing temperatures the monomer concentration increases and therefore, the slope of &, versus temperature becomes different from the classical one, for example an increase of with increasing temperature [ 1571 can be observed. By addition of derivatives of benzoic acid with a longitudinal dipole moment like .c-@o,

105


/

3801.

N+Cr

N+cr

-

--"

A

01

0.2

XB-

0.3

Figure 29. Phase diagram of the acids A and B according to [158].

and F*COOH

to the following acids exhibit liquid crystalline phases C i H i i e O O H

(cr 361

N

401

a)

(A)

and C,HI,Nr+-COOH

(cr382 N 396 a)

(B)

a stabilization of the nematic phase could be observed. An example for it is given in Fig. 29. Surprisingly, an increase of the clearing temperature is observed. An explanation for this effect can be the formation of mixed associates e.g.

If this idea is correct one should expect an increasing dielectric anisotropy and a dielectric relaxation effect of E; at low frequencies. The last one can be observed only if there is a longitudinal dipole moment.

Experimental data by addition of 1, 3.5, 8 and 15 mol% of C to A are presented in Figs. 30 and 31 [I.%]. There is a clear evidence for the existence of mixed associates. A chemical variation of the components results a stronger (B/C) or weaker (B/D) increase of the dielectric increment A,, depending on the overall dipole moment in the direction of the molecular long axis (Fig. 32) [159]. The relaxation frequencies do not depend on the concentration but depend on the chemical structure of the associates (Fig. 3 3 ) . There are a lot of different possibilities for formation of associates by hydrogen bondings [160]. Due to the high conductivity it is difficult to prove its existence by dielectric measurements which has been done previously [161]. Special interactions with hydrogen bonding at a surface can be responsible for the shift of the relaxation frequencies by addition of the very small particles of aerosil. As an example, relaxation frequenciesf,,, of a nematic mixture M with and without aero-

106


0

360

4 00

380

0.05 'C,D

0.10

015

Figure 32. Dielectric increment of the low frequency relaxation for different mixtures [159].

420

TIK-

Figure 30. Static dielectric constants of the mixtures of A and B. The numbers are related to xB [158].

0

0.5

1.o

1.5

2.0

2.5

A&'-

2.6

1000

2.7

2.8

TI K

Figure 31. Cole-Cole plots of different mixtures of A a n d B . Tandx,aregiven [158].

Figure 33. Dielectric relaxation frequencies of the mixtures at different concentrations [ 1591.

sil are compared with each other in Fig. 34 [ 1621. This effect depends on the surface treatment. Similar results were obtained by Rozanski and Kremer for the reorientation around the long molecular axis in anapore [ 1631 and earlier by Aliev et al. in different porous glasses [ 1641.

There are strong tendencies to an antiparallel order in the short range produced by steric interactions as shown in Section 2.2.2 of this chapter. In such cases the addition of compounds with different molecular shape should destroy theseforces. Classical examples for them are swallow-tailed compounds

2.2.5


107

L

14.4 N

-

M + Aerosil

I

4

IY

c

c 14.1 -

13.8

13.5I 3.35

3.3 9

.-

3.L 3

3.4’‘

1000 TIK

[137, 1651 or molecules with an angular [135] or ‘h’-like molecular shape [138]. Systematic investigations were especially done on the swallow-tailed compounds

(A) which are mixed with 1,4-bis-4-n-hexylbenzoylox y -benzene

Figure 34. Comparative dielectric relaxation measurements on a mixture M and a mixture with aerosol (different cells) (1621.

end of the phase transition T NIswas taken. As it can be seen there is a systematic change in the molecular interaction from B to F. This tendency could be confirmed by dielectric measurements. The respective data of the dielectric measurements on the system A/F are given in Fig. 38. It can be clearly seen that the antiparallel correlation of the swallow-tailed molecules is destroyed by addition of 60 mol% of F. For comparison, the

and the derivatives of 1,4-bis-[4-n-octyloxybenzoyloxy]-2-n-substituted-benzenes.

R=-OCH, -C,H, -C,,H,, -C,H,,

cr cr cr cr

371 333 327.5 325.5

N N N N

399.5 392 342.5 352

is C is D is E is F

Two phase diagrams, namely the mixtures of A/B and A/F representing the extreme cases are given in Figs. 35 and 36. For comparing, the slope of the SmAINphase transition temperatures is plotted in Fig. 37 versus the molar fraction x ~ - For ~ . the mixtures, the mean temperature of the beginning and the

t-

330

320

I

(A10

-

0.5 xF

IF)

Figure 35. Phase diagram of the swallow-tailed compound A with the laterally branched F [ 1371.

108

2.2

-

K-

330


(A10

0.5

1(B)

4.01

i"

---- --____

3.51,

xB

320

340

Figure 36. Phase diagram of A and B [165].

,

,

360

380

TIK-

Figure 38. Static dielectric constants of A and F and a mixture with the given molar tractions 11371.

A

0.5

1

'0-F-

Figure 37. Relative phase transition temperatures N/S, of B - F [165].

I

I

static dielectric anisotropies 20 K below the N/I transition are plotted versus the concentration (Fig. 39). By chance the A%-values of the pure compounds C, E and F are about -1 and therefore, the data can be directly compared. As demonstrated in Fig. 39, addition of F results in the strongest increase of Ae, with concentration due to the strongest destruction of the antiparallel order. For C only a weak destruction of the antiparallel dipolar order of A was detected. How sensitive are these effects with respect to the

A

I

0.5

1

'c,E,FFigure 39. Static dielectric anisotropies of a mixture of the swallow-tailed compound A and the respective components 20 K below the beginning of the clearing process [165].

molecular shape can be seen by comparing of E and F. Despite of the lower clearing temperature of F this heptyl substituted derivative is a more effective destroyer of the short range order of A.

2.2.6 References

The last example demonstrates how sensitive the orderldisorder equilibrium depends on the molecular architecture. Dielectric measuements can help us to understand such complicated relations which are also very important in the life sciences.

2.2.6 References [ 11 P. Debye, Polare Molekeln, Hirzel Verlag, Leip-

zig 1929. [2] C. P. Smyth, Dielectric Behaviour and Structure, McGraw-Hill Book Co., New York, 1995, pp. 239-259. [3] A. Budo, E. Fischer, S . Miyanoto, Phys. Z. 1939, 40,337-345. [4] E. Fischer, F. G. Frank, Phys. Z. 1939, 40, 345 - 352. [ 5 ] J. P. Parneix, C. Legrand, D. Decoster, Mol. Cryst. Liq. Cryst. 1983, 97, 163- 176. [6] M. F. Bone, A. H. Price, M. G. Clark, D. G. McDonnell, Liq. Cryst. Ordered Fluids 1984,4, 799 - 830. [7] H. Kresse, W. Weissflog, F. Kremer, A. Schonfels, Cryst. Res. Technol. 1992, 27, K5-KI0. [8] J. Jadzyn, L. Hellemans, M. Stockhausen, C. Legrand, G. Czechowski, Z. Naturforsch. Teil A 1994,49, 1077- 1080. [9] J. Jadzyn, C. Legrand, N. Isaert, A. Cartier, P. Bonnet, G. Czechowski, B. Zywucki, J . Mol. Liq. 1994,62, 55-63. [lo) D. Lippens, C. Druon, J. M. Wacrenier, J. Phys. Colloq. (Orsay, Fr) 1979, 3, 306-309. [ 111 G. P. Johari, Phil. Mag. B 1982,46, 549-564. [I21 H. R. Zeller, Phys. Rev. A 1981,23, 1434- 1436. [ 131 H. R. Zeller, Phys. Rev. A 1982,26,1785- 1787. [14] H. Kresse, S . Ernst, W. Wedler, D. Demus, F. Kremer, Be% Bunsengesell. Phys. Chem. 1990, 94, 1478-1483. [ 151 H. Kresse. P. Hartmann, W. Schafer, I. Szulzewsky, Liq. Cryst. 1991, 10, 127-133. [16) J. K. Moscicki, Solid State Commun. 1976, 20, 481 -483. [I71 V. K. Agarwal, V. P. Arora, A. Manisingh, J. Chem. Phys. 1977,66,28 17 - 2820; Mol. Cryst. Liq. Cryst. 1978, 45, 1 17 - 125. [I81 G. K. Gupta, V. P. Arora, V. K. Agarwal, A. Manisingh, Mol. Cryst. Liq. Cryst. 1979, 54, 234- 244. (191 B. Bahadur, R. K. Sarna, A. K. Garg, V. K. Agarwal, Mol. C v s t . Liq. Cryst. 1983,100, 137-144. [20] N. X. Phuc, J. Krawczyk, D. Chrusciel, J. Chrusciel, J. A. Janik, J. M. Janik, K. Otnes, H. Kresse, I. Natkaniec, S . Urban, S . Wrobel, Liq. Cryst. 1986,1,561-572.

109

1211 K. Clendowska, D. Chrusciel, J. A. Janik, H. Kresse, H. Stettin, K. Otnes, T. Stanek, S . Urban, S . Wrobel, Liq. Cryst. 1988, 3, 13391354. [22] W. Maier, A. Saupe,Z. Naturforsch., TeilA 1958, 13, 564-566. [23] A. J. Martin, G. Meier, A. Saupe, Symp. Furuday Soc. 1971,5, 119- 133. [24] M. J. Bradshaw, E. P. Raynes, Mol. Cvst. Liq. Cryst. 1981, 72, 73-78. "251 J. Thoen, G. Menu, Mol. Cryst. Liq. Cryst. 1983, 79, 163-176. [26] H. Kresse, F. Kremer, Phys. Stat. Sol. ( a ) 1990, 118, 119-122. [27] L. Onsager, J. Am. Chem. Soc. 1936, 58, 1486- 1493. [2S] W. Maier, G. Meier, Z. Naturjorsch., TeilA 1961, 16,262-267. [29] J. G. Kirkwood, J . Chern. Phys. 1939, 7, 911 -919; H. Frohlich, Trans. Furaday Soc. 1948,44,238-243. [30] Landold-Bornstein, Zahlenwerte und Funktionen II,6, Springer-Verlag, Berlin 1959, pp. 607613. [ 3 11 V. N. Tsvetkov, Kristullografya 1969,14,681686. [32] V. N. Tsvetkov, E. I. Ryumtsev, 1. P. Kolomiets, A.P. Kovshik, Dokl. Acad. Nauk SSSR 1972, 203, I 122- 1125. [33] H. Kresse, P. Schmidt, Z. Phys. Chern. (Leipzig) 1975,25b, 987-989. [34] R. T. Klingbiel, D. J. Genova, R. T. Criswell, J. P. Van Meter, J. Am. Chem. Soc. 1974, 96, 7651-7655. [ 3 5 ] W. Weissflog, H. Kresse, Z. Chem. 1979, 19, 256- 257. [36] H. Kresse in Dielectric Behaviour of Liquid Crystals, Advances in Liquid Crystals, Vol. 6 (Ed. G. H. Brown), Academic Press, New York, 1983; a) 120-123, b) 126, c) 133- 136, d) 142. [37] M. A. Osman, Z. Nuturforsch., Teil B 1979, 34, 1092- 1095. [38] M. A. Osman, L. Revesz. Mol. Crysr. Liq. Cryst. Lett. 1980,56, 133-138. [39] W. Weissflog, H. Kresse, A. Kolbe, 2. Chem. 1980,20,259- 260. [40] J. Ruoliene, P. Adomenas, A. Tubelyte, V. Sekausas, V. A. Grozhik, Mol. Cryst. Liq. Cryst. 1981, 78, 21 1-216. [41] M. Schadt,J. Chem. Phys. 1972,56,1494-1497. [42] M. Schadt, F. Muller, J . Chem. Phys. 1976, 65, 2224- 2230. [43] M. Schadt, Phys. Lett. A 1977, 60, 421 -423. [441 M. Schadt, Mol. Cryst. Liq. Cryst. 1981, 66, 639 - 656. [45] P. G. Gerber, Z. Naturjorsch., Teil A 1982, 37, 266 - 270. [46] M. Schadt, Mol. Cryst. Liq. Cryst. 1982, 89, 77-92.

110

2.2


[47] M. Schadt, R. Buchecker, F. Leenhouts, A. Boller, A. Villinger, M. Petrzilka, Mol. Cryst. Liq. Cryst. 1986, 139, 1-25. [48] R. Steinstrasser, Angew. Chem. Int. Ed. Engl. 1972,II, 633-634. [49] L. Pohl, R. Eidenschink, J. Krause, D. Erdmann, Phys. Lett. A 1977,60,421-423. [SO] R. Eidenschink, D. Erdmann, J. Krause, L. Pohl, Angew. Chem. 1978,90, 133. [Sl] L. Pohl, R. Eidenschink, J. Krause, G. Weber, Phys. Lett. A 1978,65, 169- 172. [52] W. H. DeJeu, C. J. Gerritsma, Th. W. Lathouwers, Chem. Phys. Lett. 1972, 14,503-506. [53] C. J. Gerritsma, P. Van Zanten, Phys. Lett. A 1972,42, 127-128. [54] W. H. DeJeu, J. Van der Veen, Phys. Lett. A 1973, 44,277 - 278. [ S S ] W. H. DeJeu, Th. W. Lathouwers, P. Bordewijk, Phys. Rev. Lett. A 1974,32,40-43. [56] W. H. DeJeu, Th. W. Lathouwers, Z. Nuturforsch., Teil A 1974, 29A, 905 -9 11. [57] W. H. DeJeu, Th. H. Lathouwers, Mol. Cryst. Liq. Cryst. 1974,26, 225 -294. [58] W. H. DeJeu, Th. H. Lathouwers, Mol. Cryst. Liq. Cryst. 1974,26, 235-243. [59] W. H. DeJeu, Th. H. Lathouwers, Z. Naturforsch., TeilA 1975, 30, 79-82. [60] W. H. DeJeu, J. Van der Veen, Mol. Cryst. Liq. Cryst. 1977,40, 1- 17. [61] M. A. Osman, Z. Naturforsch., Teil B 1979,34, 1092- 1095. [62] H. Schad, M. A. Osman, J. Chem. Phys. 1981, 75, 880-885 [63] M. Osman, H. Schad, H. R. Zeller, J. Chem. Phys. 1983, 78,906-914. [64] H. Schad, S. M. Kelly, J. Chem. Phys. 1984,81, 1514-1515. [65] S. M. Kelly, H. Schad, Mol. Cryst. Liq. Cryst. 1984,110,239-261. [66] H. Schad, S. M. Kelly, Z. Naturjorsch., TeilA 1985,40,932-943. [67] H. Schad, S. M. Kelly, Mol. Cryst. Liq. Cryst. 1986,133,75-83. [68] T. Inukai, F. Furukowa, H. Inoue, K. Terashima, Mol. Cryst. Liq. Cryst. 1983, 94, 109- 118. 1691 Y. Goto, Kikan KagakuSosetsu 1994,22,40-59. [70] D. Demus,Y. Goto, S . Sawada,E. Nakagawa, H. Saito, R. Tarao, Mol. Cryst. Liq. Cryst. (Proc. 15thInt.Liq. Cryst. Conf., Budapest 1994) 1995, 260, 1-22. [71] K. Miyazawa, Y. Goto, Mol. Cryst. Liq. Cryst. (Proc. 15th Int. Liq. Cryst. Conf., Budapest 1994) 1995,260,277-286. [72] C. 3. Alder, E. P. Raynes, J. Phys. D 1973, 6, L33 -L36. [73] M. G. Clark,E. P. Raynes, R. A. Smyth,R. J. A. Tough, J. Phys. D 1980,13,2151-2164. [74] M. J. Bradshaw,D. G. McDonnel1,E. P. Raynes, Mol. Cryst. Liq. Cryst. 1989, 6 , 515-523.

[75] D. G. McDonnell, E. P. Raynes, R. A. Smyth, Liq. Cryst. 1989,6, 515-523. [76] T. J. Phillips, J. C. Jones, D. G. McDonnell, Liq. Cryst. 1993,15,203-215. [77] J. W. Baran, J. Kedzierski, Z. Raszewski, J. Zmija, Electr. Technol. 1979,12, 107- 114. [78] Z. Raszewski, Liq. Cryst. 1988,3, 307-322. [79] Z. Raszewski, J. Kidzierski, J. Rutkowska, J. Zielinski, J. Zmija, R. Dabrowski, T. Opara, Proc. SPIE - Int. SOC.Opt. Eng. 1993, 1845, 32.5 -332. [80] Z. Raszewski, J. Kedzierski, J. Rutkowska, J. Zielinski, J. Zmija, R. Dabrowski, T. Opara, Mol. Cryst. Liq. Cryst. (Proceedings of the 14th Int. LC Conf. Pisa 1992) 1993,14,1715-1724. [81] E. I. Ryumtsev, A. P. Kovshik, P. V. Adomenas, Yu. N. Denite, V. N. Tsetkov, Kristallografija 1978,23, 144- 148. [82] E. I. Ryumtsev, A. P. Kovshik, A. V. Salnikov, L. V. Poloudina, Kristullografiju 1986, 31, 1170-1174. [83] V. N. Tsvetkov, N. V. Tsvetkov, L. N. Andreeva, Dokl. Acad. Nauk. 1992,324,1000- 1005. [84] E. I. Ryumtsev, A. P. Kovshik, D. A. Ragimov, S. G. Polushin, Zh. Fiz. Khim. 1993,67,602-605. [85] N. V. Madsuhudana, S. Chandrasekhar, Liq. Cryst., Proc. Int. Con$ Bungalore 1973, 1975, 57-68. [86] B. R. Ratna, R. Shashidhar, Pramana 1976, 6, 278-283. [87] P. P. Karat, N. V. Madsuhudana, Mol. Cryst. Liq. Cryst. 1977,42, 1067- 1075. [88] B. R. Ratna, R. Shashidhar, Mol. Cryst. Liq. Cryst. 1977,42, 1195- 1202. [89] B. R. Ratna, R. Shashidhar, Mol. Cryst. Liq. Cryst. 1978,45, 103- 106. [90] B. R. Ratna, R. Shashidhar, M. Bock, A. Goebel-Wunsch, G. Heppke, Mol. Cryst. Liq. Cryst. 1983,99,285-295. [91] B. S. Srikanta, N. V. Madsuhudana, Mol. Cryst. Liq. Cryst. 1983, 103, 111-125. [92] S. Chandrasekhar, Mol. Cryst. Liq. Cryst. 1985, 124, 1-20. [93] M. F. Grebenkin, V. A. Seliverstov, L. M. Blinov, V. G. Chigrinov, Kristallografija 1975,20, 984-990. [94] V. V. Belyaev, V. G. Chigrinov, Kristallografija 1978,23,811-815. [95] M. I. Barnik, L. M. Blinov, A. V. Ivashenko, N. M. Shtykow, Kristallografija, 1979,24,811816. [96] L. Bata, G. Molnar, Chem. Phys. Lett. 1975,33, 535-538. [97] L. Bata, A. Buka, Actu Phys. Polon. A 1978,54, 635 -641. [98] A. Buka, L. Bata, Mol. Cryst. Liq. Cryst. 1986, 135,49- 64. [99] J. Jadzyn, P. Kedziora, Mol. Cryst. Liq. Cryst. 1987,145, 17-23.

2.2.6 References [I001 J. Jadzyn, G. Czechowski, N. Shonova, Liq. Cryst. 1988,3, 1637-1641, [loll J. Jadzyn, G. Czechowski,Acta Phys. Polon. A 1988, 74, 105- 109. [lo21 D. Baumann, G. Czechowski, J. Jadzyn, Acta Phys. Polon. A 1989, 75, 697-703. [lo31 J. Jadzyn, G. Czechowski, Liq. Cryst. 1989,4, 157- 163. [ 1041 P. Kedziora, J. Jadzyn, Proc. SPIE - Inr. Soc. Opt. Eng. 1993,1845,333-339. [lo51 P. Maurel, A. H. Price, J. Chem. Soc. Faraday Trans. 2 1973,69, 1486- 1450. [I061 V. K. Agarwal, A. H. Price, J. Chem. Soc. Faraday Trans. 2 1974, 70, 188-192. [I071 M. Daves, R. Moutran, A. H. Price, M. S . Beewers, G. Williams, J. Chenz. Soc. Faraday Trans. 2 1976, 72, 1447-1458. [ 1081 A. Buka, P. G. Oween, A. H. Price, Mol. Cryst. Liq. Cryst. 1979, 51, 273-284. [lo91 A. Buka, A. H. Price, Mol. Cryst. Liq. Cryst. 1985,116, 187-195. [llO] A. K. Garg, V. K. Agarwal, B. Bahadur, Mol. Cryst. Liq. Cryst. 1985, 130, 1 1-24. [ 1 I I ] V. P. Arora, V. K. Agarwal, J. Phys. Soc. Jpn. 1978,45, 1360- 1363. [112] G. K. Gupta, V. K. Agarwal, J. Chem. Phys. 1979, 71,5290-5292. [ I 131 G. K. Gupta, V. P. Arora, V. K. Agarwal, Mol. Cryst. Liq. Cryst. 1979,54, 237-243. [114] G. K. Gupta, A. K. Gark, V. P. Arora, V. K. Agarwal, Proc. Nucl. Phys., Solid State Phys. Symp. 1982, 24C, 435-436. [ 1 IS] P. G. Cummins, D. A. Dunmur, N. E. Jessup, Liq. Cryst. Ordered Fluids 1979,2, 341 -350. [ 1 161 P. G. Cummins, D. A. Dunmur, D. A. Laidler, Mol. Cryst. Liq. Cryst. 1975, 30, 109- 121. [117] D. A. Dunmur, W. H. Miller, Mol. Cryst. Liq. Cryst. 1980, 60, 241 -292. [ 1181 H. Kresse, P. Schmidt, D. Demus, Phys. Stat. Sol. ( a ) 1975, 32, 315-320. [ I 191 H. Kresse, K. H. Lucke, P. Schmidt, D. Demus, Z. Phys. Chem. (Leipzig) 1977,258,785-787. [120] H. Kresse, Chr. Selbmann, Z. Phys. Chem. (Leipzig) 1978, 259, 897-904. [I211 H. Kresse, S. Konig,D. Demus, Z. Chem. 1978, 18, 152-153. [I221 H. Kresse, J. Pietscher, S. Konig, W. Weissflog, H. J. Deutscher, Z. Phys. Chem. (Leipzig)1978, 259,779-783. [I231 H. Kresse, W. Weissflog, Z. Chem. 1979, 19, 59-60. [ I241 H. Kresse, K. Sauer, A. Wiegeleben, D. Demus, A. Drzymala, J. Chem. 1979,19, 145-146. [ 1251 W. Weissflog, P. Mijckel, H. Kresse, D. Demus, Z. Chem. 1979, 19,291-292. [I261 H. Kresse, G. Pelzl, Phys. Stat. Sol. ( a ) 1980, 57, K149-Kl51. [127] H. Kresse, Sh. Tschimeg, D. Demus, Z. Phys. Chem. (Leipzig) 1981,262,612-620.

111

[1281 H. Kresse, Z. Phys. Chem. (Leipzig)1981,262, 801-805. 11291 H. Kresse, M. Keil, W. Weissflog, Cryst. Res. Technol. 1983, 18, 563-567. [I301 H. Kresse, K. Worm, W. Weissflog, Z. Chem. 1985,25,64-65. [I311 R. Krieg, H.-J. Deutscher, H. Kresse, B. Stecker. Z. Chem. 1987,27, 292-293. 11321 P. Bordewijk, W. H. DeJeu, J . Chem. Phys. 1978,68, 116- 118. (1331 W. Maier, G. Meier, Z. Naturforsch., TeilA 1961, 16, 470-477. (1341 H. Kresse, P. Rabenstein, H. Stettin, S . Diele, D. Demus, W. Weissflog, Cryst. Res. Technol. 1988,23, 135-140. (1351 D. Girdziunaite, C. Tschierske, N. Novotnk, H. Kresse, A. Hetzheim, Liq. Cryst. 1991, 10, 397-407. 11361 H. Kresse, W. Weissflog, Phys. Stat. Sol. (a) 1988,106, K89-K91. [137] H. Kresse, P. Rabenstein, Phys. Stat. Sol. ( a ) 1987,100, K83-K85. (1381 H. Kresse, S. Haas, S. Heinemann, F. Kremer, J. Prak. Chemie 1991,333,765-773. [139] P. E. Cladis, Phys. Rev. Lett. 1975, 35, 48-50. (1401 L. Longa, W. H. DeJeu, Phys. Rev. A 1982, 632- 1647. [I411 P. Kedziora, J. Jadzyn, Liq. Cryst. 1989, 4, 157-163. [142] B. R. Ratna, R. Shashidhar, K. V. Rao, Proc. Int. Liq. Cryst. Con$, 8th (1979), Mol. Cryst. Liq. Cryst. 1980, 3, 135- 142. [143] C. Legrand, J. P. Parneix, A. Chapoton, Nguyen Huu Tinh, C. Destrade, Mol. Cryst. Liq. Cryst. 1985, 124, 277-285. 11441 J. Jadzyn, G. Czechowski, Liq. Cryst. 1989, 4 , 157-163. [I451 G. Pelzl, S . Diele, I. Latif, W. Weissflog, D. Demus, Cryst. Res. Techno/. 1982,17, K78-K82. [ 1461 S . Chandrasekhar,MoZ. Cryst. Liq. Cryst. 1985, 124, 1-20. [ 1471 J. Moscicki, H. Kresse, Ad!,,. Mol. Relax. Int. Proc. 1981,19, 145-150. [148] H. Weise, A. Axmann, Z. Naturforsch., Teil A 1966,21, 1316-1317. [149] G. Heppke, J. Kayed, U. Miiller, Mol. Cryst. Liq. Cryst. 1983, 98, 309- 3 19. [I501 H. Kresse, P. Rabenstein, D. Demus, Mol. Cryst. Liq. Cryst. 1988, 154, 1-8. [ 1.5 11 H. Kresse, H. Stettin, F. Gouda, G. Anderson, Phys. Stat. Sol. ( a ) 1989, 11, K26S-K268. [I521 A. Stieb, G. Baur, German Patent 2328667 (6.6.1973), E. P. Raynes, British Patent 1463979 (25.9.1973), H. Kresse, F. Kuschel, D. Demus, DDR Patent 107561 (26.9.1973). [I531 M. Schadt, Mol. Cryst. Liq. Cryst. 1982, 89, 779 -792. [154] H. Stettin, H. Kresse, D. Demus, Cryst. Rex. Trchnol. 1989, 24, 121- 129.

112


(15.51 H. Kresse, C. Selbmann, D. Demus,Mol. Cryst. Liq. Cryst. 1978,44, 179- 190. [156] C. J. F. Bottcher, 0. C. vanBelle, P. Bodewijk, A. Rip, Theory of Electric Polarization, vol. I, 2nd edn., Elsevier, Amsterdam 1993, 200203. [157] H. Kresse, K.-H. Lucke, P. Schmidt,D. Demus, Wiss. Zeitschr. Univ. Halle 1977,26, 147- 154. [158] H. Kresse, S. Konig, D. Demus, Wiss. Zeitschr. Univ. Halle 1978,27,47-52. [1591 H. Kresse, N. K. Sharma, W. Weissflog, Kristall und Technik 1981, 16, 101 - 107.

[160] C. M. Paleos, D. Tsiouvas, Ang. Chem. 1995, 107,1839-1855. [161] H. Kresse, I. Szulzewski, S. Diele, R. Paschke, Mol. Cryst. Liq. Cryst. 1994,238, 13-19. [162] S. Tschierske, 0. V. Jaroshchuk, H. Kresse, Cryst. Res. Technol. 1995,30, 571-575. [163] S. A. Rozanski, F. Kremer, SPlE 1995, 2372, 32-37. [164] F. M. Aliev, Mol. Cryst. Liq. Cryst. 1994, 243, 91 - 105. [ 1651 S. Heinemann, H. Kresse, W. Weissflog, Cryst. Res. Technol. 1993,28, 131 - 136.


2.3 Diamagnetic Properties of Nematic Liquid Crystals Ralf Stannarius

2.3.1 Magnetic Quantities Common nematic liquid crystals represent diamagnetic fluids. Molecular diamagnetism in non-ordered isotropic materials in general, as well as the mean diamagnetic polarizability in ordered materials, is temperature independent. However, due to thermal expansion of the material the volume susceptibility is not constant but decreases with increasing temperature.' It is therefore sometimes convenient to introduce the temperature independent quantities the susceptibility per mole, or x ( ~ ) ,the mass susceptibility, which are related to by

x

x'~', x

x(~= ) M,X/p

(m3 mol-'1

and X(m)= X I P

(m3 kg-')

where M,,, is the molar mass of the substance and p is the mass density.

The anisotropic magnetic properties of nematics and the interactions of the director with external magnetic fields are described by a symmetric second rank diamagnetic susceptibility tensor 2. The magnetic moment per volume induced in the nematic liquid crystal by an external magnetic field H is

M=xH and correspondingly the magnetic free energy per volume is given by 1 Fmag= - 2

= - 1 pLg H (1 ~

2

x

XGU = 4 z x ( c g r )

+x)H

(1 1

where 1 is the unit tensor and p0 is the vacuum permeability. The shape of depends upon the symmetry of the ordered phase. has diagonal shape in a laboratory fixed frame (x,y, z ) where the z axis is parallel to the director n

x

x

7 ;,] 0

'

SI notation is used for the magnetic equations and quantities. As, particularly in older publications, magnetic susceptibilities are given in cgs electromagnetic units, we present such experimental data in both cgs and SI units. The dimensionless volume susceptibility can be converted from cgs to SI using the formula

( H + M )H

~

xL,

0

with xII 0), and decreases with increasing the birefringence with respect to the free litemperature. The temperature dependence gand [16]. The inverse case has also been is pronounced in the neighbourhood of observed [62, 64, 651. TN-1. It should be emphasized that at the The experimental results can be easily transition to the isotropic liquid the birefrinunderstood on the basis of equations that gence does not disappear continuously but correlate the refractive indices with the modiscontinuously, indicating a phase transilecular polarizability anisotropy and the orientational order. For a merely qualitative tion of first order.

2.4.4 1,70

Dispersion of n,, no and An

133

Combination of Eqs. (6) and (7) gives

1.65

As for elongated molecules the longitudinal molecular polarizability a, is greater than T 1*60 C the transverse polarizability a,, n, must be greater than n,; this explains the positive 1,55 nematic isotropic sign of the birefringence. According to Eq. (8), the magnitude of the birefringence depends on the molecular polarizability anisotropy (a,- q),the orientational order S and the density p. I I I I 80 100 120 140 160 180 200 Whereas the temperature dependence of 91"C+ n1 is determined by the temperature dependence of p, the temperature change in n, and Figure 4. Temperature dependence of the refractive n, with temperature is mainly influenced by indices in the nematic (nc, no) and isotropic phase ( n l ) of 4-n-butylphenyl-4-(4-n-butylbenzoyloxy)ben- the temperature dependence of a, and a,, zoate (A=589 nm). (Adapted from Rettig [63]). respectively, which, according to Eqs. (7 a) and (7 b), is the result of the change with interpretation it is sufficient to use the equatemperature of S. With increasing temperations proposed by Vuks [66], which are ofture the density as well as a, decrease, givten applied to nematic liquid crystals: ing rise to the decrease in n, with increasing temperature. The characteristic shape of the no curve can be explained by the inverse temperature changes in p and a,. For example, for ma(d-1)- P____ 'NA'ao (6 b) terials with relatively high polarizability an(n2'2) 3MEo isotropy a relatively strong increase in a, with increasing temperature is found, which where n2=(n2+2n2)/3,p i s the density, NA leads to a positive temperature coefficient is Avogadro's number, M is the molar mass, of n,. Materials with smaller polarizability E,, is the permittivity of the vacuum, and a, anisotropy show a smaller change in a, with and a, are the average polarizabilities partemperature. Therefore, if the two influencallel and perpendicular to the optical axis rees (a,, p ) are of the same order of magnispectively. These can be expressed by the tude, a flat minimum of the n, curve results. longitudinal ( a , )and transversal (q)polaThe strong drop in the birefringence on rizabilities of the molecules [67]: approaching TNPIsotransition is due to the a, = a + 2 ( a l - a t ) S (7 a) strong decrease in S. 3 a, = a - -1 ( a ,- a, ) S 2.4.4 Dispersion of n,, no 3 ~

~

~

where S is the orientational order parameter and a is the average polarizability: a=(a,+2%)/3.

and An

The dispersion of the refractive indices over a wider wavelength region has been studied

134

2.4 Optical Properties of Nematic Liquid Crystals

by several authors [17, 42, 43,46, 49, 51, 52,55, 56,69,70,72,73]. Figure 5 presents the dispersion curves for n,, no and An for the nematic phase of 4-n-pentyl-4-cyanobiphenyl in the wavelength region 400- 800 nm at 25 "C [70]. It can be seen that the dispersion of the refractive indices is normal, meaning that they decrease with increasing wavelength. Furthermore, the dispersion of

1*65 1.60

i 4

1

I

I

I

I

I

400

500

600

700

il /nm+ (b)

I

800

I

0,26

024

t OSZ2 % 0,20

n, is clearly greater than that of no (whereas the dispersion of n, is intermediate between those of n, and no). According to quantum mechanical theory, the molecular polarizability in the ground state at the wavelength A is proportional to the sum over all quantum transitions: (9) wherefok is the oscillator strength, LC) is the angular frequency and wokis the angular frequency of the O+k transition. It follows from Eq. (9) that the band with the highest oscillator strength and the longest resonance wavelength will make the largest contribution to the molecular polarizability. For rod-like mesogenic molecules the longest wavelength electron transition is mostly directed parallel or nearly parallel to the long molecular axis. Therefore the longwave absorption band of a planar oriented nematic layer shows a distinct dichroism in the visible or ultraviolet (UV) region; that is, the absorption of the extraordinary ray (electric vector of the light parallel to the optical axis) is much larger than that of the ordinary ray (electric vector perpendicular to the optical axis) [7 11. That means, that also the effective oscillator strength parallel to the optical axis (A,) is greater than that perpendicular to the optical axis (fi).According to Wu [72] the wavelength dependence of the mean polarizabilities a, and a, of a nematic phase can be expressed by a single band approximation (see also [68]):

0.18

I

4M)

I

500

I

600

I

700

I

800

il/nm+ Figure 5. Dispersion curves for (a) n, and no and (b) An in the nematic phase of 4-n-pentyl-4-cyanobiphenyl(6=25"). (Adapted from Wu and Wu 1701).

where5, andf, are the average effective oscillator strengths parallel and perpendicular to the optical axis, respectively (A is the wavelength; A* is the resonance wavelength).

2.4.5 Refractive Indices of Mixtures

In general, for calamitic liquid crystals is satisfied so that, according to Eq. (lo), not only is n, greater than no, but also the dispersion of n, (a,) is greater than the dispersion of no (ao).The isotropic liquid exhibits an average absorption (Al >As>ti);that is, the dispersion of nI is expected to be between that of n, and no (see Fig. 3). On the basis of Vuks' formula (Eq. S), Wu [72] derived a simple dispersion equation for the birefringence:

hl>fi

where G depends on the density and on the anisotropy of oscillator strengths JI-fi at the resonance wavelength A*. In the IR region APA*, so that Eq. (1 1) is simplified to

An(T,A)= G(T)A*2

(12)

In accordance with the experimental results [17, 511 the birefringence in the IR region is expected to be nearly independent of the wavelength and mainly determined by the electronic transition moment. The contribution of the molecular vibrational bands to the birefringence is limited to the vicinity of these resonance bands. In the IRregion, positive and negative dispersion is observed. When the absorption of the extraordinary ray is more pronounced than that of the ordinary ray the dispersion is positive, and vice versa [17, 511. A more detailed analysis of the dispersion of n,, no and An has been made [70,73]. Whereby not only the long-wave electronic band but also two further bands are involved in the dispersion equation. Besides a o+o* transition in the vacuum UV region (at &) two z+n* transitions at longer wavelengths A, and & (UV or visible) are considered. In this way more exact

135

dispersion relations for n,, no and An are derived, which can be confirmed by the experimental data. In the visible region, for A+& the following simplified equation is satisfied [70, 731:

where & is the o+ o* resonance wavelength, Al and & are the rc -+ rc* resonance wavelengths, and Go, G, and G2 are coefficients that depend on the density andJI-fi. The contributions of the three bands (i. e. of the o and rc electrons) have been calculated quantitatively. It was found that the longest wavelength band (A)makes the primary contribution to the birefringence because this band has the largest absorption anisotropy. However, the rc electrons make a smaller contribution to the absolute values of the refractive indices n, and no [70, 731.

2.4.5 Refractive Indices of Mixtures In order to achieve an optimum contrast for special electro-optical effects nematic liquid crystals should have definite values of birefringence. In most cases matching of refractive indices can be achieved by mixing two or more single components. Therefore the birefringence as a function of the concentration is of special interest. As first shown in binary mixtures of homologous 4,4'-bis(alky1oxy)azoxybenzenes [74], the refractive index of a mixture (n12) can be calculated from those of the single compounds by a simple additive relation: n12 = x1 n1

+ x2 n2

(14)

where x1 and x2 are the mole fractions, n1 and n2 are the refractive indices (n, or no)of

136

2.4

Optical Properties of Nematic Liquid Crystals

components 1 and 2, respectively, provided that the indices are related to the same reduced temperature TIT,-, . The additivity rule was confirmed in a four-component mixture of 4,4'-disubstituted phenylbenzoates [63]. Furthermore, the polarizability anisotropy of a mixture ( A q J is obtained using the additivity formula [76-791 Aa,2

= XI Aa1

+ ~2 Aa,

(15a)

where x,, x2 are the mole fractions, and A a l and A$ are polarizability anisotropies of the pure components 1 and 2. From birefringence data of mixtures an average order parameter S1, was defined which was found to satisfy in good approximation the additivity rule for a constant reduced temperature

s,, = X I

s1

+ x, s,

0,155 0,150

3

0,145

0,140 0,135 0.130

Figure 6. Birefringence in the nematic phase of six homologous 4-cyanophenyl-4-n-alkylbenzoates as function of the number of carbon atoms rn in the alkyl chain (T/TN-,=0.97). (Adapted from Rettig [63]).

(15b)

where S, and S2are the order parameters of the pure compounds 1 and 2 [75 -771. However, Palffy-Muhoray et al. [78] showed that, in a binary mixture of cyanobiphenyls, the birefringence and also S, related to a constant reduced temperature deviates clearly from the additivity behaviour. A theoretical treatment of the birefringence (and the orientational order) in mixtures is given elsewhere [78-801.

T/7"-, where TN-I is the nematic +isotropic transition temperature. The striking feature is the clear alternation (odd-even effect) of the birefringence. The alternation in An is obviously the result of the alternating change in the molecular polarizability anisotropy caused by the alternation in the C-C bond angle in the terminal aliphatic chains. However, the alternation in the orientation order probably also plays a role [27].

2.4.6 Birefringence in Homologous Series

2.4.7 Determination of Molecular Polarizability Anisotropy and Orientational Order from Birefringence Data

The birefringence of the nematic phase in homologous series was first studied by Pelzl and Sackmann [9], and has been the subject of many subsequent papers [ l 1, 12,27, 34,38,40,44,60, 61, 81-84]. As a representative example, in Fig. 6 the birefringence (A=589 nm) in the nematic phase of six homologous 4-cyanophenyl-4-n-alkyloxybenzoates is plotted against the number of carbon atoms in the alkyl chain [63]. All values are related to the same reduced temperatures

If the principal refractive indices n, and no are correlated with the molecular polarizability anisotropy a,- a, (alrepresents the longitudinal polarizability and a, represents the transverse polarizability), it must be taken into consideration that the local field acting on the molecules within the nematic phase differs from the external field. Sever-

2.4.8

Relationships between Birefringence and Molecular Structure

a1 theoretical approximations have been derived in order to describe the local field in nematic liquid crystals [40, 66, 85 - 921 and have been compared [93-951. According to these models the average polarizability parallel (a,) and perpendicular (a,) to the optical axis can be determined from the principal refractive indices (n, and no, respectively). In most cases the approximations reported by Neugebauer [85] or Vuks [66] are used (for the latter, see Eq. 6). Combining Eqs. (7 a) and (7 b), it follows that ae-ao

a, -at

=s

(16)

Thus, if the orientational order S (e. g. from nuclear magnetic resonance (NMR), electron spin resonance (ESR) or dichroism measurements) is known, the molecular polarizabilities a, and q can be determined [8, 21, 37, 93-95]. InmostcasesEq. (16)is used to calculate the orientational order when the molecular polarizability anisotropy a, -a, is available. In a few cases a, -a, has been obtained by refractive index measurements on a solid monocrystal, provided that the molecular long axes are known with respect to the optical axes [6, 19,22, 671. Sometimes a, -a, has been calculated from bond polarizabilities [24, 29, 781. In most cases a, -a, has been obtained using the extrapolation procedure first proposed by Haller et al. [ 3 3 ] , where log (a,-a,) or log @,la,) is plotted against a reduced temAt some temperaperature ( T - TNpI)/TN-I. ture away from TNpIthe curve obtained is nearly a straight line and can be extrapolated to T=O (S=l), giving a, -q [13, 14, 25, 28,29,33-36,59,78,81,82,89,93]. Tough and Bradshaw [96] have described an extrapolation method of obtaining the order parameter and the molecular polarizability anisotropy from the measured birefringence by fitting the results to a mean field function of temperature (see also [82-841). Using this

137

method, Dunmur et al. [26] were able to calculate the higher order parameter P,(cos 0).

2.4.8 Relationships between Birefringence and Molecular Structure The principal refractive indices n, and n, and the birefringence An =ne-no of 40 nematogenic compounds (i1=589 nm) for a temperature T,-,-T= 10K, are listed in Table 1. It follows from Eq. (8) that at a constant reduced temperature the magnitude of the birefringence is mainly determined by the molecular polarizability anisotropy a,-%, but also by the molar volume V = M / p . On the other hand, a, -a, depends strongly on the structural features of the molecules. As can be seen from Table 1 some general relationships between molecular structure and birefringence can be derived: 1. Since aromatic rings have a higher polarizability anisotropy than alicyclic rings, the replacement of aromatic rings by alicyclic rings leads to a decrease in a, -a, and thus to the decrease of the birefringence (compare compounds 1-3; 6 and 7; 15 and 16; 18 and 19; 21-23). 2. Linkage groups that enhance the degree of conjugation between the aromatic rings (indicated by increasing J,-fi and by the shift in the long-wave absorption band to longer wavelength) give rise to an increase in a, -a, and the birefringence (compare the increase of An in the series 20,35,32, 33,31 and 27).Nematic liquid crystals with highly polarizable linkage groups such as acetylene, diyne, enyne or endiyne groups [97 - 1001exhibit a relatively high birefringence (An 20.3). However, these materials are not listed in the table because their birefringence is related to higher TN I - Tand is obtained from binary mixtures using an extrapolation procedure.

138


Table 1. Principal refractive indices and birefringence of selected nematic materials at the k 5 8 9 nm and TN-I-T= 10 K ne

n0

An

Refs.

1

1.494

1.521

0.173

30

2

1.571

1.482

0.089

30

3

1.496

I .455

0.041

30, 102

4

1.694

1.523

0.171

29

5

1.702

1.529

0.173

29

6

1.660

1.507

0.153

103

7

1.553

1.472

0.08 I

14

8

1.595

1.490

0.105

91

9

1.545

1.490

0.055

103

10

1.634

1.519

0.115

103

11

1.625

1.503

0.122

103

12

1.622

1.494

0.128

103

13

1.652

1.522

0.130

103

14

1.663

1.496

0.167

103

15

1.599

1.460

0.139

63

16

1.480

1.433

0.047

63

17

1.629

I .465

0.164

8

18

1.635

1.506

0.129

63

19

1.533

1.469

0.064

63

20

1.605

1.491

0.114

29

21

1.603

1.497

0.106

63

22

1.524

1.466

0.058

103

23

1.490

1.452

0.038

103

24

1.549

1.481

0.068

103

No.

Structure

139

2.4.8 Relationships between Birefringence and Molecular Structure

Table 1. (continued) ne

n"

An

Refs.

25

1.829

1.565

0.264

5

26

1.800

1.521

0.279

5

27

1.791

1.521

0.270

22

28

1.688

1.507

0.181

24

29

1.836

1.544

0.292

19

30

1.791

1.541

0.250

9

31

1.761

1.511

0.245

24

32

1.740

1.553

0.187

18

33

1.728

1.532

0.196

104

34

1.697

1.525

0.172

24

35

1.712

1.528

0.184

63

36

1.626

1.483

0.143

63

37

1.588

1.507

0.08 1

103

38

1.602

1.493

0.109

103

39

1.593

1.487

0.106

103

40

1.570

1.490

0.08

103

No.

Structure

3. Lateral substituents diminish a, - a, and the birefringence (compare compounds 36 - 40). The birefringence of nematic side-chain polymers is of the same order of magnitude as that of analogous low molar mass nematics [31, 1011.Plate et al. [lo11 measured the birefringence in the nematic phase of a sidechain polymer A and that of the low molar mass analog B at the same reduced temper-

ature T/T,-,=0.95 (A=633 nm), and found that:

nc

A: B:

1.660 1.696

no 1.540 1.509

An 0.120 0.187

140


It can be seen that the chemical bonding of the mesogenic units to the polymeric backbone leads to a decrease in birefringence, which is obviously caused by the decrease in the orientational order.

2.4.9

References

0. Lehmann, Ann. Phys. 1905,18,796-807. E. Dorn, Phys. Z. 1910, 11, 777-780. P. Gaubert, C. R. Acad. Sci. 1911, 153, 11581161. C. Mauguin, Bull. Soc. Chim. Belg. 1927,36,172 - 177. 0. Pellet, P. Chatelain, Bull. Soc. France, Mineral. 1950, 73, 154- 172. P. Chatelain, Bull. Soc. France, Mineral. 1955, 78,262-266. W. Maier, in Landolt- Bornstein, Zahlenwerke und Funktionen aus Physik, Astronomie, Geophysik und Technik, Vol. IY8, Springer-Verlag, Berlin, 1962, pp. 553-556. W. Maier, K. Markau, Z. Pkys. Chem. NF 1961, 28, 190-202. G. Pelzl, H. Sackmann, Symp. Faraday Soc. 1971,5,68-88. G. Pelzl, R. Rettig, D. Demus, Z. Phys. Chem. (Leipzig)1975, 256, 305 - 3 11. V. N. Tsvetkov, E. I. Ryumtsev, I. P. Kolomiets, A. P. Kovshik, N. L. Gantseva, Opt. Spectrosc. 1973,35,880-883. E. I. Ryumtsev, A. P. Kovshik, I. P. Kolomiets, V. N. Tsevtkov, Kristallgrafiya 1973,18, 12461249. S . Sen, P. Brahma, S. K. Roy, D. K. Mukherjee, S. B. Roy, Mol. Cryst. Liq. Cryst. 1983, 100, 327 - 340. M. Takahashi, S. Mita, S. Kondo, Mol. Cryst. Liq. Cryst. 1986, 132, 53-64. D. Riviere, Y.Levy, C. Imbert, Opt. Commun. 1978,25,206-210. C. Versace, G. Cipparrone, D. Lucchetta, D. Pucci, M. Ghedini,Mol. Cryst. Liq. Cryst. 1992,212, 313-318. P. Lampen, E. H. Korte, A. Blumenberg, SPIE Con$ 1991,1575,284-285. M. Brunet-Germain, C. R. Acad. Sci. B. 1970, 271, 1075-1077. N. V. Madhusudana, R. Shashidhar, S . Chandrasekhar, Mol. Cryst. Liq. Cryst. 1971,13,61-67. Y. Poggi, J. Robert, J. Borel, Mol. Cryst. Liq. Cryst. 1975,29,311-322. H. Schulze, W. Burkersrode, Exp. Tech. Phys. 1975,23,369-374. J. Shashidara Prasad, H. S. Subramhanyuam, Mol. Cryst. Liq. Cryst. 1976, 33, 77-82.

[23] R. G. Horn, J. Phys. (Paris) 1978,39, 105- 109. [24] R. Somasekhar, D. Ravannasiddaiah, M. S. Madhava, H. S. Subramhanyam, D. Krishnamurti, Mol. Cryst. Liq. Cryst. 1978, 45, 243256. [25] R. Desai, R. Pratap, Mol. Cryst. Liq. Cryst. 1981, 75, 287-293. [26] D. A. Dunmur, D. A. Hitchen, Hong Xi-Jun, Mol. Cryst. Liq. Cryst. 1986, 140, 303-318. [27] E. G. Hanson, Y. R. Shen,Mol. Cryst. Liq. Cryst. 1976,36, 193-207. [28] I. H. Ibrahim, W. Haase, Z. Naturforsch. Teil a, 1976,31, 1644- 1650. [29] I. H. Ibrahim, W. Haase, J. Phys. (Paris) 1979, 40, 191- 198. [30] I. H. Ibrahim, W. Haase, Mol. Cryst. Liq. Cryst. 1981,66, 189-198. [31] N. A. Vaz, G. W. Smith, G. P. Montgomery, W. D. Martin, Mol. Cryst. Liq. Cryst. 1990,198, 305 -321. [32] 1. Haller, H. A. Huggins, M. J. Freiser, Mol. Cryst. Liq. Cryst. 1972, 16, 53-54. [33] I. Haller, H. A. Huggins, M. R. Lilienthal, T. R. McGuire, J. Phys. Chem. 1973, 77,950-954. [34] G. R. Van Hecke, B. P. Santasiero, L. J. Theodore, Mol. Cryst. Liq. Cryst. 1978,45, 1-20. [35] R. K. Sarna, B. Bahadur, V. G. Bhide, Mol. Cryst. Liq. Cryst. 1979, 51, 117- 136. [36] R. K. Sarna, V. G. Bhide, B. Bahadur, Mol. Cryst. Liq. Cryst. 1982, 88, 65-79. [37] V. G. Rumyantsev, P. D. Beresin, L. M. Blinov, I. N. Kompanets, Kristallografiya 1973, 18, 1104-1106. [38] V. A. Groshik, Z. V. Adomenas, Kristallografiya 1978,23, 1087- 1089. [39] D. A. Balzarini, Pkys. Rev. Lett. 1970, 25, 114-115. [40] W. H. de Jeu, P. Bordewijk, J. Chem. Pkys. 1978, 68, 109-115. [41] C. C. Huang, R. S. Pindak, J. T. Ho, J. Phys. (Paris) Lett. 1974,35, L185-187. [42] R. Chang, Muter. Res. Bull. 1972, 7, 267-278; Mol. Cryst. Liq. Cryst. 1973, 28, 1-8, Mol. Cryst. Liq. Cryst. 1975,30, 155-165. [43] W. Kuczynski, B. Stryla, Mol. Cryst. Liq. Cryst. 1975,31,267-273. [44] R. Chang, F. B. Jones, J. J. Ratto, Mol. Cryst. Liq. Cryst. 1976,33, 13- 18. 1451 M. Laurent, R. Journeaux, Mol. Cryst. Liq. Cryst. 1976,36, 171-178. [46] R. Chang, Mol. Cryst. Liq. Cryst. Lett. 1976,34, 65-69. [47] W. Kuczynski, P. Pieranski, W. Wojciechowski, B. Stryla, Mol. Cryst. Liq. Cryst. 1977, 34, 203 -209. [48] F. Leenhouts, E. Van der Woude, J. Phys. (Paris) Lett. 1978,39, L249-251. [49] T. Akahane, T. Hashimoto, T. Tako, Jpn. J. Appl. Phys. 1980,19, 1419- 1420.

2.4.9 References [ S O ] R. Moldovan, M. Tintaru, S. Frunza, T. Beica, S. Polosan, Cryst. Res. Technol. 1996, 31, 951 -955. 1511 S.-T. Wu, U. Efron, L. D. Hess,Appl. Phys. Letr., 1984,44,1033-1035;Ap~I.Opt. 1984,23,3911. [52] H. Mada, S. Kobayashi, Mol. Cryst. Liq. Cryst. 1976, 33, 47 - 53. [53] F. Kuschel, R. Rettig, G. Pelzl, D. Demus, Cryst. Rex Technol. 1981, 16, K43-45. 1541 P. Palffy-Muhoray, D. A. Balzarini, Can. J . Phys. 1981,59,515 -520. 1.551 M. Warenghem, C. P. Grover, Rev. Phys. Appl. 1988,23, 1169- 1178. [56] M. Warenghem, G. Joly, Mol. Cryst. Liq. Cryst. 1991,207,205-218. [57] K. C. Lim, J.-D. Margerum, SPlE Displ. Technol. 1992,1815,99- 104. [58] K.-C. Lim, J. T. Ho,Mol. Cryst. Liq. Crysr. 1978, 47, 173- 177. [59] M. Gasparoux, J. R. Lalanne, B. Martin, Mol. Cryst. Liq. Crysr. 1979,51, 221 -246. [60] M. Takahashi, S. Mita, S . Kondo, Phase Trunsit. 1987, 9, 1 - 10. [61] E. F. Gramsbergen, W. H. de Jeu, J. Chem. Soc., Furuday Trans. 2 1988, 84, 1015- 1021. [62] D. W. Bruce, D. A. Dunmur, P. M. Maitlis, M. M. Manterfield, R. Orr, J. Matec Chem. 1991,1,255-258. [63] R. Rettig, Thesis, Halle/S, 1979. 1641 W. Pyzuk, E. Gorecka, A. Krowczynski, Liq. Cryst. 1992, 11, 797 -802. 1651 W. Pyzuk, E. Gorecka, A. Krowczynski, J. Przedmojski, Liq. Cryst. 1993, 14, 773-784. 1661 M. F. Vuks, Opt. Spectros. 1966, 20, 644-65 1. 1671 A. Saupe, W. Maier, Z. Nuturforsch. Teil u 1961, 16,816-824. 1681 I. Abdulhalim, Mol. Cryst. Liq. Cryst. 1991,197, 103- 108. [69] E. M. Averyanov, V. Y. Zyryanov, V. V. Adomenas, V. V. Bykova, Opt. Spectrosk. 1988. 64, 544-552. [70] S.-T. Wu, C.-S. Wu, SPIE Displ.Technol. 1992, 1815, 179-187. 1711 A. Saupe, Z. Naturforsch. Teil a 1963, 18, 336347. [72] S.-T. Wu, Phys. Rev. A 1986, 33, 1270- 1274. [73] S:T. WU, C.-S. WU, J. Appl. Phys. 1989, 66, 5297 -5301. [74] P. Chatelain, M. Germain, C. R. Acud. Sci. 1964, 259, 127- 130; M. Brunet-Germain, Mol. Crysf. Liq. Cryst. 1970, 11, 289-303. 1751 S . Chandrasekhar, N. V. Madhusudana, J. Phys. (Paris) 1969, 30, C4-24. 1761 S. Denprayoonwong, P. Limcharoen, 0.Phaovibul, I. M. Tang, Mol. Cvst. Liq. Cryst. 1981,69, 313-326. [77] 0. Phaovibul, P. Sungsittayakorn, P. Limcharoen, I. M. Tang, Mol. Cryst. Liq. Cryst. 1981, 73, 81 -93.

141

(781 P. Palffy-Muhoray, D. A. Dunmur, W. H. Miller, D. A. Balzarini, Liquid Crystals and Ordered Fluids, Vol. 4, Plenum, New York, 1984, pp. 615-641. I791 E. M. Averyanov, Kristallogrufiyu 1981, 26, 673 - 676. [80] P. Palffy-Muhoray, D. A. Dunmur, A. Price, Chem. Phys. Lett. 1982, 93, 572-577. I811 A. Hauser, R. Rettig, F. Kuschel, D. Demus, Wiss. Z. Univ. Hulle XXXV’86M. 1986,5,72- 80. 1821 A. Hauser, D. Demus, Wiss.Z. Univ. Hulle, XXVII’88M, 1988,3, 137- 141. [83] A. Hauser, D. Demus, Z. Phys. Chem. (Leipzig) 1989,270, 1057- 1066. 1841 A . Hauser, M. Hettrich, D. Demus, Mol. Cryst. Liq. Cryst. 1990, 191, 339-343. [85] H. E. J. Neugebauer, Can. J . Phys. 1954, 32, 1-15. [86] D. A. Dunmur, Chem. Phys. Lett. 1971, 10, 49-51. [87] A. Derzhanski, A. G. Petrov, C. R. Acad. Bulg. Sci. 1971, 24, 569-577. [88] D. Barbero, R. Malvano, M. Omini, Mol. Cryst. Liq. Cryst. 1977, 39, 69- 86. [89] P. Palffy-Muhoray, D. A. Balzarini, D. A. Dunmur,Mol. Cryst. Liq. Cryst. 1984,110,315-330. [90] D. A. Dunmur,R. W.Munn, Chem. Phys. 1983, 76, 249-253. [91] E. M. Averyanov, V. A. Zhuikov, V. Ya Zyryanov, V. F. Shabanov, Mol. Cryst. Liq. Cryst. 1986,133, 135-149. [92] P. Adamski, Mol. Matel: 1994, 3, 157- 162. 1931 A. Hauser, G. Pelzl, C. Selbmann, D. Demus, S . Grande, A. G. Petrov, Mol. Cryst. Liq. Cryst. 1983,41,97-113. (941 N . V. S . Rao, V. G. K. M. Pisipati, P. V. Datta Prasad, P. R. Alapati, Mol. Cryst. Liq. Cry.st. 1986,131, 1-21. (951 N. V. S. Rao, V. G. K. M. Pisipati, P. V. Datta Prasad, P. R. Alapati, D. M. Potukuchi, A. G. Petrov, Bulg. J . Phys. 1989, 16, 93- 104. [96] R. J. A. Tough, M. J. Bradshaw, J. Phys. (Paris) 1983, 44, 447-454. [97] S.-T. Wu, U. Finkenzeller, V. Reiffenrath, J . Appl. Phys. 1989,65,4372-4376. [98] M. Hird, K. J. Toyne, G. W. Gray, S. E. Day, D. G. McDonnell, Liq. Cryst. 1993, 15, 123- I SO. [99] Y. Goto, T. Inukai, A. Fujita, D. Demus, Mol. Cryst. Liq. Cryst. 1995, 260, 23 - 38. LlOO] A. Fujita, Y. Goto, E. Nakagawa, Liq. Cryst. 1994,17,699- 707. 1011 N. A. Plate, R. V. Talroze, V. G. Shibaev,Makromol. Chem. Macromol. Symp. 1987,12,203228. 1021 S. Sen, K. Kali, S . K. Roy, Bull. Chem. Soc. Jpn. 1988,61,3681-3687. 1031 G. Pelzl, D. Demus, unpublished results. 1041 V. V. Belyaev, A. B. Kusnetsov, Opf. Shurn. 1993, 7, 25-29.


2.5 Viscosity Herbert Kneppe and Frank Schneider

2.5.1 Introduction This section covers experimental methods for the determination of shear and rotational viscosity coefficients of monomeric nematic liquid crystals and experimental results on this topic. Polymeric nematic liquid crystals are dealt with in Chap. V in Vol. 3 of this Handbook. The hydrodynamic continuum theory of nematic liquid crystals was developed by Leslie [l, 21 and Ericksen [3, 41 in the late 1960s.The basic equations of this theory are presented in Vol. 1, Chap. VII, Sec. 8. Since then, a great number of methods for the determination of viscosity coefficients have been developed. Unfortunately, the reliability of the results has often suffered from systematic errors leading to large differences between results. However, due to a better understanding of flow phenomena in nematic liquid crystals, most of the errors of earlier investigations can be avoided today.

2.5.2 Determination of Shear Viscosity Coefficients 2.5.2.1 General Aspects According to Chap. VII, Sec. 8 of Vol. 1 of this handbook, there are three main viscosity coefficients q1 to q3 with different orthogonal orientations of the director n to the direction of the flow velocity v and the velocity gradient grad v.

ql: n I1 gradv 772:

n II v

q3: n Iv,

It

I gradv

(3)

A further viscosity coefficient qI2has to be taken into account if the director lies in the shear plane and is neither parallel to the flow velocity nor parallel to its gradient. If the director lies half way between velocity and its gradient, the resulting viscosity is 7745 =

1

1

(771+ 7 7 2 ) + 4 7712

(4)

The coefficient qI2is usually small in comparison to q1 and q2. The methods used to determine shear viscosity coefficients can be divided into three

2.5.2

Determination of Shear Viscosity Coefficients

groups: mechanical methods (capillary flow, movement of a plate) - dynamical light scattering - special methods with restricted applications (acoustic impedance, ultrasonic attenuation, torsional shear, backflow) -

These methods are discussed separately, below.

2.5.2.2 Mechanical methods Flow in a Flat Capillary Usually, the laminar flow of a nematic liquid crystal through a capillary with a rectangular cross-section (Fig. 1) is studied [5-91. For rectangular capillaries with large aspect ratios b/a the shear gradient across the width b can be neglected. For a long capillary the volume flow V is given by V=-. a3bAp 121 q where a is the capillary thickness, 1 is the capillary length and A p is the pressure difference across the capillary. By changing the director orientation, each of the four shear viscosity coefficients of a nematic liquid crystal can be determined. The director can be aligned by means of electric or magnetic fields. The geometric factor a3b11 is usually obtained by calibration using a substance of known viscosity. The reliability of

L

I

143

the results can be very high if special attention is paid to a number of problems. These are discussed below.

Choice of Aspect Ratio. Because of the finite aspect ratio of the capillary there are velocity gradients in the a and b directions. To determine a certain viscosity coefficient, the influence of the gradient in the b direction should be negligible. For a given aspect ratio this influence is large in the case of q3, where the gradient in the b direction affects the measurement via the usually large viscosity coefficient q There is no influence of other viscosity coefficients in the case of q2. The apparent viscosity coefficients can be extrapolated to an infinite aspect ratio [ 101. For example, in the case of ql the correction amounts to 4% for b/a=8 and 171 l q 3=4Director Alignment. Usually magnetic fields are used for the director alignment. Alignment by electric fields is simpler, but the versatility of the magnetic alignment (e. g. rotation of the field) is far greater, and there are no complications due to the electrical conductivity of the liquid crystal. There are two effects that lead to a deviation of the director orientation from the field direction: surface alignment and flow alignment. If the direction of the surface alignment and the magnetic field H differ, the alignment of the director within a surface layer of thickness

h

will be influenced by surface alignment [ 111. Here k is a mean elastic coefficient and Figure 1. Flow experiment for the determination of the viscosity coefficients q,, q2 and q3 in a flat capillary.

Xa = XU-

XL

(7)

is the anisotropy of the magnetic susceptibility. The apparent viscosity coefficient is

144

2.5

Viscosity X

given by [8]

1 $" - L qi +a%~s ( U )

t

(8)

where q iis one of the main shear viscosity coefficients and qs the viscosity coefficient that would be observed for perfect surface alignment in the whole sample. For a typical nematic liquid crystal and a magnetic induction of 1 T the thickness of the surface layer 5 amounts to about 3 ym. For a=0.5 mm and q S = 2q i this effect causes an error of about 2%. Larger errors result for larger values of qs/qi.A plot of the inverse apparent viscosity coefficient as a function of the inverse field strength should give a straight line. This allows extrapolation to infinite field strength and elimination of the influence of surface alignment. Errors due to surface alignment can be avoided by using large capillary thicknesses a, large magnetic fields and suitable surface orientations. With the exception of the case of q3,a velocity gradient in the liquid crystal is coupled with a torque on the director (flow alignment). The balance between the magnetic and shear torque leads to an inhomogeneous director orientation. The deviation between the director orientation and the field direction is given by [8, 121

@ - @ , = 6 - Y-

a/2

(9)

for small deviations, where @ and Q0 denote the orientation of the director and the field with respect to the flow velocity (Fig. 2). The coefficient 6 depends on the director orientation:

Figure 2. Flow in a flat capillary with weak anchoring at the capillary walls. The director orientation deviates from the direction of the magnetic field due to flow alignment. Upper part: velocity profile, lower part: vector field of the director for @, = 90". @,, denotes the direction of the magnetic field.

where q (a)is the viscosity

q(@= ) q1sin2 @ + 712 cos2 @

+ 7lI2 sin2

cos2 @

(1 1)

For H+m, a measurement with @0=900 gives ql, and one with QO=O O gives q2.For finite field strength the following equations are obtained for the apparent viscosity coefficients ([8, 121; the numerical factors are incorrect in both these papers):

1 1 P1 =-+7lapp

171

771

with

and ~

1 -- 1 7lapp

with

712

P2

712

2.5.2 Determination of Shear Viscosity Coefficients

145

tubes As already mentioned, this effect has no influence on the determination of q3.As, usually, la3161aJ,this effect is more pronounced in the determination of 77,. It can cause severe problems, as can be shown for a typical nematic liquid crystal such as pol; f a c e s c a p i l l a r y nernati; l i q u i d c ry s t a 1 4-methyloxybenzylidene-4'-n-butylaniline (MBBA). The viscosity coefficients and Figure 3. Capillary system betwen the pole faces of an electromagnet. The temperature regulation of the the anisotropy of the magnetic susceptibilcapillary system is not shown. ity at room temperature are $=-0.15 Pas, q,=0.19 Pas, q2=0.031 P a s , ~ ~ = I . 8 ~ 1 0 - ~ . In order to keep the systematic error caused by flow alignment within 1% for a magnetused as reservoirs for the liquid crystal. In ic induction of 1 T and a capillary thickness order to cancel gravitational forces the capof 0.5 mm, the pressure gradient has to be illary is arranged horizontally. The air or nismaller than I0 Pa/cm and the volume flow trogen pressure on either side of the capilmust be smaller than 0.5 mm3/s for a capillary can be regulated separately. A small pressure difference (10- 100 Pa) forces the lary width of 10 mm. Many problems will be encountered in measuring these small liquid crystal to flow through the capillary. quantities. Errors from flow alignment can The movement of the meniscus in one of the be avoided by using small capillary thickreservoirs allows the determination of the nesses, small pressure gradients and large volume flow. If the reservoirs on both sides magnetic fields. of the capillary are connected to closed vessels the volume flow can also be calculated from the decrease in the pressure difference Hagenbach - Couette Effect. The developbetween these vessels. ment of the velocity profile at the beginning Problems arise from the underpressure of the capillary (Hagenbach-Couette efcaused by the surface tension of the liquid fect) leads to a deviation from the Hagencrystal on both sides of the capillary. For Poiseuille law. This deviation is small for small tube radii this underpressure is in the large capillary lengths and small pressure same order of magnitude as the admissible gradients. pressure differences. The influence of the differences in the radii of curvature of the Experimental Set-ups. The above-menmenisci, of different wetting properties of tioned requirements regarding the experithe surfaces or minor impurities on the surmental set-up are partly contradictory, espefaces is disastrous. cially if one requires a measurable volume The pressure difference can be increased flow. Furthermore, the strength of the magif longer capillaries are used. With folded netic field is limited. Therefore, any expericapillaries (Fig. 4) [8, 91 lengths of about mental set-up is the result of a compromise 1 m have been realized, and these allow a between these contradictory requirements. pressure difference of several 100 Pa. Thus Most set-ups are modifications of the conthe influence of the difficulties just disstruction shown in Fig. 3. A rectangular cussed can be reduced. However, the incapillary with a thickness of 100-500 pm creased volume of liquid crystal needed to and an aspect ratio of 20 - 50 is connected fill the capillary is a disadvantage of the on both sides to larger tubes. The tubes are

146

2.5 Viscosity

I 1

\1 Figure 4. Cross-section of a folded Capillary system.

I I I

Liquid crystal Plate

I

Container

,, , I

method, and it should thus only be used in investigations where high precision is required. The various director orientations for the determination of the different viscosity coefficients can be achieved by rotation of the capillary or the magnetic field. If the set-up is optimized with respect to a minimal gap between the pole shoes, as shown in Fig. 3, separate set-ups are required for each of the viscosity coefficients. The viscosity coefficient qI2 is usually determined by a measurement of ql, q2 and 7745 according to Eq. (4). As qI2 is small compared to the measured quantities, the measurement should be performed in such a way that the unavoidable errors in the measurements cancel out. Therefore, the coefficients q,, q2 and q45 should be determined in the same capillary, and the different director orientations should be achieved by a rotation of the magnet or the capillary. Due to the high demands on the precision of measurement, determinations of qI2are rare. Movement of a Plate

In this method the liquid crystal is filled in a container having a circular or rectangular cross-section (Fig. 5). A thin plate suspended from a wire or glass rod is submerged in the liquid crystal. The force on the suspension during an upward or downward movement of the container or the damping of an oscillation of the plate gives a measure of the viscosity of the liquid crystal [13 - 161.

Figure 5. Determination of viscosity coefficients by means of the force on a plate in a nematic liquid crystal during vertical movement of the liquid crystal.

The great advantage of this method over capillary flow is the high sensitivity of dynamometers, which allows the forces acting on the plate to be kept very small. Therefore, the velocity gradients and the influence of flow orientation can be kept low. In addition, because of the large container dimension, the influence of the surface orientation at the plate and the container walls can be neglected. The movement of the plate is coupled with a three-dimensional balancing flow. For isotropic liquids the influence of this flow can be taken into account by calibration with an isotropic liquid of known viscosity. For liquid crystals the influence is more complicated due to the fixed director orientation. The orientations of the velocity and the velocity gradient with respect to the director are different around the plate, and the effective viscosity also varies. Therefore, all viscosity coefficients contribute to the measured apparent viscosity. With a proper geometry the contribution of the unwanted viscosity coefficients can be minimized and the viscosity that is effective at the plate surface can be determined. Due to the complex geometry, a calculation of the velocity profiles, or at least an estimation of the error in the measurement,


is difficult. To date all results obtained using this method contain large systematic errors. These errors can partly be avoided and probably estimated by using a rectangular and flat container (see Fig. 5 ) . Although the first determination of viscosity coefficients by Miesowicz [13] were done at a geometry very similar to this, systematic investigations of the influence of the geometry have yet to be done. To determine q2the direction of the magnetic field and plate movement must coincide. This causes many mechanical problems. Sometimes no magnetic field is applied, in which case the viscosity is determined under flow alignment. The procedure cannot be used for larger flow alignment angles.

147

The strong scattering of visible light is a characteristic feature of nematic liquid crystals. The scattering can be attributed to thermally induced fluctuations of the director orientation. In principle, the elastic coefficients of the liquid crystal can be determined from the intensity of scattered monochromatic light. The viscoelastic ratio, i.e. the ratio of the viscosity coefficient to the elastic coefficients can be obtained from the line width or intensity modulation of the scattered light [ 17-22]. The broadening of the line width of monochromatic light by director fluctuations amounts to 100- 1000 Hz and is in-

accessible for classical optical detection. If the scattered light interferes with the exciting light an intensity modulation with the same frequency is observed, and this is easily detectable. This method is called ‘light beating spectroscopy’ or the ‘heterodyne technique’. Interference within the scattered light leads to a similar effect and this method is called ‘self-beat spectroscopy’ or the ‘homodyne technique’ [23]. Several set-ups for the detection of the scattered light are possible. Figure 6 shows four typical arrangements that differ in the direction of incident and scattered light to the polarization axes and the director orientation. The intensity of the scattered light is high if the polarization axes of incident light and scattered light are perpendicular to each other. Usually the incoming light strikes the sample under normal incidence; in this case a goniometer with one arm can be used. An apparatus for the investigation of light scattering using the homodyne technique is shown schematically in Fig. 7. A small part of the sample is illuminated by polarized light from a laser with a power of some milliwatts. The scattered light is detected from a small spot of the sample under the angle by a photomultiplier tube. The current fluctuations are analysed by a real-time spectrum analyser or stored for subsequent computer-assisted analysis. The measurement is repeated for different scattering angles. Some set-ups allow for variation of

geometry 2

Figure 6. Scattering geometries: k , and k,, wavevectors for the incoming and scattered light, respectively; i andf, polarization vectors.

2.5.2.3 Light Scattering

geometry 1

148

2.5 Viscosity polarizer

sample

Q laser

Y

tube

the director orientation by means of electric or magnetic fields. The optical spectrum S,(v) of the light scattered by the long-range orientational fluctuations is given by [24]

Figure 7. Block scheme of a homodyne set-up.

light; V the scattering volume; E, the amplitude of the electric field; c the velocity of light; and R the distance between the scattering volume and the point of observation. If no is a unit vector parallel to the optical axis, and e2 and e l are two unit vectors the directions of which are defined as nox q and e2 xn,, respectively, then the geometric factor G, is given by G, = ,i . f o + i, .fa

(20)

where

and qI1and q1 are the components of q with respect to the optical axis. The scattered light consists of two Lorentzian-shaped modes, a=land a = 2 , with equal angular centre frequency w, and different widths Ama. By proper choice of the scattering geometry, single fluctuation modes can be observed.

q=ki -kf

(19)

where kiand kf are the wavevectors within the nematic liquid crystal (i.e. the differences in the directions and lengths of the wavevectors inside and outside the sample have to be taken into account). E ~ = E ~ ~ -is- E ~ the anisotropy of the dielectric constant; m, the angular frequency of the incoming light; m the angular frequency of the scattered

If the scattering vector q is normal to the optical axis no (geometry 1)

2.5.2


results. That is, two fluctuation modes, the splay and the twist mode, having different half-widths are observed. If the scattering vector is parallel to the optical axis (special case of geometry 2)

Ka ( 4 ) = k33

149

The angle between the polarization directions of incident and scattered light enters the geometric factor G,. It takes a maximum value for perpendicular directions, if the other angles are kept constant. The spectral distribution of the light intensity fluctuation can be obtained by an autoconvolution of the optical spectrum [ 2 5 ] :

results. That is, the scattered light consists only of one Lorentzian band, the bandwidth of which is determined by the bend mode. The fluctuation modes with the corresponding displacements &, and &, of the director in the el and e2directions are shown in Fig. 8. The modes are named according to the effective elastic coefficients. The main term for a viscous director rotation is, in all cases, the rotational viscosity yl. The additional terms are caused by the backflow. The backflow term in the splay geometry is very small, and therefore its determination is difficult.

’

bend

twist

Figure 8. Uncoupled fluctuation modes in the q n plane (6n,) and perpendicular to it (6n2).

The spectrum consists of the superposition of three Lorentzian functions. Two of them show the two-fold half-width of the corresponding term in the optical spectrum. The half-width of the third is the sum of the first two half-widths. By changing the scattering geometry the contributions of the single terms can be extracted. In geometry 1 the direction of the scattering vector q nearly coincides for small scattering angles 8 with the directions of k j and k,, as the length of ki and kf differ due to the different refractive indices. For both cases of geometry 1 shown in Fig. 6 the geometric factor G, nearly vanishes and the half-width of the spectrum is determined only by the twist mode. Unfortunately, the transition from one mode to another covers such a broad range of scattering angles that the separation of the modes is difficult. At small scattering angles the scattered light partly interferes with the incident light by means of which the scattered light contains components with half-widths corresponding to the heterodyne technique. However, in principle it is possible, by using suitable fit procedures, to determine all the Leslie coefficients from

150

2.5

Viscosity

the angle dependence of the light scattering under different geometries. A comparison of the light scattering method with mechanical methods shows that: -

-

-

-

The sample volume and the consumption of liquid crystals in light scattering experiments can be kept extraordinarily low. Some of the Leslie coefficients can easily be determined by light scattering, while others, such as q,are virtually unaccessible. The experimental set-up used for light scattering is relatively simple. However, the primary results are viscoelastic ratios and elastic coefficients determined using the light scattering method are not very precise. Due to the presence of many sources of error, the reliability of results obtained by light scattering cannot compete with that of mechanical methods.

It should be mentioned that, for certain classes of liquid crystals (polymeric liquid crystals, smectic liquid crystals), the light scattering method allows the determination of the viscosity coefficients, whereas their measurement by means of mechanical methods is very difficult.

2.5.2.4 Other Methods Besides the methods described in the foregoing chapters, several other methods have been proposed that have not received greater attention as they are either more inaccurate or they only allow the determination of a few Leslie coefficients or shear viscosities. These methods are mainly based on: -

ultrasound investigations [26- 301, torsional shear flow [31-351, and effects due to backflow during a director rotation after a sudden change in an applied field [36-391.

Shear viscosities under flow alignment can be studied using commercial viscosimeters.

2.5.2.5 Experimental Results The anisotropic shear viscosity coefficients q,, q2, q3 and q12have been determined only for a few liquid crystals. In contrast there have been many investigations of the shear viscosity coefficient under flow alignment. The reason for this might be that the effort required to determine .the anisotropic coefficients is greater by far. Viscosity coefficients determined under flow alignment are often used to estimate the switching times of liquid crystal displays. For basic research they are less important. Temperature Dependence The behaviour of the coefficients ql, q2and q3will be discussed for a liquid crystal having a broad nematic range and no anomalies. A mixture of nematic liquid crystals with similar structures is well suited to this purpose, and the example used here is Nematic Phase V, a former product of Merck, which consists of a eutectic mixture of the two isomers of 4-methoxy-4’-n-butylazoxybenzene (65 mol%) and the two isomers of 4-methoxy-4’-ethylazobenzene (35 mol%). The nematic phase ranges from 268 K (melting point) to 347 K (clearing point). The mixture exhibits a sharp clearing point. Figure 9 [9] shows the shear viscosity coefficients ql, q2and q3in the nematic phase and the isotropic shear viscosity as a function of temperature in an Arrhenius plot. At low temperatures far from the clearing point, the curves of the shear and rotational viscosity coefficients are parallel to each other, i.e., the ratios qi/qjand yl/qj remain more or less constant. For a given temperature the activation energies of the coefficients are the same, but they change with

2.5.2


151

1 "7i In Pa s

0

Y1 In Po s -1

-2

-3

-4

-5 I

I

I

1

2.8

3.0

3.2

3.4

temperature. The activation energy varies between 55 kJ/mol for low temperatures and 30 kJ/mol for higher temperatures. In the isotropic phase one obtains an activation energy of 25 kJ/mol, which is in good agreement with the activation energy for other isotropic liquids having similar structures. By analogy to isotropic liquids, the bending in the Arrhenius plot can be described by the equation of Vogel

To amounts to 180 K for this liquid crystal. With the exception of the neighbourhood of the clearing point, the order ??l

>y1 >773

>772

(30)

is valid over the whole phase range. This is a general rule for common nematic liquid crystals, and is predicted by a series of microscopic models [40 -431.

,

3.6

I

3.8

Figure 9. Shear viscosity coefficients q,, q2 and q3,rotational viscosity coefficient y, and isotropic shear viscosity coefficient qisoas a function of temperature for the liquid crystal Nematic Phase V. T c , Clearing point temperature.

In the neighbourhood of the clearing point the influence of the order parameter, which undergoes a rapid change in this region, becomes visible. According to theory, all shear viscosity coefficients approach a common value for a vanishing order parameter, which corresponds to an isotropic viscosity. Due to the density change at the phase transition this formal isotropic viscosity cannot be obtained from an extrapolation of the isotropic viscosity into the nematic phase. The predicted relation between shear viscosity and degree of order is of the form [431

where i j is the just discussed isotropic reference viscosity and f, (&, S,) is a linear function of the Legendre polynomials S2 and S,, where S2 corresponds to the usual order parameter.

152

2.5 Viscosity

The temperature dependence of q 2 changes its sign shortly below the clearing point. f i is negative for q2 and its absolute value decreases rapidly with increasing temperature at the clearing point. Multiplication by 17, which decreases with increasing temperature, leads to the observed change of sign. Direct comparison of experimental data and theoretical predictions is difficult. Like the case of isotropic liquids, there is no theory that allows the calculation of the reference viscosity for liquid crystals. Furthermore, experimental values for S4 are not known with sufficient precision. It has been shown empirically [44] that a relation of the form

qi = aijk V j bijk q k

(32)

is valid for the viscosity coefficients. This follows from Eq. ( 3 1) under the assumption that f1

a.. Y f. J

1

(33)

A simple example isf, =aiS2. The observed viscosity for a director orientation in the shear plane changes between the extreme values q1 and q2.The exact angular dependence is given by

17(@)

= 772 + (171 - 172) sin2 @ + 1712 sin2 CDcos2 ~i

(34)

The contribution of q12exhibits its maximum at @ =45 'and is usually small because of the small coefficient. As this coefficient can only be determined from the angular dependence of the viscosity, its determination is difficult. In the first investigation by Gahwiller [ 5 ] ,even the sign obtained for qI2 was incorrect. Therefore, and because of the minor interest this coefficient has been investigated only for a few liquid crystals. Theory and later determinations [5, 8, 44-46] show that this coefficient is negative for usual liquid crystals.

A discussion of the influence of molecular form and structure on the shear viscosity coefficients is desirable but impossible on the basis of the available experimental data. The number of liquid crystals that have been investigated is small and the coefficients determined with different methods show different accuracies. The following list summarizes the most important investigations:

Schiff bases [5-8, 14, 47, 481; cyanobiphenyls [9, 15,44, 46,49-511; esters [44, 461; - azoxybenzenes [9, 16,44,45].

-

Divergence a t a Phase Transition to a Smectic A Phase If there is a phase transition from a nematic to a smectic phase, pretransitional effects are observed in the neighbourhood of the transition [9,44,49-511. Figure 10 [9] shows this behaviour for 4-n-octyloxy-4'cyanobiphenyl (SOCBP) with a nematic smectic phase transition at 340.3 K. Pretransitional effects cause a divergence of the shear viscosity coefficient q2 and the rotational viscosity yl. The apparent divergence of the shear viscosities ql and q3(open circles in Figure 10) is an experimental artifact caused by an inhomogeneous surface orientation. Despite of the extrapolation to infinite field strength, which normally eliminates the influence of surface alignment (see Sec. 2.5.2.2 of this Chapter) a deviation remains in this temperature region because of the divergence of some of the elastic coefficients. Only a surface orientation parallel to the magnetic field or very large magnetic fields (several Tesla [51]) allow reliable determination of the viscosity coefficients. Of course this is also valid to a minor extent for the determination of q2.


153

-2.5 7)

In -2-

Po s -3.c

In 1 Y

Po s

-3.5

Figure 10. Shear viscosity coefficients q , , q2 and q 3 , rotational viscosity coefficient y, and isotropic shear viscosity coefficient q,,, as a function of temperature for

-4.0

4-n-octyloxy-4'-cyanobiphenyl (SOCBP). The phase

?PO

L 2.80

I

I

2.85

2.90

Theory and intuition show that at a transition from a nematic to a smectic A phase, where the mobility is restricted to two dimensions, the viscosity coefficient q 2 , which is coupled with a movement in the forbidden dimension, will diverge. The divergence can be described by the expression [52-541 772

=7720+4T-Tis)-"

(35)

where 17; is the non-divergent part of the viscosity. Values between 0.33 and 0.5 have been predicted for the exponent v. Because of the large number of adjustable parameters a fitting of experimental data to this equation and to Eq. (31) for the temperature dependence of 17; is easy, as can be seen from Fig. 10, the solid curves in which were calculated using this method. On the other hand, the obtained exponents cannot be used for the verification of theories, as the experimental values vary between 0.36 and 1.05. A main problem is the determina-

2.95

transition from the nematic to the smectic phase occurs at T N s .

tion of q;, which can only be extrapolated from the temperature dependence of q2 at temperatures where the divergence can be neglected. Due to several uncertainties this extrapolation always involves large errors. Graf et al. [9] have suggested a procedure that also takes into account the non-divergent viscosities q1 and q3. Because of experimental problems and insufficient sharpness of the transition point, it is also impossible to make measurements at temperatures so close to TNs that the non-diverging part can be neglected. The fitting procedure itself is a further source of error. In the case of the elastic constants, the non-diverging part is almost independent of temperature. Therefore, the divergence of elastic constants is considerably better suited to the verification of theories about pretransitional effects. Figure 11 [51] shows the temperature dependence of the kinematic viscosities v, = 77, /p for a mixture of the liquid crys-

154

2.5 Viscosity

rection of flow. Under usual conditions this angle is small and the observed viscosity qo nearly equals q2. A more precise relationship is

-6-

In&,

-

770 = 772 -a3

-8 -

-10

3.2

3,4

'"

1 a K T

'8

Figure 11. Kinematic shear viscosity coefficients v,, v, and v, of a re-entrant nematic mixture as a function of temperature in the nematic, smectic and re-entrant nematic phases.

tals 4-n-heptyl-4'-cyanobiphenyl, 4-n-octyloxy-4'-cyanobiphenyl and 4-n-pentyl4"-cyanoterphenyl in the ratio 73 : 18 :9 by weight. Besides a nematic and smectic A phase, this mixture exhibits a re-entrant nematic phase at low temperatures. All phases are stable and the transitions are almost second order. The kinematic viscosity v, diverges on both sides of the smectic phase. The viscosity v, shows the same activation energy in all phases and only small steps at the transitions. As for the non-divergent part of v,, the viscosity v, shows in the re-entrant nematic phase an exact continuation of the course in the nematic phase. There is still no plausible explanation for the complicated course of v,. Shear Viscosity under Flow Alignment During shear flow of a nematic liquid crystal without applied field the director in the bulk of the sample will normally be aligned in the shear plane at an angle a0to the di-

(36)

which is obtained assuming that a, =O. Due to the simplicity of the measuring technique, the viscosity under flow alignment has been investigated for many liquid crystals and has been used to predict the switching time of liquid crystal displays. For basic research the knowledge of this quantity is of minor interest. A comprehensive summary of experimental data on 77, up to 1988 has been presented by Belyaev [55]. A comparison of data within homologous series and in dependence on the molecular structure is also given in this summary. The curve shown in Fig. 12 [56] for the liquid crystal 4-ethoxybenzylidene-4'-nbutylaniline ( 2 0 . 4 ) is representative of the temperature dependence of 7,. Although an untreated capillary was used, wall effects can be neglected because of the high shear rates. The sign change in the temperature dependence slightly below the clearing point is more pronounced than for 77, because the flow alignment angle increases there [57], and this leads to a large contribution from 771 to 770. The curve for 4-n-penty loxybenzylidene4'-n-butylaniline ( 5 0 . 4 ) shows some remarkable deviations from this course [56]. These are caused by pretransitional effects from a smectic phase at low temperatures. Due to these effects the range of flow alignment is limited to a small region below the clearing point. At lower temperatures the director begins to tumble and a viscosity between q1 and q2 is observed. This leads to the pronounced minimum in the q, curve for 5 0 . 4 . A further deviation is caused by the divergence of qo at the transition to the smectic phase.

2.5.3

155

Determination of Rotational Viscosity

Tube 1 . 7 7 p

71,

Tube 2, 131 p

m Pas

3.6 -

3.2

A

.

Tube 3, 2 5 4 ~ Tube 4. 5 1 6 p

-

2.82.4

-

0.001

I

0.01

I

0.1

I

1

3

Figure 12. Apparent viscosity measured in a capillary as a function of temperature for 4-ethoxybenzylidene4’-n-butylaniline ( 2 0 . 4 ) and the homologous pentoxy compound 5 0 . 4 in the nematic and isotropic phases. Tc, Clearing point temperature.

Figure 13. Apparent viscosity q, of 4,4’-dimethoxyazoxybenzene (PAA) obtained from measurements in capillaries of different diameters and homeotropic alignment at the inner capillary surface versus the volume velocity divided by the capillary radius.

Even at high shear rates the director orientation in a layer near the inner capillary surface is still determined by the surface orientation. The thickness of this layer depends on the shear rate. Therefore, the apparent viscosity depends on the shear rate and the pressure gradient over the capillary, and it only approaches a constant value for high shear rates. This dependence can be calculated using the Leslie - Ericksen equation (see Chap. VII, Sec. 8.1 of Vol. l of this Handbook, Viscous Flow under the Influence of Elastic Torques). Investigations of the effective shear viscosity under flow alignment and with known surface orientation can therefore be used to verify the predictions of the Leslie-Ericksen theory. According to the theory, the effective viscosities for a given liquid crystal, at a given surface orientation and a fixed temperature, should be a universal function of the ratio V/R, where the volume velocity Vand the capillary radius R can be changed independently. Figure 13 shows the result of a corresponding investigation by Fischer and

Fredrickson [ 5 8 ] , which confirms this prediction.

2.5.3 Determination of Rotational Viscosity 2.5.3.1 General Aspects Rotation of a director at an angular velocity 0 in a sample of volume V is coupled with a torque

M=y1@V

(37)

on the sample (see Chap. VII, Sec. 8.1 of Vol. 1 of this Handbook), where yl is the rotational viscosity coefficient. Correspondingly, the sample exerts a torque-M on the director. The switching time of a liquid crystal display is proportional to the rotational viscosity. Therefore and due to its strong temperature dependence, y, is one of the most important material constants of liquid crystals for electrooptical applications.

156

2.5 Viscosity

2.5.3.2 Experimental Methods with Permanent Director Rotation Mechanical methods utilize Eq. (37) for the determination of the rotational viscosity f i . If a rotating magnetic field H is applied to a nematic sample, the director will follow the rotation up to the critical velocity

(see Chap. VII, Sec. 8.1 of Vol. 1 of this Handbook), where xais the anisotropy of the magnetic susceptibility, which must be positive for this method. After a settling time the director rotates with the same velocity as the applied field and there is a constant phase lag between field and director. The torque according to Eq. (37) exerts a corresponding torque on the sample suspension, which can easily be determined [59, 601. Figure 14 shows a simple set-up, where the torque is measured via the twisting of the suspension wire. The torque obtained for a sample of some cubic centimetres of a usual nematic liquid crystal with positive magnetic anisotropy can be measured for adequate angular velocities with no problems. In order to increase the critical velocity one should apply fields that are as large as pos-

sible. Therefore, the diameter of the sample vessel and the surrounding thermostated water jacket (not shown in Fig. 14) should be kept small. The method is not suitable for nematic liquid crystals with negative magnetic anisotropy, as the director of these substances will finally evade to the direction of the rotation axis. In principle, Eq. (37) can only be applied if the director of the complete sample rotates with the angular velocity of the rotating field. At the inner surface of the vessel molecules attached to the surface determine the director orientation. This anchoring cannot be broken by magnetic fields of usual strength. Figure 15 shows an enlarged top view of a sample in a vessel with homeotropic surface alignment. After one revolution of the field the field line of the director exhibits two inversion walls [61]. Without an efficient mechanism for the annihilation of inversion walls the whole sample will be filled with inversion walls after a short time and the overall torque will be drastically reduced. Fortunately, this type of inversion wall is unstable against a rotation of a pair of walls with reverse sense around the x axis. After a rotation of 90" the inversion walls approach each other and are annihilated. Nevertheless there will always be a layer at the vessel wall where the director does not follow the rotating field. The thickness

T

Figure 14. Determination of the rotational viscosity. The sample is suspended in a rotating magnetic field.

Figure 15. Inversion walls in a nematic liquid crystal (LC) in a rotating magnetic field after one revolution.

2.5.3

of this layer exceeds the magnetic coherence length 5 under the given conditions. For a common liquid crystal 2 5 is of the order of 20 pm at 0.3 T and its influence can be neglected for sample diameters above several millimetres [62]. For very viscous materials the critical velocity according to Eq. (38) becomes small and the time required to reach the equilibrium torsion of the suspension wire is very long. The critical velocity is proportional to the square of the field strength, which should be as high as possible. Due to the necessary rotation of the magnet, permanent magnets with a moderate field strength are commonly used. Rotation of an electromagnet is possible [63], but this procedure is not advisable. Larger fields and larger sample volume are possible if the sample rotates instead of the magnetic field, and electromagnets can then be used [62]. The torque on the suspension wire must then be measured in a rotating system, which requires some effort. The rotation of the sample can be monitored by means of a laser beam, which is reflected from a mirror attached to the sample vessel. The reflected laser beam is detected twice in every revolution by a photodiode. If the suspension is rotated by a computer-controlled stepper motor and the photodiode interrupts a timer on the computer, the phase lag between motor and sample vessel can be determined without and with field, and the rotational viscosity can be calculated from the difference between these phase lags. The uncertainty in the determination of the rotational viscosity with this method can be as small as 1%.

2.5.3.3 Relaxation Methods In relaxation methods a non-equilibrium orientation of the director is produced and the time constant for the relaxation to equilib-


157

rium is determined. The driving torque can be of elastic type or exerted by magnetic or electric fields. The relaxation process can be followed by optical methods, or by measurement of the dielectric constant or the torque on the sample in a magnetic field. Accordingly, many relaxation methods have been developed for the determination of rotational viscosity. Most of the methods use small sample volumes. This often gives rise to an inhomogeneous director rotation, and backflow effects (see Chap. VII, Sec. 8.1 of Vol. 1 of this Handbook) lead to a faster relaxation, as for a homogeneous rotation.

Methods with Thin Layers The relaxation of a deformation of the director field in a thin layer is observed. The liquid crystal is placed between two glass plates with a given surface orientation. The deformation is produced by appyling electric or magnetic fields. In the first realization of this method, Cladis [64] used a homogeneous planar orientation of the undeformed director (Fig. 16). For liquid crystals with positive magnetic anisotropy the orientation of the director can be twisted between the glass plates by application of a magnetic field perpendicular to the relaxed orientation and parallel to the glass plates. If the field strength slightly exceeds the critical value there will be only a minor deformation and the relaxation after switching off the magnetic field will follow an exponen-

planar o r i e n t a l i o n

Figure 16. Director field of a nematic liquid crystal with a planar surface orientation and an applied magnetic field.

158

2.5

Viscosity

tial law. The relaxation of the deformation angle @between the director orientation in the sample and at the surface is given by

(39) 2

z-I/lan2k22

~

Yl ~

a

~

c

2

(40)

The relaxation time constant z is proportional to the rotational viscosity coefficient. Furthermore, it depends on the layer thickness a and the elastic coefficient k,, or the anisotropy of the magnetic susceptibility and the critical field strength H, for this geometry. Two of these quantities have to be determined in a separate experiment. As the director rotation is within the plane of the boundaries, there are no disturbing backflow effects. This is the main advantage of this method. For the same reason, the director rotation cannot be detected by usual optical or dielectric methods, but is determined by observing the conoscopic interference figure in a polarizing microscope. The figure consists of two hyperbolas, the orientation of which depends on the angle distribution @ (y ) in the layer. The determination of the hyperbola rotation gives the mean relaxation time. As for small deformations, the relaxation time does not depend on z ; the mean value agrees with the relaxation time constant z. The elastic coefficient k,, can be measured using the same apparatus. If the applied magnetic field greatly exceeds the critical strength, the relaxation will be non-exponential. The hyperbola rotation must then be calculated by means of the Leslie-Ericksen equations, and the rotational viscosity y, is determined by a fit of the calculated hyperbola rotation to the observed one. A disadvantage of this method is that it is difficult to follow the rotation of the interference figure by eye or by means of automatic equipment.

All other methods start with a director deformation the relaxation of which takes place in a plane perpendicular to the boundaries. In this case standard methods for the determination of the director orientation, which are also applied to the determination of elastic constants, can be used (e.g. light intensity measurements behind crossed polarizers or measurement of the dielectric constant). Usually a cell with planar surface orientation is used. By means of a magnetic [65] or electric [66] field perpendicular to the plates and somewhat larger than the critical value, a small splay deformation of the director is produced. The relaxation to the planar equilibrium orientation after switching off the field is followed by the methods discussed above. In contrast to the twist deformation, inhomogeneous rotation of the director causes a shear flow in the cell, which is called backflow. The observed relaxation time for a small deformation will be shorter than the analogue to Eq. (40)

which has to be used for this geometry. If an effective rotational viscosity is calculated according to Eq. (41) it may be some 10% smaller than yl [65]. For the relaxation of a bend deformation in a cell with homeotropic surface orientation the correction for the backflow is even larger. The influence of backflow is a great disadvantage of relaxation methods in the case of precise measurements. Methods with Thick Layers If all dimensions of a sample exceed the magnetic and the dielectric coherence lengths,

2.5.3

and

respectively, it can be treated as a thick layer. The rotation of the director by means of a magnetic field is homogeneous across the sample, with the exception of a small boundary layer 5, and backflow can be neglected. In the method described by Gerber [67], the director of a liquid crystal sample in a cell with a thickness of 1 mm is orientated by a magnetic field at the beginning of the experiment. After a small change in the direction of the magnetic field the relaxation of the director to the new equilibrium position is followed by measurement of the dielectric constant. The relaxation time is given by

z=

Y1

Po Xa H 2

(43)

The anisotropy of the magnetic susceptibility has to be determined otherwise. In the method described by Bock et al. [68], the liquid crystal is filled in an ampulla which is suspended from a torsion wire in a constant magnetic field. The suspension of the wire is rotated by a certain angle and the relaxation of the ampulla to the new equilibrium position is observed. The method is very useful for samples with high viscosity. If the oscillation period of the system is negligible relative to the relaxation time, and if the director orientation is not far from its equilibrium position, an exponential relaxation is observed with the time constant


159

Rotational viscosities can also be determined by means of electron spin resonance (ESR) or nuclear magnetic resonance (NMR) experiments [69-711. For low viscosity materials the sample is rotated around an axis perpendicular to the magnetic field. For high viscosity materials the sample is rapidly rotated by a small angle and the relaxation observed. Both methods allow the determination of the angle A between director and field direction. For the continuous rotation with an angular velocity +IY smaller than the critical one (see Eq. 38) one obtains [691 sin 2 4 = 2YlV P O Xa H~

(45)

The anisotropy xaof the magnetic susceptibility must be determined in a separate experiment. The relaxation time after a rapid rotation by a small angle obeys Eq. (43). For angles above 45", and especially for angles around 90°, the director relaxation will be strongly inhomogeneous due to backflow [36]. This effect can be utilized to determine shear viscosities besides the rotational viscosity for high viscosity and polymeric material s. For low demands on the accuracy, the rotational viscosity can also be estimated from the switching time of a liquid crystal display [72]. The switching times in a cell of thickness a are given by ton =

Y1 a2 E, E,

U 2 - krC2

and

(44)

where V is the sample volume and D is the torsion constant of the wire. Both quantities can easily be determined.

where k is the appropriate elastic constant, U is the voltage across the cells and E, is the anisotropy of the dielectric constant.

160 2.5.3.4

2.5 Viscosity

Experimental Results

There are good reasons for the large interest in the rotational viscosity coefficient First, the switching time of displays on the basis of nematic liquid crystals is mainly determined by the rotational viscosity of the liquid crystal used (see Eqs. 46 a and 46 b). Secondly, there is no analogue to the rotational viscosity in isotropic liquids.

x.

Temperature Dependence Figure 9 shows the typical temperature dependence of "/1. At low temperatures the course of yl is parallel to the courses of the other viscosities, that is, the activation energies of about 30-50 kJ/mol are equal and the observed bending for the rotational viscosity in the Arrhenius plot can also be described by the equation of Vogel (Eq. 29). In contrast to the other viscosities, the rotational viscosity strongly decreases in the neighbourhood of the clearing point. This can be attributed to the special dependence on the order parameter. Because of the vanishing rotational viscosity in the isotropic phase, and for symmetry reasons, the leading term in the order parameter dependence is of second degree. Therefore, the temperature dependence of the rotational viscosity is often described by an equation of the form 173,741 y1= AS2(2') exp (2) (47) T-T,

where different expressions are used for the temperature dependence of the order parameter; for example, the ansatz of Haller [75]. Data covering several orders of magnitude could be fitted to this equation within the experimental errors. The temperature Todepends on the glass transition temperature Tg. Schad and Zeller [76] proposed the following relation between these temperatures To = Tg- 50 K

(48)

It is known that the temperature dependence of the viscosity of polymeric materials can be described as a universal function of the difference T-Tg. Schad and Zeller have shown that the rotational viscosity for a large number of liquid crystal mixtures used for displays can also be described by such a universal function if the influence of the order parameter in the neighbourhood of the clearing point is not taken into account. Divergence at a Phase Transition to a Smectic A Phase

A divergence of the rotational viscosity is observed in the neighbourhood of transitions to smectic phases as the molecular rotation will be hindered by the pretransitiona1 formation of the smectic layer structure. Figure 10 shows this effect for 80CBP [9]. The divergence can be described by an equation similar to Eq. (35) [52-541: (49) The difficulties in the experimental verification of this equation are the same as for the already discussed shear viscosities. It is nearly impossible to separate the divergent from the non-divergent part. As can be seen from Fig. 10, the divergence is less pronounced for the rotational viscosity, and thus in this case it is even more difficult to extract the divergent part. Although the accuracy in the determination of yj is normally higher than for the shear viscosity q2,this advantage is annihilated by the large contribution of the non-divergent part yp. The experimental values for v [71,77,78] are comparable with the theoretical value of 0.33 [79]. Influence of the Molecular Structure The influence of the molecular structure on the rotational viscosity has been investigated for a number of liquid crystals. Investi-

2.5.3

gations of homologous series can give information about the influence of the chain length. Figure 17 shows the result for the homologous di-n-alkyloxyazoxybenzenes [go]. Apart from the influence of the order parameter in the neighbourhood of the clearing point, an increase in the rotational viscosity with chain length is observed for constant temperature. This general trend has superimposed on it an odd-even effect, which leads to higher values for liquid crystals with an even number of carbon atoms in the alkyl chain. The reason for this effect might be that the increase in the chain length is larger for odd to even than for even to odd changes of the number of carbon atoms. A corresponding effect is also observed for the clearing temperature, as can be seen in Fig. 17. The rotational viscosity and the high clearing point of the ethyloxy homologue show this behaviour in an extreme manner. The exceptional behaviour of the first members of a homologous series of liquid crystals is observed for many properties. The heptyloxy homologue exhibits a smectic C phase at low temperatures. Therefore, the

-6’

‘

2.4

2.6

2.8

I

Figure 17. Rotational viscosity coefficients y, of the homologous di-n-alkyloxyazoxybenzenesas a function of temperature. The numbers on the curves denote the length of the alkyl chain.


161

rotational viscosity diverges, which leads to the relatively large absolute values. A reversed odd-even effect is observed for alkyl substituted compounds, such as din-alkylazoxybenzenes [81] where the homologues with an even number of carbon atoms show a smaller rotational viscosity. This observation can be explained by the rule presented for the alkyloxy compounds if the influence of the oxygen atom and the CH, group on the form of the side chain are assumed to be similar. The series of 4-n-alkyloxybenzylidene4’-n-butylanilines (mO .4) [56] exhibits no odd - even effect if the rotational viscosities are divided by the square of the order parameter (Fig. 18). ‘

Yl =

Yl 3

In comparison to the above discussed dialkyl- and dialkylazoxybenzenes, it has to be taken into account that only one chain length is changed, which should reduce the oddeven effect. The divergence at the nematic - smectic phase transition causes an addi-

I

28

I

30

I

3 2

I

34

Figure 18. Rotational viscosity coefficient divided by the order parameter squared as a function of temperature for the homologous series of 4-alkyloxybenzylidene-4’-n-butyl-anilines (mO ’4).

162

2.5 Viscosity

tional increase in the rotational viscosities for 4 0 . 4 and 5 0 . 4 at low temperatures. There is only a rudimentary microscopic theory for the chain length dependence of the rotational viscosity. The molecules are treated in these theories as hard rods or ellipsoids, and thus the increasing flexibility of the chains with increasing chain length is not taken into account. For hard ellipsoids Baalss and Hess [41] found that y1 = p 2 with p = -a and a % b b

(51)

where a describes the length of the long and b the length of the short molecular axis. Polar substituents in the side chains and in the core increase the rotational viscosity [55, 821. This rule fails when comparing alkylcyanobiphenyls with Schiff bases of comparable length. Although the lengths of 1 0 . 4and the more polar n-pentyl- or n-hexylcyanobiphenyl are nearly equal, the rotational viscosities of the latter compounds are smaller rather than larger. It is known that there is an anti-parallel ordering of the cyano compounds, which reduces the polarity. On the other hand, this aggregation should lead to an enhanced viscosity. There is at present no theory available that can deduce the rotational viscosity from molecular properties in liquid crystals of such complexity. Low rotational viscosities, which are necessary for outdoor or video applications of liquid crystal displays, are obtained in mixtures with unpolar substances having short side chains such as, for example, dialkylcyclohexylphenyls or the corresponding alkenyl compounds [83, 841. Lateral substituents lead to a viscosity increase as well as the substitution of hydrogen atoms at the benzene ring by halogens. The effect is small for fluorine atoms and increases in the sequence F < C1< Br [55]. The influence of a lateral cyano group is more pronounced.

There have been no systematic investigations on lateral alkyl substituents [55], but it can be expected that the rotational viscosity increases with the volume of the substituent. Different rings in the central core and the insertion of lateral groups change the molecular packing density, which exerts an essential influence on the shear and the rotational viscosity (Fig. 19) [55, 851. Obviously, the reason for the large differences in the rotational viscosities of alkyl- and alkyloxycyanobiphenyls is the different packing density. Other explanations are not very convincing [82]. A summary of experimental results on the rotational viscosities of homologous series and parameters for the description of the temperature dependence with the help of different equations can be found in the review by Belyaev [%].

Figure 19. Rotational viscosity coefficient "/1 at 25 "C as a function of the free volume coefficient vfg= 1- k,, where k, is the molecular packing coefficient: (1) alkyloxycyanobiphenyls; ( 2 ) alkylbicyclooctylcyanobenzenes; (3) alkylpyridylcyanobenzenes; (4) alkylcyanobiphenyls; ( 5 ) alkylcyclohexylcyanobenzenes. The crosses show the rotational viscosity for some members of the homologous series and the lengths of the vertical lines give the accuracy of measurement.

2.5.3 Determination of Rotational Viscosity

Mixtures of Liquid Crystals For liquid crystal displays, mixtures of liquid crystals are always used. Therefore, there is an essential interest in models that predict the rotational viscosity of mixtures from the rotational viscosities of the pure components. With the exception of mixtures of very similar compounds, the dependence of the shear viscosity of isotropic liquids on the mixture composition is normally complex. Due to the additional dependence on the order parameter, one cannot expect a simple concentration dependence for the rotational viscosity of liquid crystals. Figure 20 shows the rotational viscosities of a series of mixtures between the ester LC1 ~

c

0

0

~

0

~

c

0

~

c

C2H5

163

points of both components are about 76 "C. In the mixture the clearing point exhibits a flat minimum at 74.5"C. Because of the larger molecular length, the rotational viscosity of the three-ring ester is considerable higher than that of the mixture of the tworing esters. The activation energies of the pure components are similar and, therefore, the temperature dependence of the rotational viscosity is similar for all mixtures. For almost equimolar mixtures there is a broad nematic phase range, and the positive bending at low temperatures discussed above can be observed. The different curves are almost equidistant, i.e. the logarithms of the rotational viscosities at constant temperature should depend linearly on the mole fraction xi. Fig6 H 1 3 ure 21 shows the corresponding plot. The curves are slightly bent and the equation

and an ester mixture LC2 composed of

In 71'

50 wt% 4-n-PentYloxYPhenYl-4'-methOXYbenzoate and 50 wt% 4-n-octYloxY-4'-nProPYloxYbenzoate [86]- The

which is also valid for the shear viscosity of similar isotropic liquids, is a good approximation of the real dependence. As the rotational viscosities of the pure components differ strongly, a stronger bending will be observed for a linear plot. For mixtures of dissimilar compounds, for example polar and unpolar liquid crystals, neither of the plots will give simple dependences. Even maxima or minima are sometimes observed [86, 871. Equation (52) is normally used for the estimation of the rotational viscosity of mixtures that have to be optimized for display applications. As the mixture must fulfil several demands it consists of a large number of compounds (even including non-mesogenic compounds) with strongly varying

-

I

1000 K T

ln?'Ll

+-

2'

In y1,2

(52)

164

2.5 Viscosity 1

Y1 In Pa s C

4 5'

50'

55O 60' -1

6 5' 69' 72'

--L

-

7

tal or liquid crystal mixture for small concentrations. Sometimes, other measures of composition are used instead of the mole fraction. The method can be improved by taking into account the change in the degree of order by the compound added. If the properties of the unknown mixture do not differ too much from the standard, the rotational viscosity can be estimated to within 10%.

Figure 21. Rotational viscosity of mixtures of the esters LC1 and LC2 (see text) as a function of the mole fraction of LCI.

1 I

the influence of the changing order parameter dominates the pressure dependence. If the logarithm of the rotational viscosity at constant pressure is plotted versus the inverse temperature, the curves for higher pressure can be obtained from the curve at atmospheric pressure by shifting along the abscissa. Neither the activation energy nor the absolute value of the viscosity at the

Pressure Dependence

Like the shear viscosity of isotropic liquids, the rotational viscosity of liquid crystal depends on pressure. Figure 22 [88] shows the pressure dependence for the liquid crystal MBBA at 85.2 "C, which is well above the clearing point temperature at atmospheric pressure. Similar to the clearing temperature, one can define a clearing pressure for the transition from the nematic to the isotropic phase at constant temperature. For pressures much higher than the clearing pressure the pressure dependence of the rotational viscosity resembles the dependence of the shear viscosity of isotropic liquids, and can be described by similar equations. Slightly above the clearing pressure

12

I

I

1.6

2.0

4

Figure 22. Rotational viscosity of MBBA as a function of pressure at 85.2"C.

165

2.5.4 Leslie Coefficients

procedure allows a reliable prediction of the non-divergent part from measurements made far from the transition point. A disadvantage is the expensive experimental equipment needed for high pressure investigations.

2.5.4 l/T').lOOO I

K

1

Figure 23. Rotational viscosity of MBBA as a function of the difference 1/T- l/T*, where T* is the temperature of the clearing point at the measurement pressure.

clearing point seem to be functions of the applied pressure. Figure 23 shows that all curves obtained for MBBA between 1 and 2500 bar and between 20°C and 90°C can be brought into coincidence if a proper temperature scale is used. For the pressure dependence of the clearing point T * ( p ) the equation of Simon and Glatzel [89]

(53) was used, and the parameters T:, a and c were fitted to the experimental data. T: is the clearing temperature at 0 bar, which barely differs from the clearing temperature at atmospheric pressure. A main problem in evaluating the divergence of the rotational viscosity in the vicinity of a smectic phase is the separation of the non-divergent part. An additional determination of the pressure dependence can be very advantageous. First, the pressure dependence can be studied directly, as the pressure dependence of the non-divergent part is less pronounced than its temperature dependence. Secondly, the above discussed

Leslie Coefficients

The six Leslie coefficients a, to a, are the material constants in the stress tensor of the Leslie - Ericksen equations (see Chap. VII, Sec. 8.1 of Vol. 1 of this Handbook). The coefficients must be known for any calculation of flow phenomena and director rotations by means of the Leslie-Ericksen equations such as, for example, for the prediction of the transmission curve during the switching of a liquid crystal display. Because of the Parodi equation [90]

(54) there are five independent coefficients that have to be determined experimentally.

2.5.4.1 Determination from Shear and Rotational Viscosity Coefficients The shear viscosity coefficients q,, q2, q, and q,* and the rotational viscosity coefficient yl form a complete set of independent coefficients from which the Leslie coefficients can be determined with the help of the Parodi equation. The corresponding equations are given in Chap. VII, Sec. 8. l of Vol. 1. Figure 24 [74] shows the Leslie coefficients for MBBA as a function of temperature. Due to the different dependence on the order parameter (see Chap. VII, Sec. 8.1 of Vol. 1 of this Handbook), the coefficients exhibit different bending above the clearing point. The temperature dependence of a, differs greatly from that of the other coefficients, as it is not a real viscosity.

166

2.5 Viscosity

-2

la,l

In Po s

-4

J

-6

Figure 24. Leslie coefficients aiof MBBA (T,=45.1 "C) as a function of temperature (a,, a27 a3,

The complete set of coefficients for MBBA at 25 "C is [74]: a, =-0.018, a,= -0.110, a,=-O.OOll, a 4 ~ 0 . 0 8 2a5=0.078 , and a6=-0.034 Pas. As a, and a, are differences of two nearly equal terms, they are less accurate than the other coefficients. If the flow alignment angle cD0 is known, a, can be calculated from the relation

:4

tan@, =

-

(55)

with better accuracy. This has been used for the determination of the coefficients shown in Figure 24 and the set of coefficients for MBBA given above. It is known that the flow alignment of nematic liquid crystals with a low temperature smectic phase or a long alkyl chain can only be observed in the neighbourhood of the clearing point. The flow alignment angle decreases strongly with decreasing temperature and vanishes at a certain temperature [91, 921. Obviously, a, becomes positive below this temperature. Figure 25 shows the ratio %la, for 4-n-hexyloxybenzylidene-

%a.

4'-aminobenzonitrile (HBAB) [91]. As a,is always negative, a, becomes positive below 92 "C. Theory predicts [52-541 that only the Leslie coefficients a,, %, and a6 diverge at a transition to a smectic A phase.

2.5.4.2 Determination by Means of Light Scattering The study of light scattered by a nematic sample allows the determination of the viscosities q [ ( q ) and q;(q) (see Eqs. 17 and 18), which are mainly determined by the rotational viscosity coefficient y,, but also contain other coefficients because of the backflow. In principle, all coefficients can be determined with different accuracies by a suitable choice of the scattering geometry. The influence of the small coefficient a, is normally neglected. For 4-n-pentyl-4'-cyanobiphenyl, Chen et al. [93] found the following values at 25 "C: a,=-0.086, 0!3=-0.004, a4=0.089, a5=0.059 and -0.031 Pa s.

2.5.5

References

167

Figure 25. Ratio of the Leslie coefficients a3/@of HBAB as a function of temperature.

2.5.4.3 Other Methods As the transmission curve of a liquid crystal display during the switching process depends on all the Leslie coefficients due to backflow effects, it is possible to determine the coefficients from the transmission curve. In analogy to light scattering, the coefficients are obtained with different accuracies [38, 391. The investigation of torsional shear flow in a liquid crystal [3 1 - 351 allows the determination of quantities from which some Leslie coefficients can be determined, if one shear viscosity coefficient is known.

2.5.5

References

[I] F. M. Leslie, Q. J. Mech. Appl. Math. 1966, 19, 357-370. [2] F. M. Leslie, Arch. Ratl. Mech. Anal. 1968, 28, 265 -283. [3] J. L. Ericksen,Arch. Ratl. Mech. Anal. 1966,23, 266-275. [4] J. L. Ericksen, Mol. Crysf. Liq. Cryst. 1969, 7, 153- 164. 151 Ch. Giihwiller, Phys. Lett. A 1971, 36, 311312.

[6] Ch. Gahwiller, Mol. Cryst. Liq. Cryst. 1973,20, 301-318. [7] V. A. Tsvetkov, G. A. Beresnev, Instrum. Exp. Techn. 1977,20, 1497- 1499. [8] H. Kneppe, F. Schneider, Mol. Cryst. Liq. Cryst. 1981,65,23-38. 191 H.-H. Graf, H. Kneppe, F. Schneider, Mol. Phys. 1992,77,521-538. [lo] F. Schneider, Z. Naturforsch., Teil u, 1980. 35, 1426- 1428. [ 1 I ] P. G. de Gennes, The Physics ofLiquid Crystals, Clarendon Press, Oxford, 1975, p. 82. [I21 G. J. O’Neill, Liq. Cryst. 1986, I , 271-280. [13] M. Miesowicz, Bull. Acad. Polon. Sci. Lett. 1936,228-247. [14] J. W. Summerford, J. R. Boyd, B. A. Lowry, J. Appl. Phys. 1975,46,970-97 1. [15] L. T. Siedler, A. J. Hyde, in Advances in Liquid Crystal Research andApplications (Ed.: L. Bata), Pergamon Press, Oxford, 1980, pp. 561 -566. [I61 H . X . Tseng, B. A. Finlayson, Mol. Cryst. Liq. Cryst. 1985, 116, 265-284. [I71 Groupe d’Etude des Cristaux Liquides (Orsay), J. Chem. Phys. 1969, 51, 816-822. [I81 D. C. van Eck, W. Westera, Mol. Cryst. Liq. Cryst. 1977, 38, 3 19- 326. [I91 D. V. van Eck, M. Perdeck, Mol. Cryst. Liq. Cryst. Lett. 1978,49, 39-45. [20] E. Miraldi, L. Trossi, P. Taverna Valabrega, C. Oldano, Nuov. Cim. 1980,60B, 165- 186. [2 11 J. P. van der Meulen, R. J. J. Zijlstra, J. Physique 1984,45, 1347- 1360. [22] F. M. Leslie, C. M. Waters, Mol. Cryst. Liq. Cryst. 1985, 123, 101- 117.

168

2.5 Viscosity

[23] H.Z. Cummins, H.L. Swinney, Prog. Opt. 1970,8, 135-200. [24] D. C. van Eck, R. J. J. Zijlstra, J. Physique 1980, 41,351-358. [25] C. T. Alkemade, Physica 1959,25,1145- 1158. [26] P. Martinoty, S. Candau, Mol. Cryst. Liq. Cryst. 1971,14,243-271. [27] K. A. Kemp, S. V. Letcher, Phys. Rev.Lett. 1971, 27, 1634- 1636. [28] Y. S. Lee, S. L. Golub, G. H. Brown, J. Phys. Chem. 1972, 76,2409-2417. [29] F. Kiry, P. Martinoty, J. Physique 1977, 38, 153-157. 1301 S. D. Hunnisett, J. C. A. van der Sluijs, J. Physique 1983,44, L-59-L-63. [31] J. Wahl, F. Fischer, Opt. Comm. 1972, 5, 341 -342. [32] J. Wahl, F. Fischer, Mol. Cryst. Liq. Cryst. 1973, 22,359-373. [33] K. Skarp, S. T. Lagerwall, B. Stebler, D. McQueen, Phys. Script. 1979, 19, 339 - 342. [34] J. Wahl, Z. Naturforsch., Teil a, 1979, 34, 818-831. [35] K. Skarp, S. T. Lagerwall, B. Stebler,Mol. Cryst. Liq. Cryst. 1980, 60, 215-236. [36] P. Esnault, J. P. Casquilho, F. Volino, A. F. Martins, A. Blumstein, Liq. Cryst. 1990,7,607628. [37] H. Gotzig, S. Grunenberg-Hassanein, F. Noack, Z. Naturforsch., Teil a, 1994,49, 1179-1187. [38] R. Hirning, W. Funk, H.-R. Trebin, M. Schmidt, H. Schmiedel, J. Appl. Phys. 1991, 70, 42114216. [39] H. Schmiedel, R. Stannarius, M. Grigutsch, R. Hirning, J. Stelzer, H.-R. Trebin, J. Appl. Phys. 1993, 74,6053-6057. [40] N. Kuzuu, M. Doi, J. Phys. SOC. Jpn. 1983, 52, 3486- 3494. [41] D. Baalss, S. Hess, Z. Naturforsch. Teil a, 1988, 43,662-670. [42] H. Ehrentraut, S. Hess, Phys. Rev. E 1995, 51, 2203 -2212. [43] M. Kroger, H. S. Sellers, J. Chem. Phys. 1995, 103, 807-817. [44] H. Kneppe, F. Schneider, N. K. Sharma, Ber. Bunsenges. Phys. Chem. 1981,85,784-789. [45] W. W. Beens, W. H. de Jeu, J. Physique 1983, 44, 129- 136. [46] H. Herba, A. Szymanski, A. Drzymala, Mol. Cryst. Liq. Cryst. 1985,127, 153- 158. [47] V. A. Tsvetkov, in Advances in Liquid Crystal Research and Applications (Ed.: L. Bata), Pergamon Press, Oxford, 1980, pp. 567 - 572. 1481 M. G. Kim, S. Park, S. M. Cooper, S. V. Letcher, Mol. Cryst. Liq. Cryst. 1976, 36, 143- 152. [49] A. G. Chmielewski, Mol. Cryst. Liq. Cryst. 1986,132,339-352. [50] L. LCger, A. Martinet, J. Physique 1976, 37, C3-89 - C3-97.

[51] S. Bhattacharya, S. V. Letcher, Phys. Rev. Lett. 1980,44,414-417. [52] W. L. McMillan, Phys. Rev. A 1974, 9, 17201724. [53] F. Jiihnig, F. Brochard, J . Physique 1974, 35, 301-313. 1541 K. A. Hossain, J. Swift, J.-H. Chen, T. C. Lubensky, Phys. Rev. B 1979,19,432-440. [55] V. V. Belyaev, Russ. Chem. Rev. 1989, 58, 9 17- 947. [56] F.-J. Bock, H. Kneppe, F. Schneider, Liq. Cryst. 1986, I, 239-251. [57] S. Hess, Z. Naturforsch., Teil a, 1975, 30, 1224- 1232. [58] J. Fisher, A. G. Fredrickson, Mol. Cryst. Liq. Cryst. 1969, 8, 267-284. [59] V. Tsvetkov,Acta Physicochim. URSS,1939,IO, 555-578. [60] J. Prost, H. Gasparoux, Phys. Lett. A 1971, 36, 245 - 246. 1611 P. G. de Gennes, The Physics of Liquid Crystals, Clarendon Press, Oxford, 1975, p. 180. [62] H. Kneppe, F. Schneider, J. Phys. E 1983, 16, 512-515. [63] F. Hardouin, Thesis, Bordeaux, 1978. [64] P. E. Cladis, Phys. Rev. Lett. 1972, 28, 16291631. [65] F. Brochard, P. Pieranski, E. Guyon, Phys. Rev. Lett. 1972, 28, 1681- 1683. [66] H. Schad, J. Appl. Phys. 1983,54,4994-4997. [67] P. R. Gerber, Appl. Phys. 1981, A26, 139- 142. [68] F.-J. Bock, H. Kneppe, F. Schneider, Liq. Cryst. 1988,3,217-224. [69] F.-M. Leslie, G. R. Luckhurst, H. J. Smith, Chem. Phys. Lett. 1972,13, 368-371. [70] R. A. Wise, A. Olah, J. W. Doane, J. Physique 1975,36, Cl-l17-C1-120. [71] D. van der Putten, N. Schwenk, H. W. Spiess, Liq. Cryst. 1989,4, 341 -345. [72] E. Jakeman,E. P. Raynes,Phys. Lett. 1972,39A, 69-70. [73] W. Helfrich, J. Chem. Phys. 1972, 56, 31873188. [74] H. Kneppe,F. Schneider, N. K. Sharma, J. Chem. Phys. 1982, 77,3203- 3208. [75] I. Haller, H. A. Huggins, H. R. Lilienthal, T. R. McGuire, J. Phys. Chem. 1973, 77, 950-954. [76] H. Schad, H. R. Zeller, Phys. Rev. A 1982, 26, 2940 - 2945. [77] C.-C. Huang, R. S. Pindak, P. J. Flanders, J. T. Ho, Phys. Rev. Lett. 1974,33,400-403. [78] A. F. Martins, A. C . Diogo, N. P. Vaz,Ann. Phys. 1978,3,361-368. [79] P. G. de Gennes, Sol. State Commun. 1972, 10, 753 -756. [80] A. C. Diogo, A. F. Martins, Mol. Cryst. Liq. Cryst. 1981,66, 133- 146. [81] J. W. van Dijk, W. W. Beens, W. H. de Jeu, J. Chem. Phys. 1983, 79,3888-3892.

2.5.5 References

[82] P. R. Gerber, M. Schadt, Z. Naturforsch., Teil a, 1982.37, 179- 185. [83] R. Eidenschink,Mol. Cryst. Liq. Cryst. 1983,94, 119- 125. [84] H. Takatsu, K. Takeuchi, Mol. Cryst. Liq. Cryst. 1986, 138,231-244. 1851 V. V. Belyaev, M. F. Grebenkin, V. F. Petrov, Russ. J. Phys. Chem. 1990, 64, 509 - 5 12. [86] H. Kneppe, F. Schneider, Mol. Cryst. Liq. Cryst. 1983,97,219-229. [87] M. F. Grebyonkin, G. A. Beresnev, V. V. Belyaev, Mol. Cryst. Liq. Cryst. 1983, 103, l - 18.

169

1881 H. Dorrer, H. Kneppe,E. Kuss,F. Schneider, Liq. Cryst. 1986, 1 , 573-582. 1891 F. Simon, G. Glatzel, Z. Anorg. Allg. Chem. 1929,178, 309-316. 1901 0. Parodi, J . Physique 1970, 31, 581-584. [Yl] Ch. Gahwiller, Phys. Rev. Lett. 1972, 28, 1554-1556. 1921 W. W. Beens, W. H. de Jeu, J. Chew. Phys. 1985, 82, 3841 -3846. 1931 G.-P. Chen, H. Takezoe, A. Fukuda, Liq. CryAt. 1989,5,341-347.


2.6 Dynamic Properties of Nematic Liquid Crystals R. Blinc and I. MuieviE The nematic liquid crystalline state is characterized by long-range orientational order of the average direction of the long molecular axis. Similar to the case of a Heisenberg ferromagnet it is a state of a spontaneously broken continuous orientational symmetry of the high temperature phase, that is, of the isotropic liquid phase. As a consequence, the spectrum of collective excitations of the nematic director field is expected to be gapless in the long-wavelength limit and the so-called Goldstone mode should exist [ 1-31. For finite wavelengths, the collective dynamics of bulk nematics can be described within the hydrodynamic equations of motion introduced by Ericksen [4-81 and Leslie [9-111. A number of alternate formulations of hydrodynamics [12-181 leads essentially to the equivalent results [19]. The spectrum of the eigenmodes is composed of one branch of propagating acoustic waves and of two pairs of overdamped, nonpropagating modes. These can be further separated into a low- and high-frequency branches. The branch of slow modes corresponds to slow collective orientational relaxations of elastically deformed nematic structure, whereas the fast modes correspond to overdamped shear waves, which are similar to the shear wave modes in ordinary liquids.

In the long-wavelength limit, the relaxation rates for both modes are proportional to q2 which is characteristic of hydrodynamic modes. Here q is the wave-vector of the overdamped mode.

2.6.1 Quasielastic Light Scattering in Nematics One of the most striking phenomena in nematic liquid crystals is their milky and turbid appearance, similar to the appearance of colloidal solutions. This phenomenon was first intensively studied by Chatelain [20-261 who found that light, scattered from the nematic sample, is strongly depolarized; the polarization of the scattered light is perpendicular to the polarization of the incident light. He attributed this phenomenon to the anisotropy of the nematic fluid. By comparing scattering properties of nematics to the scattering properties of particle suspensions, he concluded that strong scattering of light in nematics originates from thermal fluctuations of swarms or domains of the size of the wavelength of light. In 1968 de Gennes introduced the concept of orientational normal modes in nematic liquid crystals that could successfully clarify the nature of this extraordinarily

2.6.1 Quasielastic Light Scattering in Nematics

strong scattering of light. Similar to the phonon collective excitations in 3D solids, orientational normal modes in liquid crystals can be considered as plane-wave-like, spatially coherent excitations of the director field n (r,t ) , which determines the mean orientation of the long molecular axis. In contrast to phonons in solids, the excitations in liquid crystals are always overdamped because of the viscosity. De Gennes [27] considered the effect of such a thermally excited and overdamped orientational plane wave 6 n (r,t ) = 6n,(t) eiqr on the optical properties of nematic and found that it is directly reflected in the fluctuation of the dielectric tensor field 6~(r,t ) :

6rv = (El, - E l ) (6n;noj+ 6njnoi)

(1)

Here E,, and are the eigenvalues of the dielectric constant for optical frequencies in a direction parallel and perpendicular to the equilibrium director no= (nox,nqy,no& respectively. In the single scattering (Born) approximation the projection of the scattered electric field amplitude E,yis [28]:

171

excitation that contributes to the scattering: q = ki - kf

(4)

It can be seen from Eqs. (1) and (3) that the scattering cross section is proportional to the mean square amplitude of the excitations that contribute to the scattering. Using the elastic free-energy expansion, the thermally excited mean square angular fluctuation per unit volume is . (5) ( 12) = kg , i=lor2 K3q; + K i q : + A x H 2

lan.

Here the equilibrium direction of the long molecular axies is along the z-axis and the wave-vector of the excitation is in the x--z plane, as shown in Fig. 1. K , is the bend elastic constant, K , is the splay elastic constant and K2is the twist elastic constant. The magnetic field H is applied in the z-direc-

and the differential scattering cross-section per unit solid angle of the outgoing beam is

f' Here &(r, t ) is the Fourier transform of the fluctuating part of the dielectric tensor, f and i are unit vectors describing the polarization directions of the scattered and incident beams, respectively, c is the speed of light in the medium, Ei, and (0 are the amplitude and the frequency of the incident light, respectively, and r is the distance between the sample and detector. The wavevectors of the incident ( k ; ) and scattered light ( k f )determine the wave-vector of the

Figure 1. Geometry of the problem (a) the excitation 6 n of the nematic director field no is decomposed into two orthogonal components; (b) definition of the wave-vector of the excitation.

172

2.6 Dynamic Properties of Nematic Liquid Crystals

tion and A x is the diamagnetic anisotropy of the nematic. One can see that in the limit of small wave-vectors and zero external field, the amplitude of fluctuations of the direction of the local optical axis can be very large, which results in very strong scattering of light in nematics and their milky appearance. From the expression ( 5 ) one can see that waves propagating perpendicular to the nematic director (qz=O) can be either pure splay or pure twist modes. For the splay mode 6n, =6n,+O (see Fig. 2a) whereas for the twist mode 6n2= 6n, # 0 (Fig. 2 b). Alternatively, waves propagating along the director (ql=O) can be only pure bend modes (Fig. 2c). For a general direction of the wave-vector we have a mixture of both polarizations: bend-splay or bend-twist modes. The relaxation rates of the two elastic deformation modes are

I'

where q i(4) is a wave-vector-dependent effective viscosity [28]. The dynamics of the collective excitations can be determined conveniently by photon autocorrelation spectroscopy, which is also called self-beating, time-resolved Rayleigh or quasi-elastic light scattering spectroscopy [29]. Here the time autocorrelation function of the scattered light intensity G2(2) is measured, which, in the heterodyne detection regime, is given by: G2(2) = ( I ( t )Z(t+z)) OC

Re {(6&if(4,0)6&$(4,2)))

Because 6Eif(q, t ) =f &(q, t )i where i and f a r e the polarizations of the incident and scattered light, respectively, we can select the appropriate component of the dielectric tensor fluctuation (and thus the corresponding director excitation) by choosing the proper combination of polarizations. In this way it is possible to isolate a given branch of excitations in nematics. In the case where a single mode contributes to the quasielastic scattering, the autocorrelation function will show a single-exponential G'2'(t) e-t'z(q) dependence, which allows for the determination of the relaxation rate of the overdamped excitation z-'(q). In general, in the limit of small wave-vectors the dispersion relation for the eigenmodes q2. Here, Ki is parabolic, z;'(q) = (Ki/qi) and q iare the elastic modulus and the viscosity for the selected eigenmode. By measuring the angular dependence we can thus determine the ratio Ki/qi. From Eqs. (3) and ( 5 ) we see that by measuring the q-dependence of the intensity of quasi-elastically scattered light one can determine the corresponding elastic constant. In combination with relaxation rate measurements one can thus determine viscoelastic properties of nematics. General reviews of the light scattering phenomena in liquids and liquid crystals can be found in the work of Berne and 0~

I:

Figure 2. Modes of pure splay (a), twist (b) and bend ( c ) .

(7)

2.6.2

Pecora [29], de Gennes [28], Litster [30] and Sprunt and Litster [3 11.

2.6.2 Nuclear Magnetic Resonance in Nematics Magnetic resonance methods have been used extensively to probe the structure and dynamics of thermotropic nematic liquid crystals both in the bulk and in confined geometry. Soon after de Gennes 1271 stressed the importance of long range collective director fluctuations in the nematic phase, a variable frequency proton spin-lattice relaxation (TI) study [32] showed that the usual BPP theory [33] developed for classical liquids does not work in the case of nematic liquid crystals. In contrast to liquids, the spectral density of the autocorrelation function is non-Lorentzian in nematics. As first predicted independently by Pincus [34] and Blinc et al. [3S], collective, nematic type director fluctuations should lead to a characteristic square root type dependence of the spin-lattice relaxation rate T;&, on the Larmor frequency w,: The characteristic frequency dependence TI 0~ wlJ2 is a direct result of the gapless Goldstone mode type nature of the director fluctuations. The constants C , and C, depend on the magnitude of the nematic order parameter, the viscoelastic constants, the molecular geometry of the spin positions and the orientation of the director with respect to the external magnetic field. Director fluctuations are however not the only spin-lattice relaxation mechanism in nematics. Translational self-diffusion of nematic molecules modulates the inter-molecular nuclear dipole-dipole interactions and induces - as first emphasized by Vilfan, Blinc and Doane 1361, another contribution

Nuclear Magnetic Resonance in Nematics

173

to T,' which can be in the low frequency limit expressed as: Here C, and C, denote temperature dependent parameters characteristic of the diffusion mechanism. Still another contribution T;&, comes from the individual molecular reorientations around the short axis and internal rotations. We thus have several competing relaxation mechanisms

1-I +-+- 1 ?(DF)

q(Diff.)

1 T(R)

which may be separated due to their different Larmor frequency, angular and temperature dependences. NMR has been used in bulk nematics for the detection of order director fluctuations, the indirect determination of the diffusion constants and the study of the local dynamics of molecules and molecular segments. In confined nematics NMR has been used as the basic technique for the determination of the configuration of molecular directors and the interaction of the liquid crystal molecules with the surface. A large number of NMR investigations has been devoted to the study of dynamic processes in nematics. A list of pioneering papers is given in reviews by Boden [37, 381, Tomlinson [39], de Gennes [28],Noack [40],VoldandVold [41] and Nordio [42]. More recent references can be found in Dong [43]. Principles of NMR are discussed by Torrey 1441, Abragam [33], Pfeifer 1451, Krueger [46], Harmon and Muller 1471, Noack (481, and Held and Noack [49]. Theory of NMR in liquid crystals is discussed by Pincus [34], Blinc et al. 1351, Lubensky [ S O ] , Doane and Johnson [51], Visintainer et al. [52], Sung 1531, Samulski 1541, Doane and Moroi [SS], Cabane [S6] and Doane et al. [57].

174


2.6.3 Quasielectric Light Scatteringand Order Fluctuations in the Isotropic Phase The collective dynamics in the vicinity of the Isotropic +Nematic phase transition was first discussed theoretically by de Gennes [ 5 8 , 591. He uses a Landau-type free energy expansion in terms of the nematic order parameter S = (3 cos26 - 1) or equivalently in terms of a macroscopic ten1 to sor order parameter Qap =xap - 3xYySap, describe the static and dynamic properties of the I + N transition. Here zapis the diamagnetic susceptibility tensor. De Gennes introduces the concept of a correlation length 5 as a measure for the spatial dimensions of the nematic-ordered regions in the isotropic phase. Close to the phase transition point I”, fluctuations in the magnitude of the nematic order parameter create metastable, short range-ordered regions (SQ(0) SQ ( r ) )= exp (- r / c ) with a typical dimension of the order of a correlation length. Once created, these regions relax back to the isotropic liquid with a relaxation rate 7-l. When approaching the phase transition, the correlation length is expected to grow, 5 = {,(T/T,- 1)-1’2,wheres the relaxation rate is expected to slow down,

The critical slowing down of the order parameter fluctuations and the divergent behavior of the correlation length in the vicinity of the I + N transition was first observed in the quasi-elastic light scattering experiments performed by Litster and Stinson [60], and later by Stinson et al. [61-631 and Chu, Bak and Lin [64, 651. The results of Litster and Stinson are shown in Figs. 3 and 4. There are other quasi-elastic light scattering studies in the isotropic phase of MBBA [66-681 as well as other substances

- I

/

n

u

-40

I

,

I

,

I

56

48 52 TEMPERATURE [‘C)

,

60

Figure 3. Critical slowing down of nematic excitations in the isotropic phase of MBBA [60].The upper curve represents raw data and includes finite instrumental line-width. The lower curve shows data, corrected for the temperature dependence of the transport coefficient. 24 -

-

-t

b

16

-

x

N

.&

I

-1%

8-

7

>I

I

I

I

[69, 701. The observations are in quantitative agreement with the mean-field model of de Gennes. Rayleigh scattering in the pretransitional region of chiral nematics was first studied by Yang [71] and later by Harada and Crooker 1721 and Mahler et al.

2.6.4

Nuclear Magnetic Resonance and Order Fluctuations in the Isotropic Phase

[73]. The results agree qualitatively with the observations in nonchiral nematics. Pretransitional dynamics in the isotropic phase of nematics was also studied by other optical methods. Wong and Shen [74, 751, Flytzanis and Shen [76] and Prost and Lalanne [77] have used the optical Kerr effect to induce nematic ordering in the isotropic phase. Using a Q-switched laser they could measure the relaxation time of the induced birefringence. They found a good agreement with the Landau-de Gennes theory (see Fig. 5) and with the results of Stinson and Litster. The optical Kerr effect in the isotropic phase of the alkoxyazoxybenzene homologous series is reported by Hanson et al. [78] and the same technique was used by Coles [79] in the studies of the dynamics of alkyl cyanobiphenyl homologs. Using the transient grating optical Kerr effect in the picoand nanosecond time scale, Deeg et al. [80] studied 5CB dynamics in a large temperature interval above T, . They observed a deviation of the collective reorientation relaxation rates from the Landau-de Gennes behavior at temperatures 40 K above T,. This is in the regime when the correlation length is smaller than approximately three molec-

I75

ular lengths. On the picosecond time scale they could resolve an additional temperature-independent relaxation process that was attributed to the reorientations of individual molecules within a correlated region. A similar observation was reported by Lalanne et al. [81] for MBBA. The same technique was used by Stankus et al. [82] in a study of pretransitional dynamics of the isotropic phase of MBBA on the nanosecond time scale. Well above T, they also observe deviations from the Landau-de Gennes theory. A molecular statistical theory was used by Ypma and Vertogen [83] in the treatment of the I -+N pretransitional effects. Recently, Matsuoka et al. [84] have used a novel light beating spectroscopy over the range of lo4 to lo9 Hz in the studies of pretransitional dynamics of 6CB. There are other reports on the study of pretransitional dynamics in polymeric and lyotropic nematics. Quantitative measurements of ratios of Frank elastic constants and Leslie viscosities in the pretransitional range of poly-y-benzyl-glutamate polymeric nematic are reported by Taratuta et al. [85]. McClymer and Keyes [SS-881 report light scattering studies of pretransitional dynamics of potassium laurate-decanol-D,O system. An interesting study of a magneticfield induced I + N phase transition in a colloidal suspension is reported by Tang and Fraden [891.

2.6.4 Nuclear Magnetic Resonance and Order Fluctuations in the Isotropic Phase

Figure 5. Relaxation time of the order parameter as determined from the optical Kerr effect in MBBA 1241. The solid line is a best fit of the form z=(T-T,)-'.

The first NMR evidence of large fluctuations in the magnitude of the nematic order parameter tensor in the isotropic phase above T, has been obtained by the I4N linewidth measurements at 3 MHz in PAA [90]. As T, is approached from above the line-

176


width increases critically but the first order transition to the nematic phase occurs before a true divergence is reached. A similar anomalous increase has been seen in the deuterium spin-spin relaxation rate TT1 of linkage deuterated MBBA within -5 "C of the isotropic-nematic transition by Martin, Vold and Vold [91]. These authors also pointed out that there is no similar anomaly in the T;, and that the spectral density function shows normal, non-critical behavior over a frequency range 5 -75 MHz. The frequency and temperature dependencies of the proton T,' of PAA at the nematic-isotropic transition have been measured by Woelfel [92]. At high Larmor frequencies he finds a strong frequency dependence of the proton T , in the isotropic phase up to 40°C above T, but no critical temperature dependence as T+T,. At low Larmor frequencies (e.g. at 7 MHz and 30 kHz), on the other hand, T I is nearly frequency independent but decreases critically as T +T, from above (Fig. 6).

A similar study has been performed in MBBA by Dong et al. [93]. The dispersion of the proton T , in the isotropic phase of 5CB, PAA and MBBA has been precisely studied by the field cycling technique by Noack and coworkers [94-961. The above results can easily by understood within the Landau-de Gennes theory, The relaxation rate for nematic short range order fluctuations with a wave-vector q is:

' ;z = zi'(1 + q 2 t 2 ( T ) ) where zo=qt2(T)/K corresponds to the correlation time for the q=O mode. t ( T )is the correlation length, K is an average elastic constant and q an average viscosity. The spectral density at the Larmor frequency o, is obtained as a sum over all relaxational modes J I ( @ L ) =1~

03

J d z C (1QqI2) 0

4

. exp[-z/z,] exp(-iwLz)

(13)

where the mean square fluctuation in the magnitude of the nematic order parameter associated with the q-th mode is I

I

1

T1 S

I'

For small Larmor frequencies a,+ zilone finds 1

so that T , is strongly T-dependent but independent of the Larmor frequency. In the case of large Larmor frequencies, oL$zi'

Figure 6. Temperature dependence of proton T , in PAA at different Larmor frequencies [92].

T , depends on the Larmor frequency, but is not strongly T-dependent as indeed observed.

2.6.6

Nuclear Magnetic Resonance and Orientational Fluctuations below T,

2.6.5 Quasielastic Light Scattering and Orientational Fluctuations below T, The first time-resolved Rayleigh scattering experiment was performed in the nematic phase of PAA by Durand et al. [12,97,98]. Using polarization selection rules [27], they were able to resolve the two collective modes (splay-bend and twist-bend) which showed the predicted q2 dispersion (see Fig. 7). The temperature dependence of the relaxation rates and scattered intensity in MBBA was studied by Haller and Litster [99, 1001. They found a good agreement with the Orsay Group theory of normal modes in liquid crystals. Fellner et al. [ l o l l report temperature dependencies of the elastic constants and viscosities in MBBA, as calculated from the light-scattering data using the normal modes concept. Experimental details and the analysis of the spectrum of the scattered light intensity are discussed by Van Eck and Zijlstra [ 1021 and Van der Meulen and Zijlstra [ 1 03 - 1051. They have also determined the viscoelastic properties of nematics OHMBBA and APAPA.

177

Viscoelastic properties are reported for the homologous series of nCB [ 1061, 5CB [ 107-1091, mixtures of 5CB and side chain polymers [ 1101, mixtures of PAA and chain polymer liquid crystals [ 1 111, mixtures of side-chain and low molar mass mesogens [112] and nematic solutions of rodlike polymers [ 1 131. The literature reports other measurements of the three Frank elastic constants and viscosity coefficients [ 1 141 181. Quenching of the nematic fluctuations in the presence of an electric field is discussed by Martinand and Durand [ 1 161 and Leslie and Waters [107]. The magnetic-field quenching of fluctuations is discussed by Malraison et al. [ 1191. copii. and Ovsenik [ I201 have observed the second-harmonic scattering of light on orientational fluctuations in nematics. Further theoretical considerations of the light scattering and the spectrum of fluctuations can be found in the work of Litster et al. [121], Langevin and Bouchiat [122, 1231, Alms et al. [124], Gierke and Flygare [125], Parsons and Hayes [126], Dzyaloshinskii et al. 11271, Miraldi et al. [128], Fan et al. [129] and Faber [ 1301. Extensive and general overviews of the subject are given by de Gennes [28], Chandrasekhar [ 1311, Litster [30] and Belyakov and Kats [132].

2.6.6 Nuclear Magnetic Resonance and Orientational Fluctuations below T,

Figure 7. The first observation of the normal mode dispersion in nematic liquid crystals 1121.

The fluctuations in the magnitude of the nematic order parameter are reduced in importance as long range orientational ordering takes place below T,. The effect of these fluctuations on T,' in the nematic phase has been discussed by Freed [133]. The fluctuations in the magnitude of the nematic ordering are for T

Figure 13. Magnitude of the nonlinear refractive index in the pretransitional region of MBBA 1751. The solid line is a best fit of the form (T-Tc)-’.

182


cinity of the Fredericksz transition are discussed by Ong [ 1451 and surface effects by Pan et al. [147]. Whereas single beam experiments measure the response of a medium at q = O , the so-called transient grating (or four wave mixing) experiments measure the response of a medium at nonzero q. Here two coherent laser beams cross each other at a small angle, resulting in an intensity grating due to interference of both beams. This intensity grating in turn induces a refractive index grating because of (i) Kerr effect in the isotropic phase, (ii) heating of the sample due to the absorption of light and the resulting change of the refractive indices n ( T ) , and (iii) collective molecular reorientation due to the torque imposed by the optical electric field and optical anisotropy [148]. The intensity and time dependence of the induced transient grating is measured by the third beam (probe beam) that diffracts (fourth beam) from the grating. The transient grating Kerr effect experiments were performed in the isotropic phase of 5CB [SO, 1491 and MBBA [82] over a very large temperature interval. For very short (picosecond) time scales, an additional noncritical relaxation was observed that was attributed to the individual molecular motion. Far above T,, a deviation of the relaxation rates from the de Gennes theory was observed [80]. Dynamic four wave mixing experiments in the nematic phase were performed by Eichler and Macdonald [150] and Khoo et al. [151, 152) using picosecond lasers. They have observed that the short excitation pulse is followed by a delayed reorientation process, indicating a large inertial moment. The observed dynamics were explained by flow-alignment theory, taking into account translational motion of the molecules under the action of the optical field. Build-up and decay times of the diffraction grating were

measured by DrevenSek and CopiE [ 1531 as a function of a grating wave-vector in ZLI1738. They were able to measure bend and splay elastic constants and the corresponding viscosities.

2.6.8 Dielectric Relaxation in Nematics In a dielectric relaxation experiment, the linear response of a sample to an oscilating and spatially uniform ( q = O ) electric field is measured. The bulk nematic (non-polar) collective excitations with a nonzero wavevector q thus cannot contribute to the linear response of a nematic. The exception is here a trivial coupling of an external electric field to the q=O (Goldstone) mode, which represents an uniform rotation of a sample as a whole and is as well non-polar. This leads to the conclusion that the dielectric relaxation experiment will measure the response of individual nematic molecules to an applied electric field. Similar to the case of an isotropic liquid, the relaxation rates of the individual molecular motion are expected to be observed in the 100 MHz to GHz frequency region. The influence of individual molecular motion on the dielectric relaxation was first considered by Martin, Meier and Saupe 111541. Whereas the onset of the nematic ordering will not drastically influence the rotation around the long molecular axis, the motion around the short molecular axis will be strongly hindered by the nematic order. As a result, we expect four dielectric relaxation mechanisms (see [ 1551). These are the relaxations of a ,ul dipole moment along the long molecuar axis in a direction (1) around the nematic director and (2) perpendicular to the nematic director as well as the relaxations of a y, dipole moment perpendicular to the long axis, in a direction (3) around

2.6.9

Pretransitional Dynamics Near the Nematic-Smectic A Transition

and (4) perpendicular to the nematic director. The first observation of the dielectric relaxation was reported by Maier and Meier [ 1561in the MHz range and later by Axmann [ 1571 in the GHz range by Meier and Saupe [158]. The dielectric relaxation in nematics can be conveniently described by the so-called Cole-Cole equation for the complex dielectric constant E (0)

Here E~ and E, are the static and infinite frequency dielectric constants, u) is the frequency of the measuring field, z,is the relaxation time of a given relaxation process and the parameter a measures the polydispersivity of the relaxation process. In the so-called Cole-Cole plot the imaginary dielectric constant E” is plotted versus the real dielectric constant E’ for various frequencies, as it is shown in Fig. 14. The maximum of E” determines the relaxation time 2,. Dielectric relaxation phenomena were investigated in different nematic materials like PAA [ 159- 1621,MBBA [ 163- 1691,nitriles [ 170-1731 and other mesogens [ 1741771. A recent review of rotational dynamics and conformational kinetics in liquid crystals can be found in Ferrarini [178]. The linear electric field response can be measured in either a frequency or time-do-

1 .

6.0

Figure 14. Cole-Cole plots of a dielectric constant [175].

183

main experiment. Whereas in the frequency domain ( 1 mHz to 10 MHz), the complex electric current through the capacitor (sample) is measured at a given frequency of a measuring electric field, in a time domain measurement (100 kHz to 10 GHz), a response of a sample to an electric pulse with very short rising time is measured [179]. The time-domain spectroscopy (TDS) technique was for the first time applied to study the dielectric behavior of liquid crystals by Bose et al. [ 180,18 I]. They report the splitting of a single relaxation frequency at the phase transition into the nematic phase of 7CB and 8CB.

2.6.9 Pretransitional Dynamics Near the Nematic-Smectic A Transition Among the phase transitions in liquid crystals, the N +A phase transition is of particular importance from the theoretical point of view and has attracted a significant attention of both experimentalists and theorists during the past two decades. We shall limit the discussion to the light-scattering and dynamical aspects of the phase transition. General aspects of this phase transition can be found in the work of Litster [30], Litster et al. [182], Anisimov et al. [183], Vithana et al. [ 1841and Garland and Nounesis [ 1851. The smectic A phase is characterized by the onset of a one dimensional (1D) density modulation p =po { 1 + Re [ Y eiqoZ] } along the long molecular axis. Here Y= 1 Yoleic is the smectic order parameter [ 1861,qo=2nld is the wave vector of the density modulation and d is a distance between the layers. As the smectic order parameter is analogous to the order parameter in superconductors, de Gennes has predicted a number of analogies between superconductors and smectics A. In particular, smectics A tend to expel twist

184


and bend deformations (in analogy to the Meissner effect), because these contribute the energetically costly term rotn to the elastic free energy. As a consequence, the bend and twist elastic constants are expected to diverge at the N -+ s, transition [ 1861 whereas K l should remain noncritical. The divergence of the elastic constants is of the form 6 K i ( T ) { ( T )where { ( T )is smectic correlation length in the nematic phase. Dynamical aspects of the transition have been considered by McMillan [ 1871, Brochard [ 1881 and Jahnig and Brochard [ 1891, leading to the conclusion that certain viscosity coefficients should also exhibit critical enhancement near T,. This should be reflected in the relaxation rates of thermally excited fluctuations of the nematic director. In particular, the twist mode relaxation rate should be independent of temperature if the phase transition is mean-field-like and should diverge if the phase transition is helium-like. The first observation of a critical enhancement of the K2elastic constant was reported by Gruler [190] and Cheung et al. [ 1911. Delaye et al. [ 1921 reported the first observation of a critical behavior of the K2 elastic constant near the N -+ S, transition in CBOOA using Rayleigh scattering. They observed an increase of the elastic constant by more than an order of magnitude, as shown in Fig. 15. Pretransitional behavior of twist and splay elastic constants was also measured in CBOOA by Chu and McMillan [193]. The splay is not renormalized, whereas the twist elastic constant shows a mean-field like divergence. They also report slowing down of the twist mode near T,, which is in apparent disagreement with both mean-field and helium-like models. A similar slowing down of the twist mode was observed by Delaye [ 1181. Pretransitional bend mode behavior is reported by Birecki and Litster 0~

rc

q' I

I

I

0.1

1

I 10 T-T,("K)

Figure 15. Divergence of the elastic constant K22 versus temperature for small (curve a) or large angle (curve b) scattering [192].

[ 1941, Birecki et al. [ 1141 in CBOOA and Von Kanel and Litster [ 1951 in 40.8. Sprunt et al. [ 1961compare X-ray and light scatter-

ing data on the pretransitional dynamics in 80CB, 8CB and 8S5. Very extensive high resolution light scattering experiments have been performed at Kent State University [ 184,197-2001 to determine the critical exponents for twist and bend elastic constants in 80CB, 8S5, 9S5, and 609. The pretransitional enhancement of the elastic constants is in reasonable agreement with the scaling laws [ 1891 and the critical behavior is close to a 3D XY, helium-like behavior.

2.6.10 Dynamics of Nematics in Micro-Droplets and Micro-Cylinders Nematic liquid crystals confined to a small volume of submicron size have recently been extensively studied because of their potential use in optical devices [201]. These materials consist of a random dispersion of

185

2.6.10 Dynamics of Nematics in Micro-Droplets and Micro-Cylinders

nematic microdroplets in a solid polymer and are characterized by a relatively large surface to volume ratio. Both the nematic ordering and the molecular dynamics in the nematic micro-droplets differ considerably from those found in bulk nematics. In addition to the bulk relaxation mechanisms, two specific effects are observed. In the MHz region, the nuclear spin-lattice relaxation rate is dominated by the cross-relaxation between liquid crystal nuclei and the surface polymer protons. In the kHz region, on the other hand, the molecular rotation induced by translational diffusion in the spatially varying director field is the dominant relaxation mechanism [202]. The configuration of molecular directors within a spherical micro-droplet depends on the boundary conditions imposed by the surrounding material, on the temperature and the elastic constants of the liquid crystal and on the strength of the external electric or magnetic fields. If the splay, twist and bend elastic constants are almost equal, the structure is, in the absence of external fields, either: -

-

bipolar with two surface singularities (i.e. point defects) at the axis of cylindrical symmetry (i.e. at the poles) if the molecules are anchored parallel to the polymer surface (tangential boundary conditions), (Fig. 16a), or radial (star-like) with a defect in the center of the droplet if the molecules are anchored normally to the surface (perpendicular boundary conditions) (Fig. 16b). The resulting structure is spherically symmetric.

In the presence of an external magnetic field it is convenient to introduce the magnetic coherence length 5M

112

= (POKIAX)

B

-1

(28)

which describes how far the order is imposed by the surface into the droplet inte-

a

b

Figure 16. Bipolar (a) and radial (b) configuration of the nematic molecular directors in polymer dispersed nematic microdroplets [202].

rior. Here A x is the anisotropy of the magnetic susceptibility of the liquid crystal. For t M > R ,where R is the droplet radius, the effect of the magnetic field B is negligible. For t M < R , the inner part of the droplet is practically uniformly aligned along the magnetic field B. In the radial case the configuration changes for R/

42 44 Temperature ( " C ) 38

LO

~6

4a

Figure 20. (a) Deuterium NMR spectra of SCB-Bd, in nucleopore microcavities in the isotropic phase at T=33.75 ?O0.O3"C.The solid lines are theoretical fits [210] and (b) Deuteron quadrupolar splitting versus temperature for R = 0.1 pm. The insert shows the surface induced order parameter profile in the isotropic phase at T-T* = 1.48 K 12101.

der parameter So within the layer lo is temperature independent as it is governed by local interactions. This monolayer is followed by an exponentially decaying order towards the center of the cylinder: S ( r ) = So exp[-(R - lo - Y)/ ny, which, however, requires a biaxial deformation [65]. Compensation can be performed by using one or two foils stacked between the STN layer and

218

3

Applications

for laptop displays where the required maximum operation temperature is about 50 "C. Further improvement of the film compensation technique was reported for FSTNLCDs with four films [72]. Figure 24. Configuration of a stretched film with refractive indices n, (parallel to the deformation axis) and nY,n, (perpendicular to the deformation axis).

the polarizer [66-691. In the case of two foils these can either be stacked on one side or on both sides of the STN cell. The first case results in a better viewing angle dependence while for the second case an enhancement of the contrast ratio and less coloration at oblique viewing angle are observed [70,7 11.Compared to the DSTN display, the FSTN display offers the advantages of reduced price, weight and an easier manufacturing. Film compensation is mostly used in portable applications such as laptop displays. A limiting factor of the compensation is the different dispersion of the liquid crystal mixture and the polymer foil. The wavelength dependency of the retardation is significant for polycarbonate while it is rather weak for polypropylene. The compensation effect can be adjusted by laminating polymers with different wavelengths dependencies. Another approach is to choose the retardation between the liquid crystal mixture, R ~and, the polymer foil, cpp, to be

p ~ c - @ = n -a- , with n=l,2,3,4,.. 2

(25)

This results in a wavelength independent phase difference given by

Acp = ApLC- Acpp = n z

(26)

A further problem of the film compensation technique is the different temperature dependence of the liquid crystal and the polymer foil, which limits the maximum operation temperature. However, it is sufficient

3.1.4.6 Viewing Angle and Brightness Enhancement In addition to the described compensation techniques, several other techniques have been reported to enhance the viewing angle dependency and the brightness. A system, suitable for the enhancement of the viewing angle of TFT and STN displays by external means consists of a specially designed collimated backlight and diffusing screen with the liquid crystal cell placed in between [73, 741. Recent studies on two- and four-domain structures have shown the potential improvement of the viewing angle dependence in TN and STN displays [75]. Reflective polarizers consisting of a wide waveband cholesteric film and a quarter wave foil can be optimized in their optimal properties to achieve improvement of the brightness by (70-80)% [76].

3.1.4.7 Color Supertwisted Nematic Displays For transmissive displays, color operation can be achieved by RGB (red, green, blue) color filter technology. RGB filters are manufactured on the interface between the I T 0 layer substrate and the polyimide layer by dyeing, pigment-dispersion, printing or electrodeposition. The thickness of the color filters varies around (0.8-3.5) pm depending on the production technique. The color filters are arranged as parallel stripes on the substrate, which increases the number of necessary columns by a factor of three. With three colors and n different achievable gray levels n3 different colors can be displayed. The transmission of such

3.1

a colored STN display is only (4-5)% of a black and white operated STN-display and consequently the use of color filters is not suitable for reflective operation. An alternative method to achieve a transmission of about 10% is the so-called subtractive color mixing [77-791. However, even this transmission ratio is not sufficient for a colored reflective display. One technique for the realization of a reflective colored STN display showing four colors (White, orange, blue and green) without the need for colorfilters makes use of the electrically controlled birefringence technology [ 801, Figure 25 shows the luminance as a function of the applied voltage. The applied voltage across a pixel results in a specific orientation of the molecules which determines the color. The requirements for the realization of a reflective colored STN display are: a large retardation, cp=dAn, value of about 1.5, - an optimization of polarizer orientations, and - a compensating foil to achieve a black and white status. -

3.1.4.8 Fast Responding Supertwisted Nematic Liquid Crystal Displays As described in Sec. 3.1.4.4, the response speed of a STN display can be reduced by decreasing the layer thickness and adequate increase of the birefringence of the liquid crystal mixture to obtain the necessary retardation value for an optimized contrast. However, in fast responding STN displays operated with Alt -Pleshko addressing the r.m.s. condition is not fulfilled and a phenomenon called frame response becomes apparent [8 11. Frame response means that the liquid crystal molecules in an activated pixel undergo a significant relaxation towards the unactivated state within the frame period, resulting in reduced contrast and

TN, STN Displays

219

White Orange

Green

u,,

+

_ _ _ _ _

Us

Voltage

Figure 25. Luminance as a function of the applied voltage for a reflective colored STN display.

flicker of the display. The transmission behaviour of a pixel of a slow- and a fast-responding LCD switched to the activated light state by Alt-Pleshko addressing is shown in Fig. 26 [17]. The fastest acceptable response speed to suppress frame response using Alt-Pleshko addressing is about 120 ms for dual scan VGA (Mux 240) and about 175 ms for dual-scan XGA (Mux 384) [8 11. The occurrence of frame response can be reduced by an increase of the frame frequency. However, this is limited by the low pass filtering action of the panel meaning that the pixel does not receive any voltage at high frequencies. In the Alt-Pleshko technique every row is addressed once per frame with a selection pulse of amplitude, S . The effect of frame response can be reduced by splitting the select pulse, S, into many pulses of smaller amplitude which are distributed over the frame period without the necessity to increase the frame frequency. Addressing techniques for fast responding STN displays are: active addressing (abbreviation is AA), where all rows are selected at a time [82, 831, - multi-line addressing (abbreviation is MLA), where several rows are selected at a time [84].

-

N scanning lines are divided into N/L subgroups, where each subgroup contains L scanning lines. For Alt - Pleshko addressing

220 liaht

3

I

Applications

slow LCD \

mation state of the display. The r.m.s. voltage across a pixel element is given by

fast LCD

I

(Uu) = F J 1- 2c Zu + Nc2

4

I

where F is given by IT

16.7177s

Figure 26. Transmission behavior of a pixel of a slowand a fast-responding LCD switched to the activated ‘light’ state by Alt-Pleshko addressing.

L= 1, for active addressing L = N , while typically for multiline addressing the value of L =4 ...7. AA and MLA require a different set of row and column signals from Alt -Pleshko addressing. These will be considered in the following: The signal for row i and columnj at time t are described by functions F,(t) and Gj(t). The voltage across pixel ij is given by Uij(t) = F , ( t ) - Gj(t)

(27)

A detailed mathematical analysis shows that the row functions F,(t) must be a set of orthonormal functions to obtain an optimum selection ratio. The time dependent column signals Gj(t) must be calculated by summation of the product of a matix element Zii and the row functions Fi(t) over the number of scanning lines L per subgroup N/L: Gj (t)=

(29)

CC1~E ( t ) L

i=l

The matrix elements are set Zij =+ 1for anonselected state and Zii=-l for the selected state. The coefficient, c, is a proportionality constant, which is independent of the infor-

and T is the frame period. Equation (30) has the value F , i f j = k and is zero, if j # k. Setting c = 1/ f l the optimized selection ratio is given by

which corresponds to Eq. (10) for AltPleshko addressing. Detailed information about row waveforms for multiple-line addressing are given by Scheffer and Nehring [17]. In general AA will require more drivers than MLA. For MLA with seven selected rows at a time the lower driving limit is 30 ms for a dual-scan VGA and 50 ms for a dual-scan XGA display [73]. These values are smaller by a factor four than for the Alt - Pleshko addressing technique.

3.1.5 Liquid Crystal Materials for Twisted Nematic and Supertwisted Nematic Display Devices The quality of any LC-display is strongly determined by the physical properties of the LC-material. To achieve the highest display quality it is essential to select and optimize the materials for the given LC-cell parameters and requirements. On the other hand it is impossible to find one single LC-materia1 which fulfills all the material require-

3.1

ments. Therefore mixtures of up to 20 LCcomponents are usually used in LC-devices. Some of these materials are universal useful basic components, others are ‘specialists’ for the adjustment of properties such as birefringence An, dielectric anisotropy A&, ratio of elastic constants K,,/K, I etc. Commercially used LC-structures can be divided into the following groups: materials with high optical anisotropy, An materials with high positive A& (benzonitrile type) materials with moderate A& (fluoro aromatics) materials for the adjustment of the elastic constant ratio K3,1K, dielectic neutral two and three ring basic materials materials with extreme high clearing point In Tables 3 to 11, mesophases, dielectric anisotropies A&, birefringence values An, rotational viscosities yl and ratios of elastic constants K,,IK,, are given. All data was experimentally evaluated in the laboratories of Merck KGaA. The values of A&, An and yl were determined by measurement in a nematic host mixture (ZLI-4792) and extrapolation to 100%. The ratios of K33/K11 are those measured in a nematic host mixture while the values in brackets are those determined from mixtures of homologues.

3.1.5.1 Materials with High Optimal Anisotropy As described in Sec. 3.1.22 and 3.1.4.2 it is essential to adjust the birefringence, An, for a given cell gap, d, to achieve an optimal display performance. Since the switching time, z, strongly depends on d (Eqs. 19 and 20) materials with high A n are required. The refractive indices (ne, no) of liquid crystals are determined by the molecularpo-

TN, STN Displays

22 1

larizabilities and therefore depend mainly on the extent of conjugated x-bonding throughout the molecule [ 181. The optical anisotropy (An=ne-no) of LC materials increases with the increasing number of aromatic rings and x-bonded linking- or terminal groups (compare Table 5, Structures 3.1, 3.3 and 3.4). The main problem in the design of high An materials is the insufficient UV-light stability of such highly conjugated structures [85]. Commercially used high An LC materials (Table 3) are mainly based on cyanobiphenyl (Structures 1.1 and 1.2) and tolane structure (Structures 1.3 to 1.7).

3.1.5.2 Materials with Positive Dielectric Anisotropy The dielectric anisotropy A&of LC-materials is defined by A&= E,,- E ~where , E~~and are the dielectric constants parallel and perpendicular to the director. From the Maier and Meier theory it can be seen that both the polarizability anisotropy A a and the per, of the LC molemanent dipole movement U cule determine the dielectric anisotropy [86]. As given in Eqs. (3), (4),(19) and (20), A& is a quantity of paramount importance, as its magnitude directly determines the interaction between LC and the electric field. The A& value of LC-mixtures has to be adjusted for the desired threshold voltage. Currently available materials with highly positive A& are mainly based on benzonitrile structures (Tables 4 and 5). Introduction of heterocyclic ring systems (Structures 2.5 and 2.6) or ester links (Structures 2.7 and 3.5) lead to an increase of A&compared with the corresponding non-heterocyclic and directly connected systems. Unfortunately, the effectivity regarding A& of the benzonitrile structures is decreased by a local antiparallel ordering of the dipole moments [87]. The degree of antiparallel correlation

222

3 Applications

Table 3. Commercially used materials with high optical anisotropy. Structure

No.

1.1

C

5

H

l

w

C

Mesophases ["C]

Birefringence, An

Ref.

C 23 N 35 I

0.237

[911

C 131 N 240 I

0.324

[92,931

C 65 N (61) I

0.301

[941

C 109 N 205 I

0.223

[951

C 99 N 245 I

0.255

W, 961

C 96N 240 I

0.21 1

I971

C 8 4 N 1441

0.240

t971

N

Table 4. Commercially used two-ring materials with high positive dielectric anisotropy. Mesophases ["C]

A&

An

y, [mPas]

K,-,IK,,

C 23 N 35 I

22

0.237

112

(1.66)

C 45 N 46 I

21

0.136

116

2.0

C 68 N 74 I

23

0.170

180

2.1

C39N(-Il)I

26

0.123

98

1.83

-

C 59 N (42) I

29

0.124

121

(1.71)

c 5 H , f c ) region is characterized by periodic parallel striations of a much shorter period (a few micrometers) than the Williams domains [23]. Above the threshold, these striations move, and bend and give rise to what has been called a chevronpattern(Fig. 5 ) [8-12,17,23-261. In this regime, the threshold is determined by a critical field rather than a critical voltage. The threshold field strength increases with the square root of the frequency. The spatial periodicity of the chevron pattern is also frequency dependent; it is

Figure 5. Chevron pattern. After de Gennes [ 121.

found to depend inversely on the square root of the frequency. The relaxation time of the oscillating chevron pattern is very short, of the order of a few milliseconds, while that of the stationary Williams domain is 100 ms for a 25 pm thick sample. The oscillatory domain regime is therefore sometimes called a fast turn off mode [ 1 1,12,30]. This regime is also called a dielectric regime, as space charges are not able to followthefieldinthisregime[lO-l2,28].The chevron pattern also gives way to turbulence at about twice the threshold field. An applied magnetic field parallel to the initial orientation of the director increases the threshold voltage in the conduction regime, but has no effect on the dielectric regime except to increase the spacing between the striations.

-

3.3.4

Theoretical Explanations

The basic mechanism for electric field induced instabilities is now very well understood in terms of the Carr-Helfrich model based on field induced space charges due to conductivity and dielectric anisotropies [ 16, 3 I]. Helfrich [ 161 made derivations for only DC fields, which were further extended to AC fields by Dubois-Violette and co-

248

3.3 Dynamic Scattering

workers [17, 181. Another somewhat accepted model, applicable only to DC fields, is the Felici model [32], which is based on charge injection in the liquid crystal and not on its dielectric and conductivity anisotropies. DC and low frequency AC voltages produce electrohydrodynamic instabilities in the isotropic phase of liquid crystals also, the threshold being comparable to that in the nematic phase. The Felici model is applicable only for DC fields. When the frequency becomes more than llt, (usually 10 Hz), where t, is the transit time of the ions, charge injection does not take place, showing that this is not the primary mechanism for AC field instabilities in the nematic phase.

-

3.3.4.1 Carr - Helfrich Model The current carriers in the nematic phase are ions whose mobility is greater along the preferred axis of the molecules than perpendicular to it. Because of conductivity anisotropy, space charges will accumulate with signs as shown in Fig. 6 at the distortion maxima and minima. The applied field acts on the charges to give rise to material flow in alternating directions, which in turn exerts a torque on the molecules. This is reinforced Ez

t

/

by the dielectric torque due to the transverse field created by the space charge distribution. The torque increases with an increase in the electric field. With increasing field, the torque may offset the counterbalancing normal elastic and dielectric torques, and the system may become unstable. The resulting cellular flow pattern and director orientation are sketched in Fig. 3. Based on this physics, Helfrich developed the theoretical model for Williams domains and explained most of the experimentally observed phenomena [lo- 12, 16,28, 311. He calculated the threshold voltage for Williams domains, V,,

K33

(1)

0.75).

Effect of Thickness

Figure 10 exhibits the effect of the cell spacing d on the threshold characteristic, contrast ratio, and transmission using the same mixture. These measurements show that for an increase in the cell gap from 5 to 11 pm a significant gain in the contrast ratio (-7fold) is achieved with a small loss in transmission (7.6% overall and 32% of the initial transmission). This increase in contrast ratio is achieved primarily due to increase absorption in the off state of the cell due to increased cxd. A secondary reason for this increase can be explained as follows. As men-

3.4.8.6

3.4.8.7

Impact of the Order Parameter

Impact of the Host

As discussed in Sec. 3.4.2, the birefringence, dielectric anisotropy, elastic constant, and transition temperatures of dichro-

280

3.4 Guest-Host Effect

04

Figure 9. Isocontrast curves for (a) 90" twisted and (b) nontwisted Heilmeier cells.

3.4.8 70 60

r; 70

0

2

28 1

Heilmeier Displays

0

50

10

0

E

5

2

4

6

8

w

10

VOLTAGE 0

60

10

12

14

0

2

4

6

8

10

12

14

VOLTAGE (V)

Figure 10. Effect of cell gap on the threshold characteristic and contrast of a Heilmeier display. The transmittances of cells with 5, 8, and 1 1 prn cell gaps are 23.6%, 20.0%, and 16.0%, respectively. Operating voltage, 10 V.

Figure 12. Impact of polarization efficiency on the threshold characteristic of a Heilrneier display. The transmittance of the cells made with polarizers having polarization efficiencies of 65%, 75%, 85%. 92%, 96.9%, 99.5%, and >99.9% are 20.35%, 17.57%, 16.80%, 16.70%, 16.567~~ 16.02%, and 15.98%, respectively.

ciency of the polarizer (Fig. 12), and hence a high-efficiency polarizer with good transmission must be used for this application. The polarization efficiency should be kept above 99% and as close to 100%as possible. 0.60

0.65

0.70

0.75

0.80

Order Pameter

Figure 11. Theoretical calculation of contrast ratio versus order parameter. (After Ong [ 1001).

ic mixtures are more or less those of the host. The viscosity of the mixture and the order parameter of the dyes are also highly dependent on the host. The host should have low viscosity, high dielectric anisotropy, high birefringence, wide operating temperature range, and low K , I . Moreover, it must produce a very high order parameter and good solubility for the dye.

3.4.8.8 Impact of the Polarizer The contrast ratio of a Heilmeier display is highly dependent on the polarization effi-

3.4.8.9

Color Applications

For monochrome applications, one can either put a monochrome color filter inside the cell or use monochromatic back-lighting. For Heilmeier displays, there is another way to get a monochrome display: by using monochromatic pleochroic dyes [26]. For full-color display, color filters must be used. Heilmeier displays exhibit better color performance than TN displays, as the chromaticity of the pixels does not change much at large viewing angles.

3.4.8.10 Multiplexing Heilmeier displays can be multiplexed only for low levels, as the threshold characteristic is not sharp enough for high level multiplexing. The 90" twisted geometry provides

282


a better threshold characteristic for multiplexing compared to parallel (0") alignment. Positive mode Heilmeier displays, with pleochroic dyes in a negative dielectric anisotropy liquid crystal, exhibit sharp threshold characteristics and are good candidates for moderate-level multiplexing. Heilmeier displays also do not show unwanted memory effects. In active-matrix displays they can exhibit better gray scale characteristics than the TN mode. However, since the advent of first minimum TN LCDs, Heilmeier displays are rarely used in active-matrix LCDs.

3.4.9 Quarter Wave Plate Dichroic Displays The operational principle of the quarter wave plate dichroic display is shown in Fig. 13 [ 18- 201. The incident unpolarized light becomes almost linearly polarized after passing through the dichroic layer, as the pleochroic dye absorbs the component of the E vector of unpolarized light parallel to its long molecular axis. This linearly polarized light is then converted to circularly polarized light by passing through the quarter wave plate. Upon reflection from the metallic reflector the original circularly polarized light is changed to opposite-handed circularly polarized light which, after passing through the quarter wave plate, is converted to linearly polarized light with its polaDichroic Mixture

I I \ 'I,.

LO/J

i14plate

,

,

"

/

-

rization axis rotated by 90". This re-entrant reflected light has its electric vector parallel to the long molecular axes of the dye molecules, and hence is absorbed by the pleochroic dyes. In the quiescent state, the cell looks colored or black, depending on the dye composition. On application of the electric field, dye molecules, along with the liquid crystal, are aligned in the direction of the field. In this geometry, the electric vectors of the light are more or less perpendicular to the long axis of the dye, and hence the light is not absorbed. Therefore, in the activated state the cell looks clear. In place of parallel alignment on both pieces of glass, a 90" twisted or 270" twisted geometry can also be incorporated. In these geometries the display generates light or clear pixel information on a colored or dark background. By giving homeotropic alignment and using a liquid crystal host of negative dielectric anisotropy one can make a display exhibiting dark pixels on a light background. The procedure for making a good reflective quarter wave plate display (CR > 12 :1) has been described elsewhere [19]. To obtain a transflective mode quarter wave plate display [20] one can replace the reflector by a transflector, put another quarter wave plate at 45" to the rub, and put a high efficiency polarizer parallel to the rub. This cell basically operates as a reflective mode quarter wave plate cell with front lighting and a Heilmeier cell with backlighting.

Linear Polarizer

.

-

Transflactor

(a) QUIESCENT STATE

(b) ACIWATEDSTATE

Figure 13. The structure and operational principle of a transflective mode quarter wave plate LCD in reflective mode: (a) quiescent state; (b) activated state.

3.4.10 Dye-doped TN Displays

3.4.10 Dye-doped TN Displays Dye-doped TN has the same cell geometry as TN, except for the fact that the liquid crystal fluid is doped with a small amount of dye. The addition of dye increases both the contrast ratio and the viewing angle. Only a few studies on dye-doped TN LCDs have been reported [15, 16,25-27, 1021. Scheffer and Nehring [27] have given a detailed theoretical analysis of dye-doped TN LCDs. The threshold characteristic of the dyedoped TN display is very similar to that of a TN display (see Fig. 4). The contrast ratio of a dye-doped TN LCD is heavily dependent on the polarization efficiency of the polarizer, and thus polarizers with very high polarization efficiency (> 99%) should be used. The threshold and operating voltages also increase slightly with an increase in thickness. The contrast ratio shows a similar effect to the Gooch Tarry curve in TN displays. The contrast ratio has been found to maximize at the first and second Gooch Tarry minima [16, 881. It has been found that the incorporation of dyes broadens the Gooch Tarry minima [16, 271. The addition of a small amount of dichroic dye decreases the values of the maxima and increases

283

the values of the minima. The positions of maxima and minima are found to be essentially unaffected by the absorption. The effect of actually increasing the transmission for certain values of d A d Aby the addition of dye is a consequence of dichroism of the dye and does not occur for isotropic dyes. The dichroism of the dye causes the two eigenmodes to be absorbed in different amounts so that they do not interfere destructively so efficiently in the second polarizer [27]. This effect is even more pronounced at higher dye concentrations. At still higher concentrations the maxima and minima disappear altogether, leaving a monotonically decreasing function. Figure 14 shows the impact of the dye concentration on the contrast. It has been found that the contrast ratio of dye-doped TN with 90" twist is higher than or equivalent to TN for only a small amount of dye concentration. For higher dye concentration the contrast ratio decreases, primarily due to the fact that the cell tends to become more Heilmeier like rather than remaining in the TN mode. However, in spite of the lower contrast ratio and transmission, dye-doped TN cells with higher dye concentration provide wider viewing angles, and more achromatic background. The decrease in contrast ratio oc-

1 0

1

2

3

4

DYE (D12) CONCENTRATION (in %)

5

6

Figure 14. Impact of dye concentration on the contrast of a dye-doped TN display.

284


curs basically due to the different amounts of absorption of the two eigenmodes. It has been observed that, by reducing the twist angle below 90" in a dye-doped TN mode display, the contrast ratio can be increased further [27]. The threshold voltage does not shift appreciably in dye-doped TN but the operational voltage Vop does. Vop increases with dye concentration. The contrast ratio is found to increase for dye-doped TN compared to TN. Figure 5 shows the viewing angle dependence of dye-doped TN compared to TN and Heilmeier cells; it is better than TN but inferior to Heilmeier at large angles. The contrast of dye-doped TN is much higher than that of both TN and Heilmeier displays. Table 2 shows the percent transmission and contrast ratio of dyedoped TN, TN, and Heilmeier displays. It is clear from the table that the incorporation of dye reduces the percent transmission slightly, but improves the contrast greatly at large angles. This is because TN operates solely on birefringence, while dye-doped TN operates on absorption too. The switching time of dye-doped TN is slightly more than that of TN, but there is no appreciable difference (Table 3). To get the best results with dye-doped TN displays the liquid crystal fluid must have low viscosity, appropriate dielectric anisotropy, and birefringence. The dyes must have all the advantages already discussed in the Sec. 3.4.8 on Heilmeier displays.

3.4.11 Phase Change Effect Dichroic LCDs Phase change dichroic LCDs are the most widely commercialized displays of all the dichroic LCDs. They are based on the cholesteric-nematic phase change effect [ 1031061 and do not require polarizers. The liquid crystal mixture used is a long pitch (- 2- 5 pm) cholesteric material with an appropriate amount (- 2 -6%) of dichroic dyes [12, 15-17, 107-1141. The usual alignments on the glass plates are homogeneous, homeotropic, or hybrid. Homogeneous alignment could be nonunidirectional or unidirectional, with any angle between the buffing directions of the two plates (e. g. 0", 90" or 180"). The display also works without any alignment treatment on the glass. The theoretical treatment for phase change dichroic LCDs is given by White and Taylor [17], Saupe [107], and Scheffer and Nehring [12]. Figure 15 shows the Alp dependence of the eigenwave absorption constants a, and a, as calculated from the theory. For a detailed theoretical treatment of the subject, the reader is referred to the articles by Bahadur [16] and Scheffer and Nehring [12]. The unpolarized light entering the liquid crystal is propagated in polarized modes. For propagation of these modes in a cholesteric liquid crystal, there are four possible types of A versusp dependence [ 12, 16, 108-1101:

Table 3. Switching speed of Heilmeier, dye-doped TN, and TN displays [16]. (")

Tdelayin on (ms)

Trise (ms)

To, (ms)

Heilmer display (10.38 pm)

0 45

15 14.5

25 24.5

40 39

3 3

63 54

66 57

106 96

Dye-doped TN (5.00 pm)

0 45

10 6

26 23

36 29

12

I

29 28

41 35

77 64

TN (5.00 pm)

0 45

14 15

23 24

37 39

14 9

28 25

42 34

79 73

Display

Pitch

Tdelay in off (ms)

Tdecay

3.4.1 1 Phase Change Effect Dichroic LCDs

-

OO

I

1

I !

I

2

i

3

IVPIFigure 15. Alp dependence of the eigenwave absorbances a, .d and q . d for the typical case where n,=1.7, n,=1.5, ae.d=lO.O, q . d = l . O , il=500nm, and d= 10 Fm. The region between dashed lines is the selective reflection band. (After Scheffer and Nehring [121).

Case I: p % A This case, in the nonabsorbing mode, is described by Mauguin and Berreman [ 115 - 1171. The polarized modes follow the twist, and the nematic liquid crystal simply behaves as a waveguide. In a perfectly ordered system, the dichroic dye dissolving in a long-pitch host absorbs only a single component of the E vector. The absorption of unpolarized light is only 50% of maximum, limiting the contrast ratio of only 2: 1. This ratio can be increased to more than 2 :1 by using (1) one polarizer (Heilmeier mode), (2) two polarizers (dye-doped TN mode), ( 3 ) a dichroic dye mixture composed of pleochroic and negative dichroic dyes 11181, or (4) a double cell.

285

Case 11: p - Aln This case, analyzed by Fergason [ 1191 and others [ 1161, gives rise to irridescent colors due to Bragg reflection. We also see the reflection of this band in the case of an absorbing mode cholesteric (Fig. 15). However, one component of the polarized light always gets absorbed. Case III: p 5 A h , This case is described in White and Taylor 1171, Saupe [107], and by others [12]. In this case both the normal modes of the elliptically polarized light have a component parallel to the local liquid crystal director and the long axis of the dichroic dye. Hence more than 50% of the unpolarized light can be absorbed. As is clear from Figure 15, this region shows the maximum absorption (maximum average absorption occurring at Alp n,). The absorption depends on the pitch of the cholesteric which, along with the principal refractive indices nlland nl, determines the eccentricity of the polarized modes. The other important parameters include the order parameter of the dye, its absorbance, and the cell thickness. Although, theoretically, this is the most desired region for operating phase change displays, practical displays are not operated in this region as a very high operating voltage is required due to the very small pitch in this region (see Eq. 17).

-

Case IV: A
Aln, ( p - 1-5 pm) As is clear from Figure 15 in this region too, both the normal modes of elliptically polarized light get absorbed by the dyes, although q,d, in this case, is smaller compared than that in the region p IAln,. However, due to moderate operating voltages, this is the region in which phase change displays are operated. The cells are usually prepared with either ho-

286


mogeneous or homeotropic alignment, with a cell thickness of usually more than 4-5 times the pitch of the dichroic mixture (-2-5 pm). Sometimes hybrid alignment (homeotropic on one plate and homogeneous on the other) is given. Irrespective of the alignment, the central layers adopt the planar Grandjean arrangement, with the helix axis perpendicular to the glass surfaces.

3.4.11.1 Threshold Characteristic and Operating Voltage The threshold characteristic of a phase change dichroic display is shown in Fig. 16. With slowly increasing voltage, the cell seems to go from Grandjean to a scattering focal conic and from there to a homeotropic nematic texture. On reducing the voltage the same effect is observed in reverse order. The first major jump in the threshold characteristic corresponds to the transition from Grandjean or planar to fingerprint or focal conic texture, and the second is for focal conic to nematic texture. The critical unwinding voltage V, for the cholesteric -ne-

matic phase transition can be calculated as [103]:

This equation was derived for an infinitely thick cholesteric layer where there is no torque exerted by the boundaries and cholesteric material has its natural pitch. However, it holds reasonably well for practical devices with large d/p ratios, and in particular for White-Taylor displays with homeotropic boundaries having no forced pitch. The threshold characteristic shows a noticeable hysteresis. The winding voltage V, is given by (see Fig. 16)

where k22and k,, are the twist and bend elastic constants, respectively. V, is found to With homeotropic be smaller than V,.

Figure 16. Threshold characteristic of a phase change dichroic display: (--) homogeneous alignment; (- - - - ) homeotropic alignment. Voltage (V)

287

3.4.1 1 Phase Change Effect Dichroic LCDs

alignment the threshold characteristic shifts towards lower voltage. Homeotropic alignment generates lower threshold and operating voltages (see Fig. 16). Eq. (17) also shows that threshold and operating voltages are directly proportional to the cell gap and inversely proportional to the pitch of the mixture and the square root of A&.Thus, to reduce the operating voltage, the cell thickness must be reduced and the pitch and A& increased. However, increasing the pitch reduces the contrast. To obtain the appropriate contrast and operating voltage we recommended that dlp be kept at about 4-6 for directly driven applications, especially for avionic use. With smaller d/p ratios (d/pO >O O

>O O O

Theoretical contrast ratioa) ~~

1 2 3 4 5 6

Aa=q,-aL,dichroism of the dichroic dye.

Vth) and the use of polarized light. In planar cells the E vector is parallel to n. In homeotropic cells the E vector agrees with n after the dielectric reorientation. b, The director n is tilted by a small angle with respect to the layer normal.

3.4.13 Positive Mode Dichroic LCDs

Positive Mode Dichroic LCDs Using a i1/4 Plate

3.4.13.2

W4 displays do not need polarizers. One can get a positive mode A/4 display using the same two-cell geometries and materials as discussed in an earlier section.

Positive Mode Double Cell Dichroic LCD

3.4.13.3

The same geometry and materials can be used as discussed for single cell positive mode LCDs (see Sec. 3.4.13).

Positive Mode Dichroic LCDs Using Special Electrode Patterns

3.4.13.4

A positive mode dichroic LCD [16, 1271 can be demonstrated by using special electrode patterns even in the case of pleochroic dyes embedded in a liquid crystal of positive dielectric anisotropy. In this case the voltage is applied to the whole visible area and is removed only from the desired segmented areas.

Positive Mode Phase Change Dichroic LCDs

3.4.13.5

The molecular structure of a long-pitch cholesteric mixture is determined both by the cell gap and the type of alignment [ 13- 161. If the cell gap is sufficiently large, the structure is always helicoidal in the bulk of the layer, irrespective of the homeotropic or homogeneous alignment on the surface [ 13- 161. If the cell gap is below a critical thickness d,, where

the helix is unwound in the presence of a homeotropic alignment and the whole structure is homeotropic nematic [ 1201. Two versions of cells using this property have been proposed using a pleochroic dye

295

in a liquid crystal host of positive dielectric anisotropy [ 1281. The operational principle ofboth types of cell is that the area surrounding the picture element has homeotropic alignment and a cell gap less than d,, resulting in a nonabsorbing homeotropic nematic structure. In the first geometry the areas surrounding the pixels undergo homeotropic treatment, while the pixel areas receive homogeneous alignment [ 1291.The cell gap is less than d,. In the second geometry the alignment on the whole cell is homeotropic, but the cell gap is adjusted in such a way that the pixel areas have a cell gap more than d,, while the remaining area is less than d,. These proportions result in an absorbing helicoidal structure in the pixel areas and a nonabsorbing homeotropic one in the remaining area [ 1281. On application of the electric field, the helicoidal structure is destroyed and the liquid crystal molecules adopt a homeotropic structure, with the result that only the nonactivated pixels remain dark. The control logic for this display is inverted with respect to that required for the White-Taylor type with negative contrast. Another way of obtaining apositive mode phase change type display is to use a pleochroic cholesteric mixture of negative dielectric anisotropy [ 16, 1291. The surface treatment is homeotropic and cell thickness d is chosen to be less than d,. In the quiescent mode the cell is in the homeotropically aligned nematic state, and hence pleochroic dyes do not absorb the light. On aplication of the field, the molecules become parallel to the glass plates and also adopt the heliocoidal structure. In this situation the light is absorbed by the dyes. A display of this type has the advantages of positive contrast, brightness, wider viewing angle, lower operating voltage, and multiplexing capability [ 16, 1291, but has low contrast. A very high order parameter dichroic mixture with a very low optical anisotropy is need-

296


ed to obtain sufficient contrast for this display.

3.4.13.6 Dichroic LCDs Using an Admixture of Pleochroic and Negative Dichroic Dyes These dichroic LCDs have a dichroic mixture containing both pleochroic (L) and negative dichroic (T) dyes, these having absorption wavelengths in different parts of the spectrum [53, 1181. The display can be made in Heilmeier, TN, and phase change mode. If a liquid crystal mixture of positive dielectric anisotropy is used to make a dichroic mixture using these L and T dyes, and is filled in a cell having homogeneous alignment, both L and T dyes will absorb in the quiescent state, and the cell will have the complementary color of the dichroic mixture. This color can be changed by changing the ratio of L and T dyes. On application of the field, the dye molecules, together with the liquid crystal molecules, become aligned in the direction of the field. Only the T dye absorbs in this geometry, and its complementary color becomes the observed color. These displays do not require polarizers and can be operated at low voltage like TN displays. Their excellent brightness and contrast are much less dependent on the order parameter compared to other guest-host displays [ 1181. Schadt [ 1181 also derived the detailed analytical expressions describing the dependence of transmission and color effects on the dye order parameter, the direction of the dye’s transition moment, and the elastic and dielectric properties of the liquid crystal mixture. The viewing angle and threshold voltage have been calculated and compared with experimental values. Using tetrazine dye (T) and anthraquinone dye D27 (L), Schadt developed a display exhibiting bright-red characters on a bright-blue background [ 1181. This display

can also be operated with a single polarizer in the Heilmeier mode [ 1181.Pelzl et al. [54] have reported a similar display.

3.4.14 Supertwist Dichroic Effect Displays Supertwist dichroic effect (SDE) displays have a twist of approximately 3 x/2, instead of n/2 as in the case of the popular TN mode LCDs, and hence are called supertwisted LCDs 129-311, The 3n/2 twist imparts a very steep slope to the threshold characteristic of the cell. This means it has a lower value of AV/Vth, and hence can handle a higher level of multiplexing. However, the threshold characteristics of 3 n/2 displays, unaided by dye or the interference of ordinary and extraordinary rays, has low contrast. The dyes absorb the leakage and enhance the viewing angle and contrast. Two types of SDE display can be made, one by using a Heilmeier geometry (by using a single polarizer), and the second by using the phase change or White-Taylor mode. However, SDE displays did not become popular due to their lower contrast, lower brightness, and slower switching speed compared to other supertwist displays.

3.4.15 Ferroelectric Dichroic LCDs Surface stabilized mode ferroelectric LCDs [31-351 show bistability, i. e. both the 8and the -8 position are equally stable. A pulse of one polarity is used to switch from 8 to -8,while a pulse of opposite polarity is used to switch from -8 to 8. The molecules can remain in either of these states (8 or -8)for a long time without any applied voltage. In the case of GH ferroelectric LCDs, the ferroelectric mixture contains an appropriate

3.4.16 Polymer Dispersed Dichroic LCDs

amount of dichroic dyes. Ferroelectric dichroic LCDs have a very fast switching speed (-100 ps or less), wide viewing angle, and good contrast [35].

3.4.15.1 Devices Using A Single Polarizer For a dye dissolved in a ferroelectric host in a single polarizer device, the orientation is rotated through twice the tilt angle (28) of the guest - host material on changing from one switched state to the other. If the polarizer is aligned with the dye direction to generate maximum absorption (dark state), then the switched state ( @ = 2 8 )would be lighter. One can also make a display exhibiting dark characters on a light background by initially aligning the polarizers perpendicular to the long axes of the pleochroic dye molecules. For maximum contrast a tilt angle of 45" is required. Only a few ferroelectric liquid crystals have such a high tilt angle. Fortunately, a 10-90% change in intensity may be achieved with a tilt of only 27" [35], making commercially available ferroelectric host and dichroic mixtures, with a typical tilt angle of 22-25', useful for this application. Another single polarizer DGHFE mode LCD uses an anisotropic fluorescent dye in the ferroelectric mixture [35].

3.4.15.2 Devices Using No Polarizers

-

A ferroelectric liquid crystal with 8 22.5" and a high pleochroic content can be used entirely without a polarizer by using a 2 4 plate [32] with a reflector. In the off-state the incoming light is selectively absorbed along the homogeneous alignment n in the cell. A quarter wave plate is placed along or perpendicular to the director. The nonabsorbed radiation (- 50%)in the ideal case vibrates perpendicular to the dichroic director and is reflected back unaffected. In the onstate n is turned 45" to the axis of the A14 plate; the nonabsorbed orthogonal vibration

297

is thus split up and components retarded corresponding to a double pass 2 i1/4=A/2. The polarization plane is therefore rotated by 90" and the radiation is absorbed on its way back into the liquid crystal. Coles et al. [35] made another ferroelectric dichroic device without polarizer, using a double layer surface stabilized mode DGHFE. The optimum tilt angle required for this geometry is 22.5".

3.4.16 Polymer Dispersed Dichroic LCDs A polymer dispersed liquid crystal (PDLC) film [36-39, 130- 1321, with a pleochroic dye dissolved in it, possesses a controllable absorbance as well as a controllable scattering. This combination can be exploited to generate high-contrast displays. For polymer dispersed dichroic LCDs, Fergason's NCAP systems are found to be better than Doane's PDLC systems [36 - 391. Unlike to other dichroic LCDs where we strictly require dichroic dyes only, one can use isotropic as well as dichroic dyes in these kinds of devices. Vaz observed a larger than expected color change between the on and off states of dichroic PDLC shutters, even with dichroic dyes with small order parameters (0.2) and dichroic ratios (1.7) [37]. This is explained on the basis of increased path length (i.e. more than the film thickness) due to multiple scattering in the off mode, which consequently increases the off-state absorbance. The contrast ratio of the dyepolymer system can be improved significantly by incorporating dichroic dyes with high order parameters and extremely low solubilities in the polymer [36-39, 1311. These displays provide much higher brightness and wider viewing angles than TN displays. Two optical processes are at work in these displays: switchable absorbance due to dye alignment, and electrically controlled

298


light scattering. When the display is excited, the light entering the film experiences a low absorbance and minimal scattering. The color reflector in the back is seen clearly with high brightness and color purity. In the quiescent state, incoming light is both strongly absorbed and scattered. The strong absorption by the pleochroic dyes gives the film a dark appearance. The scattering effect enhances the absorption and causes a fraction of the light to be reflected before reaching the colored reflector. This ensures that the light reflected from the display in the unexcited state possesses a very low color purity and hence looks more neutral or black. The color difference properties of the film can be optimized by varying various parameters of the film, such as film thickness, dye concentration, dye order parameter, and the level of scattering. The scattering is controlled by the liquid crystal birefringence and the droplet size distribution.

3.4.17

Dichroic Polymer LCDs

It is now well established that polymer nematic liquid crystals can be aligned by an electric field and surface forces, in more or less the same way as low molecular weight nematic liquid crystals [ 133- 1351. To generate dichroic polymeric LCDs, either dichroic dyes are dissolved in nematic polymers, or side-chain dye moieties are attached in nematic copolymer structures [ 133- 1351.As the pleochroic dye has its absorption transition dipole defined relative to its chemical structure, rotation of the dye produces a change in absorption of the guest-host cell when observed in polarized light. Several types of effect have ben reported and many more are possible, analogous to the low molecular weight nematic counterpart (as discussed in Sec. 3.4.83.4.16). Some of these are: Heilmeier type,

using pleochroic dyes in liquid crystal polymer of positive dielectric anisotropy; guest-host cells, using a dichroic liquid crystal polymer in a low molecular weight liquid crystal host; and polymeric ferroelectric dichroic LCDs. However, their use in display devices is strongly restricted by their slow response time. The reason for this is that the viscosity of side-chain liquid crystals is some orders of magnitude greater (depending on the temperature) in relation to the glass transition temperature and the degree of the polymerization of the polymer. One of the most promising potential uses of liquid crystal polymers is in optical storage devices [133, 1351. The information is written using a He-Ne laser. Images are stable over a long period of time (at least 4 years under ambient conditions), and are erasable by applying an electric field. The absorption of the laser beam is facilitated by incorporating a dye into the polymer [ 1361. Ferroelectric polymeric materials are fascinating because, in principle, they can have the fast switching speed of ferroelectric materials together with the processibility of polymers. Dichroic properties can be achieved either by dissolving dichroic dyes in ferroelectric polymers or by inserting dichroic groups in the polymer. Using a little imagination one can form all types of dichroic ferroelectric LCDs using polymeric ferroelectric dichroic mixtures in place of ferroelectric dichroic liquid crystal mixtures.

3.4.18 LCDs

Smectic A Dichroic

In these displays usually a thin layer of SmA material (- 10- 15 pm) is sandwiched between I T 0 coated glass plates with homeotropic alignment. When the layer is heated above the isotropic temperature and

3.4.20

is cooled back to the SmA phase via a nematic phase, it generates: (1) a focal conic scattering texture in the absence of the field, and (2) a clear homeotropic texture if cooled in the presence of an electric field [137]. These properties of SmA phases have been used in making various kinds of laseraddressed [ 137, 1381 and thermal-addressed [40, 41, 1381 SmA displays. Incorporation of pleochroic dyes converts the scattering state into an absorbing state [40, 41, 137, 1381. The homeotropic state will remain clear in this case too. In spite of a lot of research and demonstrations, thermally and electrically addressed displays have not become a commercial product [40, 41, 1371. The main reasons for this are their high power consumption and limited operating temperature range. Moreover, the advent of supertwist displays closed the market sectors where they could have been utilized.

3.4.19 Fluorescence Dichroic LCDs Some attempts have been made to replace normal dichroic dyes with fluorescent type dichroic dyes [16, 59-61, 139- 1411. Fluorescence is a two-step process involving absorption at a given wavelength and reemission at a longer wavelength, and is associated with electronic transitions which, relative to dye-molecule geometry, are directional in space. Thus the change in the orientation of the fluorescent dye molecule changes the absorption and subsequent emission intensity. Depending on the polarization of the incident and transmitted light, sample thickness, and concentration, it is possible to produce an increase or decrease in the light level. These fluorescent dyes can be excited either by UV light or light of shorter wavelengths in the visible spectrum

References

299

(such as blue light for exciting green, and yellow for exciting red fluors). These fluors can be excited either directly or indirectly through a liquid crystal. For example, a green fluorescent dye can be excited directly by blue light or indirectly with ultraviolet light. In the latter case the UV energy is absorbed by an appropriately formulated liquid crystal host, and subsequently transferred to the fluorescent dye. The fluorescent LCDs combine the visual impact and good viewing angle of emissive displays with the desirable features of LCDs, such as long voltage operation and low power consumption. Both Heilmeier [ 1391 and phase change [61] type fluorescent dichroic displays have been reported. When stimulated from the rear, indirect excitation is preferred because the exciting light is invisible and the display then has a dark appearance on a bright colored background. The display can also be excited from the front. In the frontlit mode, the phase change version is preferred over the Heilmeier mode, as the polarizer blocks UV light and attenuates any blue light passing through it. Acknowledgments Thanks are due to Urmila, Shivendra, and Shachindra Bahadur for their untiring help in preparing this manuscript. This article is dedicated in loving memory to my aunt, Mrs Sushila Srivastava, who passed away recently after a brave fight against cancer.

3.4.20 References [ l ] G. H. Heilmeier, L. A. Zanoni, Appl. Phys. Lett. 1968, 13, 91. [2] G. H. Heilmeier, J. A. Castellano, L. A . Zanoni, Mol. Cryst. Liq. Cryst. 1969, 8, 293. [3] B. Bahadur, Mol. Cryst. Liq. Cryst. 1983, 99.

34s. [4] E. Sackmann, in Applications ($Liquid Crystu/s (Eds.: G. Meier, E. Sackmann, J. G. Grabmaier), Springer-Verlag, New York, 1975. [S] J. W. Emsley, J. C. Lindon, N M R Spectroscopy Using Liquid crystal Solvents, Pergamon Press, New York, 1975.

300


161 C. Schumann, in Handbook of Liquid Crystals (Eds.: H. Kelker and R. Hatz), Verlag Chemie, Weinheim, 1980. [7] C. L. Khetrapal, R. G. Weiss, A. C. Kunwar, Liquid Crystals- Applications and Uses, Vol. 2 (Ed.: B. Bahadur), World Scientific, Singapore, 1991. [8] A. Saupe, G. Engler, Phys. Rev. Lett. 1963, 11, 462. [9] A. Carrington, G. R. Luckhurst, Mol. Phys. 1964,8,401. [lo] D. L. Uhrich, Y. Y. Hsu, D. L. Fishel, J. M. Wilson, Mol. Cryst. Liq. Cryst. 1973, 20, 349. [ I13 W. J. Leigh, in Liquid Crystals - Applications and Uses, Vol. 2 (Ed.: B. Bahadur), World Scientific, Singapore, 1991. [12] T. J. Scheffer, J. Nehring, in Physics and Chemistry of Liquid Crystal Devices (Ed. J. G. Sprokel), Plenum Press, New York, 1979, p. 173. [13] T, J. Scheffer, Phil. Trans. R. SOC., London Ser. A, 1983,309, 189. [14] T. Uchida, M. Wada, Mol. Cryst. Liq. Cryst. 1981, 63, 19. [15] B. Bahadur, Mol. Cryst. Liq. Cryst. 1991, 209, 39. [16] B. Bahadur, in Liquid Crystals - Applications and Uses, Vol. 3 (Ed.: B. Bahadur), World Scientific, Singapore, 1992. 1171 D. L. White, G. N. Taylor, J. Appl. Phys. 1974, 45,4718. [I81 H. S. Cole, R. A. Kashnow, Appl. Phys. Lett. 1977,30,619;SID Digest, 1977,8,96; GE-CRD Report No. 77CRD059,1977. [19] B. Bahadur, SPIE, Opt. Test. Meteorol. II, 1988, 954, 574. 1201 B. Bahadur, K. Wan, C. Prince, L. Krzymien, J. Tunnoch, Mol. Cryst. Liq. Cryst. 1992,220,155. [21] T. Uchida, H. Seki, C. Shishido, M. Wada, SlD Digest, 1980, 11, 192. [22] H. Seki, T. Uchida, Y. Shibata, Proc. SID 1984, 25, 275. 1231 K. Sawada, Y. Masuda, Proc. SID 1982,23,241. [24] K. Sawada, S. Kudoh, F. Kadoo, Y. Endoh, Y. Nakagawa, Y. Masuda, SID Digest 1985,78. 1251 G. A. Dir, V.J. Hull, Proc. Int. Disp. Res. Con$, 1985, 83. [26] B. Bahadur, Development of a High Resolution (Phase II) Liquid Crystal Display System - Llquid Crystal Mixture and Process Development, LSL Report, April 1989. [27] T. J. Scheffer, J. Nehring, J. Appl. Phys. 1984, 908,56. [28] K. Wan, D. Lewis, B. Bahadur, SID Digest 1994, 25, 601. B. Bahadur, K. Wan, US Patent 5589965,1996. [29] C. M. Waters, E. P. Raynes, V. Brimmell, Mol. Cryst. Liq. Cryst. 1985, 123, 303. [30] C. M. Waters, V. Brimmell, E. P. Raynes, Proc. SID 1984, 25, 261, Jpn. Displ. 1983,398.

1311 B. Bahadur, Supertwisted Dye Effect, Supertwisted Birefringence and Ferroelectric Liquid Crystal Displays, Litton Data Images Report, March 1986. [32] S. T. Lagerwall, J. Wahl, N. A. Clark, Proc. Int. Displ. Res. Con$ 1985,213. [33] K. Kondo, S. Era, M. Isogai, A. Mukoh, Jpn. J. Appl. Phys. 1985,24, 1389. [34] H. J. Coles, H. F. Gleeson, Mol. Cryst. Liq. Cryst. Lett. 1988, 6, 53. 1351 H. J. Coles, H. F. Gleeson, J. S. Kang,Liq. Cryst. 1989, 5, 1243. 1361 P. S. Drziac, R. Wiley, J. McCoy, SPZE, Liq. Cryst. Chem. Phys. Appl. 1980,41. [37] J. W. Doane, in Liquid Crystals - Applications and Uses, Vol. 1 (Ed.: B. Bahadur), World Scientific, Singapore, 1990. [38] J. L. Fergason, SZD Digest 1985, 68; US Patent 4435047, March 6,1984. 1391 P. S. Drzaic, Liquid Crystal Dispersions, World Scientific, Singapore, 1995. 1401 S. Lu, D. H. Davies, Mol. Cryst. Liq. Cryst. 1983, 94, 167. 1411 W. Harter, S. Lu, S. Ho, B. Basler, W. Newman, C. Otaguro, SID Digest 1984, 15, 196. [42] B. Bahadur, R. K. Sarna, V. G. Bhide, Mol. Cryst. Liq. Cryst. 1981, 75, 121. 1431 H. Seki, T. Uchida, Y. Shibata, Mol. Cryst. Liq. Cryst. 1986, 138, 349. 1441 R. J. Cox, Mol. Cryst. Liq. Cryst. 1979,55, 1. [45] G. W. Gray, Chimica, 1980, 34, 47; Dyes Pigments 1982,3,203. 1461 H . V. Ivashchenko, V. G. Rumyantsev, Mol. Cryst. Liq. Cryst., 1987, 150A, 1. [47] M. G. Pellatt, I. H.C . Roe, J. Constant, Mol. Cryst. Liq. Cryst. 1980, 59, 299. [48] F. C. Saunders, K. J. Harrison, E. P. Raynes, D, J. Thompson, Proc. SID 1983,24, 159. [49] J. Cognard, T. H. Phan, Mol. Cryst. Liq. Cryst. 1981, 68, 207. [50] X. Q. Yang, J. R. Wang, G. D. Ren, Mol. Cryst. Liq. Cryst. 1991, 199, 1. 1511 S. Imazeki, M. Kaneko, T. Ozawa, A. Mukoh, Mol, Cryst. Liq. Cryst. 1988, 159, 219. [52] G. Pelzl, H. Schubert, H. Zaschke, D. Demus, Krist. Techn. 1979, 14, 817. [53] G. Pelzl, H. Zaschke, D, Demus, Displays 1985, 141. [54] Literature on Dichroic dyes, Mixtures and Hosts from BDH (England), E. Merck (Germany), Hoffman La Roche (Switzerland) Mitsui (JaPan). [55] T. J. Scheffer, J. Appl. Phys. 1982, 53, 257. 1561 B. S. Scheuble, G. Weber, L. Pohl, R. E. Jubb, SIR Digest 1983, 176; Proc. SID 1984, 25, 25. [57] G. Heppke, B. Knippenberg, A. Moller, G. Scherowsky, Mol. Cryst. Liq. Cryst. 1983, 94, 191.

3.4.20 References [58] U. Claussen, A. Brockes, E. F. Kops, F. W. Krock, R. Neeff, SlD Digest 1984, 209; Proc. SlD 1985,26, 17. [591 E. Wolarz, D. Bauman, Mol. Cryst. Liq. Cryst. 1991, 197, 1. [601 S. Sato, M. M. Labes, J. Appl. Phys. 1981, 52, 3941. R. W. Filas, M. M. Labes, 1981,52,3949. [611 M. R. Lewis, M. C. K. Wiltshire, A. Cuddy, J. Stanford, I. Sage, J. Griffiths, S. Tailor, Proc. SlD 1988, 29, 233; Eurodisplay 1987, 149. [62] S . Aftergut, H. S. Cole, Jr., Mol. Cryst. Liq. Cryst. 1982, 89, 37. [63] H. Seki, C. Shishido, T. Uchido, M. Wada, Mol. Cryst. Liq. Cryst. 1981, 66, 209. [64] S. Ohmi, A. Watanabe, K. Hara, Jpn. Displ. 1986, 282; Proc. SlD 1987, 28, 123. (651 H. Seki, T. Uchida, C. Shishido, Jpn. J . Appl. Phys. 1980,19, L501. [66] S . Aftergut, H. S. Cole, Mol. Cryst. Liq. C y s t . 1990, 188, 147; Proc. SID 1990, 31, 317; SlD Digest 1990, 21, 95. [67] F. Jones, T. J . Reeve, Mol. Cryst. Liq. Cryst. 1981, 78, 201. [68] J. K. Foitzik, W. Haase, Mol. Cryst. Liq. Cryst. 1987,142,55; 1987, 149,401. [69] F. Jones, F. A. Kirby, Mol. Cryst. Liq. Cryst. 1984,108, 165. [70] S. Imazeki, A. Mukoh, T. Yoneyama, M. Kaneko, Mol. Cryst. Liq. Cryst. 1987, 145, 79. [71] A. Bloom, P. L. K. Hung, Mol. Cryst. Liq. Cryst. 1978,44, 323. [72] S. Yano, S. Kato, M. Kano, Y. Kamijo, Mol. Cryst. Liq. Cryst. 1985, 123, 179. [73] T. K. Attwood, J. E. Lydon, F. Jones, Liq. Cryst. 1986, I , 499. [74] M. A. Osman, L. Pietronero, T. J. Scheffer, H. R. Zeller, J . Chem. Phys. 1981, 74, 5377. [75] B. Bahadur, in Liquid Crystal -Applications and Uses, Vol. 2 (Ed.: B. Bahadur), World Scientific, Singapore, 1991. [76] B. Bahadur, Mol. Cryst. Liq. Cryst. 1984,109, 1. [77] S. Morozumi, in Liquid Crystals -Applications and Uses, Vol. 1 (Ed.: B. Bahadurj, World Scientific, Singapore, 1990. [78] J. Cognard, Mol. Cryst. Liq. Cryst. 1981, 7 8 (Suppl 11, 1. [79] T. Uchida, H. Seki, in Liquid Crystals - Applications and Uses, Vol. 3 (Ed.: B. Bahadurj, World Scientific, Singapore, 1992. [80] J. M. Geary, J. W. Goodby, A. R. Kmetz, J. S . Patel, J. Appl. Phys. 1987, 62, 4100. [81] S. Matsumoto, M. Kawamoto, N. Kaneko,Appl. Phys. Lett. 1975,27, 268. [82] Homeotropic aligning agents from E. Merck, Germany (such as ZLI-2570), and Nissan Chemical Ind., Japan (such as RN 722), etc. [83] H. Seki, Y. Itoh, T. Uchida, Y. Masuda, Jpn. J. Appl. Phys. 1990, 29, L2236; Mol. Cryst. Liq. Cryst. 1991, 199, 151.

30 1

[84] Low tilt (for TN) and high tilt (for STN) producing polyimides from Hitachi (Japan), Japan Synthetic Rubber (Japan), Nissan Chemicals Inc. (Japan). [851 H. Fukuro, S . Kobayashi, Mol. Cryst. Liq. Cryst. 1988, 163, 157. [861 M. R. Lewis, M. C. K. Wiltshire, Appl. Phys. Lett. 1987, 51, 1197; R. W. Filas, SID Digest 1984,206. [87] B. 0. Myrvold, Mol. Cryst. Liq. Cryst. 1991, 202, 123. [881 C. H. Gooch, H. A. Tarry, Electron. Lett 1974, 10, 2; J. Phys. D 1975, 8 , 1585. [89] P. Kassubek, G. Meier, Mol. Cryst. Liq. Cryst. 1969, 8, 305. [90] A. J. Hughes, D. G. McDonnell, S. Hedges, Displays, April 1987, 69. [91] M. Kawachi, K. Kato, 0. Kogure, Jpn. J. Appl. Phys. 1978, 17, 1245. [92] Information sheets for polarizers from Polaroid Corp., USA, Nitto, Japan, Sanritsu, Japan. [93] R. W. G. Hunt, Measuring Colouv, Ellis Horwood, Chichester, 1987. [94] A. Bloom, E. B. Priestley, ZEEE Trans. Electron. Dev., 1977, ED24, 823. [95] Euro-Fighter Project Definition Phase, Final Report-Report No. EFJ-R-EFA-000-107, October 1987. [96] E. Jakeman, E. P. Raynes, Phys. Lett. 1972, 39A, 69. [97] K. M. Bofingar, H. A. Kurmier, M. R. Romer, J. D. E. Beubert, German Patent 4699636 (E. Merck, Darmstadt, Germany). [98] US Military Standard MIL-L-85762. [99] F. Gharadjedaghi, J . Appl. Phys. 1983, 54, 4989. [loo] H. L. Ong,J. Appl. Phys. 1988,63, 1247; H. L. Ong, Proc. SlD 1988, 29, 161. [ l o l l G. Schauer, W. Wiemer, Eurodisplay 1990, 122. [lo21 D. Potzsch, H. Baeger, F. W. Nickol, E. Purtzel, H. Voss, Proceedings of 12th Freiburger Arbeitstagung Fliissigkristulle, Freiburg, Germany, 1982. [lo31 P. G. de Gennes, J. Prost, The Physics o f L i q uid Crystals, 2nd edn. Oxford University Press, London, 1993. [lo41 M. J. Press, A. S. Arrott,J. Phys. 1976,37,387. [lo51 B. Kerllenvich, A. Coche, Mol. Cryst. Liq. Cryst. 1985, 124, 149; 1983, 97, 103. [ 1061 P. R. Gerber, Z. Naturforsch. a 1981, 36, 7 18. [lo71 A. Saupe, J . Chem. Phys. 1980, 72, 5026. [ 1081 H. S. Cole, Jr., S . Aftergut, J . Chem. Phys. 1978, 68, 896. [lo91 S . Aftergut, H. S. Cole, Jr., Appl. Phys. Lett. 1981, 38, 599. [I101 T. Ishibashi, K. Toriyama, K. Suzuki, M. Satoh, Proc. lnt. Display Res. Conf. 1990, 186; Proc. SID 1983, 24, 152.

302


11111 D. Jones, B. Desai, SOC.Autorn. Engrs 1980, 91; J. Mech. Engng 1981, 331. [112] M. Schadt, P. Gerber, Mol. Cryst. Liq. Cryst. 1981, 65, 241. [113] P. W. Ross, B. Needham, D. Coates, Eurodisplay 1981, 55. 11141 Data sheets from dichroic LCD manufactures such as Litton Data Images, Ottawa, Canada, Goodrich Aerospace Displays, Hatfield, USA, and Stanley Electric Co., Tokyo, Japan. [ 1151 C. Mauguin, Bull. SOC.Fr. Mineral. 1911, 34, 71. 11161 H. de Vries, Acta Crystallogr. 1951, 4, 219. [117] D. W. Berreman, J. Opt. SOC.Am. 1973, 63, 1374. 11181 M. Schadt, J. Chern. Phys. 1979, 71,2336. [119] J. L. Fergason, Appl. Opt. 1968, 7, 1729. [120] F. Fischer, Z. Nuturforsch. a 1976,31,41. 11211 J. F. Clerc, Displays, July 1985, 148. [122] G. Gharadjedaghi, A. E. Lagos, Proc. SID 1982,23,237. 11231 W. A. Crossland, B. Needham, P. W. Ross, Proc. SID 1985,26,237. 11241 S. Mitsui, Y. Shimada, K. Yamamoto, T. Takamatsu, N. Kimura, S. Kozaki, s. Ogawa, H. Morimoto, M. Matsuurd, M. Ishii, K. Awane, SID Digest 1992,437. [125] C. Casini, US Patent 4516834, May 14, 1985. [126] H. L. Ong, Jpn. J. Appl. Phys. 1988,27, 2017. [127] C. S. Oh, G. Kramer, Displays, January 1982, 30. [128] F. Gharadjeadaghi, E. Saurer, IEEE Trans., Electron. Dev. 1980, ED27, 2063.

[129] F. Gharadjedaghi, Mol. Cryst. Liq. Cryst. 1981, 68, 127. [130] J. L. West, R. Ondris, M. Erdmann, SPZE, Liq. Cryst. Disp. Appl. 1990, 57, 76. [ 1311 P. S. Drzaic, A. M. Gonzales, P. Jones, W. Montoya, SID Digest 1992, 571. [132] P. Jones, W. Montoya, G. Garza, S. Engler, SID Digest 1992,762. [133] H. Finkelmann, W. Meier, H. Scheuermann, in Liquid Crystals -Applications and Uses, Vol. 3 (Ed.: B. Bahadur), World Scientific, Singapore, 1992. [134] R. Simon, H. J. Coles, Liq. Cryst. 1986, I , 281. 113.51 H. J. Coles, Faraday Discuss. Chern. SOC. 1985, 79, 201. 11361 C. Bowry, P. Bonnett, M. G. Clark, presented at the Euro Display Conference, Amsterdam, September 1990. [ 1371 D. Coates in Liquid Crystals-Applications and Uses, Vol. 1 (Ed.: B. Bahadur), World Scientific, Singapore, 1990. [138] T. Urabe, K. Arai, A. Ohkoshi, J. Appl. Phys. 1983,54, 1552; Proc. SID 1984,2.5,299. [139] R. L. Van Ewyk, I. O’Connor, A. Moseley, A. Cuddy, C. Hilsum, C. Blackburn, J. Griffiths, F. Jones, Displays 1986, 155; Electron. Lett. 1986,22,962. 11401 L. J. Yu, M. M. Labes, Appl. Phys. Lett. 1977, 31,719. [141] D. Bauman, K. Fiksinski, Eurodispluy 1990, 278.


Chapter IV Chiral Nematic Liquid Crystals

1 The Synthesis of Chiral Nematic Liquid Crystals Christopher J. Booth

1.1 Introduction to the Chiral Nematic Phase and its Properties Chiral nematic liquid crystals, as the name suggests, are optically active variants of nematic liquid-crystalline compounds; the incorporation of a chiral centre imparts properties which are unique to the chiral nematic phase and are responsible for their utilisation in a variety of differing display technologies and other related applications. The term cholesteric liquid crystal was originally used to describe this phase, and originates from the structural nature of the earliest chiral nematic liquid crystals which were derivatives of cholesterol [ 1,2]. Nowadays, the term chiral nematic is used primarily because the materials are clearly derived from nematic type liquid crystals [3, 41. Despite these differences in definition, the terms cholesteric and chiral nematic phase are interchangeable and it is common to find references to either term in the literature. The incorporation of a chiral centre into a formerly nematic structure (or alternatively of a chiral non-mesogenic dopant into a nematic host) results in the induction of a

macroscopic helical twist distortion in the bulk of the sample [ 5 , 6 ] .As a consequence the chiral nematic phase can be described as having helical orientational order or being a single twist structure [4]. The director ( n ) may precess through 360"; the distance over which this occurs is called the pitch length ( p ) , and this is shown simplistically in Fig. 1

1

pitch length, p

Figure 1. Diagram of the structure of the chiral nematic phase.

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1 The Synthesis of Chiral Nematic Liquid Crystals

All interest in the unique optical properties of the chiral nematic phase stems from the two-fold optical activity of the phase [5, 6-91. That is, the mesophase displays (1) molecular optical activity - the phase being composed of optically active molecules and (2) macromolecular optical activity - arising from the macroscopic helical twist induced by the chiral molecules in the phase (sometimes termed form chirality). These features are of immense importance technologically, as many of the applications of such materials depend on one if not both of these phenomena. As would be expected for any optically active molecule, a chiral nematogen should rotate the plane of plane polarized light. This is indeed the case, but in contrast to other optically active materials (e.g. sugars), very large values of rotation are observed (ca. lo3 deg. mm-’ [5]); this may be attributed to the relative phase retardation of the right and left handed components of the plane polarized light as they encounter different refractive indices associated with the macroscopic helical twist of the phase. Rotation of the plane of polarized light usually occurs when the pitch length of the chiral nematic phase is very much longer than the wavelength of the incident light (i.e. p %-A).A second optical property associated with this phase is circular dichroism, whereby the chiral nematic phase will transmit one circularly polarized component of light whilst reflecting the other circularly polarized component. Which circularly polarized component becomes reflected or transmitted depends on the handedness of the macroscopic twist associated with the chiral nematic phase; a right handed helix will transmit the right-handed component whilst reflecting the left-handed circularly polarized component [4]. However, the most noted feature of the chiral nematic phase is its ability to reflect incident white

light selectively, provided that the incident light has a wavelength of approximately the same order as the pitch length of the phase (i.e. il= p ) . Coherently reflected light components experience constructive interference from other reflected wavefronts, giving rise to iridescent colour play (various analogies with Bragg reflection are possible, assuming normal incidence of the light beam). The wavelength or waveband of the reflected light is related to the pitch length by Eq. (1) [8]:

AA=An.p

(1)

where An = optical anisotropy of the phase (or birefringence). The optical purity (or the width) of the selectively reflected component ( A n ) may be modulated to some degree by manipulation of the optical anisotropy ( A n ) of the phase (this is usually achieved by controlling the sp2 or sp3 nature of the mesogen’s chemical structure). Special mention must also be made for the case of obliquely incident light on a chiral nematic phase; here the reflection band is shifted to shorter wavelengths and results in an angle-dependent effect to the viewer. However, this is outside the scope of this chapter and readers are referred to references [lo-121. These optical properties are observed only when the mesophase is in the planar or Grundjeun texture, that is where the helical/optical axis is perpendicular to the glass substrates when a sample is constrained between a microscope slide and cover slip [ 131, and the molecules lie in the substrate plane. There is a second common texture associated with the chiral nematic phase, where the helical axes of domains in the bulk sample are randomly aligned, and this is sometimes referred to as the pseudo focalconic texture; light undergoes normal scattering when the sample is in this texture [5, 131. This texture is easily mechanically

1.2 Formulation and Applications of Thermochromic Mixtures

disturbed to give the selectively reflecting planar texture. Certain chiral nematic liquid crystals (or mixtures) are found to exhibit thermochromism, that is, temperature dependent selective reflection; here the pitch length of such materials or mixtures is often found to have an inverse relationship with temperature and can depend on the nature of the material’s mesomorphism. Thermochromism is found to be at its most spectacular in materials which display chiral nematic phases and underlying smectic phases; this is exemplified for a material with an I-N*SmA* sequence (on cooling) and is shown schematically in Fig. 2. Here the pitch length gradually lengthens from the blue end of the electromagnetic spectrum (i.e. p = 0.4 pm), but an altogether more rapid increase in pitch length is experienced as the chiral nematogen is cooled towards the smectic A phase. This is best explained by the gradual build-up of smectic order on approach to the N*-SmA* transition, and results in startling colour play through to the red end of the electromagnetic spectrum (p=O.7 pm) as the helical structure of the phase becomes unwound (indeed the SmA* phase may be considered as having an infinite pitch length). It should be noted that not all chiral nematogens are either as responsive or behave in precisely

305

the same manner, and indeed some materials are notable for being exceptions to this rule of thumb [ 141. As an aside, it may be of interest to the reader that although selective reflection is usually a phenonemon associated with calamitic liquid crystalline systems, various multiyne materials have recently been demonstrated to show selective reflection as well as a helix inversion in chiral discotic nematic phases [15, 161.

1.2 Formulation and Applications of Thermochromic Mixtures Rarely, if ever, does one particular chiral nematic compound display “ideal” behaviour, which would make it suitable for use in a given application, and normally carefully formulated mixtures of a variety of mesogenic and non-mesogenic components, which may have very different thermodynamic properties, are used. Formulation of mixtures is frequently a complex trade-off of one property over another and is usually achieved by application of the Schrodervan Laar equation [ 17 -201, which allows the thermodynamic characteristics of a par-

1

I

I I I I

I I

Pitch

I I

Length

I

P)

I

I I

I I

Smecuc A*

1 I I I

I

I

C h i d Nematic

Temperature (“C)

I

Isouoplc Liquid

Figure 2. The pitch length- temperature dependence of a chiral nematic liquid crystal.

306


ticular mixture to be predicted theoretically (with some accuracy) before recourse to actual experimental formulation of the mixture. Practical commercial thermochromic mixtures must have the following general characteristics: low melting points, wide operating ranges (i.e. -50- 150“C), short pitch lengths and underlying smectic A* phases to induce the spectacular pretransitional unwinding of the helix of the chiral nematic phase, which results in a visible thermochromic effect. It is usual to employ racemic or partially racemized compounds, as these have the effect of compensating the twist induced by other chiral components, enabling the fine tuning of the colour playtemperature characteristics, although this sometimes has the undesired side effect of extending the blue selective reflection range [3,5,21]. Similarly, the mixing of polar and non-polar liquid-crystalline components may result in the formation of injected smectic phases; these may also be exploited to give wider operating temperature ranges (they are also reported as preventing the extension of the “blue-tail’’ phenomenon) 1221. The colour purity of a thermochromic mixture (An),is related to the birefringence (An) of the mixture, and as mentioned earlier, this may be controlled by judicious selection of components which are either aromatic (sp2 hybridised), or alicyclic (sp3 hybridised) or a combination of the two (sp2- sp3) [ 171. The commercial synthesis of a wide variety of modern chiral nematic materials has made many of these points a little easier to address, in contrast to times when the choice of materials was limited to unstable cholesterol derivatives, azo-compounds, and Schiff’s bases; nevertheless, the final formulation of a mixture is still a complicated process. As may now be more clearly appreciated, the potential uses of chiral nematic liquid crystals depend on either the twisting pow-

er or the thermochromic response of the chiral nematic phase (N”). The former macroscopic property was initially the reason for most of the commercial interest in the use of chiral nematic liquid crystals; here chiral components were employed in electro-optic displays to counter reverse twist domain defects (in low concentrations ca. 1-10% wt.wt) and to sustain the helical twist induced by surface alignment in both the twisted nematic display and supertwist display modes [23, 241. Chiral nematic dopants may also be employed to induce short pitch lengths in White - Taylor Guest - Host displays (this prevents waveguiding of light in the off-state 117, 251) or as circularly dichroic filters 1261. However, the major applications of chiral nematic liquid crystalline materials are in thermometry, medical thermography, non-destructive testing, pollutant sensing, radiation sensing, surface coatings, cosmetics, and printing inks for decorative and novelty applications [3, 51; all of these applications employ either the selective reflective properties or the thermochromic response of the chiral nematic phase, or both. In many of these applications, the thermochromic liquid crystal mixture is rarely utilised as a thin, neat film, but rather as a microencapsulated slurry which is incorporated into a coating; microencapsulation of the thermochromic mixture is usually achieved by complex coacervation using gelatin and gum-arabic to form the microcapsule walls [27]. The reasons for microencapsulation are firstly economic and secondly to protect against and prevent attenuation of the optical properties of the chiral nematic liquid crystals, which are often prone to chemical and photochemical degradation during use. However, this may be reduced to some extent by use of UV filters or free-radical scavengers [3]. The availability of microencapsulated ‘inks’ have led to the increased use of the materials simply

1.3 Classification of Chiral Nematic Liquid Crystalline Compounds

because they may be applied to a variety of surfaces (paper, plastic, fabrics, and metal) by a variety of widely used techniques, e.g., airbrush, screenprinting, gravure, or flexographic means) [3, 281.

1.3 Classification of Chiral Nematic Liquid Crystalline Compounds Despite the wide variety of chiral nematic liquid crystals (and of course low molar mass chiral liquid crystals in general), it is possible to sub-divide them into three class types, according to the relationship of the chiral moiety and the liquid-crystalline core [29]. Firstly, we consider type I; here the chiral centre (or multiplicity of chiral centres) is situated in a terminal alkyl chain attached to the effective liquid-crystalline core. As will be seen later, it is entirely possible that the compound can have two or more chiral terminal groups associated with the molecule. Type I materials are probably the most frequently encountered chiral nematic liquid-crystalline compounds, often

3 07

because of their relative ease of synthesis and because of the availability of suitable chemical precursors. Secondly, type I1 materials: here the chiral centre may be trapped between two liquid-crystalline core units, and the structure resembles a dimer or a twinned molecule. Here, in principle, it is possible to modulate the properties of the molecule by variation of the length of the flexible spacer which carried the chiral group; this is believed to occur via processes which restrict the freedom of rotation about this central axis. However, this type of material has the disadvantage that the core units, which are usually polarisable in nature (i.e. sp2-hybridised carbon skeleton) are separated by a non-polar region (i.e. sp3hybridised carbon skeleton), preventing effective conjugation of the cores which usually leads to destabilisation of any liquidcrystalline characteristics. Thirdly and finally, type 111: here the chiral centre is in some way incorporated into the effective liquid-crystalline core: for example see Fig. 3 . In type 111 materials asymmetry may be achieved either by the presence of a chiral atom in the core or by a particular structural feature which results in gross molecular asymmetry. This stuctural type may be

Type I; terminal chiral chains appended to a liqmd-crystallme core

Type II: flexible chiral spacer chain between two liquid-clystalline cores

Type III: chiral point or structural molecular asymmetry within the liquid-crystalline core

Figure 3. The classification of chiral liquid crystals according to the position of the core unit and chiral moiety.

308

1

The Synthesis of Chiral Nematic Liquid Crystals

of use when attempting to gain the greatest coupling effect between the chiral centre and core to produce strongly twisting dopants. All three types of material are schematically illustrated in Fig. 3. Many of the compounds used as examples in this chapter to illustrate the three classes of chiral nematic structure are not necessarily compounds in which the presence of a chiral nematic phase or its properties were of primary importance to the researchers concerned in the work; for instance some of the materials were developed as potential ferroelectric dopants, but happened to show a chiral nematic mesophase. Also in many cases, the synthetic techniques used and the hazardous nature of some of the reagents employed, along with the poor chemical or photochemical stabilities of the mesogens, would almost automatically preclude their use in any commercial applications (i.e., thermography). However, such materials are of scientific interest in that they help to illustrate the many potential variations of novel molecular structures which may result in a chiral nematic mesophase.

1.3.1 Aspects of Molecular Symmetry for Chiral Nematic Phases Having defined the different forms of chiral nematogen structure with regard to the positioning of the chiral moiety relative to the liquid-crystalline core unit, it is now necessary to describe further and more precisely the exact nature of this structural relationship. It has been understood for many years that optical properties, such as helical twist sense and the direction of rotation of plane polarised light, depend intimately on the absolute spatial configuration of the chiral centre, the distance the chiral centre is sep-

arated from the core, the electronic nature of the substituents attached to the chiral centre and the overall enantiomeric purity of the system in question. These molecular features may be more clearly appreciated with reference to the schematic structure of a type I chiral liquid crystal shown in Fig. 4. Firstly, the absolute configuration of an organic compound is determined using the Cahn, Ingold and Prelog sequence rules which relate the atomic number of the groups attached to the chiral centre to their relative priority over one another (the higher the atomic number, the higher the priority; i.e. C1 has higher priority than H). The resulting order of increasing priority may then be designated as being either (R)- or (S)-; that is rectus or sinister (right or left forms) [4, 301. Additionally, it is necessary to define the distance of the chiral centre from the core (rn + l), as it has been found that the helical twist sense of the resultant chiral nematic phase alternates from odd to even numbers of atoms [ 311. This may be illustrated by considered the following two (S)-4-alkyl-4’-cyanobiphenyls(A and B), in Fig. 5 . Subsequent experimentation by contact studies with other chiral systems (R)- and (S)-, of differing parity revealed the following helical twist sense relationships, entries 1 to 4 in Table 1. These results form the basis of a set of empirical rules termed the Gray and McDonnell rules [ 3 2 ] and are particularly useful in predicting the properties of a chiral nematic phase of a given com-

X and Y may represent polar or non-polar groups; m and p = integers.

Figure 4. A representation of a type I chiral liquid crystal.

1.3 Classification of Chiral Nematic Liquid Crystalline Compounds

309

mathematically as

P = (P .C J 1

A

Abs. config ...(3)-;parity (m+1) ...2 (even, e); rotation of plane polarized light ...d; twist sense...LH.

B Abs. config ...(Sj-; parity (m+1) ...3 (odd, 0):

rotation of plane polarized light ...I; twist sense...RH

Figure 5. The relationship between twist sense, parity, and absolute configuration demonstrated for two chiral nematogens.

pound. The first four entries in Table 1 all correspond to materials which have an electron donating substituent at the chiral point (i.e. CH,-, +I). Electron withdrawing groups, such as C1 or CN (-1) were later demonstrated effectively to reverse these empirical twist sense rules; entries 5 to 8 in Table 1 all reflect this electronic structural change [ 3 3 ] . Finally, the other property which is also strongly dependent on molecular symmetry associated with the chiral centre is the twisting power, P, which is usually expressed Table 1. Rules relating twist sense to absolute configuration, parity and the electronic nature of the substituents at the chiral centre. Absolute configuration

Parity

Electronic nature of substituent

1. ( S ) (S)-

e

+I +I +I +I -I -I -I -I

2. 3. 4. 5. 6. 7. 8.

(R)(R)(S)(5’)(R)(R)-

0

e 0

e

0

e

o

Rotation of plane polarized light

Helical twist sense LH RH RH LH RH LH LH RH

(2)

where p =pitch length, c, = concentration of the chiral solute species, i; a right or left handed system is usually denoted by P being either positive (+) or negative (-), respectively [34, 3.51. This mathematical relationship is usually only applicable to systems which contain low concentrations of the chiral dopant (i), usually bicyclo[2.2.2]octyl> cyclohexyl [5]. This entire class of stable, colourless chiral nematogens turned out to be commer-

During the late 1980s the highly optically pure intermediate (R)-2-(4-hydroxyphenoxy)propanoic acid (RHPP; ee >97% [70]) was employed as the basis of a series of novel thermochromic liquid crystals. RHPP is a bifunctional structure and theoretically allows for extension of the molecule along the molecular long axis at either terminal functional group, to give structures which may be classified as type I or type I1 materials. Additionally, the chemical nature of these groups could be modified to give other varieties of polar linkage (e.g. C 0 2 H converted to either CN or CH,OH), to give variation in the thermodynamic properties of the different structures. Initial work revealed that chiral nematic phases were only obtained when the carboxylic acid moiety of RHPP was converted into either a simple alkyl ester or a cyano group. This behaviour is highlighted by the ( R ) and (R,S)-alkyl 2-( 4-[4-(truns-4-pentylcy-

320


Table 5. Transition temperatures and phase assignments for a series of (R)-and (R,S)-2-{4-[4-(truns-4-pentylcyclohexyl)benzoyloxy]phenoxy) propanoates and a propanonitrile.

Compound no.

61 62 63 64

65

Z C02C3H7 C02C3H7 C02C4H9

C02C4H9

CN

Configuration

Transition temperature ("C)

(R)-

Cr 67.2 (SmA* 60.5) N* 77.9 I Cr 77.0 (Cryst B* 35.8 SmA* 67.9) N 82.0 I Cr 58.1 (SmA* 46.2) N* 67.3 I Cr 70.6 Cr 77.5 (Cryst B* 19.2 SmA* 51.4 N 70.9) I Cr 122.3 (SmA* 92.9) N* 151-6 I

(R)-

(RS)(R)-

clohexyl) benzoyloxy] phenoxy } propanoates (61 - 64) and (R)-2-{4-[4-(truns-4pentylcyclohexyl)benzoyloxy]phenoxy } propanonitrile (65) [71, 721, whose chemical structures and transitions are given in the Table 5. However, analytical determinations performed using 'H nmr and the chiral shift reagent, (+)-europium tris-(D-3-heptafluorocamphorate) revealed that these materials had inherently low enantiomeric excesses (ee). The ee values of the propyl (61) and butyl esters (63) were found to be between 0.69-0.75 on integration of the areas for the aromatic protons ortho to the carboxylate moiety of the trans-4-pentylcyclohexylbenzoate core. The low values of ee have been attributed to the presence of the electronwithdrawing carbonyloxy or cyano groups a to the chiral centre, which readily facilitates racemization, even during the relatively mild synthetic processes performed previously during the synthesis of the compounds. It is also interesting to note that the independently synthesized racemic modifications of these propyl and butyl esters (62 and 64) have noticeably higher melting points and clearing points when compared with their (R)-enantiomers (61 and 63). This behaviour has been noted before in other chiral systems and is an indication of the general influence and importance of enan-

tiomeric purity on a compound's physical properties [72]. This problem of low enantiomeric purity (ee) was circumvented by removing the electron withdrawing group. This was achieved by the reductive cleavage of a benzyl ester function to give the alcohol, using lithium aluminium hydride, and resulting in a series of materials derived from the compound (R)-2-(4-benzyloxyphenoxy)propan1-01(68) [73]. The synthetic route employed is outlined in Scheme 6. The first step involves heating (R)-benzyl 2-(4-hydroxyphenoxy)propanoate (66) with benzyl bromide and potassium carbonate in butanone to give the dibenzyl compound 67. Compound 67 was the reduced to (R)-2-(4-benzyloxyphenoxy)propan-1-01 (68) using lithium aluminium hydride in dry tetrahydrofuran at room temperature. The alkylation of compound 68 was then achieved using sodium hydride and the appropriate alkyl halide in dry N,N-dimethylformamide at room temperature to give the (R)-1-alkoxy-2-(4-benzyloxyphenoxy)propanes (69-75) as colourless oils. These compounds were then debenzylated using hydrogen and palladium-on-charcoal at room temperature and pressure to give the chiral phenols (76-82) which were then subsequently esterified with the appropriate two ring core acid using dicyclohexylcarbo-

1.5 Type I Chiral Nematic Liquid Crystals

32 I

PhCH?Br,

LiAM4, THF, Nr NaH, AlkylBr, H3C

H3C 6 8 0 H

OCnHznil

69-15

H2, Pd-C, EtOH Core Acid, DCC, DMAP, CH2C12,RT H3C

OCnHznil

83-101

76-82

H3C

a = trans- 1,4-cyclohexyl, 1.4-phenyl or 2-fluorophenyl.

b = 1,4-phenyl or 2,3-difluoro-1,4-phenyl. n=lt06

diimide (DCC) and 4-N,N-dimethylaminopyridine (DMAP) to give the target compounds 83-101. Proton NMR and chiral shift reagent studies on various (R)-1-alkoxy-2-{4-[4-(truns4-pentylcyclohexyl)benzoyloxy]phenoxy ] propanes (83 and 84) failed to resolve the presence of any of the other enantiomer, indicating that the material was optically pure (ee 20.98, within experimental error) and that this system was now inherently stable to racemization.

OCnHzn+1

Scheme 6. Synthesis of ( R ) -1alkoxy-2-[4-(4-substituted)phenoxylpropanes.

The methyl to hexyl terminal chain homologous all showed chiral nematic phases, although their phase ranges decreased from 15.2 to 4.4"C as the homologous series was ascended. The most interesting feature of the phase behaviour of these materials was the occurrence of Blue phases near the clearing points of the higher homologues of the series (butyl to hexyl, compounds 83 to 88). This is clearly the result of damped or restricted rotation of the bonds attached to the chiral centre caused by both the prox-

Table 6. The transition temperatures and phase assignments for the ( R ) -1-alkoxy-2- (4-[4-(tran.s-4-pentylcyclohexyl)benzoyloxy]phenoxy Jpropanes.

Compound no.

n

Transition temperatures ("C)

83

I 2 3 4 5 6

Cr, 69.3 Cr, 83.5 Cryst B* 85.5 SmA* 107.5 N* 122.7 I Cr, 43.4 Cr, 59.7 Cryst B* 80.1 SmA* 105.1 N* 112.4 I Cr 54.8 Cryst B 73.9 SmA* 95.8N* 100.8 I Cr 48.8 Cryst B* 73.6 SmA* 89.5 N* 93.7 BP 94.0 I Cr 46.3 Cryst B* 68.1 SmA* 83.2 N* 86.7 BP 86.7 I Cr 44.5 Cryst B* 62.8 SmA* 74.0 N* 78.4 BP 78.4 I

84

85 86

87 88

322


imity of the liquid-crystalline core and the presence of longer peripheral alkyl chains [29]. The transition temperatures and phase assignments are given in Table 6. The esters with 4’-pentylbiphenyl cores were somewhat disappointing in their phase behaviour; all materials showed smectic A* and crystal B* phases; and only the methoxy compound 89 displayed a short chiral nematic phase (3.8 “ C ) .

H3C‘

bCH3

89; Cr 73.3 CrystB* 93.3 SmA* 131.6 N* 135.4 I (“C) [73]

The use of lateral fluoro-substituents in liquid crystals chemistry is well known for influencing physical properties, particularly in supressing smectic phases, as well as depressing both melting points and clearing points [74-791. By use of 2’-fluoro- and 2,3-difluoro-substituents in the biphenyl core, it proved possible not only to reduce both the melting points and clearing points, but also drastically to lower the thermal stability of the smectic A* phases, often to such a degree that room temperature iridescent chiral nematic phases were observed for a number of compounds in two different, but related, series. The acids providing the two different fluoro-substituted cores (4’pentyl-2’-fluorobiphenyl-4-carboxylicacid and 4’-pentyl-2,3-difluorobiphenyl-4-carboxylic acid) were synthesized by well-documented techniques for low temperature lithiation, carboxylation and formation of the boronic acids from aryl bromides as well as palladium (0) catalysed cross-coupling procedures [80-831. It is important to stress the versatility of these methods, the increased use of which has led to the accessibility of numerous structures throughout liquid crystal chemistry, which were previously thought to be too difficult to synthesize easily.

In the first of these fluoro-substituted series, the (R)-1-alkoxy-2-[4-(2’-fluoro-4’pentylbiphenyl-4-carbonyloxy)phenoxy]propanes (90-95), it was found that the 2’-fluorosubstituent destabilizes the ability of the molecules to pack efficiently to such a degree that they prefer to form chiral nematic phases over the more ordered smectic phases observed in their non-fluoro-substituted parents (see compound 89) [841. The first five materials show monotropic smectic A phases at correspondingly low temperatures; furthermore the butyl, pentyl, and hexyl homologues did not crystallize above a temperature of -40 “C (potentially an advantage for microencapsulation). The transition temperatures of this series are shown in Table 7; the clearing points are seen to decrease very rapidly from 8 1.2 to -6.1 “C. A similar, but less rapid decrease in thermal stability of the SmA phase is also observed. The propyloxy and butyloxy compounds (92 and 93) are both of interest in that they show highly iridescent chiral nematic phases at or around room temperature. Spectroscopic measurements, indicate that the homologues of this series have pitch lengths which vary in magnitude between 0.30 and 0.32 ym. Table 7. The transition temperatures and phase assigments of (R)-1-alkoxy-2-(4-(2’-fluoro-4’-pentylbiphenyl-4-carbonyloxy)phenoxy]propanes. F

Compound no.

90 91 92 93 94 95

n 1

2 3

4 5 6

Transition temperatures (“C) Cr 54.3 (SmA* 24.5) N* 81.2 I Cr 40.6 (SmA* 4.9) N* 50.1 I Cr 36.2 (SmA* 6.0) N* 47.4 I Cr -(SmA* -4.1) N* 18.6 I Cr - (SmA* -10.0) N* 7.7 I Cr N* -6.1 I

1 .5

Type I Chiral Nematic Liquid Crystals

323

propanonitrile [72] and (R)-1-methoxy-2( 4- [4-(trans-4-pentylcyclohexyl)-benzoylfluoro-4’-pentylbiphenyl-4-ylcarbonyloxy)- oxyl-phenoxy }propane (83) [73], revealed phenoxylpropanes (compounds 96 to 101), that they show opposite helical twist senses the transition temperatures listed in Table 8, (the compounds are left handed and right show that as would be expected, the inhanded, respectively) as would be predictsertion of a second fluoro-substituent aped for materials with electron acceptor and pears to have little extra effect on the cleardonor groups at the chiral centre [32, 33, ing point over that of the 2’-fluoro-substi851. Interestingly, certain composition mixtuted series [84]. tures displayed either TGBA* phases mediating the chiral nematic to smectic A* tranThe melting points, clearing points and sitions or twist inversion phenomena in the the N*-SmA* temperatures are indeed all chiral nematic phase. slightly higher than for the corresponding The use of the stable, optically pure 2’-fluoro homologues; the SmA* phases all ( R ) -1-alkoxy-2-(4-substituted-phenoxy)occur enantiotropically, indicating greater propane system in conjunction with the apthermodynamic stability, unlike the precedpropriately fluoro-substituted liquid-crysing SmA* phases of the 2’-fluoro series (90 talline cores offers great potential for mateto 95). This overall result may be partly due rials which are suitable for use in thermoto the shielding of the 3-fluor0 substituent chromic mixture formulations [SS]. by the carboxylate linkage and the fact that the second fluoro-substituent effectively makes the liquid crystal core no broader 1.5.5 Miscellaneous Type I (i.e. the second fluoro-substituent has little Chiral Nematic Liquid Crystals effect on the overall geometrical anisotropy of the molecule). The former examples of type I materials are Binary mixture studies involving the not the only examples of the class; many chiral nematogens (R)-2- [(2’-fluor0-4’other forms of novel side chains have also pentylbiphenyl-4-carbonyloxy)phenoxy lbeen investigated. These miscellaneous chiral nematic systems include the following types of material: (R)-and (5’)-l-methylalkTable 8. The transition temperatures and phase assignments of (R)-1-alkoxy-2-(4-(2,3-difluoro-4’-pen- oxy derivatives (102) [87, 881; derivatives of (S)-P-citronellol (103) [89]; (R)-2-chloty l biphenyl-4-carbonyloxy)phenoxy]propanes. ropropanol and (S)-2-ethoxypropanol(lO4) F F 190, 9 11; (S)-2-chloropropyl derivatives (105) [29, 921; (S)-2-halogeno-4-methylpentyl derivatives (106) [29, 931; materials with (2S,3S)-3-propyloxirane groups (107) Compound n Transition temperatures (“C) [29,94]; and (R)-4-(1-propoxyethyl)phenyl no. derivatives (108) [95]. These materials will 96 1 Cr 34.3 SmA* 41.4 N* 85.6 I not be covered in great detail, as many of 97 2 Cr 17.5 SmA* 45.6 N* 74.5 I them were synthesized as potential ferro98 3 Cr 18.2 SmA* 25.1 N* 54.1 I electric materials, nonetheless, they high99 4 Cr 1.4 SmA* 9.5 N* 32.8 I 100 5 Cr 2.6 SmA* 13.6 N* 35.8 I light the use of other novel chiral side 101 6 Cr 0.6 SmA* 15.8 N* 42.1 I chains. Turning now to the second fluoro-substituted series, (R)-l-alkoxy 2-[4-(2,3-di-

324


102; (S)-Abs config.; Cr 71.8 SmC* 89.8 N* 137.4 I ("C) [87, 881 A

103; Cr 79.5 SmC* 116.6 N* 150.0 I ("C) [89]

OCzH5

104; Cr 27.9 (Sm2 16.9) SmA* 45.2 N* 50.3 I ("C) [90,91]

ci 105; Cr 102.6 SmA* 137.0 N* 166.0 I ("C) [29,92]

106;Cr 67.8 SmC* 79.9 SmA* 96.8 TGB A* 100.4N* 128.3 BP 129.4 I ("C) [29, 931

107; R=C,H,; Cr 59 (SmCg 46.2 SmCZ 46.8 SmCt) Ng 106.3 NE 112.1 NE 158.1 BPI 162.9 BPI1 164.6 I ("C) [29, 941

Some of these materials were readily available from commercial sources, others were not and have had to be synthesized from convenient precursors. This has often led to two distinct types of approach: firstly, by employing mild synthetic methods which somehow preserve the optical activ-

ity of a particular system; secondly, where the former method was not possible, asymmetric induction methods have been employed. Here the chiral moiety may be synthesized stereospecifically, for example by employing a-amino acids such as (S)-alanine, (S)-leucine, (S)-valine, or (2S,3S)-isoleucine [29, 92, 931, or by using chiral catalysts or auxiliaries [94,95]. These catalysts and auxiliaries allow a reaction to take place at one specific face of the transition state complex during the reaction, thereby leading to a preponderance of one isomer over others (see also the Sharpless asymmetric epoxidation in Sec. 1.7.3 of this Chapter). One of the more unusual and elegant examples of the uses of a chiral catalyst is in the synthesis of the novel mesogen (R)-1(4'-nonyloxybiphenyl-4-y1) 4-( 1 -propoxyethy1)benzoate (108) [95]; this is outlined in Scheme 7. The achiral starting material, methyl 4-acetylbenzoate (109) was enantioselectively reduced using borane in the presence of the chiral oxazaborolidine (110) (itself synthesized from (S)-(-)-2-diphenylhydroxymethy1)pyrolidine and BH3 : THF [96]) to give the optically active benzyl alcohol (lll),in 89% ee. The (R)-4-( l-propoxyethy1)benzoic acid (112) was then obtained in a 25% yield after the sequence of base hydrolysis, propylation and base hydrolysis procedures. Compound 112 was then esterified in the standard manner to give the target compound (108). (R)-1-(4'nonyloxybiphenyl-4-y1) 4-( 1-propoxyethyl)benzoate (108) showed only a very short chiral nematic (N*) phase of range 0.5 "C, after undergoing a direct SmC*-N* phase transition at 104.5 "C.

1.6 Type 11 Chiral Nematic Liquid Crystals 110, BH,, THF.

H3C02C H:*

325

* H3CO&

3

111

109

I

NaOH, MeOH; (ii) NaH, CSH,I; (iii) NaOH, MeOH (I)

C9H,90 ~

O

Z

C

~

-

c OC3H7

(i) SOCI,; (ii) ArOH, pyridine. H

3

H 0 2 c ~ c H 3 OC3H7

112 108; Cr98 SmC' 104.5 N* 105 I ("C) [95]

110 [961

Scheme 7. Asymmetric synthesis of (R)-l-(4'-Nonyloxybipheny1-4yl) 441-propoxyethyl)benzoate.

1.6 Type I1 Chiral Nematic Liquid Crystals

1.6.1 Azomethine Ester Derivatives of (R)-3-Methyladipic Acid

Achiral twin compounds, which possess two liquid-crystalline cores separated by a flexible spacer, are now well known and documented. As well as being pre-polymer model systems, they also give large variations in transition temperatures which are dependent on the length of the flexible spacer and frequently give incommensurate smectic phases [97- 1001. However, examples of chiral materials which may be categorized in this manner are not numerous, and the majority of these examples concern the use of flexible, chiral linking groups based upon (R)-3-methyladipic acid [ 1011051, derivatives of lactic acid [106, 1071or optically active diols 11081 between two liquid-crystalline moieties. This class of chiral materials, however, remain an interesting subject in that, in principle, it is possible to modulate and sterically restrict motion about the chiral centres by varying the length of the flexible linking spacer unit.

The first examples of this kind of material belong to a homologous series of bis-azomethines (113-114) which have the general structure represented in Table 9 [loll. The materials were prepared by esterification of (R)-3-methyladipic acid with 4-hydroxybenzaldehyde to the bis-[bforrnylphenyl] (R)-3-methyladipate. This was then condensed with the appropriate 4-alkoxyaniline to give the desired bis-azomethine dimer. In this homologous series, only the early members (ethoxy, butoxy and hexyloxy, compounds 113 to 115) showed chiral nematic phases; the transition temperatures of these materials are given in Table 9.

326


Table 9. The transition temperatures and phase assignments of diesters derived from the chiral3-methyl adipic acid and 4-hydroxybenzylidene-4'-alkoxyanilines.

Compound no.

n


113

2 4 6

Cr 156.3 N* 236.6 I Cr 154.6 Sml 158.5 Sm2 169.3 N* 210.9 I Cr 122.8 Sml 140.0 Sm2 174.7 SmA* 190.0 N* 195.5 I

114 115

~~~

~

Where Sml and Sm2 represent unidentified smectic phases.

1.6.2 Novel Highly Twisting Phenyl and 2-Pyrimidinylphenyl Esters of (R)-3-Methyladipic Acid A more recent continuation of this theme using (R)-3-methyladipic acid, was the systematic study of dimeric or twin structures which are capable of forming highly twisted helical structures [ 102- 1051.These examples, differ from the previously mentioned bis-azomethines in that they employ 2-pyrimidinylphenyl (116 and 117) and phenyl core units (118); they were made simply by esterification of (R)-3-methyladipic acid with the appropriately substituted phenol using dicyclohexylcarbodiimide (DCC) and the catalyst 44,N-dimethylaminopyridine (DMAP). The structures and phase transitions of members of these two classes are given in structures 116 to 118.

The transition temperatures for the 2-pyrimidinylphenyl based compounds (116 and 117) clearly show that they display only rather short range, monotropic chiral nematic phases. Bearing this in mind, it is not surprising that the smaller twin with a phenyl core (118) does not form a chiral nematic phase. Studies which employed these three materials as dopants have shown conclusively that the chiral nematic phases of the test mixtures have particularly short pitch lengths ( p = 16- 22 pm) and right handed twist senses. This contrasts noticeably with the monomeric materials which have similar structures, for example (S)-4-(4-[2-(4hexyloxyphenyl) - 5 -pyrimidinyl] -phenyl } 3-methylpentanoate (119), which has a considerably longer pitch length ( p = 79 pm).

119; Cr 118.2 (SmC* 185.4) N* 195.8 I ("C); p = Fma, LH-helix [102, 1031

It has been suggested that the marked difference in pitch lengths between the twins and monomeric materials is due in part to the further restriction of rotational motion about the chiral centre caused by the presence of a second bulky core moiety, result-

116; n = 7; Cr 139.6 (N* 136.9) I ("C); p = 19 pm', RH-helix [102-1041 117; n = 8; Cr 130.9 (N* 127.7) I ("C); p = 22 pm",RH-helix [102-1041

C8H170 - @ 0 2 c & C 0 2 ~

OC,H

17

118; mp = 56.7"C, p = 16 pna, RH-helix [102-1041

a Corresponds to a measurement made with a 2 wt% mixture in 6CB.

1.7 Type 111 Chiral Nematogens

ing in a more tightly twisting helical structure. However, if this was entirely true, then a similar increase in spontaneous polarization of the induced SmC* phases, which are also present in the test mixtures doped with twins, should also be observed. This is not the case, and this may possibly be due to the transverse dipole of the twin aligning perpendicularly to the C2 axis of the chiral smectic C phase [ 1021.

1.6.3 Chiral Dimeric Mesogens Derived from Lactic Acid or 1,2-Diols

327

(R,R)-2,3-butandiol, has shown the diesters to have high helical twisting powers (p) when used as dopants in suitable nematic mixtures. However, only one of these materials is known to show a liquid-crystalline phase; this is a derivative of (R,R)-2,3-butanol (122) [IOS]. The high thermal stability of the chiral nematic phase is not surprising, considering the size of the liquid-crystalline core (4'-(trans-4-pentylcyclohexyl)biphenyl-4-carboxylic acid); the chiral nematic phase occurs between 212 and 255 "C. C5H11

C5Hll

Other attempts have been made to employ the (R)-2-oxypropanoyloxy moiety as a chiral spacer between identical [ 1061 and dissimilar [7 1, 1071 liquid-crystalline core systems, typical structures are given by compounds 120 and 121.

122; Cr 212 (SmX* 197) N* 255 I ("C) [lo81

This compound has been demonstrated to give highly twisted chiral nematic phases when used as a dopant and shows a helix in-

120; Cr 104.9 (SmA* 80.4 N* 83.7) I ("C) [lo61

Compound 120 shows a short monotropic chiral nematic and smectic A* phase, whilst 121 shows a short enantiotropic chiral nematic and a monotropic smectic A* phase. From this it may be concluded that the lactic acid derived (R)-2-oxypropanoyloxy moiety is not particularly suited to sustaining liquid crystal phases; this may either be partly due to poor conjugation between the liquid crystalline cores or because of the non-linear nature of molecules. Research on diesters derived from the optically active diols, (S)- 1,2-propandiol and

version at approximately 60°C in a commercially available wide range nematic mixture.

1.7 Type I11 Chiral Nematic Liquid Crystals This class of chiral mesogen contains many structurally unusual and interesting liquid

328


crystal materials. Here the chirality is imparted by the presence of either a chiral atom situated within the core, or by the generation of gross molecular asymmetry as a result of the core’s overall spatial asymmetry. It may also be recalled from an earlier section on molecular symmetry (Sec. 1.3.1), that the chirality of a liquid-crystalline system may be increased if the chiral centre is brought closer to the mesogenic core, due to restricted motion of groups around the chiral centre [29]. This increase in chirality may manifest itself in many ways, such as the shortening of helical pitch length or the increase in spontaneous polarisation of a chiral dopant. Therefore, it may be appreciated that incorporation of the asymmetric centre in the core, to create a chiral core, is an attractive method of trying to develop a mesogen capable of forming a very highly twisted helical structure (i.e. a short pitch chiral nematic phase). Examples of these less common systems include the following compound types: twistanol (or tricycl0[4.4.0.0~~~]decane) derivatives [ 1091; cyclohexylidene ethanones [ 110, 1111; chiral oxiranes [112,1131; chiral 1,3-dioxolan4-ones [ 1141; substituted stilbene oxides [ 1151; chiral dioxanyl derivatives [ 1161; nitrohydrobenzofuran derivatives [ l 171 and cyclohexanes [ 118,1191. Although many of these systems show chiral nematic phases, their usefulness is severely limited for a number of reasons; the awkward and expensive synthetic routes, the necessity for inefficient and frequently impractical resolution techniques, and in many cases their ultimate chemical or photochemical instability.

1.7.1 Tricyc10[4.4.0.0~~~]decane or Twistane Derived Mesogens

has been incorporated into a number of liquid-crystalline (R)-(+)-8-alkyltwistanyl 4-(trans-4-pentylcyclohexyl)benzoates or 4’-pentylbiphenyl-4-carboxylates(130-132), some of the members of these series are reported as showing chiral nematic phases [ 1091.The twistane ring system has D, symmetry and may be viewed as consisting of four fused boat form cyclohexyl rings which all twist in the same sense; using the Cahn, Ingold and Prelog selection rules, the two enantiomeric forms may be classified as having P- or M-helicity [30]. The (R)-(+)8-alkyltwistanol moiety was prepared by use of a six step synthetic route, starting from the disubstituted cyclohexan- 1,5dione (123) shown below in Scheme 8. The first two steps, that is the stereoselective cyclization in the presence of (S)-(-)proline to give the bicyclic diketone (124) and the hydrogenation of the double bond formation during the condensation step to give compound 125, are crucial in setting up the appropriate stereochemistry necessary for the acid-catalysed cyclization step which results in the formation of the basic twistance core (126). Of the five materials synthesized in this way, only three show chiral nematic liquid crystal phases, as listed in Table 10. It is also of interest to note that compounds 131 and 132 are reported to show anomalous pitch dependency in their chiral nematic phase; the pitches are both reported to increase from 1.1 to 1.6 pm with increasing temperature.

1.7.2 Axially Chiral Cyclohexylidene-ethanones

Solladie and Zimmerman have reported a series of novel chiral liquid crystals which The optically active twistane ring, more are believed to be the first to incorporate a correctly named tricyc10[4.4.0.0~,~]decane, molecular unit which possesses axial chiral-

1.7

128

329

126

127

I LiAlH4

Type 111 Chiral Nematogens

ArCOCI,

OH pyridine

C5Hll

129

130-132 where R = C3H7 or CSH11.

Scheme 8. Synthesis of (R)-(+)-8-twistanol containing mesogens.

Table 10. The mesomorphic behaviour of (R)-(+)-8twistanol derivatives. where R1 = alkyl, alkoxy, nitrile and R2 = alkyl or mcthyleneoxy.

Compound no.

X

R

Transition temperatures ("C) H

130 131 132

Ph") Ph Ch")

C3H, C,H,, CSH,,

Cr 94.2 N* 119.2 I Cr71.8N" 126.41 Cr 65.0 N* 124.7 I

Figure 7. (a) The general structure of a cyclohexylidene ethanone. (b) Axial chirality of the cyclohexylidene moiety.

Where Ph denotes 1,4-phenyl and Ch denotes trans1,4-cyclohexyl.

')

ity; these are the substituted biphenylyl cyclohexylidene ethanones of the general structure shown in Fig. 7(a) [110, 11 11. The axial chirality is the consequence of two perpendicular planes associated with the R, and hydrogen substituents on the C-4 carbon atom of the cyclohexyl ring and the alkene substituents, R , and H; this is more clearly seen in Fig. 7(b). The optically active compounds were obtained by a series of elegant stereoselective reactions, outlined in Scheme 9. The chiral sulfoxide (134) was obtained from the reaction of the Grignard reagent of

a bromo-(4-substituted cyclohexy1)methane (133) and (S)-(-)-methyl sulfinate. Compound 134 was then stereoselectively acylated using lithium di-isopropylamide (LDA) at -78 "C with an appropriately substituted aroyl chloride, to give the diastereoisomeric sulfoxides (135- 136). The (R,R)-and (S,R)-diastereoisomers may both be obtained as either the thermodynamic or the kinetic product of the reaction process. The final step involves the stereoselective pyrolytic elimination of the sulfoxide group to give the ( S ) - or (R)-cyclohexylidene ethanones (137 and 138) from the diastereoisomeric (R,R)- or (S,R)-sulfoxides (135 and 136).

330


(i) LDA, THF, -78 OC; (ii) ArCOC1, -78 'C.

Table 11. Mesomorphic behaviour of a variety of arylcyclohexylidene ethanones.

Compound no. 139 140 141

Configuration

(0 (0

(9-

Rl

R2


C5H1 1

CHZOCZH,

CH3 CN

C5H1 1 C5H11

Cr 43 SmX* 63 N* 67 I Cr 65 N* 124 I Cr 102 SmX* 113 N* 135 I

SmX* = represents an unidentified smectic phase.

Of the seven optically active cyclohexylidene ethanones synthesized, only three showed chiral nematic phases; these materials are listed in Table 11 . However, the conjugated nature of these materials makes them particularly photochemically unstable; irradiation of a racemic cyclohexylidene ethanone with UV light has been shown to result in the rapid isomerization of its double bond in a few hours to give compounds of the general structure (142), as well as the oxidation product, 4'-pentylbiphenyl-4-carboxylic acid.

142

Nonetheless, despite this poor photochemical instability, these materials un-

equivocally prove that materials possessing axial chirality are capable of forming chiral nematic phases.

1.7.3 Chiral Heterocyclic Mesogens A number of heterocyclic type I11 systems have been investigated, primarily as ferroelectric dopants, but a number of the materials do display short (sometimes unstable) chiral nematic phases. Notable examples of systems based on three-membered ring heterocycles are probably best demonstrated by the materials containing the (2R,3S)-2oxirane carboxylic acid unit [ 1121 and trans-stilbene oxides [ 1 151. The synthesis of the oxirane units is of interest as it is achieved by use of the Sharp-

1.7 Type 111 Chiral Nematogens

less asymmetric epoxidation procedure by treatment of either cis- or trans-allylic alcohols with a stoichiometric mixture of L-(+)diethyl tartrate, titanium isopropoxide and t-butyl hydroperoxide at low temperature to give the appropriate epoxide [ 112,113,120, 1211. This process is demonstrated in the synthesis of (2R,3S)-(-)-4-heptoxyphenyl 3- [truns-4-(truns-4-pentylcyclohexyl)cyclohexyl]oxirane-2-carboxylate (146) shown in Scheme 10 [113]. The use of a further mild oxidation and neutral esterification methods ensure that ring opening of the epoxide ring is minimized. As can be seen from the transition temperatures of compound 146, the chiral nematic phase has quite a high thermal stability, presumably a direct result of the two cyclohexane rings which are known to promote high clearing points [49]; the material also has an underlying smectic A phase. Interestingly, this form of epoxide is somewhat more stable than other examples (i.e. compound 107 [94]) because the electron-withdrawing carboxyl moiety reduces the basicity of the oxirane ring, reducing the tendency towards ring opening processes.

-

CSHll

OH

143

Ti('OPr)4,L-(+)-DET, 'BuOOH, CH2Cl2,-23 "C.

144

C5hl

' I

RUC13, NaI04, CC14, CH,CN, H20, RT. 0 CO2H

* *

145

4-hcptoxyphenol, DCC, DMAP, C H Z C I ~RT. ,

33 1

Larger chiral heterocyclic core systems have been synthesized, for example chiral 1,3-dioxany1-4-ones (147) [ 1141 methyldioxanyl (148) [I 161 and 2-alkyl-2,3-dihydrobenzofuran (149) [ 1171 derived mesogens, and the phase behaviour and transition temperatures of these materials are shown below.

147: Cr 71 SmC* 75 N* 85 I ("C) [ I 141

148; Cr 52 SmA* 57.4 N* 100.5 I ("C) [ I 161

CeHi70

w z

C6H13

149; Cr 115 SmC* 140 SmA* 183 N * 185 I ("C) 11171

1.7.4 Chiral Mesogens Derived from Cyclohexane A number of elegant attempts have also been made to employ chiral cyclohexane rings as part of the liquid-crystalline core; the approaches to these materials have usually involved the use of either enantiospecific aluminium trichloride catalysed Diels -Alder reactions (150) [ 1181 or the chiral reducing agent alpine boramine on unsaturated cyclohexyl derivatives (151) followed by palladium (0) catalysed coupling procedures [119]. However, the full development and potential of such mesogens still remains a relatively unexplored field.

146; Cr52.0 SmB* 121.0 SmA* 159.7 N* 167.5 I ("C) [I131

Scheme 10. Synthesis of (2R,35')-(-)-4-Heptoxyphenyl 3-[trans-4-(truns-4-pentylcyclohexyl)cyclohexyl Ioxirane-2-carboxylate.

150: Cr 79 S2 94 S , 113 SmC* I32 SmA* I33 N* 150 I ("C) [I181

332


H,CO‘

151; Cr 120.1 SmA* 127.4 N* 139.9 I (“C) [119]

1.8 Concluding Remarks As has been stressed throughout this chapter, the development of chiral nematic liquid-crystalline materials has often taken its lead from the inadequacies and unsuitability of many of the existing materials which have been employed in particular technological roles. This materials development process is perhaps most clearly evident in the development of the stable, colourless ester derivatives which utilise the (S)-2-methylbutyl side chain, particularly as this evolution is easy to trace from the early sterolbased mesogens, to the chiral azobenzenes through to the chiral azomethine mesogens. As well as being commercially successful, these materials also led to the development of ground rules which relate the nature of the chemical structure to the physico-chemical properties. This has most importantly led to a certain degree of selectivity in the manipulation of properties during the process of choosing a material for any given application. The fact that these materials have relatively simple structures, especially when compared with those of the ‘exotic’ chiral nematogens, is of benefit and importance in that is makes them more readily accessible and therefore more economically viable at a commerical level. Nevertheless, the advent of certain synthetic methods (i.e. the palladium (0) catalysed cross-coupling reactions) has led to a number of notable issues such as improvements in the synthesis of known materials, improvements of physical characteristics as a result of minor

structural modifications (i.e., use of lateral fluoro-substituents) and the generation of entirely novel and frequently exotic chiral mesogens (i.e., twistanol derivatives or cyclohexylidene ethanones). These ‘exotic’ chiral systems demonstrate the myriad of structural variations possible, despite some being highly impractical. Nevertheless they are of great interest from a purely scientific stand point; these materials have usually been used to probe experimentally some facet of the relationship between chirality and molecular structure.

1.9 References [1] F. Reinitzer, Monatsh. Chem. 1888, 9,421. [2] L. Lehmann, Z. Phys. Chem. 1889,4,462. [3] I. Sage in Liquid Crystals: Applications and Uses, Vol 3 (Ed.: B. Bahadur), World Scientific, Singapore 1992, Chapter 20. [4] J. W. Goodby, J. Muter. Chem. 1991, 1, 307318. [5] D. G. McDonnell in Thermotropic Liquid Crystals (Ed.: G. W. Gray), John Wiley, Chichester 1987, Chapter 5. [6] D. M. Makow, Colour Research andApplication 1979,4,25-32. [7] J. L. Fergason, Sci. Am. 1964,211, 77-85. [8] J. L. Fergason, Mol. Cryst. 1966, 1 , 293-307. [8] J. L. Fergason, Mol. Cryst. 1966, 1, 309-323. [9] J. L. Fergason, Appl. Optics 1968, 7, 17291737. [lo] D. W. Berreman, T. J. Scheffer, Phys. Rev. Lett. 1970, 25, 557. [ l l ] R. Dreher, G. Meier, Phys. Rev. A 1973, 8, 1616- 1623. [12] A. Saupe, G. Meier, Phys. Rev. A 1983, 27, 2196 -2200. [13] Y. Bouligand, J. Phys. (Paris) 1973, 34, 603614. [14] T. Harada, P. Crooker, Mol. Cryst. Liq. Cryst. 1975,30,79-86. [15] D. Kriierke, H.-S. Kitzerow, G. Heppke, V. Vi11, Ber. Bunsenges. Phys. Chem. 1993, 97, 13711375. [16] M. Langner, K. Praefcke, D. Kriierke, G. Heppke, J. Muter: Chem. 1995,5,693-699. [17] Ian Sage in Thermotropic Liquid Crystals (Ed.: G. W. Gray), John Wiley, Chichester, 1987, Chapter 3.

1.9 References [ 181 D. Coates in Liquid Crystals: Applications an,d

Uses, Vol 1 (Ed.: B. Bahadur), World Scientific, Singapore, 1990, Chap. 3. [I91 D. S. Hulme, E. P. Raynes, K. J. Harrison, J. Chem. Soc., Chem. Comm. 1974,98-99. [20] I. Schroder, Z. Phys. Chem. 1893, / I , 449-465. [21] Liquid Crystal Information Booklet, Merck UK Ltd, Poole, Dorset, UK. [22] J. Constant, D. G. McDonnell, E. P. Raynes, Mol. Cryst. Liq. Cryst. 1987, 144, 161 -168. [ 2 3 ] E. P. Raynes, Electron. Lett. 1973, 9, 118. [24] P. A. Breddels, H. A. van Sprang, J. Bruinink, 1. Appl. Phys. 1987, 62, 1964-1967. [25] D. L. White, G. N. Taylor, J. Appl. Phys. 1974, 45,4718-4723. [26] M. Schadt, Ben Sturgeon Memorial Lecture, The British Liquid Crystal Society Conference. 28-30 March, 1993, Manchester, UK. [27] J. E. Vandegaer in Microencupsulation ProceSse.7 and Applications (Ed.: J. E. Vandegaer). Plenum Press, New York, 1974, Chapter 2. [28] Uncredited article, Polym. Paint. Col. J., 1990, 180 (4255), 118. [29] J. W. Goodby, A. J. Slaney, C. J. Booth, I. Nishiyama, J. D. Vuijk, P. Styring, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1994, 243, 231 -298. [30] R. S . Cahn, C. K. Ingold, V. Prelog, Angew. Chem. Int. Ed. 1966, 5, 385-415. [31] G. W. Gray, D. G. McDonnell, Electron Lett. 1975, 11, 556. 1321 G. W. Gray, D. G. McDonnell, Mol. Cryst. Liq. Cryst. 1977,34. 21 1-217. [33] J. W. Goodby. Science 1986, 231, 350. [34] G. SolladiC, R. G. Zimmermann, Angew. Chem. Int. Ed. Engl. 1984, 348-362. [35] G. Gottarelli, G. P. Spada, Mol. Cryst. Liq. Cryst. 1985,123,377-388. [36] J. March, Advanced Organic Chemistry: Reactions, Mechanisms and Structure, 3rd ed. WileyInterscience, New York, 1985, Chap. 4, pp 107 109. [37] C. J . Booth, D. A. Dunmur, J. W. Goodby, J. S . Kang, K. J. Toyne, J. Muter. Chem. 1994, 4 , 747-759. [3 8 ] G. Friedel, Ann. Phys. (Paris) 1922, 18, 273. [39] F. M. Jaeger, Rec. Trav. Chim. 1906,25, 334. [40] E. M. Barrall 11. R. S . Porter, J. F. Johnson, J. Phys. Chem. 1967, 71, 1224- 1228. [41] G. W. Gray, J . Chem. Soc. 1956, 3733. [42] H. Baessler, M. M. Labes, J. Chem. Phys. 1970, 52,631-637. [43] H. Baessler, P. A. G. Malya, W. R. Nes, M. M. Labes, Mol. Cryst. Liq. Cryst. 1970,6,329-338. [44] F. F. Knapp, H. J. Nicholas, J . Org. Chem. 1968, 33,3995 -3996. [45] F. F. Knapp, H. J. Nicholas, J. P. Schroeder, J . Org. Chem. 1969,34,3328-3331. [46] F. F. Knapp, H. J. Nicholas, Mol. Cryst. Liq. Cryst. 1970, 6, 319-328.

333

[471 D. Demus, H. Zaschke, Fliissige Kristalle in Tabellen /I, VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig, 1984. [481 C. J. Booth, J. P. Hardy, 0. C. Lettington, K. J. Toyne, J. W. Goodby, G. W. Gray, Unpublished results, 1991. [49] K. J. Toyne in Thermotropic Liquid Crystals (Ed.: G. W. Gray), John Wiley, Chichester, 1987, Chapter 2. [50] J. March, Advanced Organic Chemistry: Reactions, Mechanisms and Structure, 3rd ed., Wiley Interscience, New York, 1985, Chapter 1 I , p471. [S11 M. Tsukamoto, T. Ohtsuka, K. Morimoto, Y. Murakawi, Jup. J. Appl. P h y . 1975, 14, 13071312. [S2] Y. Y. Hsu, D. Dolphin, Mol. Cryst. Liq. Cryst. 1977,42,319-325. [53] J . A. Castellano, Ch. S . Oh, McCaffrey, Mol. Cryst. Liq. Cryst. 1974, 27, 419-429. [S4] G. Heppke, H. Marschall, P. Nurnburg, F. Oestreicher, G. Scherowsky, Chem. Ber. 1981, 114,2501 -2518. [ S 5 ] P. Keller, Ann. Phys. (Paris) 1978,3, 139- 143. [56] D. Dolphin, Z. Muljiani, J. Cheng, R. B. Meyer, J . Chem. Phys. 1973,58, 413. [57] W. Helfrich, Ch. S. Oh, Mol. Cryst. Liq. Cryst. 1971,14,289-292. [58] D. Coates, K. J. Harrison, G. W. Gray, Mol. Cryst. Liq. Cryst. 1973, 22, 99- 122. [59] D. Coates, G. W. Gray, Mol. Cryst. Liq. Cryst. 1976, 34, 1 - 5 . [60] E. M. Elashvili, G. S . Chilaya, S . M. Aronishidse, M. I. Brodzeli, K. G. Dshaparidse, Svohshch. Akad. Nuuk. Gruz. SSR 1976,81, 105. [61] Y. Y. Hsu, D. Dolphin, Mol. Cryst. Liq. Cryst. 1977,42,327-340. [62] J. Doucet, P. Keller, A. M. Levelut, P. Porguet, J . Phvs. (Paris) 1978, 39, 548-549. [63] G. W. Gray, K. J. Harrison, J. A. Nash, Electron. Lett. 1973, 9, 130. [64] G. W. Gray, D. G. McDonnell, Mnl. Cryst. Liq. Cryst. 1976,37, 189-21 1. [6S] B. H. Klanderman, T. R. Criswell, J . Am. Chem. SOC.1975,97, 1585-1586. [66] G . W. Gray, D. G. McDonnell, Mol. Cryst. Liq. Cryst. 1978, 48, 37 -52. [67] Y. Y. Hsu, Mol. Cryst. Liq. Crvst. 1977, 42, 263-271. (681 M. A. Tius, X. Gu, J. W. Truesdell, S . Savariar, D. K. Yang, P. P. Crooker, Mol. Crjst. Liq. Cryst. 1987, 150h, 247-255. (691 M. A. Tius, X . Gu, J. W. Truesdell, S. Savariar, P. P. Crooker, Synthesis 1988, 36-40. 1701 P. Le Gras, Personal communication, Zeneca FCMO, Huddersfield, UK, 1988. 1711 C. J. Booth, G. W. Gray, K. J. Toyne, J. P. Hardy, Mol. Cryst. Liq. C y s t . 1992, 210, 3 1 51.

334


[72] C. J. Booth, J. W. Goodby, J. P. Hardy, 0. C. Lettington, K. J. Toyne, Liq. Cryst. 1994,16,925 -940. [73] C. J. Booth, J. W. Goodby, J. P. Hardy, 0. C. Lettington, K. J. Toyne, J. Muter. Chem. 1993, 3,821 -832. [74] P. Balkwill, D. Bishop, A. Pearson, I. Sage, Mol. Cryst. Liq. Cryst. 1985, 123, 1- 13. [75] V. Reiffenrath, J. Krause, H. J. Plach, G. Weber, Liq. Cryst. 1989,5, 159- 170. [76] C. Viney, R. J. Twieg, T. P. Russell, L. E. Depero, Liq. Cryst. 1989,5, 1783- 1788. [77] C. Viney, T. P. Russell, L. E. Depero, R. J. Twieg, Mul. Cryst. Liq. Cryst. 1989,168,63 - 82. [78] C. Vauchier, F. Vinet, N. Maiser, Liq. Cryst. 1989,5, 141-151. [79] M. A. Osman, Mol. Cryst. Liq. Cryst. 1985,128, 45-63. [SO] J.-M. Fu, M. J. Sharp, V. Snieckus, Tetrahedron Lett. 1988, 29, 5459-5462. [81] S. Gronowitz, A. B. Hornfeldt, Y. H. Yang, Chemicu Scriptu 1986,26, 3 11- 3 14. [82] G. W. Gray, M. Hird, D. Lacey, K. J. Toyne,Mul. Cryst. Liq. Cryst. 1989,172, 165- 189. [83] G. W. Gray, M. Hird, D. Lacey, K. J. Toyne, J. Chem. Suc., Perkin Trans. 2 1989,2041 -2053. [84] C. J. Booth, J. W. Goodby, J. P. Hardy, 0. C. Lettington, K. J. Toyne, J. Muter. Chem. 1993, 3,935-941. [85] C. J. Booth, I. W. Goodby, J. P. Hardy, K. J. Toyne, Liq. Cryst. 1994, 16, 43-51. [86] C. J. Booth, J. W. Goodby, G. W. Gray, J. P. Hardy, K. J. Toyne, Eur. Put. Appl. 1992,230, 392. [87] K. Terashima, M. Ichihashi, M. Kikuchi, K. Furukawa, T. Inukai, Mol. Cryst. Liq. Cryst. 1986, 141,237-244. [88] T. Inukai, S. Saitoh, H. Inoue, K. Miyazawa, K. Terashima, K. Furukawa, Mol. Cryst. Liq. Cryst. 1986,141,251-266. [89] E. Chin, J. W. Goodby, J. S. Patel, J. M. Geary, T. M. Leslie, Mul. Cryst. Liq. Cryst. 1987, 146, 325 -339. [90] B. Otterholm, C. Alstermark, K. Flatischler, A. Dahlgren, S . T. Lagerwall, K. Sharp, Mol. Cryst. Liq. Cryst. 1987, 146, 189-216. [91] C. Alstermark, M. Nilsson, B. Otterholm, Mul. Cryst. Liq. Cryst. 1987, I50b, 277-287. [92] A. J. Slaney, J. W. Goodby, Liq. Cryst. 1991, 9, 849- 861. [93] A. J. Slaney, I. Nishiyama, P. Styring, J. W. Goodby, J. Muter. Chem. 1992,2, 805-810. [94] P. Styring, J. D. Vuijk, A. J. Slaney, J. W. Goodby, J. Muter Chem. 1993,3, 399-405. [95] T. Kusumoto, T. Ueda, T. Hiyama, S. Takehara, T. Shoji, M. Osawa, T. Kuriyama, K. Nakamura, T. Fujisawa, Chem. Lett. 1990, 523-526. [96] E. J. Corey, R. K. Bakshi, S. Shibata, J. Am. Chem. SOC. 1987,109,5551-5553.

[97] A. C. Griffin, T. R. Britt, J. Am. Chem. SUC. 1981,103,4957-4959. [98] J. W. Emsley, G. R. Luckhurst, G. N. Shilstone, I. Sage, Mul. Cryst. Liq. Cryst. 1984,102,223233. [99] J. L. Hogan, C. T. Imrie, G. R. Luckhurst, Liq. Cryst. 1988, 3, 645 - 650. [loo] G. S. Attard, S. Garnett, C. G. Hickman, C. T. Imrie, L. Taylor, Liq. Cryst. 1990, 7,795 -508. [loll J. Barberi, A. Omenat, J. L. Serrano, Mol. Cryst. Liq. Cryst. 1989, 166, 167-171. [lo21 A. Yoshizawa, I. Nishiyama, J. Muter. Chem. 1994,4,449-456. [lo31 I. Nishiyama, H. Ishizuka, A. Yoshizawa, Ferruelectrics 1993, 147, 193-204. [lo41 I. Nishiyama, A. Yoshizawa, Liq. Cryst. 1994, 17,555-569. [105] I. Nishiyama, M. Saito, A. Yoshizawa, Poster at the 15th ILCC, Budapest, Hungary, 1994. [lo61 M. Marcos, A. Omenat, J. L. Serrano, Liq. Cryst. 1993,13,843-850. [lo71 C. J. Booth, J. P. Hardy, J. W. Goodby, K. J. Toyne, Unpublished results. [lo81 G. Heppke, D. Lotzsch, F. Oestreicher, Z. Nuturforsch. 1987,42a, 279-283. [lo91 R. Ch. Geivandov, I. V. Goncharova, V. V. Titov, Mol. Cryst. Liq. Cryst. 1989, 166, 101103. [110] G. SolladiB, R. Zimmermann, J. Org. Chem. 1985,50,4062- 1068. [I 111 G. SolladiC, R. G. Zimmermann, Angew. Chem., Int. Ed. Engl. 1985,24, 64-65. [112] G. Scherowsky, J. Gay, Liq. Cryst. 1989, 5, 1253- 1258. [I131 G. Scherowsky, J. Gay, N. K. Sharma, Mol. Cryst. Liq. Cryst. 1990, 178, 179-192. [I141 G. Scherowsky, M. Sefkow, Mul. Cryst. Liq. Cryst. 1991,202,207-216. [115] B. F. Bonini, G. Gottarelli, S. Masiero, G. P. Spada, Liq. Cryst. 1993, 13, 13-22. [116] R. Buchecker, Oral Presentation at the 13th ILCC, Vancouver, British Columbia, Canada, 1990. [117] H. Matsutani, K. Sato, T. Kusumoto, T. Hiyama, S . Takehara, H. Takazoe, T. Furukawa, Poster at the 15th ILCC, Budapest, Hungary, 1994. [ 1181 Z. Li, B. M. Fung, R. J. Twieg, K. Betterton, D. M. Walba, R. F. Shao, N. A. Clark, Mol. Cryst. Liq. Cryst. 1991,199, 379-386. [ I 191 S. J. Lock, M. Hird, J. W. Goodby, K. J. Toyne, J. Muter. Chem. 1995,5,2175-2182. [ 1201 Y. Gao, R. M. Hanson, J. M. Klunder, S. Y. KO, H. Masamune, K. B. Sharpless, J. Am. Chem. SOC. 1987,109,5765-5780. [121] K. B. Sharpless, T. Katsuki, J. Am. Chem. SUC. 1980,102,5974-5976.


2 Chiral Nematics: Physical Properties and Applications Harry Coles

2.1 Introduction to Chiral Nematics: General Properties The discovery of thermotropic liquid crystals is generally attributed to Reinitzer [ l ] who studied compounds such as cholesteryl benzoate and cholesteryl acetate and noted that the former compound exhibited two melting points and bright iridescent reflection colors between these points. Lehmann [2] coined the phrase “liquid crystal” for such materials as a result of his extensive work on liquid-like substances and there is a lot of interesting debate in the early literature as to who actually discovered liquid crystals [3]. Lehmann certainly constructed specialized polarizing microscopy apparatus which was of fundamental importance in recognizing the selective reflection properties of such materials. It is interesting to note that at much the same time as this discovery research was being carried out on the reflection colors of birds and insects, and that Michelson also noted [4] the selective reflection in ordinary daylight of circularly polarized light from the beetle Plusiotis resplendens. It is now generally thought that

this reflection layer is formed at the late chrysalis stage by a helicoidal liquid crystalline glandular secretion that hardens into a pseudomorph on the surface [ 5 ] . This reflecting layer has a thickness of 5-20 pm, which is typical of the reflecting cholesteric films discussed later. Further, Caveney showed that this reflection was enhanced by a nontwisted half-wave plate layer naturally formed between the two such helicoidal layers [6]. This biological example of enhanced selective reflection serves to show that we have many lessons to learn from Nature which is probably the true inventor of liquid crystals and, as noted in [7], “the farther backward you can look the farther forward you are likely to see”. Studies of the early thermotropic and biological systems have led to much of our present understanding of the general properties of cholesteric liquid crystals. These will be considered herein and we will show how such properties lead to optically linear and nonlinear devices, thermal imagers, radiation detectors, optical filters, light modulators, and other technologically interesting applications in Sec. 2.5 of this Chapter.

336

2 Chiral Nematics: Physical Properties and Applications

Historically, the helicoidal liquid crystals recognized by Reinitzer, Lehmann, Michelson, Caveney et al. were called “cholesterics” after the original cholesterol esters studied by Reinitzer [l]. However, many other steroidal and nonsteroidal compounds exhibit these so-called cholesterical phases (see, for example, [8-121). Thermodynamically, the cholesteric phase is the same as the nematic phase described in the previous sections of this volume and, although both notations are often used, the cholesteric phase can be considered as just the chiral form of the nematic phase. This can be understood by considering a racemic mixture of exactly equal amounts of enantiomeric forms (S and R) of the same nematic molecule. Such a mixture would be achiral, however, a slight excess of one form over the other leads to a chiral nematic phase. It therefore seems more rational to use the notation “chiral nematic” or N*. Thus a chiral nematic phase (N*) is exhibited by neat nematic compounds or mixtures where at least one of the compounds is chiral (i.e., each molecule not superimposable on its mirror image) or where there is an excess of one enantiomer over the other. In this chapter we will not consider in depth chiral nematic systems where only a small percentage of chiral material is added to give a weak helical structure to prevent ‘reverse twist’, as in twisted nematic or supertwisted nemat-

ic devices [ 131. We will primarily be concerned with systems with a high twisting power, such that the N* helicoidal structure formed macroscopically has a pitch length ( p ) of the order of the wavelength of light (A) (see Fig. l), or more generally exhibits a high value of optical rotatory dispersion. For comparison, a typical N* material would give an optical rotation of >lo3 degrees/mm compared with -10 degreedmm for a typical sugar solution. Chiral nematic (or cholesteric) liquid crystals have the orientational order of achiral nematics, but the director (n)is constrained in a layer-like structure to precess around the helical axis perpendicular to n. A ‘layer’ one molecule thick would give a director rotation of -10-20 min of arc per layer. Thus successive ‘layers’, with molecules ‘on average’ preferring to sit at such an angle to each other, twist and describe a helix of pitch p over distances that are large in comparison to the molecular dimensions. Here it should be remembered that such ‘layers’ are composed of molecules in constant thermal agitation and the director only describes a mean macroscopic or continuum picture. Molecules can exchange between near neighbors in the N* phase just as in the N phase. The helix pattern described by the director then dominates the optical properties of the N* phase. Depending on the enantiomeric excess, the materi-

AXIS

Figure 1. Representation of the helicity in chiral nematic structures. The helix defines the z axis and the periodicity in the structure is pi2 due to the condition n =-n.

2.1

Introduction to Chiral Nematics: General Properties

als may have a right-handed (clockwise director rotation) helical structure, and there is a clear relationship between helical sense and molecular structure [ 141. If the director n (a unit vector) describes a right-handed screw along the z axis, in a right-handed coordinate system then the director in the N*< phase is given by

where @ is a constant defining an arbitrary angle with x in the x, y plane and p is the helix pitch, which is positive or negative for right-handed or left-handed materials, respectively. Note that the helix only extends in one direction and that in any one ‘layer’ the molecules appear nematic-like. Further, since n =-n the ‘true’ period of the N*phase corresponds to p12 or a 180” rotation of n . We may also define the helical wave vector k = 2 d p , which then appears in the twist term of the free energy density equation for an N* phase, i.e.,

+ X k2, ( n . V xn + k), +% k3, ( n x V xn),

,,

(2)

Here k, k,,, and k,, are the usual splay, twist, and bend elastic constants of Leslie [lS, 161 and Ericksen [17, 181 continuum theory. This theory will be considered further in Sec. 2.2.2. It is the dependency of k on p , dpld T, and d p l d P that leads to interesting reflection or transmission filters and thermometry devices or temperature and pressure ( P ) sensors, respectively. These will be considered further in Sec. 2.5. If an electric or magnetic field is applied to the system, then an additional term -W is also added to the Eq. ( 2 ) , where W=XArl ~ X ( E. n)2 or %AX ( H n12, respectively. This again has important ramifications

337

which will be considered in Secs. 2.2 and 2.4. The modified free energy density equation refers to static or time-independent properties. If pulsed fields are used, then transient changes lead to switchable bistable states, dielectric and hydrodynamic instabilities and flexoelectric phenomena [ 191, which again may be used in modulation devices. These will be considered in Secs. 2.3 and 2.5, respectively. The optical properties of chiral nematics are remarkable and are determined by the pitch, p , the birefringence, An, and the arrangement of the helicoidal axis relative to the direction and polarization of the incident light. Here we use the term light to indicate that spectral region between the material’s ultraviolet and infrared absorption bands, since this leads, for example, to the possibility of near-infrared modulators. The helical pitch may be much greater or much less than the wavelength &, provided we remain in the limit of high rotatory dispersion discussed briefly earlier. In an external field changes may occur in both the direction of the helix axis, which leads to a textural transition, or in the helical pitch p , which then leads to an untwisting of the helix itself. These effects have been reviewed recently [20, 211 and led to numerous device applications (see Sec. 2.5). The observed optical properties of chiral nematic films depend critically on the direction of the director at the surface interface and on how this propagates to the bulk material. If the director is oriented along the surface of the cell using suitable alignment agents, such as rubbed polyimide, PVA, or PTFE, then the helix axis direction (see Fig. 1) is perpendicular to the substrates, as shown in Fig. 2a. In this case, an optically active transparent planar texture is obtained. It is this texture that is normally used to observe the bright iridescent reflection colors initially observed by Reinitzer and Leh-

338


mann. If, however, the molecules are oriented normal to the substrate using lecithin, quaternary ammonium surfactants (e.g., HTAB), or silane derivatives, the competition between the helix twist and the surface forces constrains the helix axis parallel to the substrate. This is turn leads to two possible textures, i.e., fingerprint and focal conic (Fig. 2 b, c). In the fingerprint texture the helix axis, z , is aligned uniformly and a side view of the helix is observed. As a result of the director rotation, the refractive index varies in an oscillatory manner and through crossed polarizers this appears as banding reminiscent of a fingerprint. On the other hand, if the helical axis is random in the horizontal plane, we would have a 'polycrystalline' sample which becomes focal conic if the axis of the helix tilts and forms ellipses or hyperbolae. We will discuss these textures further in Sec. 2.2.1. The focal con-

ic texture is highly light-scattering and for initially describing the optical properties of chiral nematics we consider optical phenomena observed with helically twisted planar textures. Under the conditions that the pitch @) is of the order of the wavelength (A) in the medium and that the incident light (Ao)propagates along the helix axis (z), we have two primary characteristic features: a) There is a strong selective reflection of circularly polarized light having the same handedness and wavelength as the pitch inside the chiral nematic medium (see Fig. 3). This corresponds to a snapshot of the E vector of the circularly polarized light matching the helicoidal structure. The reflected light is circularly polarized with the same handedness as the incident light, which is the exact opposite of a normal mirror reflection, which has a 7c phase change on reflec-

+ LINEAR

Figure 3. Schematic diagram of selective reflection from aright-handed chiral nematic planar texture for ;1=&ln inside the liquid crystal. The linearly polarized input light may be considered as counter-propagating right-handed (RH) and left-handed (LH) circular components. The RH component in which the E field matches the sense of the helicoidal structure is back reflected due to director fluctuations, whilst the LH component is almost totally transmitted. By convention, the handedness is defined in terms of the progression of the E field vector in time relative to the observer. The RH rotating wave therefore has the same spatial structure as the chiral nematic at any time.

2.1


tion. Thus right circularly polarized light would be reflected by a right-handed helix. On the other hand, left circularly polarized light would be almost wholly transmitted through the medium without reflection. Thus if white light is normally incident on such a chiral nematic film, it appears vividly colored on reflection. The effect is best observed, as in thermometry devices, against a black background. The selective circularly polarized reflection occurs around the incident wavelength, &, (in air) as given by ;h=iip

(3)

with a bandwidth A L centered on A, given by

AA =Anp

(4)

where A n = n l ,-nl and E, the mean refractive index, is given by (n,,+ nJ2. Note that here rill is defined as parallel to the director and n1 as perpendicular to it in the same plane, and that the ratio An/& is defined only in terms of the birefringence and refractive indices of the chiral nematic material, i.e., An/;. This is of considerable importance in the design of narrow band optical filters. If p becomes very temperature-sensitive, such as, for example, when the N* phase approaches an SmA* phase on cooling, then since in the latter phase p +00 the wavelength & also diverges towards infinity. This is the basis of many thermometry devices [ 1 I]. At oblique incidence, the reflection band is shifted to shorter wavelengths and side-band harmonics appear [22]. This situation is complex to analyze because of the effect of the twisted refractive index ellipsoid associated with each ‘layer’ on the different polarization components of the incident light. We have in fact to deal with complex elliptically polarized light rather than circularly polarized reflec-

339

tions and their interactions with the refractive index. However, to a good approximation Fergason [22] showed that &, varies for polydomain samples as

where Oi and 8, are the angles of incidence and reflection at the chiral nematic polydomain sample and m is an integer. The equation is only approximate, since the derivation assumes small O,,, and A n . If Oi= Or, i.e., a planar N* sample then

4)= Pmk cos ~

[ (n)l sin

-I

sinO,

(6)

which is of the form of the often quoted ‘Bragg-like’ condition where

m A = p cos $r

(7)

where sin Oi=E sin $,., $r is the internal angle of refraction at the aidliquid crystal interface, and ilis the wavelength in the medium [23]. Experimentally, all orders (m= 1, 2,3, etc.) are observed and again the reflected polarizations are elliptical rather than circular [23-251. We will return to more exact derivations of the selective reflection properties of chiral nematic materials in Sec. 2.2.1 by solving Maxwell’s equations inside the structure. b) There is a strong optical rotatory power for incident wavelengths A,, away from the central reflection maximum at ;lo,subject to the two limiting conditions that Ai >>p or Ai AA/2

2.1


applies. This equation also shows that the polarization plane rotates in the same sense as the helix for A
p. In the case of A c p (Mauguin's regime), the plane of the polarization actually follows the rotation of the director, and the angle of its rotation on emergence from the layer corresponds exactly to the number of turns of the helix. This is the waveguide regime used in twisted nematic (TN) devices [13], where the helical pitch is much greater than the wavelength of light. In this device the full twist in the director between the upper and lower plates is 90". Thus in the field off state linearly polarized light is rotated through 90" between crossed polarizers to give a transmission state. If the chiral nematic has a positive dielectric anisotropy (i.e., A E= - and E~~and are the dielectric constants parallel and perpendicular to the director at the frequency of an applied field E ) , then the planar texture on the application of E transforms to the homeotropic state and the twist ordering is lost. Thus the incident polarization is no longer rotated in the cell and the transmitted light intensity falls to zero, i.e., extinction between crossed polarizers. Although we will not consider such a 'dilute' regime ( A c p ) further, in great detail, it represents a major applications area of display devices and illustrates another reason why we prefer to call the present materials chiral nematic or N* rather than cholesteric. There is a further geometry of practical interest for light incident on chiral nematic films, related to the pitch of the helix in which we consider light propagating in a direction normal to the helix axis, i.e., as in the fingerprint texture, but with a pitchp less than A. In this short pitch chiral nematic case, the chiral optical tensor is averaged in space and the macroscopic optic axis is collinear with the helix axis [27]. The macro-

34 1

scopic refractive index, nia, for light waves with their polarization orthogonal to the helix axis is an average of the microscopic indices nI1and n I . Since in any one 'layer' nematic liquid crystals are optically positive (nll>n,), the short pitch chiral nematic is macroscopically optically negative, i.e., R ;;"< RY. Electric fields may then be applied to such short pitch systems to deviate the effective optic axis. At low fields this gives a linear electrooptic effect [28] due to flexoelectricity [29], whilst at higher fields dielectric coupling leads to a quadratic effect, i.e., the helix deforms as the pitch increases in the field to unwind completely above a critical field. We will consider these different dielectric and flexoelectric effects in Sec. 2.2.3, and their implications for light modulation devices in Sec. 2.5. In this introduction we have outlined the important physical properties, i.e., optical, elastic, etc., of chiral nematic liquid crystals and indicated the vital role that the pitch plays in determining these macroscopic properties. In the following sections we will present more rigorous derivations of the origins of these properties. Firstly we will consider the static properties, i.e., those exhibited at equilibrium either with or without an applied field (Sec. 2.2). We will then consider time-dependent or dynamic properties, where the systems are in continuous flux or responding to a transient field (Sec. 2.3). As outlined above, both the static and the dynamic properties lead to thermo-optic, electrooptic, magneto-optic (Sec. 2.4), and even opto-optic phenomena in chiral nematics, which in turn lead to devices where the chiral nematic pitch varies from much less than the wavelength of light to much greater than A. These applications will be considered in the Sec. 2.5, where we will also speculate on possible future developments.

342


2.2 Static Properties of Chiral Nematics In the previous section we discussed the preferential use of the term chiral nematic over cholesteric. At zero pitch the chiral nematic (or cholesteric) becomes nematic. This is true on the molecular scale where the local twist is very small. In the simple 'layer' model, ignoring molecular fluctuations, the twist between layers is of the order of 0.1" for pitch lengths at optical frequencies. Therefore within this limit, and including fluctuations, the cholesteric behaves as a nematic and locally the order parameter definitions are the same for each system. For this reason, the definitions of local birefringence ( A n =q- nl) and dielec- E ~ remain ) the tric anisotropy (A&= 6, same. Parallel (11) and perpendicular (I) refer to the local director inside the material. Macroscopically we consider the director, now averaged on a long length scale, to vary smoothly throughout the material, as depicted in Fig. 1. The local order parameter is described as for a nematic, i.e., S = -(3cos2 1 8 - 1) 2

(9)

where 8 is the angle between the long axis of each molecule and the local director. Here we ignore local molecular asymmetry to define the direction of the long axis. In chiral nematics we make the same assumptions, as in nematics, that (1) the centers of mass have no long range order, (2) there is local order as defined in Eq. (9) and therefore the director n has a direction, and (3) that the states n and-n are indistinguishable. For the chiral nematic, the director is no longer arbitrary but has a preferred helical conformation (Fig. l , as defined by Eq. (1)). The helical axis z and @ are arbitrary unless the director is aligned preferentially at

a surface. We will consider how this is done experimentally in the next section. As a result of the n =-n condition, the structure is periodic along z with a spatial variation of p/2, as previously discussed. The helical wave vector k (=2n/p) has magnitude and sign. The magnitude determines the macroscopic physical properties we are interested in herein, whilst the sign defines the handedness of the helix. As pointed out in reference [30] (p. 15) for materials in which k changes sign, the macroscopic properties, such as the specific heats, remain steady across the transition from -k through zero to + k . At k=O the material behaves like a conventional nematic. Further there is no evidence from X-ray scattering of any significant differences between cholesteric and nematic phases save a slight broadening on the cylindrical distribution curve due to reduced parallelism caused by the helical twist [31]. It was Friedel [32] who first noted the similarity between the local molecular arrangements of the so-called cholesteric (or N*)and nematic phases. This is further support for the use of the more general term chiral nematic in preference to cholesteric. For very tight pitch materials (i.e., when p approaches to within 10-100 times the molecular dimensions), the structure is more akin to a layered smectic phase; locally, however, it is still nematic although the scale of the repeat unit of the helix will give X-ray scattering peaks similar to SmA materials, but for a wider layer spacing [33]. These structures are then of considerable interest for flexoelectric and dielectric devices [29]. By definition then a racemic or achiral material leads to a nematic N phase, whilst a nonracemic or chiral material leads to a chiral nematic N*phase. In the preceding discussion chirality was used only to differentiate between righthanded and left-handed structures, that is, structures in which their mirror images can-

2.2

not be superimposed. This is the definition introduced by Lord Kelvin [34]. There is, however, no absolute measure of chirality and there is no obvious way of absolutely predicting how much twist comes from the molecular chirality. Chirality is important herein in that if the individual liquid crystals are chiral (assuming a nonracemic mixture) then there will be a tendency to form a helicoidal structure of the director superimposed on the local nematic order in the nematic (and tilted smectic) phase. As discussed above, the induced helicoidal structure has a defined axis orthogonal to the local director and a defined pitch p . It is the existence of this helix and the variation of p under different conditions that leads to the use of chiral nematics in many different applications and devices (see Sec. 2.5). Before such devices can be understood, it is necessary to consider how the bulk macroscopic properties are determined by this helicoidal structure. In this section we will consider the static properties, that is, those properties as observed at equilibrium in the presence of alignment forces, applied electric or magnetic fields, and at different temperatures and pressures. We have used the heading static to indicate, under any given conditions, that we are not considering transient changes between a ‘ground’ and an ‘excited’ state, but the conditions in either end state. Time-dependent phenomena will be considered in Sec. 2.3 under the general heading of dynamic properties. The static properties important in the following section will relate to how the helicoidal pitch is a) measured and b) influences the optical properties and leads to different textures and defects. We will then examine in detail the theoretical approach to optical propagation, Bragg reflection, and transmission for normal and nonnormal incidence in chiral nematic materials. We will outline how the

Static Properties of Chiral Nematics

343

bulk elastic properties are modified by the helicoidal structure by using the continuum theory to deduce a free energy density expression both for the quiescent state and in the presence of external fields. This will then allow us to determine the helicoidal pitch behavior in the presence of external influences such as temperature, pressure, and electric or magnetic fields. Finally, we will describe how these external fields lead to different dielectric, diamagnetic, and flexoelectric phenomena in chiral nematics.

2.2.1 Optical Properties As described earlier, the spectacular optical properties of chiral nematics are determined by the helicoidal pitch, the birefringence (and refractive index), the direction and polarization of the incident light, and the arrangement of the helix axis. For normally incident light the direction of the helix axis gives rise to the three classical textures depicted in Fig. 2, and typical photomicrographs taken with crossed polarizers are shown in Fig. 6; these are: a) The planar or Grandjean texture, in which the helix axis is uniformly orthogonal to the confining glass plates. The surface alignment is often induced by rubbed polymer films. b) The focal conic texture, in which chiral nematic domains are formed with the helix axes arranged in different directions. These may be achieved without surface treatment on rapid cooling from the isotropic phase. c) The fingerprint texture, in which the helix axes are parallel to the glass plates. Surfactants are often used to produce this texture, which may be uniform or polycrystalline depending on the degree of alignment control at the surface. The

344


Figure 6. Photomicrographs of (a) planar, (b) focal conic, and (c) fingerprint textures in chiral nematics, and the schlieren texture demonstrating brushes in an apolar nematic (d); observations through crossed polarizers.

2.2 Static Properties of Chiral Nematics

name fingerprint arises, in the case of long pitch materials (i.e., p A) from the stripes observed as the helix pitch rotates through optically equivalent states with a period of p/2. IN.B. In short pitch mate-. rials ( p a i l ) , the pattern is not resolved and often takes on a fairly uniform colored appearance depending on the cell thickness, A n macroscopic (i.e., ni"-n;I"), and the direction of the input polarization.]

-

All of these textures may be switched to produce electro-, magneto, or flexo-electric effects, which will be discussed at the end of this section. The key to the use of these various effects and indeed observation of the optical properties lies in control of the director orientation at the liquid crystal-substrate interface. For the techniques to be described, we will be in the strong anchoring regime where we can ignore the k , , and k,, terms in the full free energy density expansion (see Sec. 2.2.2.1). As a result of the local similarity between nematic and chiral nematic phases, most of the alignment techniques that work for nematics [3S] work for chiral nematics. We are principally interested in two types of alignment of molecules at the surface, i.e., planar and homeotropic, in which the preferred orientation of the molecules pinned to the surface is parallel or perpendicular to the surface. Planar alignment in chiral nematics can normally be achieved by three well-known techniques: (1) SiO evaporation, (2) polymer rubbing, or (3) microgrooved surfaces. In (1), silicon monoxide ( S O ) is evaporated onto a surface to give a layer, typically 20-100 nm thick, at an oblique angle 8. For 8=60" the molecules align parallel to the evaporation plane, whilst for 0=80" they are perpendicular [36, 371. If random planar alignment is required, the SiO is evaporated at normal incidence. SiO gives a surface of

34s

very high thermal stability. In (2), i.e., polymer rubbing techniques [35, 381, a polymer such as PVA (polyvinyl alcohol), which is water soluble, or polyimide is spin-coated onto the substrate and then rubbed with a spinning velvet cloth in a unique direction. In these cases the molecules are aligned in the rubbing direction and, if necessary, speed and pressure may be used to control a small 1-5" surface pretilt. The commercially available polyimides have good thermal and chemical stability, whilst PVA is convenient for rapid testing in the laboratory. If a barrier layer is required for electrooptic applications to prevent ionic flow from the electrode layers, it is possible to evaporate the SiO normally and then spin-coat on top the polymer prior to rubbing, in order to obtain good planar alignment. A new polymer alignment technique [39] using frictiondeposited polytetrafluoroethylene (PTFE) gives excellent planar alignment of nematic and chiral nematic materials with almost zero surface tilt [40]. In ( 3 ) , as will be discussed in the thermochromic devices section (Sec. 2.5.2) fine microgrooved surfaces may be used in embossed laminated sheets [41] to give excellent planar alignment. Homeotropic alignment is usually obtained by coating the substrate surfaces with surfactants such as lecithin or HTAB [42, 431. A practical laboratory method is to deposit egg lecithin in ethanol or chloroform on the surface. The solvent evaporates to leave the surfactant with its polar head group stuck to the surface and the hydrocarbon chains pointed, on average, into the cell perpendicular to the substrates. The liquid crystal-hydrocarbon chain interaction then gives the desired homeotropic alignment. Via the elastic forces, the surface alignment then propagates into the bulk volume. Silane derivatives [44] or chromium complexes [4S] that chemically bind to glass surfaces have equally been used for homeotropic alignment.

346


The different optical textures induced by the different surface alignment conditions lead us to three common methods of measuring the helical pitch:

1. Fingerprint texture: Using homeotropic alignment and a polarizing microscope we can measure the distance between adjacent dark lines (see Fig. 6) provided the sample is illuminated with monochromatic light. As discussed earlier, the line separation is thenp/2. Since this is a visual technique, it is only easy to observe pitch lengths greater than -1.5 pm. If a polarized laser beam is used and the fingerprint texture treated as a diffracting (grating) element then this technique may be extended down to the diffraction limit to measure pitch lengths -0.6 pm, depending on the wavelength used. 2. Planar texture: Using planar alignment and by measuring the reflection or transmission spectrum of a chiral nematic

film it is possible to measure the Lax (re(transmitted) using a flected) or kin monochromator either to control the input light wavelength [ 101or using a white input light to monitor the reflected or transmitted spectrum. In the latter case we [46] have found it particularly useful to couple a simple single pass or spinning prism monochromator to a reflection microscope to measure such spectra for a large variety of materials. This is shown schematically in Fig. 7. This technique allows the spectrum to be monitored on an oscillocope instantaneously and allows pitch measurements in the range 0.2 p m < p < 1.O pm. The pitch p is related to &, by p=&,-n (see Eq. 3), where Z= (rill + n,)/2. This technique necessitates an independent measurement of nll and nI. Since these are normally measured for order parameter measurements using an Abb6 refractometer, this is no great problem. Simple diffracting ele-

Figure 7. Schematic diagram of a microscope spectrometer for measuring transmitted or reflected spectra from chiral nematic textures.

2.2

ments coupled to CCD arrays now make the detection simple and fast so that dynamic phenomena may be monitored [47]. A related technique for spectral measurement using phase-sensitive detection has also been presented [48]. 3. Focal-conic texture: Based on the diffraction equation derived by Fergason [22] for such a polydomain texture (Eq. 5 ) , e.g., HeNe laser at A=632.8 nm, the helix pitch can readily be determined. Again Z has to be determined independently, but the technique may be used for dynamic electrooptic studies. This method is limited to materials of small An,but the range of p readily measured is 1 p m < p < 2 0 pm. Supplemental to these techniques, it is also possible to use a wedge-shaped cell to measure the helical pitch in a chiral nematic [49, 501. This is a further example of the use of planar boundary conditions. In a wedge cell, with the angle a=h/L previously determined, the planar alignment produces the classical Grandjean-Cano texture with disclinations separated by a distance 1 (see Fig. 8). These disclinations arise since as the cell thickness increases the number of ‘half pitches’ through the cell also inreases to minimize the free energy. As a result of the alignment conditions, it can only do this in a quantized way. The increase thus takes


347

place in steps where disclination lines are created every time the number of half pitches is increased by one (see Fig. 9). The pitch p is then given by p = 21a =

~

21h L

where I is the distance between two disclination lines and a is the wedge angle determined by interference fringes in an empty cell. Using this technique, pitch measurements can be made readily in the range 0.8 p m
afew microm-. eters). For shorter pitch systems, in which( case the fingerprint may be too fine to observe directly (other than by diffraction), an electric field [below the critical helix unwinding (see Sec. 2.2.3)] may be used in conjunction with the shearing process to unidirectionally align the helix for materials of positive dielectric anisotropy. This is particularly useful for chiral nematics used in flexoelectric switching [29]. Pate1 and Meyer [28] showed that rubbed polyimide layers could be similarly used (N. B. without shearing) and that, on cooling from the isotropic phase in the presence of an AC field, the helix could again be uniformly aligned in the plane of the substrates. Although, as discussed in Sec. 2.2.1, the fingerprint texture may be used to measure the helical pitch, care has to be taken lest the helix axis is inclined to the substrate plane or local distortions occur at the substratel liquid crystal interface [73]. An interesting use of the fingerprint texture is to examine pitch changes with concentration in a contact preparation between a chiral and an achiral nematic. As the pitch varies from infinity in the nematic to the value of p in the neat chiral compound, the fingerprints become closer together. This effect is shown in Fig. 11b for a very short pitch cholesta-


353

nol-based organo-siloxane [74] in contact with pentylcyanobiphenyl (5CB). We will now consider in more detail some of the alignment or director field patterns around different defect structures in chiral nematics. Using the simple one elastic constant approximation (i.e., k as for the nematic case above) and the definition of the chiral director (i.e., n =(cos 6, sin 6, 0), 6 = k z , and @=O; see Eq. (1)) in the free energy density expression, (Eq. 2) gives

and V26=0. For X-screw disclinations (see the nematic wedge disclinations discussed earlier) there is a singular line along the z axis (i.e., parallel to the helix axis) and the director pattern is now given by

where m is integral as before. The simplified director patterns for s=X and 1 are shown in Fig. 12. If the elastic anisotropy is now included in the free energy density (see, for example, [59], p. 139 et seq.), then one

Optic Axis

/@//a/

/ s/I/

41t

/

/ e l f [a / /’ S=I/2

s=1

Figure 12. Representation of director patterns for s= X and 1 X-disclinations in a chiral nematic. The unfilled or filled dumbbells or pins denote the spiraling director.

354


particular value of c is favored for a disclination pair. This is important for chiral nematics where each layer may be regarded as nematic-like, but rotated about the twist axis. Since each layer is allowed only one value of c (0 or d 2 ) (see Fig. lo), the disclination pairs are expected, theoretically, to adopt a helicoidal configuration and this has been observed experimentally for s=% [75] and s= 1 [76] pair disclinations. For edge disclinations, the singular line disclination is perpendicular to the twist axis. On rotation around this line, an integral number of half pitches ( p / 2 ) are gained or lost and the pattern for s=% is as shown schematically in Fig. 13. The director pattern around such a disclination was first proposed by de Gennes [77], again in the one elastic constant approximation, with the following twist disclination type of solution

x

n = (cos 8,sin 8,o)

1

and m is again an integer. This approach has been extended to take into account elastic anisotropy by Caroli and Dubois-Violette 1781.

----c----OQ~cO----OCg.----OQCg

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

-*o--..o-.c+.o0

cs

cc

-0-

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

+-0.----0cOcO--o.0.c-c-c-c--mo-

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

4--cg

~rg-J-o-o-o.-o-o

L-c--c+-c-c-+

h

-----c------

@ - - - - a ~ ~ ~ o - - - - o o Figure 13. The director pattern for s = % X-edge disclinations in a chiral nematic. The filled in dots signify that the director is orthogonal to the plane of the figure, the dumbbells that it is in the plane, and the pins that it is tilted in a spiraling structure.

As for achiral disclinations, the Volterra process may be used to create screw or edge disclinations by cutting parallel or perpendicular, respectively, to the chiral nematic twist axis. As discussed when considering the focal conic texture, the chiral nematic may be considered as having a layered structure of period p / 2 for a given direction of n. This layered lattice can then have disclinations similar to SmA materials. In the Volterra process, if the cut is made such that the disclination line (L) is along the local molecular axis then the longitudinal (A) disclinations created are designated A+ (indicating material has to be removed) or d- (for material added) to arrive at the final configuration. If, however, L is perpendicular to the local molecular axis then these transverse (7) disclinations are similarly denoted z+ and z-. These configurations are shown schematically in Fig. 14, and it should be noted [59] that the coreless d disclinations have lower energies than the cored z structures in a chiral nematic. Also the and z(') disclinations occur in pairs to give five possible forms of dislocations and pincements or pinches (i.e., a transformation from a wall to a line) (see Fig. 15). These disclinations are most easily observed in the fingerprint texture (see Fig. 6 c), where many of these defects may be readily identified by the observant reader. As a result of the layered nature of the chiral nematic structure, like the smectic A, it can also exhibit focal-conic textures [79] and both phases exhibit screw and edge dislocations. A dislocation corresponds to a displacement of the layered structure in a - plane - o orthogonal to the layer and may be formed by the pairing of two disclinations of opposite sign. A screw dislocation has a singular line along the screw axis and is equivalent to ax-screw disclination in a chiral nematic. An edge dislocation corre-

2.2

2j.i .. 8 ::1

0-20-40-0~

................... =:'B ..................... b =..\

G-Qu-oo--o D-0C-c

q... %:;%

L p ooo-*

c+-oc-0

d........... -0 +---7F

..... o-. -6"

'

. . . .- . .0. . % .

t--S ..........

-0

Y ...........

sponds to a line defect in the y direction for a planar (x, y ) chiral nematic with its helix axis in the z direction. This line defect then forces the layer (or planes of equivalent n ) to tilt with respect to the I or unperturbed helix axis. Schematic diagrams of such singular defects are shown in Fig. 16 a,b. These edge dislocations under favorable energetic conditions can combine (Fig. 16c,d) to form a 'grain boundary' with zig-zag and quadrilateral defects [79] in chiral nematics. These are clearly evident in Fig. 17 from


355

Figure 14. The director configurations around defects leading to (a) X', (b) A+, (c) z-,and (d) r+ disclinations in a chiral nematic. The dumbbells, pins, and dots have the same significance as in Fig. 13 and the black star circles L represent the disclination lines.

Figure 15. Schematic representations of the pairing of iland z disclinations of opposite signs in a chiral nematic. The schematic diagrams show edge disclinations comprised of (a) il-and A+, (b) z-and T+, (c) r- and A+, (d) X and r+ and (e) pinches or pincements of z+ and 5-. The pins, dots, and layer lines represent the spiraling director field.

[80], where the dark banding is due to the layers of equivalent n in the chiral structure. The texture also shows in-plane linear and hyperbolic defects generated by coalescing edge dislocations in the z direction. These are similar to the focal conics formed in smectic A materials, but in the chiral nematics the length scale of the layers of equivalent n are separated by pI2, which is the order of micrometers rather than nanometers, i.e., it is a macroscopic rather than a microscopic feature.

356


I

(c)

(4

Figure 17. Optical micrograph of a chiral nematic texture exhibiting zig-zag and quadrilateral defects.

2.2.1.2 Optical Propagation (Wave Equation Approach) The large and anomalous optical rotations observed in the chiral nematic phase are not due to intrinsic spectroscopic properties, i.e., absorption or emission, of the constituent molecules, since they do not persist in the true isotropic phase (i.e., away from pre-

Figure 16. Simplified schematic diagram of (a) and (b) singular defects which combine to form grain boundaries with (c) zig-zag and (d) quadrilateral defects.

transitional effects [8 11). They must therefore be due to the transmission and reflection properties of light propagating in the helicoidal or twisted optically anisotropic liquid crystalline matrix. Based on the spiraling structure depicted in Fig. 1, this propagation has been examined theoretically in the seminal contributions of Mauguin [60], Oseen [61], and de Vries [26]. More recently Kats [62] and Nityananda [63] presented a highly accessible theoretical treatment of this work, and this will be considered below. This approach, based on the spiraling ellipsoid model for the dielectric tensor, gives ready access to the two experimentally interesting conditions of a) waveguiding >iland b) sein the Mauguin limit where p > lective optical reflection when p=A. Solution of Maxwell’s equations in this formalism leads, not only to the conditions for strong reflection of circularly polarized light and anomalous optical rotatory dispersion, which are of interest in this chapter, but also to the treatment of absorbing chiral

2.2

nematic systems, e.g., dye guest-host [82]. In the present treatment we assume (1) am ideal helix (i.e., the director of n rotates regularly and sinusoidally, (2) a semi-infinite planar structure bounded on its upper surface by an isotropic dielectric medium of the same mean refractive index as that of the chiral nematic [i.e., E=X(nll+n,)l, (3) that the birefringence is small (An=nll-n, A , the material behaves macroscopically as a variable birefringence film with A n (z) varying as a function of displacement of the orthogonal light beam relative to z, the helix axis. For p e a , the light wave interacts with many turns of the helix and the polarization experiences an average refractive index in, say, the x, y plane. In this case, if we define nfA as the macroscopic refractive index parallel to the helix axis (z) and n;OA as orthogonal, then the macroscopic birefringence is nfA-nroA. For this situation, nfA =nI in the local director n notation. The macroscopic orthogonal component is then given by (37) averaged over one pitch E(Z)= n2 (z>

where rill is parallel to the microscopic director n and e ( ~is) the in-plane (x,y ) angle between nI1(z=O) or y and n (z). Thus a microscopic positive birefringence material (A n =nI1-nl> 0) will become macroscopically negative, since nfA=nl il. In the next section we will discuss the practical Bragg diffraction properties of chiral nematic films in more detail.

2.2.1.3 Optical Propagation (‘Bragg’ Reflection Approach) In the previous section we considered the propagation of light in a chiral nematic material by solving Maxwell’s equations under the limiting conditions of (a) a planar sample, (b) a perfect helicoidal structure with its axis orthogonal to the liquid crystal layer, and (c) for A e p - d a n d A-p. For A-p we showed that circularly polarized light is reflected in a wavelength range defined by & + p A n / 2 . This formalism is the only exact way of describing the reflective, refractive, and transmissive properties of light interacting with a chiral nematic. In the present section we will use a ‘Bragg’ diffraction approach to describe these properties in the practical situation where the chiral nematic material is polydomain in nature, and where these domains may be inclined to the direction of the incident light. The term Bragg reflection is used throughout the literature, but it must be stressed that this is only a convenience. True Bragg diffraction occurs when the radiation incident on a crystal lattice has the same order of wavelength as the repeat unit of the lattice, and where the density waves of the scatter-


2.2

ing medium are discrete. In chiral nematics,, the material is in a continuum and it is the ‘local’ director that gives a layer-like structure as it precesses around the helix axis (2). Fluctuations ensure that the density wave is constant with respect to z along the axis and on the length scale of visible light. In the Bragg reflection approach, as in the figures that follow, the layers used to define the scattering or reflection geometries refer to planes of equivalent optical properties separated by d , where the local directors are orientationally aligned in the same direction with n=-n. There is a continuum of identical material, orientationally rotated ’in plane’, with respect to and in between these layers, separated byp/2 (see Eq. 1) and Anp defines the bandwidth of specularly reflected light at a wavelength A(=&/$ in the continuum. The simplest case of Bragg diffraction is shown in Fig. 20 a for an ideal planar chiral nematic. If k , is the scattering vector, arising from the structure in, and local fluctua, dielectric tensor, then tion of, ~ ( r )the

k , = k1- k ,

363

and scattered light, respectively. A more exact treatment is given in Chap. 3 of [30]. If 19~=$~=0, then for ki=-k,=k, the only allowed nontrivial solution, we have

k,=2ik or

2d=A

(41)

which is the simple ‘Bragg’ condition. As discussed in the previous section, if k>O (i.e., a right-handed helix), then right circularly polarized light is back scattered or reflected whilst the left-handed circularly polarized light is transmitted. Secondly, there is only one order of back-reflected light. For Oi > $i= &, Eq. (40) gives solutions corresponding to

2d cos $i,s = rn A or piicos$=rn&

(42)

where rn is an integer and A=&/Z. In this case [84] higher orders are allowed and the reflected light is elliptically polarized. As discussed, when solving the wave equation, the propagation of light at oblique angles is complex, since the light polarization couples neither with nIl nor nI but with values

(40)

where ki and k , are the wave vectors, which are assumed to be coplanar with the incident

I

(a)

(b)

Figure 20. Geometry for selective reflection for plainar chiral nematic films for director layers (a) perfectly aligned for internal scattering and (b) inclined at an angle a to the surface interface. All rays are assumed to be in the plane of the figures.

364

2

Chiral Nematics: Physical Properties and Applications

of n given by an angled slice across the refractive index ellipsoid. For the following discussion we will ignore these complex polarization properties of the reflected light and consider only the wavelength behavior. Unless we are considering some of the specialized reflecting films to be discussed in Sec. 2.5 of this Chapter, from a practical point of view we are only interested in intensities and wavelength. One interesting consequence of Eq. (42) is that if the monodomain is illuminated with white light and reflects back normally, say, red wavelengths, then observation at angles of 8 (or Cp internal) leads to a blue shift and this is observed in practice. Indeed, this is used in security devices, since it is an effect that is impossible to photocopy. The angular dependence of the selective reflection is one of the key features of chiral nematic thin films. In the practical world we rarely have perfect semi-infinite planar samples. Surface imperfections, preparative techniques, etc., normally lead to polydomain samples in which the planar texture is locally inclined and Cpi#Cps. This is depicted in Fig. 20b. ' O oriented . There will be many polydomains with their helix axis at different angles (a) to the substrate or liquid crystal/air interface, and each domain will selectively reflect light at some specular angle [22]. In the original model, not so far from reality in microencapsulated or polymer-dispersed chiral nematic films, Fergason assumed fictitious chiral nematic domains embedded in a medium of mean refractive index >A), of the order of the wavelength of light (A-p), or short (Asp), and these three conditions lead to quite different types of response and, ultimately, devices. Equally, the coupling might be through the dielectric, conductive, magnetic, flexoelectric, or optical properties, which in turn may have anisotropies that are positive or negative relative to the applied field. The coupling will also then depend on the direction of this applied field relative to the helix axis and the director. Thus it is possible in chiral nematic materials to observe a very wide range of electro-magnetic phenomena, with implications for theoretical understanding and experimental or practical applications. For convenience, in the following sections, the major categories will be subdivided into the effects of magnetic and electric fields applied parallel or orthogonal to the helix axis, respectively. Under these four subclasses, the effects of helix pitch, positive or negative anisotropy, field frequency, and coupling mechanisms will be considered as appropriate.

2.4.1 Magnetic Fields Parallel to the Helix Axis We will first consider a planar chiral sample with a magnetic field H applied across the sample along the z or the initial helix axis direction. The diamagnetic susceptibilities are defined as xl, and i.e., parallel and perpendicular to the local director. Since n spirals around z (see Eq. l), this gives a value of parallel to H and %(xII+x1)orthogonal to H . If Ax(=xll-x1)

xL,

x1

2.4

Field-Induced Distortions in Chiral Nematics

xL>X(xrl+xL)

is negative, then and the director n stays normal to the field at all points and the sample remains planar. If, however, then X(xI, Axis positive (xll and the director can rotate to become parallel to H (or z ) and the helix axis will try to become horizontal (i.e., move into the x,y plane). Once the helix axis is horizontal, or predominantly so through the coupling of H with a second process starts to dominate known as helix unwinding [129]. The unequivocal threshold field for this will be discussed in the next section. Essentially in this mechanism, with the helix axis orthogonal to the field, the director now starts then xlI> !4(xll to unwind since xlI This continues until the directors n are aligned along H , in which case we have unwound the helix to give a homeotropic nematic texture. This gradual transformation is commonly known as the chiral nematic (cholesteric) to nematic transition. It is not a phase transition in the thermodynamic sense, but an orientational transition within a phase at a fixed temperature. On removal of the field, the structure reverts back to helical chiral nematic form. These changes can happen if the sample is considered thick or outside the length scale on which surface forces are considered strong. If this is not the case then there will be strong competition between the surface forces trying to keep the sample planar (i.e., the helix perpendicular to the substrate) and the applied field trying to reorient the helix into the x, y

>xL),

+xL)>xL

X(xlI+xL),

>xL

+xL).

383

plane. This competition, depending on the relative strength of the two mechanisms, leads to different director distributions or distortions. At low field strengths we may assume that the director remains on average in the x , y plane with the helix axis, therefore, ‘on average’ along z. Thermal fluctuations cause the director to oscillate around thex, y plane and in the presence of an external field the director, for systems where the cell thickness d is much greater than the pitch, can couple to give layer-like or ‘Helfrich’ [130, 1311 distortions. These are shown schematically in Fig. 32. As before, the socalled corrugated layers are planes in which the director directions are equivalent (i.e., at p / 2 remembering n =-n), but regularly periodic in the x, y plane. We will discuss the threshold for this effect below. At higher field strengths the directors become more uniformly tilted at higher angles, but still with the helix axis along z. The spiral nature of the chiral nematic forces the inclined director to trace out a ‘conical’ distortion [ 132, 1331. At higher fields the helix distorts into the horizontal plane and the director may unwind as described above. It should be stressed that not all chiral nematic liquid crystals clearly exhibit all of these effects. The critical fields for each distortion are not sharp, the distortions may co-exist, since the director field is at all times continuous (unless a ‘focal-conic’ phase is formed) and these fields depend on cell dimensions,

Distorted planes of uniform director orientation \

Magnetic field

Figure 32. Schematic representation of the Helfrich or periodic distortions in a planar chiral nematic due to a magnetic field acting parallel to the helix axis (z). The lines denote equivalent director fields (in the x , y) plane ( A x > O ) and the periodicity is 21rlk,.

384


pitch lengths, magnetic susceptibilities and anisotropies, elastic constants, and quality, i.e., homogeneity, of the initial planar alignment. We will first consider the ‘Helfrich’ instability mode [130, 1341. For an unperturbed planar chiral nematic with the helix along z, the director is given by Eq. (1). If we now assume small perturbations in @ and that the director layers undulate sinusoidally by an amplitude 8 (see Fig. 32), we have n, = cos(kz + @)=r cos kz + @ sin kz ny = sin(kz + @)= sin kz + @ coskz n, = 8 cos kz

I

(106)

Equation (2) then gives the local energy density Fl as

&L L

Fl = [(kll sin2 k z + k33 cos2 kz)

aZ k&J+

[2 +

+ k22

2)

cos4 kz 7 ~

For a given undulation, 6, 3 is a minimum

a3

for -= 0 or a =0. Within the limit of small

a@

deformations, we may assume that the perturbations @ and 8 are dependent on x and z and given [ 1341 by (1 11)

where qz=m d d and m is an integer usually equal to unity. Practically, qZO or < 0). So at low frequencies for AE < 0 the undulation modes are still observed, but at higher fields the conductivity mode domi(143) nates and again leads to a scattering texture. and On removal of the low frequency field, in thick cells, the texture relaxes back to focal (Sl - 01)(Ell + El) (144) conic with residual light-scattering proper(Sl + 01)(Ell - E l ) ties. This has been described as the storage In this regime, still with AE>O, the depenmode or memory effect in chiral nematic dence on o is relatively weak and E&, desystems [162]. If a high frequency ac field creases slowly with decreasing frequency. the dielectric torque is now applied (o>q), Above this threshold field, the periodic dorestores the nonscattering planar texture mains, to be discussed later, change [160, and, just as in smectic A materials, this ef1611 to a turbulent texture similar to the dyfect can be used in electrooptic storage namic scattering mode in apolar nematics. mode devices [ 1651, since we have a low In contrast to apolar nematics, this turbulent frequency ‘write’ and high frequency texture is stored on removal of the external ‘erase’ mechanism. field [162]. For high frequencies, at which To return to the mechanism where condielectric coupling dominates, the threshold ductivity is negligible, then dielectric field is given in a slightly different form coupling dominates the periodic domain formation (see Eq. 142). Optically, the ob(145) served texture between crossed polarizers appears as a square grid pattern [ 1571 with This has been derived [ 1341in the same way a periodicity of approximately d d . The grid as Eq. (123), and is directly equivalent to it arises from the competing mechanisms of with H replaced by E and A x by Ad4n in the elastic forces trying to maintain the the expression for the free energy density planar texture, whilst the field, through the (see Eq. 117). This derivation holds for dielectric coupling, is trying to induce a finsmall AE. For the more general case, as gerprint texture with the helix axis predomfound with current chiral nematics, i.e., not inantly in the x,y plane. The original alignbased on cholesterol compounds, the Ad47c ment direction sets x and y in this model, and term is replaced by E ~ E ~ [ ~ ~ C ( ~ + E ~the ) I‘grid . pattern’ results from the refractive In the derivation of Eqs. (141) and (142), index variations as the director follows it has been assumed that A&>O, i.e., these periodic undulations. If the pitch be! ~ ( E , ~ + E ~ ) For > E ~ A&.Within the where E”,(o) is the mean square value for the threshold field of frequency o for the conduction regime at low frequencies and zc is the dielectric relaxation time given by

2.4 Field-Induced Distortions in Chiral Nematics

limit of dO are inverted to those for A o>p and (b) homeotropic surface alignment where flexoelectric coupling becomes important for p < A. In both cases the applied field E is parallel to n or orthogonal to the helix axis for such chiral nematic materials. For a chiral nematic with positive dielectric anisotropy and an electric field E orthogonal to the helix axis (z), then we observe a chiral nematic to unwound nematic transition for d>p. The analysis [ 132, 1391 of the unwinding mechanism is exactly the same as for the magnetic field case with the coupling - % A x ( n . H ) 2 replaced by -]/zA&(n . E ) 2 in the free energy density expression. The equilibrium condition (see Eq. 127) or Euler's equation then becomes

(z 7 )

kz2 d 2 y

-

AEE2sinycosy=0

(147)

Following the same solution route as for the magnetic field case leads to a coherence given by length

t2

and the pitch of the helix satisfies the condition of minimization of the free energy as given by

where F, (a)and F 2 ( a ) are complete elliptic integrals of the first and second kind as before (see Eqs. 129 and 130). Then as a+l, F , ( a ) + l , andF,(a)+.o, thecritical field for unwinding of the helix is given by

As discussed in Sec. 2.4.2, this helix unwinding corresponds to a decrease in the

392


number of regions of 180” twist or pitch walls (see Fig. 33). Thus the helix is no longer ideal and not only do the reflections occur at a longer wavelength, but higher order reflections occur and the polarization properties alter accordingly. Both second and third order reflections have been observed from such planar chiral nematic textures [168]. Further, the optical rotatory power as defined in Eq. (8) will be markedly altered to become inactive in the unwound state. Theoretically, if the influence of the cell walls is important, i.e., as in a ‘thin’ cell, then the helix unwinding is quantized and occurs in steps (of n 2dlp (0), where n is an integer) rather than as a continuous funciton with the applied field [169]. On removal of the electric field, the unwound structure relaxes to form a modulated optical structure of stripes or grids. The dynamics of the helix unwinding are described by ~1

~

A E E sintycosty=O ~ aty - k22 a2ty - at

~

az2

4n

where tyvaries from 0 to 2 TC, with solutions [170] of the form

z, =

Yl

k22 q2 fA EE2 1 8 ~

and

where z,and z, are the response times for the field induced and relaxation processes, respectively, and q is the wave vector depending on the experimental configuration. In the denominator of Eq. (15 1) the positive sign refers to q 2 k and the negative sign to q Ik, where k =2 nlp as before. Flexoelectricity arises in liquid crystals due to their shape asymmetry, i.e., ‘pear’, ‘teardrop’, ‘banana’, etc., associated with a strong permanent dipole moment. Macro-

scopically, in the absence of a field, the system does not exhibit a bulk polarization. However, application of a field induces a polarization in the field direction, due to splay or bend deformations and the effect of the molecular shape asymmetry. This effect was recognized by Meyer [171] and is known as flexoelectricity. The most general form of the flexoelectric polarization, Pflex,is given [30] by P f l e x = e s n ( v ’ n ) + e b nx ( v x n )

(153)

where e , and ebare the splay and bend flexoelectric coefficients (which may be positive or negative), respectively. As briefly discussed in Sec. 2.2.2, this gives rise to a flexoelectric contribution to the free energy density as

(154) In chiral nematics this term is then added to the free energy density expression (Eq. 2) to determine the new equilibrium in the presence of this coupling. In the following analysis it is assumed that the dielectric anisotropic coupling is negligible. If this were not the case, then dielectric reorientation processes as described earlier, where helix unwinding takes place, could influence the electrooptic effect, although a weak A E has little significant effect and helps with the surface alignment [29, 1721. In the geometry to be considered, the chiral nematic is contained between cell walls in the x, y plane with the uniform surface alignment layers designed to align the helix axis along x with the electric field applied along z (see Fig. 35). In such a ‘sandwich’ like cell [29, 173-1751, the director spirals along the x direction in the z , y plane and is therefore described by

n = (0, sine (x,t ) cos 8 (x, t )

(155)

where we have assumed that the arbitrary term @ in Eq. (l), with transposed coordi-

2.4

Field-Induced Distortions in Chiral Nematics

393

system in an electric field then becomes

Helical axis, h, optical axis, O.A.

1 F ( E ) f= ~[ k l l ( V .n)* + k22 (n . V XII + k ) 2 2 + k33( n x V xn)2] - E . [ e , n ( V . n )+eb n x ( V x n ) ] (157) Using the rotated director coordinates (Eq. 156), and making the substitution that (sin2kx),,=(cos2kx)4'z= 1 , i.e., averaging 2 over the whole system, leads to the average free energy per unit volume, F(E),, given by

F (E)f = -1 (kl I + k33)k2 sin2$

E,=O

4

Figure 35. Representation of the director (y, z) plane and the helix axis ( x = h ) for a chiral nematic undergoing flexoelectric distortion in negative ( EO) polarity electric fields ( E ) .The z axis is out of the plane of the figure towards the observer.

+ 21 k22 k2(1- cos $)2 -

1 --(ef+%)E,ksin$ 2

(158)

To minimize F ( E ) , we take the derivative

aF(E)f =0, which leads to nates allowing for the helical geometry, is 0 or IT and O = k x . The helical wave vector along x is still given by k = 2 nlp and p is defined as positive or negative for right-handed and left-handed materials as before. The helical pitch is short, i.e., p < I , so that diffraction effects due to striped textures are not observed macroscopically (viewing along the z direction) and the material is therefore optically uniaxial along the x axis. On application of an external field E,, assuming flexoelectric coupling as the dominant mechanism, the directors rotate [ 1741 through an angle $ around z to new positions defined by n, = sin0 sin$ = sinkz sin$ n, = sin0 cos$ = sinkz cos$

n, = cos0

= cos k z

(156)

Thus the optic axis of the helix is also rotated through $. The free energy density of the

a@

Within the limit of small $, then tan$= sin$ = $, which gives

Thus the field-induced tilt is linear in E, and if (e,+e,,)>O and k > O this tilt follows the field direction and reversing the field polarity reverses the tilt angle. Therefore if such a material were placed between crossed polarizers with one polarizer aligned along +$ or -9, then maximum contrast is observed for $=22.5". For the more general case, the light transmitted through crossed polarizers is given by

394

2


where Zo is the incident light intensity, p is the angle between the zero field optical axis (x) and the polarizer axis, A n is the macroscopic birefringence defined by (nFA-rzyA), where OA refers to the optical axis (i.e., parallel tox), d is the sample thickness, and A is the wavelength of light. The dynamics of this effect are described for small @ [172, 1741 by

where q is an effective viscosity for rotation of the optical axis around z , ksb=%(kll+k33),and esb=%(es+eb).Thus @ = 4, (1- exp-t’Zf)

(163)

where & is the saturation value of the rotation given by Eq. (160) for a pulsed field applied at t=O, and z, is given by Zf= q (ksb k2)-’

(164)

Thus the response time is independent of E, within the small angle limit of validity of Eq. ( 160). Experimentally, the electrooptic responseislinearupto-15’ [172,176,177], although for tilt angles greater than this the nonlinear behavior of Eq. (161) will dominate the optical response. Response times in the range of 10-100 ps have been recorded that have only a slight temperature dependence [ 1761. This can be seen from the form of Eq. (164), where it is desirable to have chiral nematic structures with a low ‘rotation’ viscosity and a high temperature independent pitch and mean splay bend elastic constant. These materials are very promising for fast electrooptic modulation [29, 1781, and in the following sections we will consider potential applications.

2.5 Applications of Chiral Nematics In the preface to the first edition of his seminal book entitled The Physics of Liquid Crystals, de Gennes wrote ‘Liquid crystals are beautiful and mysterious’ [30]. In the preface of his most comprehensive series on Liquid Crystals: Applications and Uses. Bahadur added to the de Gennes’ description the phrase ‘and extremely useful’ [ 1791. There is no liquid crystal phase to which these descriptions apply more aptly than the chiral nematic phase. The spectral reflection colors and the use of these phases in visual arts are certainly beautiful [89]. The exact solution of Maxwell’s equations for light obliquely incident on a chiral nematic film and of the Frank-Oseen and Leslie-Ericksen elastic and dynamic theories in the limit of large deformations in chiral systems, are all mysteries still to be solved. The applications of chiral nematics in twisted nematic displays [ 131, medical thermography [97], and imaging are certainly extremely useful. There are many other uses in linear and nonlinear optics, in thermal imaging, for sensors, and in novel electro- and magnetooptic devices and detectors. In the following sections we will review these applications based on the physical properties that we have already discussed. It is clear that, whilst the chiral nematic phase was the first thermotropic phase to be recognized or discovered [l-31, there are still many new inventions to be made and applications to be found [ l l , 19, 58, 147, 179-1811 for these curious chiral structures.

2.5.1 Optical: Linear and Nonlinear The optical properties of chiral nematic liquid crystals are unique in that, without ab-

2.5

sorption or energy loss, they can be used to filter or select, and reflect or transmit different polarizations and wavelengths of light spectrally from the near-ultraviolet to the near-infrared, in a range spanning -400 nm to 10 pm. In this mode they are used as passive ‘optical’ elements and if the polarization process only involves a coupling with the optical field Eoptthrough the polarizability, a, or linear susceptibility we classify this as a linear effect herein. If the coupling is with the field squared or higher, i.e., involves hyperpolarizability or n order susceptibility (n=2, 3, i.e., etc.), we will call this nonlinear. The coupling of optical effects with low frequency electric or magnetic fields will be considered in Sec. 2.5.3 as ‘active’ elements or extrinsic effects that involve director reorientation. With these definitions in mind we will outline some of the ‘passive’ or intrinsic optical applications of chiral nematics. The first application arising as a result of Eqs. (3) and (4) is in optical filters. Here the selective transmission or reflective properties are used to select a narrow spectral band [9, 181-1831, i.e., notch filters, or even a wide spectral band [ 1841,of optical frequencies. As a result of the circular polarization properties, this also leads to the production of polarizers and retardation plates [ 1811. The light reflected from a planar or Grandjean texture is either right- or left-handed circularly polarized at normal incidence. The combination of two such films of opposite handedness leads to notch and band pass filters capable of selecting bandwidths of a few nanometers or so, depending on Eqs. (3) and (4) from an unpolarized spectrum, i.e.,

xl,

x2,x3,

Thus An-0.01 and E-1.5 lead to AA 3 nm at optical wavelengths. Some

-

39s

Applications of Chiral Nematics

years ago [46] we studied a number of noncholesterol-based compounds, which verified the validity of Eq. (16.5) and demonstrated the role of Anlk in selective reflection devices. Band pass filters of this type, which required input polarizers, were described over two decades ago [ 1851, as was the ability to couple optically several of these filters to produce a multiband output [ 1811. Notch filters not requiring polarizers, but combining two films of opposite handedness, were produced [ 1851 more recently using polymeric variants [183]. A novel chiral nematic based color projection system has been demonstrated recently [ 1861, which clearly illustrates the advantages of liquid crystals. All of the functional parts, i.e., polarizers, band pass filters, and electrooptic modulators, were based on achiral or chiral nematic liquid crystals. In Fig. 36 we show the optical principles of the large aperture chiral nematic polarized light source. The conversion efficiency of the polarized color projector was close to loo%, due to the nonabsorbing nature of the chiral nematic materials used, and red-green-blue (RGB) polarized output was readily obtained from a white light source [ 1871 and used in colored twisted nematic (TN) cells. This has led to a compact efficient optical system suitable for projection TV. A different and quite remarkable application of chiral nematic wide band filters fol-

M

L

C

CNLH

QW

Figure 36. Schematic diagram of achiral nematic polarizedlight source [187], where L=lamp, M=spherical mirror, C=condenser lens, CN,, =left-handed chiral nematic filter, QW=quarter wave plate (A/4), I,=unpolarized light, I:=right-handed circularly polarized light, and Ia=polarized output light.

396

2


lows from this work [ 1881. Using direactive chiral nematic low molar mass mesogens, achiral monoreactive mesogens, and UVabsorbing dyes, it has been possible to prepare polymer films with a pitch gradient from 450 nm to 750 nm, thus giving very wide band width, ‘white’ chiral nematic reflecting films [ 1891that are now being commercially exploited [ 1841 as brightness enhancers with 80% optical gain in TN and other displays. Storage films based on low molar mass organo-siloxanes exhibiting glass transitions [190-1921 have been used to prepare self-supporting films capable of withstanding typical continuum working laser intensities, as well as for use in visual arts [193]. Laser applications, for the selective reflection of light, represent a very technologically oriented use of chiral nematic liquid crystals. It has been shown that for a pulsed Nd:YAG laser cavity end mirrors may be produced which both maintain polarization on reflection and allow single longitudinal mode selection to be attained [194]. In solid state lasers, beam apodization, in which the laser beam profile is shaped to maximize gain in the active medium, is of major importance for high powered systems [ 1951. It has been shown [196] that such apodizers may be fabricated using two chiral nematic films based on cyanobiphenyl chiral mixtures in series, in separate devices, to give a linear apodizer, and in intimate chemical contact to give a circular apodizer using refractive index gradients to modify the reflection bands. The devices had damage thresholds of 5 J/cm2 for 1 ns pulses at A= 1.054 Fm with a 3 mm spot size. Chiral nematic materials have been used for over a decade in Nd:glass laser systems for the OMEGA project with beam diameters of up to 100 mm. The use of liquid crystals in this project has been reviewed [197], and it was shown that laser waveplates, circular polar-

izers, optical isolators, and notch filters, as well as the above soft apertures, could be readily used as high performance alternatives to conventional glasses, crystals, and thin films. The unique optical properties of chiral nematics were successfully used up to power densities of joules per squarecentimeter over an 18 month period without degradation problems. This is quite clearly an area where controlled organic structures, capable of being readily ‘tuned’ to the applications in mind, have a great advantage over inorganic systems that have to be prepared from large scale crystal growth facilities. Nonlinear optical effects have been predicted and demonstrated [ 198-2001 in chiral nematic materials. The n =-n condition in chiral nematics means, in this context, that the apolar order does not lend itself to second harmonic light generation (SHG), although, using external electric fields, it is possible to excite SHG through third order (THG) processes [201-2031. The electron conjugation of the noncholesterol based materials lends itself to THG applications. It is clear that with such synthesis and the degree of molecular engineering now available, this application presents an interesting growth area. The potential is there to use poled order in chiral nematics without fully unwinding the helix in a planar structure, to use the helix pitch to generate quasi-phase matching. This would of course require transverse electric fields, but the possibilities of using glass transitions to freeze the induced optical texture potentially lead to new NLO materials. Early experiments using organo-siloxane chiral nematic structures are very promising, leading to d coefficients of the order of 1-10 pmV-’ [204]. The application of chiral nematics to THG processes has long been recognized [ 198-2001. These are passive applications in which mirrorless optical bistability has been predicted [198] and the theory modi-

2.5

fied for retro-self-focusing and pinholing effects in these materials. The latter effects were also confirmed experimentally I2051 in the presence of intense optical fields. Four wave mixing of two circularly polarized counter-propagating waves has also been predicted [200] and discussed in detail [206]. This would seem to be a further potential growth area for 'frozen' optically clear, nonresonance enhanced chiral nematic phases.

2.5.2 Thermal Effects The thermo-optical properties of chiral nematics depend critically on the helix pitch, and it is the temperature variation of this, as described by Eqs. (46) and (47), that leads to many interesting applications. Initially, simple, inexpensive, digital thermometry devices were fabricated [207] using, for example, cholesterol-based materials with a fixed pitch, a narrow temperature range, and single strip elements (each with a different clearing temperature). Many early patents are described in [ 1801 and are well worth reading! These multiple legend devices have been used as room temperature thermometers, body temperature sensors [208], and for monitoring the postoperative progress of anaesthetized patients [209]. Of particular interest in temperature sensing are two features of chiral nematic phase transitions. Firstly, as a chiral nematic is cooled towards the smectic (A or C) phase, the helix pitch diverges markedly (see Eqs. 46 and 47). Since this temperature dependent reflected wavelength spectrum, or color play, can be chosen to be over the whole visible (or UV to near IR) spectrum and be as wide as 20-30"C, or even as narrow as a few degrees, it is possible to sense temperature spectrally (even by eye) to an accuracy of a few milli-Kelvin. Optical rot-


397

atory power could similarly be used (see Eq. 8), because of thep ( t )dependency. Secondly, by using the optical texture and the quasi-permanent texture changes that occur during a heatingkooling cycle, which in turn lead to a planar to isotropic and then to a focal-conic texture sequence, it is possible to make 'maximum' thermometers [210]. The planar texture reflects light specularly, whilst the focal conic gives a scattering semi-opaque texture. The thermometer is reset by mechanical shear (i.e., weak bending of the device). A second example of this uses is in texture storage by rapid cooling into a glassy phase [21 I]. The applications of these materials and fabrication techniques have been extensively reviewed in an interesting historical sequence of decade steps [9, 11, 971. Herein we will only consider an outline of the thermal application areas and the avid reader is referred to these source references and the 700 plus references cited therein, as well as the early overviews [ 5 8 , 1801. Initially, it is useful to consider the availability of materials and preparation or fabrication techniques. Mixtures are now available [211, 2121 that cover a temperature range between circa -50°C and +150"C. Combinations of chiral nematic mesogens based on thermally stable chiral esters are used in these mixtures, and recent developments are described in the previous chapter [ 121. Essentially it is now easy to purchase A and B type mix and match materials for particular operating temperature ranges [211]. For many applications, it is the device fabrication technique that is the limiting factor rather than the availability and thermal or optical stability of the chiral nematic compounds. Chiral nematic liquid crystals are obviously fluids and in order to be used in an aligned state, they have to be contained. For good optical contrast, the background is usually black. The simplest

398


‘encapsulation’ technique is to use glass substrates, as in TN devices or plastic laminates (see [97]). Plastic blisters have equally been used for low cost ‘throw away’ devices, as have filled fibers [2 131. By far the most popular fabrication process is to use microencapsulated chiral nematics [214, 2151, which may then be formulated in inks, sprays, and pastes. Typically, a gelatin and gum arabic combination is used to form spherulites of 1-10 pm diameter and, by careful production control, these can be optimized to a diameter of -5 pm, to reduce stray light-scattering effects from the smaller capsules. These optimized capsules are then suspended in a suitable polymer binder to be coated onto the black substrate. The optics of the confinement potentially pose two problems. Firstly, spherulitic droplets, as discussed in Sec. 2.2.1.1, will contain optical defects through disclinations or dislocations. Secondly, it is not obvious that the optimally reflecting planar texture will be obtained. This problem is accentuated if, in the preparative techniques, the chiral nematic cools from a blue phase into a supercooled blue phase or even a focal-conic texture. Although the angular viewing properties of the spherulitic droplets give fairly uniform color, the displays do not show the spectacular iridescence associated with the chiral nematic phase. Some of these problems are overcome if the droplets can be deformed into flattened oblate spheroids or discs. This helps to promote the planar texture, pins the bipolar dislocations at the edges, and leads to brighter devices. A second encapsulation technique is to use polymer dispersions [2 161,in which droplets of chiral nematics are suspended in a polymer matrix through processes such as temperature or solvent induced phase separation during the crosslinking of the polymer matrix. Essentially, any of the techniques used to produce polymer-dispersed

nematic liquid crystal devices (PDLC or NCAP) [2 17-2211 for electrooptic displays may also be used for chiral nematics. A further embodiment of encapsulation procedures, which produces very bright reflectance, is to use laminated polymer sheets in which the surfaces have been prepared to give planar alignment through microgrooved gratings [41]. These may then be used in a combination of RH and LH circularly reflecting films to enhance the narrowband or indeed broadband reflections. Within these different constructional constraints, we can now review, briefly, some of the key applications areas. Biomedical thermography [222] is used extensively as a thermal mapping technique to indicate a wide range of subcutaneous medical disorders. The first use of chiral nematics to indicate skin temperature was over 30 years ago [223]. Such devices are normally constrained to indicate temperature in the 30-33°C temperature range, over which the whole color play can be exhibited. Such films have been used to indicate breast cancer [224], for placental location [225], to identify vascular disorders [226], and for skin grafting [227]. The use of chiral nematics in such areas presents an inexpensive rapid screening technique which is only indicative, since local patient and environment conditions, e.g., room and patient temperatures and internal film pressure, may lead to some false readings. This is discussed in more detail in [97]. A particular application area of increasing importance is in the nondestructive testing [228] of inanimate objects. For example, local temperature variations may be caused by structural flaws [229,230] leading to local differences in thermal conductivity, by hot spots in electrical circuits due to short circuits (here the analysis of microchips [23 11 is particularly interesting) [232-2351, by heat transfer effects in aero-

2.5

dynamic models [236], boiler surfaces [237], cookware, etc., and by faults in spacecraft [238]. In many of these applications, it is possible to study transient changes with a resolution of lo--’ s [239]. The use of chiral nematic materials for nondestructive testing has been bibliographically reviewed in references [212,240], and [97] gives an excellent recent overview. Radiation sensing has been carried out using transducers of low thermal mass to detect infrared laser light [241, 2421, microwave leakage [2431, and ultrasound [244]. Power densities as low as 1Op3 W cm-2 have been detected [245]. In these applications, the incident radiation is converted to heat using backplanes of carbon black, gold black, or metal films. The choice of backplanes is led by the application and, in the case of long wavelengths (infrared or microwave above - 10 pm), the liquid crystal may itself have intrinsic absorption bands. A particularly useful application occurs in imaging infrared laser beam emission mode structures [246], and further such devices have been used in real time infrared holograms [237]. Similarly, microwave holograms [248] and acoustic images [244] have been formed. In the very near infrared (i.e., 680-800 nm), solid state lasers have been used for write once read many times optical data storage (WORMS) at rates of 100 MHz (i.e., 10 ns exposure times) with power densities of lop9J pm-* [249], using glassforming low molar mass chiral nematics. A further large market area for the use of chiral nematics is in decorative and novel product applications that use the visual appeal of the selective reflection properties. Mood-indicating jewellery and artifacts have been produced [250], as have images on fabrics and clothing [251, 2521. Wine bottles, coffee mugs, and drink mats are another area where chiral nematics have found amusing mass applications. Three dimen-

Applications of Chiral Nernatics

399

sional visual art effects [193] and stereoscopic images [253] have also been produced. The use of chiral nematic materials in this applications field is only limited, it appears, by the imagination of the inventor and the bounds of good taste!

2.5.3 External Electric Field Effects In the previous sections we discussed the static properites of chiral nematics, i.e., textures, optical propagation, ‘Bragg’ reflections, optical rotation, pitch variation, elastic constants, and dielectric, diamagnetic, and flexoelectric phenomena, and each and every one of these properties has been used in an electrooptic device of some form. At first sight this may seem surprising, since chiral nematics are normally associated with thermal and reflective ‘passive’ devices, as discussed in the previous two sections. However, as well shall see, the chiral nature of the phase imparts some very wide ranging electrooptic (and even magneto-optic) properties to the materials. The dynamic properties, such as viscosity, texture, and defects, are important for response times and memory effects. So the natural question is, ‘what is the main parameter that allows so many electrooptic devices to be produced?’ The answer lies in Eqs. (1) and (2). It is the pitchp, produced by different twisting powers, that leads to different effective electrooptic effects. For long pitch materials of p >> A, we have light-guiding phenomena leading to twisted nematic and supertwisted nematic (TN and STN) devices based on planar textures. For intermediate pitch lengths,p - A, we have scattering (conservative or consumptive) leading to dye guest-host (DGH) displays based on focalconic or Grandjean textures. In this regime the optical rotatory power (ORP) is anoma-

400

2


lously high, and this can also be switched in an electric field to produce devices. For very short pitch systems, p > A) The majority of current commercial liquid crystal displays are based on the twisted nematic electrooptic effect using active matrices to give, for example, complex computer lap-top screens [13]. It is often overlooked that these displays are based on long pitch chiral nematic materials to remove socalled reverse twist, and the original papers [254, 2551 referred to the effect as a positive planar cholesteric to nematic phase

I

White

I

Polarisers

1 Glass Panels

U

Polarisers

change. The operation of a conventional twisted nematic is shown in Fig. 37. The basic construction is to use two orthogonal planar alignment layers separated by a distance, d , so that the director, n, twists through 90" from one surface to the other. The twisted birefringent structure rotates the plane of polarization provided, according to the Mauguin limit dAn > 21

( 166)

The threshold voltage, V,, (TN), for the transition from twisted structure to homeotropic alignment, above which polarization guiding is lost, is given [26] by &h

(TN)

=";r'

1!kl 1 -k 41 ( k 3 3 - 2k22 EO

AE

4-

2k22 d / p

(167)

The rise, z,,and decay, z, times in response to a pulsed AC field are given by

z,=

17 d2 ~0 AE(V2-

I White Light I

Figure 37. Schematic diagram of a twisted nematic electrooptic cell for (a) zero voltage and (b) a voltage above threshold, V,,(TN). Note that some chiral nematic mesogens remain anchored in a planar arrangement on the alignment surface, which then provides the coupling for the field-off decay back to the twisted structure. The weak chiral nature prevents back flow.

2.5

where q is a twist viscosity and the other terms have their usual meaning (see Sec. 2.2). Thus the finite pitch, p , of the chiral nematic phase influences the electrooptic parameter through the 2 k,,dlp term. Normally only a few weight percent of chiral dopant is added to minimize this term, whilst at the same time eliminating reverse twist. The operating parameters, the role of surface pretilt, the viewing angle, the threshold curves, multiplexability, etc., are discussed in reference [13]. In a variant of this display, the twist is increased from 90" to 180"-270", i.e., as in the STN device, to sharpen the threshold intensity-voltage curves and thereby improve multiplexability. The STN, in comparison with the TN device, has better contrast and viewing angles, but slower response times and poorer grey scale. Here again the important influence of the chiral pitch can be seen from the threshold voltage V,, (STN)

where $ is the twist angle between the two alignment layers [N. B. This reduces to Eq. (167) for $=d2.]. In the STN device the chiral compound has to be twisting sufficiently to ensure 7t < @ < ~ 1 2depending , on the shape of the theshold curve required [257]. Here clearly the threshold voltage will be greater, because of the 4 k,, dlp and $ terms. The operating parameters of STN devices are discussed in detail in references [13, 2571. In a further example [25] of long pitch 90" twisted or chiral nematic displays, dyes have been added to sharpen the threshold curve of the planar Heilmeier display [258] with the advantage over conventional TN cells of requiring only one polarizer. This improves the optical throughput,


40 1

but has also reduced contrast. Positive {J or negative ({,> dichroism (where 5 is the absorption coefficient parallel or perpendicular to n) may be used to give negative [259] or positive [260-2631 (i.e., dark symbols on a light background) optical contrast. In these devices the input polarization is the same as the alignment direction at the 'input' planar alignment layer.

2.5.3.2 Intermediate Pitch Length Systems ( p -A)

-

Intermediate pitch systems ( p A) give rise to focal-conic and planar or Grandjean textures (see Sec. 2.2.1.1), and these may be deformed in electric of magnetic fields (see Sec. 2.4). The earliest reports of electric field induced reorientation leading to electrooptic effcts are reported for scattering or focal-conic textures in [136, 1381 and for planar textures in [ 141,2641. Similar effects in magnetic fields were reported in [129, 137, 1401. The different optical effects observed at the time are accounted for by the direction of the applied field relative to the helix axis (see Sec. 2.4). As was discussed in Sec. 2.2.1.2,, for a chiral nematic phase exhibiting selective reflection, the ORD becomes anomalously large and therefore, if the helix pitch can be unwound or deformed in an electric field, the circular polarization and ORD should equally change. The latter was clearly observed and studied in some depth in [265]. These early observations set the scene for considering electrooptic devices in intermediate pitch ( p 2) chiral nematics. The focal-conic texture is inherently light-scattering in the forward direction [266] and this in itself does not provide sufficient optical contrast between 'off' and 'on' states when switched to the homeotropic texture, without the use of external polarizers. The planar to homeotropic field in-

-

402


Sec. 2.4.4) unwinds the helix to give a homeotropic state. The axis of the dye is then in the field direction and the device becomes nonabsorbing, assuming positively dichroic dyes (see Fig. 38a). In a second variant of this device, planar orientation is used to spiral the axis of the dye, following n , in the plane of the device and for zero fields this leads to a colored absorbing state. For such systems, where the pitch is too short to give light polarization guiding (see the Mauguin limit, Eq. (166)), the polarization becomes elliptical and this is readily absorbed by the dye (Fig. 38 b). For a high enough field the transition to homeotropic is again induced, and this leads to a nonabsorbing (or weakly absorbing, due to limiting 6)or clear state. The threshold voltage for helix unwinding is given by

duced transition does provide contrast with a suitable black background, but on field removal tends to relax back to a focal-conic rather than a planar texture in a fairly slow dynamic process. There have, however, been recent developments in which these effects have been utilized or improved upon to produce interesting displays. The first was the White-Taylor device [267] using anisotropic dyes and either homeotropic or planar surface alignment. The second is in using polymer-stabilized chiral nematic films to exploit the bistable nature of the planar and focal-conic textures [268]. In the White-Taylor device the chiral nematic ( p A) is doped with an anisotropic dichroic dye. With homeotropic boundary conditions and low voltages, the focal-conic texture becomes axially aligned in the plane of the device. The dye spirals with the director and the random directions of the helix axis in the plane of the device ensure that unpolarized light is absorbed uniformly in this state. Application of a high field (see

-

Input White Light c_ ____ j---____ mPolariser Glass Substrate .Transparent Electrode Homeotropic Alignment Layer Chiral Nematic (Focal Conic)

-

and for d - 10 pm and p 3 pm gives typical threshold voltages (to complete the un-

Input White Light

Input White Light

-_-I

output Coloured Light

Glass Substrate Transparent Electrode Planar Alignment Layr Chiral Nematic (Grandjean) outout Coloured Light

Output White Light

0 : LiquidCrystal With Little Attenuation

I (a) Unenergized State Focal Conic

(b) Unenergized State Grandjean

Molecule

: DyeMolecule

(c) Energized State (Homeotropic)

Figure 38. Schematic operation of the White-Taylor dye guest-host chiral nematic electrooptic cell. In (a) for zero applied field the axis of each focal-conic domain is random in the x, y plane, as therefore is the dye, using homeotropic surface alignment. In (b) the texture is planar for the zero field state and therefore the dye spirals around the z direction. In (c) the focal conic (a) or planar (b) transition to homeotropic nematic has taken place above the threshold voltage V,, (WT). The black ellipses represent the dyes in the chiral nematic matrix.

2.5

winding) of the order of 1OV. These devices are polarizer-free and have better viewing angles than TN devices, although V,, (TN) < V,, (WT) (see Eq. 170). They can also be matrix-addressed to a limited extent, and the performance of the two modes has been compared in references [269]. Negamay also be used to protive dyes duce reverse contrast. It is not, however, possible to decrease the pitch ad infinitum in these devices because of the dependence of V,,(WT) on dlp. A recent innovation in the use of chiral nematic phases has been to stabilize the focal-conic or planar textures in situ with a polymer network [268]. The helix pitch may be chosen to give bright specular reflection, and that can then be switched into a focalconic (forward-scattering) texture. Using a black background, this has led to bright, high resolution colored images with high contrast and wide viewing angles, and without the need for backlights. Devices have been fabricated using flexible polymer substrates to make lightweight displays with a 320 x 320 pixel writable-erasable screen. Applications are foreseen in electronic publishing and, using a stylus, it is possible to hand write erasable information on these displays. As with the White-Taylor device, dyes can be incorporated into the polymerstabilized chiral nematic device [270] to improve contrast between the on and off states, and it is anticipated that such dyed PDN*LC devices will find use in projection displays. The use of flexible substrates without backlighting, combined with the specular reflection properties (in unpolarized light) of chiral nematics that may be electrically switched from one bistable state to another, seems to hold great promise in the search for the Holy Grail of an electronic newspaper (2711. In the latter reference, reflective chiral nematic liquid crystals were used to produce a 200 dpi full page, passive matrix,

(tl> t,,)


403

bistable glass display with a 2240 row by 1728 column resolution. Whilst these are slow update displays, taking several seconds, they would seem ideally suited to this application. A further interesting use of the focal-conic to homeotropic texture transition is in infrared modulation [272]. Here it was found possible to modulate infrared light at A= 8 - 12 pm with a maximum transmission of 8796, a contrast of 93%, and turn on and off times of 1 ms and 125 ms, respectively. A further window examined was 3-5 pm, and this work suggests that other chiral nematic electrooptic effects could be exploited in the near infrared. In communications technology a 2x2 optical switch for fiberoptics has been developed [273] using a chiral nematic film and two switchable nematic waveplates. It has been demonstrated that this is suitable for LED or laser sources. The device worked at 1.3 18 pm and had switching times of 40 ms with -26 dB crosstalk between unselected fibers. There will clearly be further advances in this use of the unique optical properites of chiral nematics.

2.5.3.3 Short Pitch Systems ( p 2)/21

(1 1)

Here qo = 27c/Z0, the wave vector related to the layer thickness. Unlike (u2(r)),this quantity converges. Rather than a Bragg peak like a delta junction for a crystal, the calculated X-ray peaks should exhibit the following profile:

~ ( q=) l/[q,

- q0l2-"

qx = q y = 0 (12a)

2 2-11

I ( q ) cc 1/[q,2+qy1

9

q2=0

(12b)

where

17

= q i k B T/[8Z(KB)'/2]

(13)

This theoretical prediction has been confirmed by detailed X-ray diffraction studies which also enable accurate measurements of [ 111. Figure 2 displays the X-ray diffraction intensity Z(q,) as a function of the scattering wave vector qz obtained at two temperatures in the SmA phase of 8 0 C B [4'-n-octyloxy-4-cyanobiphenyl].The quasi-long-range smectic layer order gives the

2.2

I I

deviation of the experimental data from the dashed line which represents the scattering profile for a system with true long-range order. The best fits of the data to Eq. (12) convoluted with the resolution function are shown as two solid lines. The values of 77 determined from the best fits agree with the experimentally determined values of qo, K , and B. This absence of true long-range smectic order is a result of the simultaneous existence in the free energy of a solid-like elastic term for wave vectors perpendicular to the layers and a nematic term for wave vectors parallel to them. Such a system exhibiting quasi long-range order in three dimensions is at the lower marginal dimensionality below which long-range order no longer exists.

445

Smectic A Phase

Previous discussions demonstrate the importance of the compressional elastic constant B in characterizing the SmA phase. Moreover, the critical behavior of B in the immedite vicinity of the nematic (N)-SmA transition remains an important and unresolved issue. To obtain high resolution measurements of B , several experiments have been designed, (e.g. second-sound resonance [ 121 and the line width of Rayleigh scattering [13]). Well into the SmA phase, the typical value of B is about lo8 dyn/cm2. The most recent sets of experimental data resemble a power-law approach to a finite value at a continuous N-SmA transition. Figure 3 displays the compressional elastic contant B versus temperature just below the N - SmA transition temperature of SOCB. The data were obtained from the line width of Rayleigh scattering measurements [ 13). Whether the value of B approaches a finite value or zero at the SmA - N transition remains an experimentally and theoretically important question. The enhancement of surface ordering at the liquid crystalhapor interface has been well documented experi-

-m

7,8........................................................

7.4..............................

7

- 1 which indicates stronger surface damping of the layer fluctuations. Holyst et al. [15] first carried out the numerical analysis on a discrete version of the free-energy (see Eq. 14). The model offers a satisfactory explanation for the X-ray scattering data obtained from the SmI/C phase of free-standing 70.7 films at 72.5 “C [16]. The 70.7 compound is one member of the homologous series of N-(4-n-aZkyZoxybenzylidene)-4-n-aZkylanilines(n0.m).The phase consists of monolayer two dimensional SmI surface layers on SmC interior layers [ 171. High resolution data from four film thicknesses, namely 3-, 5-, 15-, and 35-layers, were obtained. The data can be fitted by a model including molecular tilt angle profiles to account for the finite tilt angle of both the SmI and SmC phases. However, the effect of surface hexatic order was not considered. Consequently, the critical test of the model should be conducted on a simpler system, namely, free-standing SmA films. Shalaginov and Romanov [ 181 have recently developed a continuum model and obtained an explicit formula for the displacement-displacement correlation function. Furthermore, both the uniaxial properties of the SmA phase and multiple reflection from the interfaces have been included in this theoretical model. It offers excellent agreement with the X-ray scattering data [9] acquired at a temperature well into the SmA phase of FPP (or H7F6EPP) [5-n-heptyl-2(4-n-perfluorohexylethanophenyl)pyrimidine]. Both the specular reflectivity and offspecular diffuse diffraction from 4-, 20-, and

2.3

Hexatic Smectic B Phase

447

[9]. Nevertheless an independent measurement of the compressional elastic constant would be extremely important. The low value of y is due to the perfluorinated tail. Subsequently, a direct measurement of surface tension confirmed this value of y [ 191. In comparison with terminal aliphatic compounds, the reduction of yand enhancement in B leads to v(=y/(BK)"2)< 1. Thus surface damping of layer fluctuations is weaker.

Figure 4. Log-log plot of the X-ray scattering intensity versus transverse scans at fixed qz for 4- and 34layer H7F6EPP films. The films are in the SmA phase. Circles and crosses indicate positive and negative q x , respectively. The values (in ,k ') of qL are 0.235 (a), 0.292 (b), 0.348 (c), 0.448 (d), 0.216 (e), 0.287 (0, 0.355 (g), and 0.429 (h), respectively. Data have been shifted for clarity. The solid lines are the best fits to the model. (Adapted from [9]).

34-layer films were measured. Figure 4 shows transverse scans obtained from 4- and 34-layer films at various fixed qz's. A broad peak with a long tail is characteristic of the Peierls -Landau instability. The theoretically fitted results are shown as solid lines. The best fitting results for both film thicknesses and various qz values yield K = l . O x IO-'dyn, B = l . O x 10'' dyn/cm2 and y= 13.0 dyn/cm. The value of K is approximately the same as that for the ordinary nematic elastic constant. The coefficient B is about two orders of magnitude larger than for ordinary liquid crystal compounds with saturated alkyl groups [ 12, 131. The more rigid part of the perfluorinated tail in the H7F6EPP compound may be the origin of this enhancement. This is consistent with the fact that the layer structure of this perfluorinated compound is better defined. The evidence is that the specular reflectivity exhibits pronounced second order peaks

2.3 Hexatic Smectic B Phase 2.3.1 Macroscopic Properties In 1971 Demus et al. [20] first reported the existence of the SmF phase in 2-(4-npentylphenyl)-5-(4-n-pentyloxyphenyl)pyrimidine. About eight years later, utilizing X-ray diffraction, Leadbetter et al. [21] and Benattar et al. [22] studied the molecular arrangement in this mesophase. A pseudohexagonal molecular arrangement was found within the smectic layers in both the SmF and SmI phases. The basic understanding of this observed pseudo-hexagonal molecular arrangement required the concept of hexatic order, developed in the context of the two-dimensional melting theory which was proposed at about the same time by Halperin and Nelson [23]. While the theorists put forth these exciting hypotheses, experimentalists [24], performing X-ray diffraction studies on various liquid crystal compounds, also demonstrated the existence of two different types of B phases with different ranges of interlayer positional correlation lengths. This observation was subsequently followed by several high resolution X-ray diffraction investigations on free-standing liquid crystal films [24-271. First, the conventional B phase in 4 0 . 8 (N-(4-n-butyloxybenzyli-

448

2 Physical Properties of Non-Chiral Smectic Liquid Crystals

dene)-4-n-octylaniline) was demonstrated to be a three-dimensional crystalline phase [25, 261. The more interesting liquid crystal mesophase exhibiting long-range bondorientational order, but only short-range positional order, the SmB,,, phase, was subsequently identified in 650BC [27]. In Fig. 5, the X-ray scattering scan along one of the “crystalline” axes (Q,, scan) displays short-range positional order, while the QI scan exhibits very weak interlayer coupling, similar to that for the SmA phase. The development of a six-fold modulation in an angular scan (with the rotation axis parallel to the layer normal) becomes apparent below the transition temperature TAB=67.9 “C (determined by high resolution heat-capacity measurements by Huang et al. [28]). This six-fold modulation indicates that the phase below TABexhibits 3 D long-range bond-orientational order. However, the size of the hexatic order domain is about 1 mm2, which was much smaller than the X-ray beam size. Extensive averaging is required to demonstrate the existence of six-fold modulation

4

650

using X-ray diffraction. This makes quantitative studies and analyses of the bondorientational order practically impossible. Employing electron diffraction with a beam size of about 1 pm2, Ho and coworkers [29, 301 obtained beautiful six-fold arcs. Figure 6 displays a reproduction of one of these photographs [30] obtained from the (a) SmA, (b) SmB,,,, and (c) B phases of

BC

Figure 5. %-averaged X-ray scattering intensity for a Qll scan (solid dots) and a QL scan (open circles) in the HexB,, phase of 650BC. Note that different scales are used for the QII and QI axes. The inset illustrates Qll the directions of three different scans, namely and QI scans. (Adapted from [27]).

x,

Figure 6 . Electron diffraction patterns from a 9-layer 54COOBC film. The entire film is in the SmA phase (a), in the HexB phase (b), and in the crystal B phase (c). (Adapted from Ref. 30).

2.3

a nine-layer 54COOBC [n-pentyl 4’-n-

pentanoyloxybiphenyl-4-carboxylate]film.

The constant intensity ring found in the high temperature SmA phase indicates the liquid-like in-polar molecular arrangement. Such a diffraction pattern is seen ubiquitously in fluids. The low temperature crystal B phase gives one set of six sharp spots. Sharp diffraction peaks are the signature of a crystal. However, much weaker second order diffraction peaks, which cannot be seen in this photograph, demonstrate that the Debye-Waller factor is very small; that is, the crystal is very “soft”. The intermediate SmB,,, phase yields the characteristic six-fold arc for the hexatic order. Although the inplane translational order remains short-ranged, the positional correlation length shows a significant increase (from approximately 2 nm to 7 nm for 650BC) through the SmA-SmB,,, transition [27]. As a result of this experimental evidence, the traditional smectic B phase has been reclassified into two different phases: the SmB,,, and B phases. By employing a symmetry argument, the existence of long range positional order in the B makes the SmA-B [28,3 11 and SmB,,,-B [30] transitions first order. The order parameter associated with the SmA- SmB,,, transition is bond-orientational order. It can be represented by YH= YHoexp (i 6 06).This order parameter places the SmA - SmBh,,-transition in the XY universality class. Thus the transition can be continuous in three dimensions and should, furthermore, exhibit Kosterlitz Thouless-like behavior in two dimensions [32]. Mechanical responses obtained from a low frequency torsional oscillator yield a finite in-plane shear modulus for 4 0 . 8 films in the crystal B phase [33, 341 indicative of a solid-like response. The hexatic B phase of 650BC yields no in-plane shear modulus, just like a liquid [35].


449

The molecular bond direction is defined by an imaginary line between one pair of the nearest neighbour molecules [23]. This means that the measurement of bond-orientation correlation requires a four-point correlation function. To date no appropriate experimental tool allows us to conduct this kind of measurement. Thus the degree of bond-orientation correlation can only be inferred indirectly. Moreover, no available physical field exists which can couple directly to the hexatic order in the hexatic B phase. Consequently, the heat-capacity measurement is one of the most powerful experimental probes used to investigate the nature of the SmA-SmB,,, transition and to complement structural identification by X-ray or electron diffraction. The pioneering X-ray work on 650BC also revealed the existence of herringbone order 1271,but a detailed investigation to determine the range of the herringbone order has not yet been performed. Despite the indication of the herringbone order, this phase is simply denoted as the SmB,,, phase. Subsequent electron diffraction studies on 8-layer 3(10)OBC films also revealed the characteristic diffraction pattern due to herringbone order [36]. As a consequence, the hexaticB phase found in nmOBC compounds may be more complicated. To test the theoretically predicted thermal properties [37,38]related to the two-dimensional liquid-hexatic transition critically, we have carefully characterized the hexatic B phase in compound 54COOBC 1301 and found that it does not display herringbone order. To make a clear distinction between these two cases, we propose to use hexatic B to denote the phase found in 54COOBC and use SmB for the phase found in the nmOBC compounds which has a clear indication of some degree of herringbone order.

450

2 Physical Properties of Non-Chiral Smectic Liquid Crystals

2.3.2 Thin Hexatic B Films

ian proposed by Bruinsma and Aeppli [43] to describe the three-dimensional SmASmB,,, transition, we considered the two dimensional version of the Hamiltonian. In the appropriate parameter space of this model, a single transition from the disordered phase to the phase with hexatic and herringbone order can be identified. Furthermore, the heat capacity anomaly can be characterized by a=0.35. Although this coupled XY model provides a plausible explanation for the liquid-hexatic transition found in the nmOBC's, no existing theory is suitable to explain the results from 54COOBC two-layer films, which lack any indication of herringbone order. Thus, our experimental results offer a unique contrast. The structural data clearly demonstrate the existence of the liquid-hexatic transition predicted by the two-dimensional melting theory [23], while the calorimetric results disagree with the related theoretical prediction. Heat capacity data from thin 3(10)OBC free-standing films of various thicknesses are shown in Fig. 8. Using information from specular X-ray diffraction [ 161,electron diffraction [44], and the evolution of this set of

Employing our state-of-the-art ac differential free-standing film calorimeter [39 -411, we have conducted high resolution heat capacity and optical reflectivity measurements on liquid crystal films as thin as two molecular layers (thickness approximately 2.5 ndlayer). Figure 7 displays the results from two-layer films of 3( 10)OBC [41] near the liquid-hexatic transition. This heat capacity anomaly shows divergent behavior, while the optical reflectivity displays a sign change in curvature in the immediate vicinity of the heat capacity peaks. These heat capacity data are very different from the theoretical prediction [37,38] which shows only an essential singularity at the two-dimensional liquid-hexatic transition temperature and a broad hump on the high temperature side. Moreover, these heat capacity data can be well-characterized by a simple power-law expression with the heat capacity critical exponent a = 0.30 f 0.05. Using Monte-Carlo simulations, we have investigated the role of herringbone order on the liquid-hexatic transition of nmOBC [42]. Based on the coupled XY Hamilton-

~"

"

73

'

"

"

'

"

'

"

'

75 76 TEMPERATURE ("C)

74

"

"I

Figure 7.Temperature variation of heat capacity and optical reflectivity obtained from 2-layer films of 3(10)OBC. The inplane molecular density was obtained directly from the optical reflectivity data. (Adapted from [41]).

2.3 7.5

5.2

(0

1

(d)

64

1

f

N=7

N=5

68 72 TEMPERATURE (“C)

76

t 9

3.2

(b)

64

N=3

68 72 TEMPERATURE (“C)

76

Figure 8. Temperature dependence of heat capacity near the SmA-SmB,,, phase transition of 3( l0)OBC. The data were obtained from 2- (a), 3- (b), 4- (c), S- (d), 6- (e) and 7-layer (f) films. Both layer-by-layer transition and sharpness of the heat capacity peaks are clearly shown.

heat capacity data from free-standing films, we can draw the following conclusion. Upon cooling from the high temperature SmA phase, hexatic order is established at the outermost layers and proceeds toward


45 1

the interior layers in a layer-by-layer fashion, for at least the first four sets of the outer layers [45]. The fact that three-layer films show two well separated transitions indicates that only two-layer films possess twodimensional thermal behavior. Careful thermal hysteresis measurements on various samples indicate that the SmA - SmB, transitions in bulk nmOBC samples and thin free-standing films are continuous [40, 41, 461. The following is a list of several counterintuitive, yet salient features: (1) Distinct layer-by-layer transitions are found associated with this continous transition. This suggests no interlayer coupling. (2) The layer-by-layer transition can be characterized by an exponent v =: 113, suggesting van der Waals-type interlayer interaction (see the discussion below). (3) Under the influence of the surface hexatic order, the transitions associated with the interior layers remain as sharp as the surface transaction. This also suggests no interlayer coupling. (4) The lower temperature heat capacity peak of 3-layer films is more than four times smaller than that of 4-layer films. This indicates a strong interlayer interaction for 3-layer films, but not for the 4-layer ones. Further experimental and theoretical advances are required to address these counterintuitive questions. Although surface enhanced order is commonly found for various liquid crystal transitions, the layer-by-layer transitions have only been characterized in the following five cases: the SmA-SmI transition of 90.4 1471, the SmA-SmB,,, transition of nmOBC [45], the SmA-SmB,,, transition of 54COOBC [48], the SmA-B transition of 40.8 [49] and the SmA-isotropic transition [50, 511. Thus far the sequence of the transition temperatures can be described by the following simple power law [ 5 2 ] :

452

2

Physical Properties of Non-Chiral Smectic Liquid Crystals

2.4

\

I

2.4.1 Physical Properties near the Smectic A-Smectic C Transition

* lo-'

'4

IO-~

lo-*

lo-'

(T(L) -To)/To Figure 9. The number ( L ) of layers of a 90.4 thick film in the SmI phase which form at the SmA/vapour interfaces on cooling is plotted as function of the layer transition temperature (T(L)).The temperature Tois a freezing temperature which is one of the fitting parameters in Eq. (15). (Adapted from [47]).

Here L gives the separation (measured in units of layers) between the nearest film/ vapor interface and the layer in question. The fittings yield L0=0.24k0.01, u=O.37 k0.02 for 90.4 [47], L0=0.31 k0.02, u=0.32k0.02 for 3(10)OBC [45], L0=0.34 k0.05, u=0.30k0.05 for 54COOBC [48] andLo=0.32k 0 . 0 1 , =0.36 ~ k0.02 for 40.8 [49]. The experimental data and fitting results near the SmA-SmI transition of 90.4 are shown in Fig. 9. The critical exponent u = 113 indicates that simple van der Waals forces are responsible for the interlayer interaction. Although the layer-by-layer transition near a first order transition has been theoretically predicted [52], that near a second order transition is totally counterintuitive. Further experimental and theoretical work is necessary to address this unresolved puzzle.

Smectic C Phase

2.4.1.1 Bulk Properties

The major difference between the SmA and SmC phases is that the latter exhibits a finite molecular tilt angle from the layer normal. While the SmA phase possesses uniaxial properties, the SmC phase shows biaxial properties. Upon heating, one usually finds the following three possible transitions from the SmC phase: SmC-isotropic, SmC-N, and SmC- SmA. In the first two cases, more than one degree of order vanishes in the given transition. For example, both the layer structure and molecular tilt disappear at the SmC-N transition. These cases are, in general, first-order transitions. Even though pretransitional behavior is not uncommon, the tilt angle shows a finite jump at the transition temperature. The order parameter associated with the SmC - SmA transition can be written as Yc= Oo exp(i4,) [53]. The amplitude Oo is the molecular tilt angle relative to the layer normal and the phase factor GC denotes the azimuthal angle of the molecular director. In 1972, de Gennes [53] argued that the SmA - SmC transition should belong to the three-dimensional XY universality class (helium-like) and might be continuous. This important observation stimulated numerous experimental efforts to investigate the nature of this transition. However, the novelty of this phase transition was revealed ten years later by careful X-ray diffraction studies [54]. Subsequent high resolution calorimetric studies by Huang and Viner [55] enabled them not only to confirm the meanfield nature of this transition, but also to pro-

2.4

pose an extended mean-field model to characterize this transition fully. The majority of the SmA - SmC transitions are found to be mean-field [56-611 and also to be in the close vicinity of the mean-field tricritical point. Thus, to describe the physical properties associated with this transition, we need the following extended mean-field free energy expansion [55, 621.

G = Go + a t I YCl2 + b I YCI4+ c JYclh (16) Here t (=(T-T,)IT,) is the reduced temperature with T, being the transition temperature. The coefficients a and c are usually positive constants. For a continuous SmA-SmC transition b > O and for a first order one b < 0. The special case, b = 0, is the mean-field tricritical point. Huang and Viner [55] proposed a dimensionless parameter to=b2/(ac) to describe the crossover temperature between the mean-field tricritical region (I t l 9 to) and the ordinary meanfield regime ( I t 1 4 to). The value of to is usually very large for most other mean-field transitions [55], (i.e. paraelectric-ferroelectric, conventional normalsuperconducting, Jahn-Teller-type transitions). Thus the I YCI6 term can be ignored. To our great surprise, most of the SmASmC transitions have to < or even as low as to= lo-'. Thus they are extremely close to a mean-field tricritical point. Various research groups have not only characterized continuous and first order SmASmC transitions, [63] but also identified systems in which the transition is tricritical [64-661. The width of the critical region may be estimated from the following Ginzburg criterion [67]:

Due to the unusually large value of the meanfield heat capacity jump (AC > lo6 erg/ cm3 K), the critical region of the SmA-SmC

Smectic C Phase

45 3

transition becomes experimentally inaccessible (tc < lo-') provided that > 1.3 nm which is slightly larger than the effective size of the molecules. Since the SmC ordering is presumably not driven by long-range interactions and the SmA-SmC transition is not at or above the upper critical dimensionality (d,=4 for the XY universality class), it is very difficult to explain the observed mean-field behavior. If the coupling to the layer undulation could be neglected, the SmA- SmC transition would be helium-like. Although the effect of layer undulation on the nature of the SmA - SmB,,, transition was considered by Selinger [68], it is extremely important to conduct extensive studies of the effect of the quasi-long-range SmA order on the molecular tilt order (SmA- SmC transition) and the bond-orientation order (SmA -SmB,,, transition). Meanwhile, it is very important to identify experimentally a system showing criticalfluctuations associated with the SmA-SmC transition [69]. In principle, with sufficient resolution, the SmA- SmC transition should exhibit an extremely rich series of cross-over behavior in an appropriate liquid crystal compound: mean-field tricritical-like ( 1 t (> to) - ordinary meanfield (to> I t I > tc) - Gaussian fluctuations (I tl= tc)-critical fluctuations (tc> I t l ) upon approaching the transition temperature. In light of the abnormal behavior of ultrasound velocity and attenuation near the SmA-SmC transition [70, 711, Benguigui and Martinoty [72] advanced a theory to explain the experimental data. They concluded that the Ginzburg crossover parameter ( t G ) determined by the static properties, (e.g. heat capacity) could be much smaller than that obtained from the measurement of the elastic constant. However, a quantitative comparison between the theoretical prediction and the experimental data is still lacking.

tetf

454

2

Physical Properties of Non-Chiral Smectic Liquid Crystals 8

From Eq. (16), one can calculate the temperature variation of tilt angle, heat capacThey are ity (C) and susceptibility given as follows:

(x).

For T > T,,

eo= o c=c,

L

0 -1.0

(184 (194

-0.6

a)

-0.2 0

0.2

T-Tc (lo

0.6

1.0

and

x-'= 2 a t

(20 4

For T < T,, 00 = { [-b+b

(1 + 3 I tI/to)'/2]/(3~)} 1'2 (18 b)

c = co+ TA((T, - T)/T,)-'/~ and

x-' = 8 a ( t l + (8ato/3)

.. .

. [ l -(1 +31tl/to)]"2

(20b)

b)

305

310

31 5

320

TEMPERATURE ( K )

325

Figure 10. (a) Temperature variation of tilt angle

Here Co is the non-singular part of the (circles) for T < T, and reciprocal of the susceptibility heat capacity. A = L Z ~ / ~ / [ ~ ( ~ C )and ' ~ ~ T (triangles) ~ / * ] for T>T, near the SmA-SmC transition of 40.7. The transition temperature Tc=49.69"C. T, =T, (1 + t0/3). These equations demonThe tilt angles are measured by X-ray (open circles) strate that the effect of mean-field triand light (solid circles) scattering. The solid line is the criticality only shows up in the region T < T, best fit to Eq. (18) with to= 1 . 3 ~ (Adapted from in which I Ycl is non-zero. Except for the [56]).(b) Heat capacity in J/cm3K versus temperature temperature variation of for T < T, many near the SmA-SmC transition of racemic 2M450BC. The solid curve is the best fit to Eq. (19) with high resolution experiments [55 -611 have to= 3 . 9 ~ 1 0 - ~ (Adapted . from [58]). been conducted to test these predictions critically. Temperature variation of both Oo(Tlo0 V and the frequency of the field increased, a focal conic texture eventually appeared. This is the point at which the material changed from positive to negative dielectric anisotropy. This was repeated for a range of temperatures (Fig. 12). In nematics, this temperature dependence is a major problem, because addressing schemes have to be complex to cope with changing voltages and frequencies as the ambient temperature changes. In smectics, the additional problem is that in the negative mode (switching from homeotropic to planar or focal conic) the focal conics are too large to cause light scattering and yet not

Polymer dispersed liquid crystal (PDLC) devices usually contain N phases as the liquid crystal material [71] and are used in vision products [72], e. g., privacy windows, projection displays [73], and direct view displays [74, 751. Cholesteric liquid crystals have also been used [76]. All these devices relax back to the original ground state when the field is removed. Ideally such films consist of diroplets of liquid crystal in a polymer matrix; the reverse situation (reverse phase) consists of a liquid crystal continuum with polymer balls dispersed within it. The latter films are not desirable, because they do not provide reversible electrooptic effects. Ferroelectric SmC* liquid crystals have also been used [77], and these give bistable

488

3 Nonchiral Smectic Liquid Crystals - Applications

devices not too dissimilar to conventional FLC devices. The light scattering appearance of a thick (> 20 pm) film of an SmA liquid crystal provides an opaque film. If doped with a colored dichroic dye, an intense color can be produced. On heating this film to the isotropic liquid, the light scattering disappears and the light path through the film is reduced such that a fairly clear film is produced. An appropriately colored background, previously hidden by the scattering film, would now be visible. This is the basis for a temperature indicator. One problem with this concept is that the liquid crystal is fluid; this problem can be overcome by containing the smectic phase in a PDLC film. By heating a PDLC film made from a liquid crystal having a smectic and an N phase, it is possible to make an electrically addressed storage device [78]. The PDLC film is heated to the temperature at which the liquid crystal is nematic and a small electric field applied to the appropriate areas using I T 0 conductors; this homeotropically aligns the N phase into a clear state and on cooling with the field applied, a transparent image on a scattering background is produced. A PDLC film containing an SmA liquid crystal can also be addressed with light from a suitable laser to produce a clear line under the influence of an applied electric field when the film cools [79]. Very recently a ‘memory type liquid crystal’, which has the characteristics of an

SmA phase, has also been used to produce a memory type device [80]. Interestingly, this device uses reverse phase PDLC so that a finer line resolution can be obtained, reversal of the process being of no importance. This device consists of a thin (6 pm) film of memory type liquid crystal and has submicrometer sized polymer balls dispersed within it and then a polymer skin on top to give.a memory type liquid crystal polymer composite (M-LCPC) (Fig. 13). This film is prepared on top of an I T 0 coated glass substrate. The film switches from scattering to clear between 200 and 300 V to provide many grey levels. The film is used in the same way as a photographic film, but in a special camera. Held 10 pm above the M-LCPC layer is a structure consisting of an organic photoconductor and an I T 0 electrode mounted on a glass substrate. A large DC field (700 V) is applied between the two I T 0 layers. When an area of the photoconductor is exposed, its resistivity drops in accordance with the energy of light and allows a field to be applied to the M-LCPC layer, which responds to the strength and duration of the field applied to it. Typical exposure time is 1/250 s for the camera shutter and the field is applied for about 1/25 s. The camera contains a lens to separate the incident image into red, green, and blue images, each of which is captured on three M-LCPC films. The films are removed from the camera, scanned with a 5000-CCD line sensor with a pixel size of 6 pm and the analog signals converted to

Figure 13. Submicrometer polymer balls in a continuum of memory type liquid crystal and a polymer cover film.

3.10 References

digital data, enhanced, and the three images combined; the final image can then be displayed on monitors or printed on conventional color printers. A resolution of 6 ym was demonstrated and the sensitivity was about I S 0 10-50; future films are expected to be I S 0 100. Compared to conventional silver halide photographs (from negative film), the images produced were much less granular. Thus this system for capturing images provides high resolution color prints very quickly, and the master images can be stored indefinitely.

3.9

Conclusions

Basic research to discover how smectic liquid crystals are affected by heat and electric fields has resulted in several effects being found, and a few of them have been extensively studied and developed into working display prototypes and early commercialization. The property of bistability is both useful and, at the same time, a problem. As yet a really long term application involving smectic liquid crystals has not been found. However, they continue to hold a fascination because they can offer many unique properties which are continually being reexplored for new applications.

3.10 References A . J. Leadbetter in Therniotropic Liquid Crystals (Ed.: G . W. Gray), Society of Chemical Industry, Great Britain 1987, Chap. 1 . G. W. Gray, J. W. Goodby, Smectic Liquid Crystals, Leonard Hill, Glasgow 1984. D. Coates, W. A. Crossland, J. H. Morrissey, B. Needham, Mol. Cryst. Liq. Cryst. 1978,41, 151. D. A. Dunmur, M. R. Manterfield, W. H. Miller, J . K. Dunleavy, Mol. Cryst. Liq. Cryst. 1978,45, 127.

489

151 D. Demus, H. D. Demus, H. Zaschke, Flin’ssige Kristalle in Tabellen, VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig 1974. 161 F. J. Kahn, Appl. Phys. 1973, 22, 1 1 1. 171 G. N. Taylor, F. J. Kahn, J. Appl. Phys. 1974,45, 4330. [8] G. W. Gray, K. J. Harrison, J. A. Nash, Electron. Lett. 1973, 9, 130. [ 91 G. W. Gray, Advances in Liquid Crystal Materiuls ,for Applications, BDH Chemicals, Dorset 1978. [ 101 G. W. Gray, K. J. Harrison, J. A. Nash, J. Chem. Soc. Chem. Commun. 1974,431. [ I 11 Merck Ltd., Licrilite Catalogue 1994. [ I21 S. LeBerre, M. Hareng, R. Hehlen, J. N. Perbert, Displuys 1981, 349. [ 131 M. Hareng, S. LeBerre, R. Hehlen, J. N. Perbert, SlD Digest of Technical Papers 1981, 106. [ 141 H. Scherrer, A. Boller, US Patent 3 952046,1976. [IS] I. Shimizu, K. Furukawa, M. Tanaka, EP Patent 037 468 B 1, 1988. [16] J. Newton, H. Coles, P. Hodge, J. Hannington, J . Muter: Chern. 1994,4(6), 869. [ 171 M. Ibn-Elhaj, H. Coles, D. Guillon, A. Skoulios, J . Phys. I / (France) 1993,3, 1807. [18] J. C. Dubois, A. Zann, A. Beguin, M o l . Cryst. Liq. Cryst. 1977, 42, 139. 1191 M. Chambers, R. Clemitson, D. Coates, S. Greenfield, J. A. Jenner, I. C. Sage, Liq. Cryst. 1989, 5(1), 153. 1201 K. Kida, M. Uchida, N. Kato, A. Mori, H. Takeshita, Chem. Express 1991, 6(7),503. [21] H. Melchior. F. Kahn, D. Maydan, D. B. Fraser, Appl. Phys. Lett. 1972, 21, 392. [22] D. F. Aliev, A. K. Zeinally, Zh. Tekh. Fiz. 1982, 52, 1669. [23] T. Urabe, K. Arai, A. Ohkoshi, J . Appl. Phys. 1983,54, 1552. [24] A. G. Dewey. J. T. Jacobs, B. G. Huth, SID Digest Technicul Papers 1978, 19. 1251 W. H. Chu, D. Y. Yoon, Mol. Cryst. Liq. Cryst. 1979, 54, 245. [26] R. Daley, A. J. Hughes, D. G. McDonnell, Liq. Cryst. 1989, 4(6), 585. [27] C. W. Walker, W. A. Crossland, Displuys 1985, 207. (281 M. Hareng, S . LeBerre, Electron. Lett. 1975, I / , 73. 1291 F. Kahn, P. N. Kendrick, J. Leff, J. Livioni, B. E. Lovcks, D. Stepner, SID Digest Technical Pupers 1987, 18, 254. [30] J. Harold, C. Steele, Proc. SID 1985, 2 6 , 141. 1311 D. Mash, GB Patent 2093206A, 1982. [32] A. Sasaki, N. Hayashi, T. Ishibashi, Jpn. Display 1983,497. [ 33] J. Harold, C. Steele, Eurodispluy Proc. (Paris) 1984, 29. [34] M. R. Smith,R. H. Burns, R. C. Tsai, Proc. SPIE 1980,200, 17 1.

490 [35] [36] [37] [38] [39] [40]

3 Nonchiral Smectic Liquid Crystals - Applications

A. G. Dewey, Opt. Engl. 1984,23, 230. G. J. Sprokel, US Patent 3 999 838, 1976. D. Armitage, Appl. Phys. 1981,52,4843. D. Coates, GB Patent 2091 1753 A, 1982. Eastman Kodak, US Patent 3 774 122, 1973. T. Nishizawa, R. Tukahara, R. Morinaka, T. Hidaka, GB Patent 2069518,1981. [41] T. Urabe, GB Patent 2 140023A, 1984. [42] V. T. Muller-Westerhof, A. Nazzal, R. J. Cox, A. M. Giroud, Mol. Cryst. Liq. Cryst. 1980,56,249. [43] K. Nakamura, 0. Yashuhiro, M. Sugimoto, J. Appl. Phys. 1989,59(2), 593. [44] A. G. Dewey, S. F. Anderson, G. Cherkoff, J. S. Feng, C. Handen, H. W. Johnson, J. Leff, R. T. Lynch, C. Marinelli, R. W. Schmiedeskamp, SID Digest Technical Papers 1983, 36. [45] A. G. Dewey, IEEE Electron Devices 1977,24, 918. [46] D. Mayden, N. Melchior, F. J. Kahn in Proc. IEEE Conference in Display Devices, 1972, p. 166. [47] M. Hareng, S. LeBerre, B. Mourey, P. C. Moutou, J. N. Perbert, L. Thirant in Proc. of the IEEE International Displays Research Conference 1982, p. 126. [48] M. Hareng, R. Hehlen, S. LeBerre, J. P. LePesant, L. Thirant in Proc. of the Electronics Displays Conference, Vol. 1 1984, p. 28. [49] S. Lu, D. H. Davies, R. Albert, D. B. Chung, A. Hochbaum, C. H. Chung, SID Digest Technical Papers, 1982, p. 238. [50] S. Lu, D. H. Davies, C. H. Chung, D. Evanicky, R. Albert, R. Traber in IEEE International Display Research Conference 1982, p. 132. [51] W. Harter, S. Lu, S. Ho, B. Basler, W. Newman, C. Otaguro in SID Symp. Digest. 1984, p. 196. [52] S. Lu, D. Buuvinhchu, US Patent 4461715, 1984. [53] M. Hareng, S. LeBerre, L. Thirant, Appl. Phys. Lett. 1974,25, 12. [54] M. Hareng, S. LeBerre, L. Thirant, Appl. Phys. Lett. 1975,27, 575. [55] W. A. Crossland, J. H. Morrissey, D. Coates, GB Patent 1569688, 1977. [56] D. Coates, A. B. Davey, C. J. Walker, Eurodisplay 1987, 96. [57] V. N. Chirkov, D. F. Aliev, G. M. Radzhabov, A. K. Zeinally, Mol. Cryst. Liq. Cryst.Lett. 1979, 49, 293.

(581 D. Coates, W. A. Crossland, J. H. Momssey, B. Needham, J. Phys. D: Appl. Phys. 1978, 11, 2025. [59] W. A. Grossland, J. H. Morrissey, D. Coates, GB Patent 1569686, 1977. [60] G. H. Heilmeier, L. A. Zanoni, L. A. Barton, Appl. Phys. Lett. 1968, 13,46. [61] B. Bahadur in Liquid Crystals - Applications and Uses (Ed. B. Bahadur) World Scientific, Singapore 1990, Vol. 1, Chap. 9. [62] C. Tani, Appl. Phys. Lett. 1971, 19, 241. [63] M. Steers, A. Mircea-Roussel, J. Physique Coll. 1976,37(3), 145. [64] W. Helfrich, J. Chern. Phys. 1969, 51,4092. [65] W. A. Crossland, D. Coates, GB Patent 1 601 601, 1978. [66] S. Matsumoto, M. Kawamoto, T. Tsukada, Jpn. J. Appl. Phys. 1975,14,7. [67] J. A. Geurst, W. J. A. Goosens, Phys. Letts. 1972,41(4), 369. [68] W. A. Crossland, P. J. Ayliffe, Proc. SID 1979, 23,9. [69] W. A. Crossland, S . Cantor, SID Digest Technical Papers 1985,16, 124. [70] D. Coates, Mol. Cryst. Liq. Cryst. 1978,49, 83. [71] J. L. Fergason, SID Digest Technical Papers 1985, 16,68. [72] Taliq Varilite and 3M Privacy Film. [73] Y. Nagoe, K. Ando, A. Asano, I. Takemoto, J. Havens, P. Jones, D. Reddy, A. Tomita, SID Digest Technical Papers 1995,26,223. [74] P. Nolan, M. Tillin, D. Coates, E. Ginter, E. Leuder, T. Kallfass, Eurodisplay 1993, 397. [75] P. Drzaic, R. C. Wiley, J. McCoy, Proc. SPIE 1989,1080,41. [76] P. P. Crooker, D. K. Yang, Appl. Phys. Lett. 1990,57,2529. [77] V. Y. Zyryanov, S. L. Smorgan, V. F. Shabanov, SID Digest Technical Papers 1992, 776. [78] M. Koshimizi, T. Kakinuma, Japanese Patent 07 36007 (95 36007), 1995; Chem. Abs. 1995, 123,70512. [79] T. Kakinuma, M. Koshimizu, T. Teshigawara, Jpn. Display (Hiroshima) 1992, 85 1. [80] M. Utsumi, M. Akada, E. Inoue, IS&T’s48th Annual Conference Proceedings 1995, p. 499.

Handbook of Liquid Crystals, Volume 2A: Low Molecular Weight Liquid Crystals I

Handbook of Liquid Crystals, Vol. 2B: Low Molecular Weight Liquid Crystals II

Handbook of liquid crystals

Liquid Crystals

Liquid Crystals

4 Volume Set, Handbook of Liquid Crystals

Textures of Liquid Crystals

4 Volume Set, Handbook of Liquid Crystals

4 Volume Set, Handbook of Liquid Crystals

Handbook of Liquid Crystals (3 Volume Set)

4 Volume Set, Handbook of Liquid Crystals

Liquid Crystals: Fundamentals

Liquid Crystals II

Chirality in liquid crystals

Advances in Liquid Crystals

Physical Properties of Liquid Crystals

Crystals That Flow: Classic Papers from the History of Liquid Crystals (The Liquid Crystals Book Series)

Thermotropic Liquid Crystals: Recent Advances

Liquid Crystals, Laptops And Life

Thermotropic Liquid Crystals: Recent Advances

Smectic and columnar liquid crystals

Bicontinuous Liquid Crystals (Surfactant Science)

Nematic and cholesteric liquid crystals

Ordered Fluids and Liquid Crystals

New Developments in Liquid Crystals

Structure and Properties of Liquid Crystals

Computer Simulations of Liquid Crystals and Polymers

Surfaces and Interfaces of Liquid Crystals

Alignment Technologies and Applications of Liquid Crystals

The physics of lyotropic liquid crystals

Computer Simulations of Liquid Crystals and Polymers

Handbook of Liquid Crystals, Volume 2A: Low Molecular Weight Liquid Crystals I

Handbook of Liquid Crystals, Vol. 2B: Low Molecular Weight Liquid Crystals II