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
. . . .
. . . .
29 29 30 30 32 33 35
. . . .
. . . . . . . . . . . . 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
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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
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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
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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
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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
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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
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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-
Structures of Calamitic Liquid Crystals
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
Phase Structures of Calamitic Liquid Crystals
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-
Structures of Calamitic Liquid Crystals
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
Phase Structures of Calamitic Liquid Crystals
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
Structures of Calamitic Liquid Crystals
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
Phase Structures of Calamitic Liquid Crystals
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
Structures of Calamitic Liquid Crystals
15
Figure 12. Structure of the alternating tilt smectic C,,, phase.
Figure 13. Bilayer structures of the tilted smectic C phase.
16
I
Phase Structures of Calamitic Liquid Crystals
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
Phase Structures of Calamitic Liquid Crystals
<
Long Range Translational Order b
Hexagonal Packing Perpendicular to theTilt Direction
lecular dynamics of these two forms are quite different from those normally observed in crystals. For example, the molecules are undergoing rapid reorientational motion about their long axes [3, 4, 441. Moreover, many internal molecular rotations, such as trans - gauche conformationa1 changes, are taking place at the same time. The rapid reorientational motion of the molecules about their long axes has led to these phases being described as anisotropic plastic crystals.
Structures of the Crystal H and K Phases 3.4.5
These two phases are equivalent to the smectic crystal E phase except for the molecules being tilted with respect to the layer
Figure 17. Structure of the crystal G phase.
planes [3,4,44, 611. There is not much experimental data available concerning the structures of these phases; however, it is assumed that the molecules are arranged in layers such that they have long-range periodic ordering. The interlayer packing is also correlated over long distances, thereby producing a crystalline structure. The packing arrangement is monoclinic with the tilt being towards the shorter edge of the packing net for the H phase and to the longer edge of the packing array in the K phase. Other variants are also possible where the tilt may be directed at an angle to both of the edges of the monoclinic unit cell. In these phases, at with crystal J and G, the molecules are still undergoing rapid reorientational motion about their long axes [69], but in this case it is assumed to be oscillatory in nature, like in the E phase [ 19, 261.
4 Long- and Short-Range Order The detailed descriptions of the structures of calamitic phases allow us to classify the mesomorphic liquid crystal state, and to place this state in context with the crystalline and amorphous liquid states [3]. Table 1describes the relationship between ordered crystals, disordered or soft crystals, liquid crystals and the isotropic liquid.
As noted in the introductory section, disordered crystals have long-range positional order whereas liquid crystals have short-range periodic order. The extent of the bond orientational order differentiates the hexatic and non-hexatic liquid crystal phases [41-43]. The positional order can be described in terms of an ideal average lattice structure
4
19
Long- and Short-Range Order
Table 1. Relationship between ordered crystals, disordered crystals, liquid crystals and isotropic liquids. Ordered crystals
Disordered crystals
Liquid crystals
Layered soft crystals Orthogonal Hexagonal B Orthorhombic E
Tilted Pseudohexagonal G J Monoclinic H K
Smectic Weakly coupled layers Short-range order
One-dimensional density wave liquid layers
Hexatic B
Smectic A SmA, SmA, SmA, SmA
Stacked hexatics Smectic F Smectic I
Smectic C SmCl SmC2 SmC, SmC
modified by a correlation function:
P (G, r ) = (exp i G . [u ( r )- u ( o ) ] )
(3)
where G is a reciprocal lattice vector and u ( r ) is a displacement at r . For true long range positional order (LRO), the positions of the molecules will repeat to infinity. Thus,
P ( G ,r ) - ( u 2 )=constant
(4)
and the X-ray diffraction pattern should become resolution limited, that is, a sharp diffraction pattern should be observed for these phases (crystals and disordered crystals). For quasi-long range order
P ( G , r ) - r-v(73
N
In the discussions concerning hexatic phases, the positional order was described as being short range, but the orientational order (bond order) was described as being long range. This three-dimensional picture is derived primarily as a result of theoretical modelling of related two-dimensional (2-D) systems. In 2-D systems, packing in a 2-D array with n-fold symmetry can be described using the order parameter
y ( r )= exp (i n O( r ) )
(7)
where 8 defines the orientation relative to a fixed direction. This can be expressed in
(5)
where F q is a temperature dependent quantity related to the elastic properties of the phase. Here the positional order decays algebraically. Finally, for the least ordered mesophases
P(G, r ) - exp (-r/{&
Nematic
Isotropic liquid
Table 2. Positional order and orientational correlation function for different two-dimensional systems (after Leadbetter [3]). P(G, r ) Two-dimensional crystal
(6)
where &,is the positional correlation length. Here the positional order decays exponentially and the molecules have short range order (SRO).
Hexatic phase
F V()'
0 (r) ( Wl2
Quasi-LRO
LRO
exp (- r/(,) SRO
Qua5i-LRO
r-""'
20
I Phase Structures of Calamitic Liquid Crystals
Table 3. Positional order and orientational correlation function for different two-dimensional and weakly COUpled systems (after Leadbetter [3]). Correlation function
Two-dimensional System
r-v
Weakly coupled 2-D system liquid crystal
(TI
(M 2
two-dimensional crystal
terms of an orientational correlation function
0( r )= (w* ( r )w(4)
(8)
and this function can have three types of behaviour analogous to P(G, r), as shown in Table 2 for two-dimensional systems. If we now extend the analogies for two-dimensional systems to weakly coupled layered systems (i.e. three-dimensional systems) as
in liquid crystal phases we obtain a set of comparisons as shown in Table 3. Here the quasi-long-range order of two-dimensional systems becomes true long-range order in the 3-D system because the layers are weakly coupled. Thus the smectic B, I and F phases could be considered as being stacked hexatic phases where the extent of the bond orientational order is long range in three dimensions.
References J. W. Goodby, Chemalog Hi-lites 1987, 11, 3. See for example: G. W. Gray, P. A. Winsor (Eds.), Liquid Crystals and Plastic Crystals, Vols 1 and 2, Ellis Horwood, Chichester, UK, 1974; H. Kelker, R. Hatz (Eds.), Handbook of Liquid Crystals, VCH, Weinheim 1980. A. J. Leadbetter, in Thermotropic Liquid Crystals, Critical Reports on Applied Chemistry, Vol. 22 (Ed.: G. W. Gray), Wiley, Chichester, UK, 1987, pp 1-27. G. W. Gray, J. W. Goodby, Smectic Liquid Crystals, Textures and Structures, Leonard Hill, Philadelphia, 1984. G. Etherington, A.J. Leadbetter, X. J. Wang, G. W. Gray, A. Tajbakhsh, Liq. Cryst. 1986, 1, 209. H. Sackmann, D. Demus, Mol. Cryst. Liq. Cryst. 1966, 2, 81. H. Sackmann, in Liquid Crystals of One- and Two-Dimensional Order (Eds.: W. Helfrich,
G. Heppke), Springer-Verlag, New York, 1980, p 19. [8] A.J. Leadbetter, M. A. Mazid, B. A. Kelly, J. W. Goodby, G. W. Gray, Phys. Rev. Lett. 1979, 43, 630. [9] A.J. Leadbetter, in The Molecular Physics of Liquid Crystals (Eds.: G. R. Luckhurst, G. W. Gray) Academic Press, New York, 1979, p 285. [lo] P. S. Pershan, G. Aeppli, J. D. Litster, R. J. Birgeneau, Mol. Cryst. Liq. Cryst 1981, 67, 205. [ l l ] J. J. Benattar, F. Moussa, M. Lambert, J. Phys (Paris) Lett. 1984,45, 1053. [12] J. J. Benattar, J. Doucet, M. Lambert, A.-M. Levelut, Phys. Rev. 1979,20A, 2505. [ 131 F. Hardouin, N. H. Tinh, M. F. Achard, A.-M. Levelut, J. Phys. (Paris) Lett. 1982,43, 327. [ 141 J. Budai, R. Pindak, S. C. Davey, J. W. Goodby, J. Phys. (Paris) Lett. 1980,41, 1371. [ 151 P. G. de Gennes, The Physics of Liquid Crystals, Oxford University Press, Oxford, 1974.
5
[16] H. Kresse, Adv. Liq. Cryst, 1983, 6 , 109. [I71 L. Bata, A. Buka, Mol. Cryst. Liq. Cryst. 1981, 63, 307. [I81 S . Chandrasekhar, N. V. Madhusudana, Proc. Indian Acad. Sci. (Chem. Sci.) 1985, 94, 139. 1191 R. M. Richardson, A. J. Leadbetter, J. C. Frost, Mol. Phys. 1982, 45, 1163. 1201 A . J. Leadbetter, R. M. Richardson, in The Molecular Physics of Liquid Crystals (Eds.: G. R. Luckhurst, G. W. Gray) Academic Press, New York, 1979, p 45 I . [21] S . Chandrasekhar, V. N. Raja, B. K. Sadishiva, Mol. Cryst. Liq. Crysr. 1990, 7, 65. 1221 K. Praefcke, B. Kohne,D. Singer, D. Demus, G. Pelzl, S. Diele, Liq. Cryst. 1990, 7, 589. (231 R. Pindak, D. E. Moncton, S . C. Davey, J. W. Goodby, Phys. Rev. Lett. 1981, 46, 1135. [24] D. E. Moncton, R. Pindak, Phys. Rev. Lett. 1979, 43, 701. [25] J. J. Benattar, F. Moussa, M. Lambert, J. Chim. Phys. 1983, 80,99. [26] A.J. Leadbetter, J. C. Frost, J. P. Gaughan, M. A. Mazid, J. Phys. (Paris) 1979,40, C3-185. [27] J . Als-Nielsen, J. D. Litster, R. J. Birgeneau, M. Kaplan, C. R. Safinya, A. Lindegaard-Andersen, B. Mathiesen, Phys. Rev. 1980, B22, 3 12. [28] J. Als-Nielsen, in Symmetries and Broken Symmetries (Ed.: N. Bocarra), IDSET, Paris, 1981, p 107. [29] A. Losche, S. Grande, K. Eider, First Specialised Colloque Ampzre, Krakow, Poland, 1973, p 103. [30] A. Losche, S . Grande, 18th Ampire Congress, Nottingham, U.K., 1974, p 201. 1311 A. De Vries, A. Ekachai, N. Spielberg, Mol. Cryst. Liq. Cryst. 1979, 49, 143. [32] A.J. Leadbetter, J. L. Durrant, M. Rugman, Mol. Cryst. Liq. Cryst. Lett. 1977, 34, 231. [33] A.J. Leadbetter, J. C. Frost. J. P. Gaughan,G. W. Gray, A. Mosley, J. Phys. (Paris) 1979, 40, 37.5. [34] F. Hardouin, A,-M. Levelut, J. J. Benattar, G. Sigaud, Solid State Comrnun. 1980, 33, 337. (351 F. Hardouin, G. Sigaud, N. H. Tinh, M. F. Achard, J. Phys. (Paris) Lett. 1981,42, 63. [36] J. Prost, Adv. Phys. 1984, 33, 1. [37] J. Prost, P. Barois, J . Chim. Phys. 1983, 80, 65. [38] B. R. Ratna, R. Shashidhar, V. N. Raja, Phys. Rev. Lett. 1985, 55, 1476. [39] D. E. Moncton, R. Pindak, in Ordering in TwoDimensions (Ed.: s. K. Sinha), North Holland Press, New York, 1980, p 83. [40] A. J. Leadbetter, J. C. Frost, M. A. Mazid, J. Phys. (Paris) Lett. 1979, 40, 325. [41] N. D. Mermin, Phys. Rev. 1968, 176, 150. [42] B. J. Halperin, D. R. Nelson, Phys. Rev. Lett., 1978,41, 121. [43] R. J. Birgeneau, J. D. Litster, J. Phys. (Paris) Lett. 1978, 39, 399. [44] A. J. Leadbetter, M. A. Mazid, R. M. Richardson, in Liquid Crystah (Ed.: S . Chandrasekhar), Heyden, London, 1980, p 65.
References
21
14.51 J. Collett, L. B. Sorensen, P. S. Pershan, J. D. Litster, R. J. Birgeneau, J. Als-Nielsen, Phys. Rev. Lett. 1982, 49, 553. (461 A.-M. Levelut, M. Lambert, Compt. rend. Acad. Sci. (Paris) 1971, 272, 1018. [47] Z. Luz, R. C. Hewitt, S. Meiboom J. Chem. Phys. 1974, 61, 1758. 1481 A.-M. Levelut, J. Doucet, M. Lambert, J. Phys. (Paris) 1974, 35, 773. [49] J. Doucet, A.-M. Levelut, M. Lambert, L. Liebert, L. Strzelecki. J . Phys. (Paris) 1975,36, 13. [SO] J. Doucet in The Molecular Physics of Liquid Crystals (Eds.: G. R. Luckhurst, G. W. Gray), Academic Press, New York, 1979, pp. 3 17-341. [Sl] A. J. Leadbetter, R. M. Richardson, C. J. Carlile, J . Phys. (Paris) 1976, 37, 65. [52] See for example: J. W. Goodby in Ferroelectric Liquid Crystals: Principles, Properties and Applicutions (Eds.: J. W. Goodby, R. Blinc, N. A. Clark, S. T. Lagerwall, M. A. Osipov, S . A. Pikin, T. Sakurai, K. Yoshino, B. Zeks), Gordon and Breach, London, UK, 1991, p. 172. [ 5 3 ] S. Dumrongrattana, C. C. Huang, Phys. Rev. Lett. 1986, 56, 464. [54] S . Dumrongrattana, G. Nounesis, C. C. Huang, Phys. Rev. 1986,33A, 2187. [ 5 5 ] A.-M. Levelut, C. Germain, P. Keller, L. LiCbert, J. Billard, J . Phys. (Paris) 1983, 44, 623. [ 5 6 ] Y. Galerne, L. LiCbert, Phys. Rev. Lett. 1990,64, 906. [57] I. Nishiyama, J. W. Goodby, J. Muter. Chern. 1992, 2, 1015. [ 5 8 ] N. Hiji, A. D. L. Chandani, S . Nishiyama, Y. Ouchi, H. Takezoe, A. Fukuda, Ferroelecrrics 1988, 85, 99. [591 N. H. Tinh, F. Hardouin, C. Destrade, J. Phys. (Paris) 1982,43, 1127. [60] F. Hardouin, N. H. Tinh, M. F. Achard, A,-M. Levelut, J. Phys. (Paris) Lett. 1982, 43, 327. [61] P. A . C. Gane, A. J. Leadbetter, P. G. Wrighton, Mol. Cryst. Liq. Cryst. 1981, 66, 247. [62] J. W. Goodby, G. W. Gray, J . Phys. (Paris), C3 1979,40, 27. [63] A. L. Leadbetter, J . P. Gaughan, B. A. Kelly, G. W. Gray, J. W. Goodby, J. Phys. (Paris) C3 1979, 40, 178. 1641 J. J. Benattar, F. Mousa, M. Lambert, J . Phyx (Paris) Lett. 1980,41, 137 1. [65] J. J. Benattar, F. Mousa, M. Lambert, J. Phys. (Puris) Lett. 1981, 42, 67. 1661 J. Doucet, A,-M. Levelut, J . Phys. (Paris) 1977, 38, 1163. [67] A,-M. Levelut, J. Doucet, M. Lambert, J . Phys. (Paris) 1974, 35, 773. 1681 J. Doucet, P. Keller, A,-M. Levelut, P. Porquet, J . Phys. (Paris) Lett. 1978, 39, 548. [69] F. Volino, A. J. Dianoux, H. Hervet, J. Phps. (Paris) 1976, 37, 5 5 .
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
Chapter I1 Phase Transitions in Rod-Like Liquid Crystals Daniel Guillon
1 Introduction A large variety of phase transitions is present in the mesomorphic state, and for many years, a considerable number of experimental and theoretical studies have been devoted to the understanding of such phase transitions. This understanding is fascinating, but also of great importance from the fundamental point of view (indeed, liquid crystals are very convenient materials for experimental studies in condensed matter physics), as well as for the use of liquid crystals in devices (for example, the temperature dependence of physical parameters such as helical pitch, elastic coefficients, etc.). So many studies concerning this topic are now reported in the literature that this chapter cannot be an exhaustive presentation of all aspects of phase transitions in calamitic liquid crystals. It deals with the most extensively studied transitions (N-I, N-SmA, SmA- SmC, SmA-SmB,,,) with developments on new trends such as phase transitions in free standing films and induced phase transitions (electrically, mechanically, etc.); the last part is devoted to less studied phase transitions, such as SmF-SmI, SmC-SmI, etc. transitions. In the whole chapter, the emphasis is put on the experimental situation with only a brief reference to the corresponding theoretical aspects (see Sec. 6.1 of Chap. VII of Vol. 1 of this handbook for a detailed description of the theo-
ries of phase transitions). All the aspects concerning transitions involving SmA,, SniA,, SmA2 phases have been excluded; these are analyzed in Sec. 6.1 of Chap. VII of Vol. 1 of this handbook. Many aspects of heat capacity measurements have been omitted too, since they are discussed in detail in Sec. 6.2.1 of Chap. VII of Vol. 1 of this handbook. For the evolution of phase transitions as a function of the chemical structure, the reader may refer to the survey of Demus et al. in Vol. 6 of [168]. Finally, the bibliography consists of two parts: the author’s references concerning the specific studies cited in the following text [ 1- 1591, and general references concerning phase transitions in liquid crystals [ 160-1681.
2 Isotropic-Nematic (I-N) Transition 2.1 Brief Summary of the Landau-de Gennes Model The simplest and best known description of the thermodynamic behavior in the vicinity of the N-I transition was given by de Gennes many years ago [ I ] . This phenomenological description of the pretransitional effects in the isotropic phase is based on the expansion of the excess free energy as a function of the order parameter S in the
24
I1 Phase Transitions in Rod-Like Liquid Crystals
following form
F = -AS2 -2
BS3 +-... CS4 3 4
In the vicinity of the transition, it is expected that A varies as A =a (7'-T * ),where T* is the second order transition temperature (B=O). As T* lies below T,, the effective transition temperature, we have (Tc- T*)= (2 B)l(9a C).When the transition is weakly first order, which is generally the case with calamitic Iiquid crystals, B is small and the quantity (T,-T*) is expected to be small too. Short range effects are of importance just above the transition temperature T,, and are responsible for the formation of small domains already exhibiting a nematic order. These effects lead to some specific physical properties [l-31; below are reported two examples of static pretransitional effects observed experimentally.
2.2 Magnetic Birefringence When a magnetic field H is applied in the isotropic phase, the free energy per mole is written as (2) a ( T - T*)S2- _ BS3 CS4 _+-...+ F= NH(S) 2 3 4
xa
where H ( S ) = ( - 1/3)xaH2S, being the anisotropy of magnetic susceptibility and and N the Avogadro's equaling number. Minimizing F leads to
(xl-xL),
S=
NXa H~ 3a ( T - T*)
(3)
As the magnetic birefringence AnM is given by AnM= Cla ( T - T*), where C is directly proportional to H 2 , the ratio H21AnM is predicted to vary as a linear function of the temperature. This, effectively,has been found
I
40
44
I
52 Tcmperature ( 'C) 48
1
1
56
60
Figure 1. Magnetic birefringence in the isotropic phase of MBBA @-methoxy benzylidene-p-n-butyl aniline). Inverse of the magnetic birefringence coefficient as a function of temperature for two samples with different transition temperatures (after [4]).
to be the case, as shown in Fig. 1 [4], where it is clear that the experimental results are in agreement with the Landau description. In this particular case, TNI- T* 1K.
-
2.3 Light Scattering The domains exhibiting nematic order in the isotropic phase (in general smaller than the optical wavelength) give rise to a scattered intensity when illuminated by light. It has been shown that this scattered intensity is quasi-independent of the scattering angle [ 5 , 61 and should vary as (T-T*)-' in the vicinity of the N-I transition [4], as shown in Fig. 2 for the isotropic phase of MBBA [41. The extension of the local nematic order in the isotropic phase can be characterized by a coherence length, 6. By precise measurements, it has been shown that 6 varies according to F=---AS2 2
BS3 +-... Cy 3 4
(4)
2
Isotropic-Nematic (I-N) Transition
25
sition temperature T,= TNr,because of the first order nature of the transition.
2.4 Deviations from the Landau-de Gennes Model -z
4
u
2
ea
2
0
44
52
48
Temper,iturz
56 (
60
C)
Figure 2. Reciprocal of the intensity of light scattering as a function of temperature In the isotropic phase of MBBA (after [4]).
N
X
./
I
d ' Q
-I>
T YC)
Figure 3. Coherence length, {, as a function of temperature in the isotropic phase for two samples of MBBA. The straight line corresponds to the following variation of {=(6.8* 1) [(T-T*)IT*]-'' A (after [61).
as represented in Fig. 3 for two sets of experiments. On apporaching the I/N transition, the coherence length, increases to reach limited values of about 10- 12 nm at the tran-
e,
Detailed observation of Fig. 2 shows a deviation from linearity very close to the transition temperature TN,. This behavior has been confirmed by many detailed analyses in other cases, where A has been measured as a function of temperature by different techniques [2-3, 8-11]. This results in a value of T* that depends on the studies reported. Other experimental results, such as the experimental temperature dependence of the specific heat [ 121 and of the order parameter [ 131, show a much more complex behavior than that described by the Landau theory [l]. Finally, the proximity of a smectic phase and the width of the nematic range seem to have a pronounced influence on the pretransitional phenomena in the isotropic phase, and in particular on the deviation from the Curie-Weiss law mentioned above for AnM. The narrower the width of the nematic range, the greater the deviations from the Curie-Weiss law. This has been interpreted as being due to smectic fluctuations in the isotropic phase, changing the temperature dependence of the nematic susceptibility [ 141. However, theoretical investigations of the nematic fluctuations [15], as well as a light scattering study on one homologous series of liquid crystal compounds [16], indicate that departures from the Curie-Weiss law and the proximity of a smectic phase are not necessarily correlated.
26
I1 Phase Transitions in Rod-Like Liquid Crystals
3 Nematic-Smectic A (N-SmA) Transition 3.1 The McMillande Gennes Approach McMillan [ 171 was the first to suggest that the N-SmA transition should in general be continuous. The smectic A phase is characterized by a density modulation in a direction z normal to the layers
where po is the mean density, I yI is the amplitude of the modulation, qs=2.nld is the wavevector of the density wave, d is the layer spacing, and q is a phase factor which gives the positions of the layer. Thus the smectic A order parameter is defined by the following complex parameter
y = I yl eiq
(6)
This situation is analogous to that of superfluid helium 4, where the order parameter is a wave function, leading to the now well known analogy between the N-SmA transition and the A. point in 4He described by de Gennes and McMillan [ 18-201. Near the transition, the free energy can be expanded as a function of y according to the relationship
where A=a(T-T:A)IT:A. As a matter of fact, the N-SmA transition may be either second or first order. It becomes first order when a coupling exists between the smectic and the nematic ordering [ 17-21]. The orientational order parameter is S=SN+6S,where SNis the order pa-
rameter in the nematic phase and 6S corresponds to the additional ortientational ordering due to the formation of smectic layers. Thus the total free energy has to contain a coupling term, -k I y126S, and the additional term ( 1 / 2 ~ ) ( 6 S )where ~ , k is a positive constant and o is a response function depending on the degree of nematic order. Minimizing with respect to 6S leads to
where C’=C-(1/2)k20. The coupling between the smectic order parameter and the orientational order parameter leads to a renormalization of the fourth order term coefficient of the free energy. When the width of the nematic phase is large, @(TAN)is small, since the nematic orientational order is saturated; as a consequence, the N-SmA transition is second order. On the contrary, when the width of the nematic phase is small, then @(TAN) is large, since the nematic order is far from being saturated, and the transition is first a order. When C‘=O (i.e., @T(A,)=2 c/L?), tricritical point appears; the location of this point is related to the ratio TNAITNI, called the McMillan criterion [20], for which a theoretical value of 0.87 has been proposed. The existence of such critical points has been extensively verified by experimental studies; however, the values of the McMillan criteria are in general higher than 0.87 and depend upon the system considered [22 - 281.
3.2 Critical Phenomena: Experimental Situation In general, in the modern theory of phase transitions, the energy of deformation of the director has to be taken into account, and
3
27
Nematic-Smectic A (N-SmA) Transition
T, = 33.712"C SAMPLER MOSAICITY = 1.70 deg Tc = 33.680"C SAMPLE MOSAICITY = 0.44 deg
I-
Figure 4. Longitudinal (& and trans-
(t1)
10
d
0.0001
-
0.001 (T-Tc)1 Tc
l
0.01
1
verse correlation lengths as a function of the reduced temperature for 8CB (n-octylcyanobiphenyl). The solid lines are least-squares fits to single power laws corresponding to v,,=0.67+0.02 and v,=0.51?0.04 (after [39]).
x
Figure 5. Susceptibility and coherence lengths of smectic A fluctuations in the nematic phase of compound 4 0 . 8 (see Table 1 ) (after [37]).
therefore the Frank-Oseen elastic contribution in the free energy has to be included. Then, it has been clearly shown that the bend
and twist elastic constants, k33 and k,,, exhibit an increase near the TANtemperature due to pretransitional smectic fluctuations
28
I1 Phase Transitions in Rod-Like Liquid Crystals
Table 1. Critical exponents from X-ray scattering of the nematiclsmectic A transition. Compound
TNAITNI
VI I
v,
Y
T8
0.660
0.70
0.65
1.22
T7
0.706
0.69
0.61
1.22
40.7
0.926
0.78
0.65
1.46
CBOOA
0.934
0.70
0.62
1.30
8S.5
0.936
0.83
0.68
1.53
40.8
0.958
0.70
0.57
1.31
0.963
0.71
0.58
1.32
0.967
0.71
0.57
1.31
0.977
0.67
0.5 1
1.26
1 oss
0.983
0.61
0.5 1
1.10
9CR
0.994
0.57
0.39
1.10
-
[22, 29-31]. Similarly, the layer compressibility constant, B, exhibits a critical variation in the vicinity of the transition. This pretransitional behavior above TANhas been recognized by de Vries [32], who, by X-ray diffraction experiments, has shown the existence of small domains with a smectic
Ref.
order within the nematic fluid; he has called these domains “cybotactic groups”. According to the theoretical approach of the extended analogy with superconductors including the smectic fluctuations, these cybotactic groups should be anisotropic and characterized by two coherence lengths of
4
Smectic A-Smectic C (SmA-SmC) Transition
tL,
the smectic order parameter, tI1 and in the directions parallel and perpendicular to the director, respectively (see Figs. 4 and 5 ) . In the helium analogy, tI1 0~ ( T - T N A ) I T N A ) - " with ~ ~ 0 . 6and 7 ,the smectic susceptibility varies as (T-TN,ITNA)-' with y= 1.32 (whereas in the mean field approach, 511 {_LOc [(T- TNA>/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 T
(10)
This leads to the well known analogy with the superfluid transition in helium [ 19,481. Using this analogy, the SmA-SmC transition may be described as continuous, and the specific heat is predicted to show a singularity
where K= (bl3 c)lI2 and to= b2/a c ; to represents the crossover temperature from mean field to tricritical behavior, and for Itl>to, 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
I1 Phase Transitions in Rod-Like Liquid Crystals
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
I1 Phase Transitions in Rod-Like Liquid Crystals
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
I1 Phase Transitions in Rod-Like Liquid Crystals
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
I1 Phase Transitions in Rod-Like Liquid Crystals
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
I1 Phase Transitions in Rod-Like Liquid Crystals
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.
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I1 Phase Transitions in Rod-Like Liquid Crystals
[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.
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Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
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<-,-COO-, -CHzCHz-. -CHZO-,
Terminal groups:
R, RO. CN. NCS. CF3, F.CI, alkenyl
-CH=N-, -N(+O)=N-, -N=N
In the 1960s and 1970s the development of electro-optical displays using nematic liquid crystals required stable molecules with specific and more demanding physical properties than those of many of the existing nematic materials. Some of the nematogens known at the time had linking groups, such as -CH=N- (generated by the reaction of an aldehyde and an amine [ 5 ] ) , -N = N- (formed by diazonium coupling 161) or -N (-0) = N- (formed by oxidation of azo compounds [6]); these types were unsatisfactory and have been less commonly
48
1
Synthesis of Nematic Liquid Crystals
ly linked to other aromatic units such as pyridine and pyrimidine. In most of the original syntheses (e.g., [17, IS]), the specific core system was used initially and terminal groups were introduced, for example, as shown in Scheme 1 for 4-alkyl- and 4-alkoxy-4’-cyanobiphenyls (see also similar reactions in Scheme 6). Biphenyl and terphenyl are reactive to direct electrophilic substitution at the terminal 4,4’- and 4,4“-positions respectively, as required for ‘linear’, lath-like structures. However, the other positions in the parent biphenyls or terphenyls are difficult or impossible to substitute directly, even with a favourable directing group present, but a way to achieving those classes of compound with lateral substituents materialized when useful coupling reactions were developed in the early 1980s [15, 16, 20-261; the Heck reaction for the vinylation of organic halides is another useful coupling reaction [27]. It is now possible to link aryl, alkynyl and alkenyl regions together in controlled steps to produce core systems with almost any substitution pattern and, because coupling routes offer the advantages of convergent synthesis and a widespread utility for certain key interme-
used in subsequent years. Records describing the development of nematic liquid crystals for display applications [7, 81, accounts of the effect of molecular structure on mesophase behaviour [ 1, 9 - 111, tabulations of liquid crystal phase transitions [12, 131, and accounts of synthetic methods [ 14- 161 show the variety of molecular structures giving nematic liquid crystals. In this short survey it is possible to consider only the syntheses involving the major classes of terminal groups, rings and linking groups. Alternative methods of synthesis are continually being discovered and several examples are given in which a more recent method is clearly superior to the original procedure.
1.2 Benzene, Biphenyl and Terphenyl Systems A vast number of liquid crystals showing nematic or other mesophases are obtained using benzene, biphenyl or [ 1,l’: 4’, 1”]terphenyl units as core systems, often with the rings connected by polarizable linkages such as ester or alkynyl functions or direct-
J(vii)
R
O
w
C
N
_(viii) “0-
Q @ N
(i) R’COCI. AlCb (ii) (a) N2HI.H20, KOH. dtgol, heat or(b) Et3SiH.CF3COzH (ref [iq) (ili) CUCN, DMF or l-rnethylWrrolidin.2-one ( v ) NaOH. Br2: dil HCI (v) SOC12: aq NH,: DMF, SOCl, (vi) Me.504. NaOH (vii) BBr3. CH& (viii) RBr, K2C03, butan-2-one or cyclohexanone
Scheme 1. Synthesis of 4-alkyl- and 4-alkoxy-4’-cyanobiphenyls
1.3 Cyclohexane Systems
diates or substrates, coupling reactions are often preferred to the original route for the synthesis of well-established nematogens such as those shown in Scheme 1; for the synthesis of the alkyl- and alkoxy-biphenyls, 4-alkyl- and 4-alkoxy-phenylboronic acids can be coupled with 4-bromobenzonitrile (cf. Scheme 7 giving examples of arylboronic couplings).
1.3 Cyclohexane Systems For many years, aromatic compounds based on benzenes, biphenyls or terphenyls were the most common core unit for liquid crystals, partly because of easier synthesis and partly because the link between highly polarizable 7c-electron systems and mesogenicity was over-emphasized. In the mid1970s it became clear that saturated systems are also excellent units when placed appropriately in relation to other planar or high polarizability regions of the core or when the cores are entirely saturated; trans1,4-disubstituted-cyclohexanes and 1,4-disubstituted-bicyclo[2.2.2]octanes(see Sec. 1.4) are the best examples of good, mesogenic, non-aromatic structures. Cyclohexane-based systems are almost invariably prepared by catalytic hydrogenation of benzene derivatives (e.g., 4-alkylbenzoic acids and 4-alkylphenols, see Scheme 6) but the 4-alkoxy systems are not often used because the alkoxy-oxygen atom is then isolated in a non-polarizable region of the product. Low temperature, low pressure procedures are possible but give mainly the cis-product whereas high pressure, high temperature hydrogenations with Raney nickel catalyst produce predominantly the trans-4-alkylcyclohexane1-carboxylic acid, if basic conditions are used, since the proton a-to the carboxylic acid function is
49
removed to generate an enolate anion which re-'ketonizes' to give the more stable transproduct. Alternatively, the cis-/trans-mixture of cyclohexanecarboxylic acids can be equilibrated by prolonged heating with thionyl chloride and subsequent hydrolysis [28, 291; enolization of the neutral acid chloride being easier than for a carboxylate anion. Such syntheses are quite lengthy and it is even more difficult to produce cyclohexylphenyl systems or cyclohexylethyl units since hydrogenation occurs mainly by cisaddition. The routes to these compounds cannot currently be achieved efficiently by coupling reactions and standard routes are as shown in Scheme 2 for PCH (2.5) [30, 311, CCH (2.6) [32, 331, and PECH (2.9) [34) precursors (the cyclohexanone starting material, 2.1, is obtained by oxidation of the cyclohexanol, 6.7, shown in Scheme 6). Two ways of achieving a trans-substitution of the cyclohexane ring in 2.4 have been reported; in one method the intermediate cisand truns-alcohols 2.2 and 2.3 are reduced selectively [30] and in the other equilibration is achieved by making use of the acidity of the benzylic hydrogen so that treatment with a strong base (KOtBu) produces the trans-compound [35]. The cyclohexane ring in phenyl cyclohexanecarboxylates and in the PCH compounds, 2.5, usually enhances nematic character relative to that of the aromatic systems and even greater enhancement is achieved with cyclohexyl cyclohexanecarboxylates or a bicyclohexyl core unit such as 2.6. The esters are prepared as outlined in Scheme 6 and the bicyclohexyl systems are obtained by the route shown in Scheme 2; a similar reduction of the aromatic ring to that shown in Scheme 6 and equilibration with thionyl chloride to give the trans-acid [28, 291 allows the terminal cyano compound to be obtained.
50
\$
1 Synthesis of Nematic Liquid Crystals
R
O
2.1
O
R&P~
0 R
e (two isomers)
Ph
2.2 2.3
R
(i) CeH5MgBr, didhyl ether; HzO (ii) Raney nickel, Hz, ethanol (iii) 10% Pd-C, H2. ethanol
PECH
(v) 1 0 % PdC, Hz.acBtic acid SOCg;b 0 (vi) see text (vii) SO.&; LiAllg. diethyl ether (viii) HBr aq, HSO4 (i) NaCN, DMSO; HOAc, HzS04 (X) SOCI, (xi) AICI,, %HE;, HpNNHz.Hz0, KOH, digol, heat (xii) see steps (IV) and (v) in scheme 1
The acid 2.8 is used to provide the acid chloride which gives a route to dimethylene linked-compounds by Friedel-Crafts acylation and reduction of the product ketone [34] and the alcohol 2.7 is used for the methyleneoxy-linked systems [36] by a direct DEAD reaction to a phenol [37] or by conversion into an alkyl halide or tosylate and reaction with a phenolate anion. Nematogenic, fused-cyclohexane systems with trans-ring junctions have been made based on decalins 138-401, perhydrophenanthrenes [40 - 421, perhydrochrysenes [43], and perhydroanthracenes, perhydronaphthacenes and perhydrobenza[a]anthracenes [44].
Scheme 2. Synthesis of 4-(trans-4-alkylcyclohexy1)benzonitriles (PCHs), trans-4(trans-4-alkylcyclohexyl)cyclohexylcarbonitriles (CCHs), and l-(truns-4-alkylcyclohexyI)-2-(4-~yanophenyl)ethanes(PECHs)
1.4 1,4-Disubstitutedbicyclo[2.2.2] octanes Like cyclohexyl systems, the bicyclo[2.2.2]octanes are usually only prepared with an alkyl terminal group and the principal route to the central intermediate (l-alkylbicyclo[2.2.2]octane with a 4-hydroxy-,4-methoxy- or 4-bromo-substituent) is shown in Scheme 3 [45, 461. All three intermediates can provide the 4-alkylbicyclo[2.2.2]octane-l-carboxylicacids (although the hydroxy or methoxy route is more direct) and the bromo compound can be used in Friedel-Crafts alkylation of aromatic compounds. The main examples of bicyclo[2.2.2]octane systems are cyanoaryl esters (3.2,X = CN [47 -491, alkyl- and alkoxy-aryl esters (3.2, X=R, OR) [48,
1.6 2,5-Disubstituted-pyridines
OH or OCH,
0
6 H or OCH,
4.3
4.4
Scheme 4. Synthesis of pheny1)- 1,3-dioxanes R-@-[alyil-X
3.1
51
4.5
5-alkyI-2-(4-substituted-
3.2
(I) CHzCHCN. base, I-BuOH 1111 KOH. HCI i l l (CH3CO)z0. CH3COzK (iv) For OH, aq. KOH, for OCH,. (CH30)3CH.HCi, CH,OH (v) NzH, H20, KOH. digol (vi) ZnErz. HEr (vit) HCOzH, AgzS04, H2S04.0 "C. ice (viii) SOCiz (ix) pyridine.a phenol, toluene. reflux 48 h, see scheme 6 (x) AICI,, ArH
Scheme 3. Synthesis of I-alkylbicyclo[2.2.2]octane4-substituted systems
50, 511 and directly linked aryl systems (3.1) [46, 51, 521; the bicyclo[2.2.2]octane core has also been compared with phenyl, cyclohexyl and a range of related cores [ 5 3 , 541.
1.5 2,5-Disubstituted1,3-dioxanes 5-Alkyl- 1,3-dioxane derivatives are acetals and are generated in an equilibrium mixture from 2-alkylpropan- 1,3-diols, 4.1, and aldehydes (Scheme 4) and the yield of product is optimized by azeotropic removal of water from the reaction mixture. A cis-/transmixture of products, with the trans-isomer predominating, is obtained and repeated recrystallization gives the pure trans-products 4.2 in 50-60% yield [55-571. The 1,3oxathiane, 4.3, 158, 591 and 1,3-dithiane, 4.4, [57,59-611 analogues of 1.3, dioxanes
have been prepared similarly from an aldehyde and the corresponding hydroxylthiol compound to give compounds of diminished mesogenicity. 2,5-Disubstituted- 1,3,2-dioxaborinanes, 4.5, are structurally similar to 2,5-disubstituted- 1,3-dioxanes but without the complication of cis-/trans-isomerism; the creation of the dioxaborinane ring is achieved by esterification of a 2-substituted-propan1,3-diol with an arylboronic acid [62, 631. For compounds of this type with a 5-aryl substituent, 2-arylpropan- 1,3-diols are required and are prepared by coupling the ethyl cyanoacetate anion and a 4-substituted-phenyl bromide or iodide [62] and the 5-alkyl-substituted- 1,3,2-dioxaborinanes 1631 are obtained from 2-alkylpropan- I ,3diols (4.1).
1.6 2,5-Disubstitutedpy ridines Pyridine rings are not particularly common as nematogenic cores partly because they are usually not superior to the pyrimidine analogues and partly because they are less easy to synthesize. Several different syntheses of pyridines have been reported [64-7 I ]
52
1 Synthesis of Nematic Liquid Crystals
but a more general approach would now involve coupling reactions to 2,5-dibromopyridine [26].
1.7 2,5=Disubstitutedpyrimidines The commonly used route to these compounds is shown in Scheme 5 172-751 but has the disadvantage that the pyrimidine ring has to be created on each occasion from the diacetal of an alkylated malondialdehyde and the amidine hydrochloride, prepared from a nitrile. The development of coupling reactions, principally of the Suzuki [20-23,251 and Negishi type [24], in the synthesis of liquid crystals [ 14- 16,261 has now provided a more direct and general pyrimidine synthesis. Useful synthons such as 5.1 [26, 761 and 5.2 [77] allow aryl and alkynyl units to be coupled selectively and transmetallation of the product at the position of the remaining halogen substituent can subsequently give hydroxy or carboxy groups.
1.8 3,6-Disubstitutedpyridazines 3,6-Disubstituted-pyridazines are attractive as core systems because the two nitrogen atoms on the side of the molecule give compounds of negative dielectric anisotropy (e.g., a value of -9.3 is reported in reference [781) without a lateral substituent being necessary. Unfortunately, the systems are not sufficiently photochemically stable for device use and are often slightly yellow; routes to pyridazines are given in references [68, 791.
1.9 Naphthalene systems Naphthalene is not easily adaptable to provide different substitution patterns but the most structurally suitable system for providing nematic phases has 2,6-disubstituents, which can fortunately be derived from the available 6-bromonaphth-2-01(1). Here selectivity of coupling can be achieved with the triflate derivatives (2 and 3 which couple preferentially at the triflate and iodo site respectively) [16, 261; the iodo compounds can be obtained from bromo compounds by an efficient procedure [80, 811.
1
I) CzHaOH, H D , conc H2S01 IN)CH30Na
sl) 1.Zdchbroelhane.POCb
Scheme 5. Synthesis of S-alky1-2-(4-cyanophenyl)pyrimidines
2, X = Br 3, X = l
6-Alkylnaphthalene-2-carboxylates[82] have been prepared in a similar way to benzoate esters and they give compounds with TN-I values = 60- 80 "C higher; comparable increases (= 80-90 "C) are obtained by replacing a benzene by naphthalene in cyanobiphenyls [83 - 851. A naphthalene ring also has several possible states of reduction ranging from the dihydro compound to the
1.1 1
fully saturated trans-decalin unit and many of these core untis have been studied in the context of terminal cyano or non-polar (e.g., alkyl/alkoxy) compounds (e.g., references [38, 84, 86-88]). For comments on decalin and perhydrophenanthrenes see Sec. 1.3.
1.10 Unusual Core Systems Many other plausible structures for generating liquid crystals have been investigated in an attempt to define the structural features which favour mesogenicity. In many of these examples the target molecules were shown to be poor mesogens and little further work has been carried out with such cores. Details of the varied syntheses are not given here, but the references shown contain at least an outline of the routes used. Cubanes, 4, [89,90] and bicyclo[ 1.1. llpentanes, 5 , [91, 921 provide a collinear arrangement of bridgehead bonds but they are poor nematogens because the angular nature of the core is not conducive to lateral, molecular associations. Derivatives of 6 [93], 7 [94,95], 8 [93 -951,9 [94,96], and 10 [97, 981 have also produced nematic phases.
4 4
4
++
5
6
8
9
10
1.11 Ester Linkages Carboxylic acid esters are extremely common as links between aromatic units [29,99, 1001 (in which they extend molecular pola-
Ester Linkages
53
rizability from one ring to the next), between saturated and aromatic rings (where a saturated carboxylic acid is preferable to an aromatic acid, e.g., aryl truns-4-cyclohexanecarboxylates [29, 1011, or aryl4-alkylbicyclo[2.2.2]octane- 1-carboxylates [48,50]) or even between two saturated rings [ 1021. Scheme 6 shows examples of benzene- and cyclohexane-based systems and includes the synthesis of some acids (6.1, 6.2 and 6.6), phenols (6.3,6.4 and 6.5) and alcohols (6.7) which are useful in general liquid crystal synthesis; some analogous bicyclo[2.2.2]octane intermediates are shown in Scheme 3. Many methods of esterification have been reported and it is normally a straightforward procedure to prepare an ester from the carboxylic acid and the phenol or alcohol. Reliable and well-established methods use the ‘acid chloridekertiary amine/hydroxy compound’ combination in an inert solvent. The procedures involve formation of the acid chloride from the acid using thionyl chloride or oxalyl chloride and then reaction with the phenol or alcohol in toluene or dichloromethane, typically in the presence of triethylamine or pyridine. These methods are still useful but direct reactions of the acids and alcohols or phenols using 1,3-dicyclohexylcarbodiimide (DCC) [ 1071 or diethyl azodicarboxylate (DEAD) [37] are now possible and would normally be chosen. The reactions proceed under mild conditions and, with convenient purification procedures, give esters in good yields. The DEAD procedure [37] is also suitable for producing ether linkages (as in -CH,O-) or ether terminal groups, from an alcohol and a phenol and may be used in preference to the ‘phenol/K,CO3/RBr/ketone solvent’ (usually acetone, butanone or cyclohexanone) method [ 1081 which requires more vigorous conditions. A complication may arise in the creation of compounds with two
54
(b)
1
Synthesis of Nematic Liquid Crystals
6.1
(iv) RO-@O,H
HO-@O,H
6.2
t(iii)
(i) R'COCI, AlC13 (ii) (a) NzH+HpO. KOH. digol, healw(b) EbSH, CF3COzH (rat [19]) (iii) Mg. C02: HCI or BuLi, CO:, HCI (re1 [103]) (ivl RBr. EtOH. H,O. NaOH: dil HCI thanQ-one i v i RBr. K.CO. BUG.B~oc~I,),; Ho,, (refs 11041and [ l 051) (vii) AlCg. C6H5N02.20 "C (viii) e.9.. (a) NWdcycbhexylcattcdiimide(DCC). 4-(Npyrmldino)pyridine,CH2C12, (b) PPhs, diethyl azodicarbaxVlafe (DEAD), THF. (c) xyleie, conc HS , O, (azeitmpic remoVal of water). (d) potassium phenolate, acid chloride, diethyl ether or toluene (ii) 10%-NaOH. Raney nickel, 200 'C, 140atmos. H, 4-5 h; immeric acids. SOCl, reflux 12-14 h (re1 [lo€.]) (x) C2H50H.Raney nickel, 200 "C, 120 atmos. Hp, 2-3 h; i s r n e n separated (i) by using CaCI, (ref el. (ii) as 3.5-dinitrobenzoateesters which were then hydmiysed(ref [29])
ivi
In many cases, similar routes can be used to prepare biphenyl and terphenyl compounds analogous to the benzene compounds shown.
ester functions in that a phenol-protected acid (see 11) or an acid-protected phenol (see 12)may be needed initially; the benzyl protecting group survives DCC or DEAD procedures and can usually be cleaved by hydrogenolysis (H,/Pd-C) [lo91 so that the released functional group can be esterified in a second step. An alternative group for protecting the phenol in such cases is the methoxycarbonyl group (see 11 b) [ 1lo], but since this group may be removed by an amine, the DEAD esterification procedure should be used rather than the method using DCC. X
G
C
W
11 a, X = PhCHlO b, X = CH3OCO 5. X = 2-telrahydwranyl
HO
0
COpCHpPh
12
Scheme 6 . Synthesis of simple esters and generally useful precursors to mesogens
1.12 Lateral Substitution Lateral substituents in core units have to be kept small in order to preserve liquid crystallinity and the most generally useful lateral substituent is fluoro. The special features of fluoro substitution, which separately or in combination may be useful, include the following: (a) a small size which usually has only a small effect on nematic thermal stability; (b) electron-attraction which may give compounds of negative dielectric anisotropy; (c) the ability to diminish or destroy anti-parallel molecular association and increase positive dielectric anisotropies; (d) a depression of melting point; (e) a reduction in the prominence of ordered smectic phases, frequently, with the consequent relevation of a nematic phase; and
1.13 4-c-(~vans-4-Alkylcyclohexyl)1 -alkyl-r- 1-cyanocyclohexanes
(f) an increase in the tendency to generate tilted phases by virtue of a lateral dipole near the end of a molecule. Coupling methods use many different organometallic systems (e.g., magnesium, [ 11I, 1121, zinc [24,113] and tin [ 114- 1171 derivatives etc.) but arylboronic acids are particularly useful because they are stable to air and moisture and can be conveniently stored and used as required; their formation at low temperatures also allows a halogen substituent to be present ortho- to the boronic acid without leading to benzyne formation. The outline of the general approach to arylboronic acid couplings is shown in Scheme 7, which also shows examples of units for selective couplings (7.1 and 7.2), convenient units (7.3 and 7.4) to achieve trifluoromethyl and fluoro terminal groups and a route to lateral 2,3-difluoro compounds. A bromo or iodo substituent is not always necessary in order to generate the organolithium and a number of directed metallation procedures are useful [ 118, 1 191. Several examples of alternative catalysts for use in coupling reactions have also been reported, such as palladium acetate 1221, tris(dibenzy1ideneacetone)dipalladium [ 1 171 and
dichloro[ 1, 1'-bis(dipheny1phosphino)ferrocene]palladium(II) [ 1201. Several other types of 'lateral' substitution are possible in addition to simple fluoro and cyano substituents. Examples have been provided of (a) longer lateral groups in the core (e.g., 13 [121, 1221); (b) lateral groups which include ring systems and so almost constitute another core region (e.g., 14 [123]); (c) substitution to give crossshaped molecules (e.g., 15 [ 124, 1251); and (d) substitution in the terminal group to give branched chains of similar size (swallowtailed compounds, e.g., 16 [ 1261).Additionally, dimeric compounds (e.g., 17 [1271291) and other extremely varied molecular shapes [ 11 have been synthesized using the methods which have been outlined here for more conventional nematogens. 13
X
~
7.1
F
O
~
~
O
Z
C
~
X
I
-Oc=,
OR
F
7.2
7.3
7.4
(i) BuLi: B(0Me)z. dil HCI (ii) 4-brarnobenzoolriie. Pd(PPh& aq NazCOs, 1.Zdtmelhoxyelhane (111)
C
CnHrn.1
RO
F
55
H202
( v ) RBr, K2C03.butan4-one (v) BuLI, RCHO ("I) P206.Lobent. P d C HZ
Scheme 7. Examples of syntheses using arylboronic acids
1.1 3 4-c-(trans-4Alkylcyclohexy1)-1-alkylr-1-cyanocyclohexanes Lateral substituents in a core have to be kept small and few in number in order to main-
56
1 Synthesis of Nematic Liquid Crystals
tain mesogenicity and although cyano is an attractive group to use as a lateral substituent [ 130- 1321 because it has a large dipole and can generate material of negative dielectric anisotropy, it is linear and projects two bond lengths away from the core so that in phenyl cores it protrudes quite severely. However, because it is a narrow unit with a small conformational energy difference, it can be placed as an axial group in cyclohexyl systems and is relatively shielded by the cyclohexane ring and gives nematogens with surprisingly high clearing points. The synthesis makes use of the acidity of the proton a- to the cyano group in compounds 2.6 (Scheme 2) and treatment with lithium di-isopropylamide and an alkyl bromide in tetrahydrofuran at -50 "C gives the 4-c(trans-4-alkylcylohexy1)- 1-alkyl-r- 1-cyanocyclohexanes with the cyano group predominantly axial [133- 1351; 1,3-dioxane systems with an axial cyano substituent have also been prepared [136, 1371.
1.14 Terminal Groups Many of the earlier schemes in this section show examples of the synthesis of alkyl, alkoxy and cyano terminal groups; alkyl and alkoxy groups are also conveniently generated in alternative ways from halides and phenols as shown in Scheme 8. If the alkynyl coupling shown in Scheme 8 for 8.1 is carried out with the phenolic triflate 8.2, then subsequent reduction of the product to the alkyl group gives a way of creating an alkyl unit at a phenolic site. Direct alkyl coupling to aryl systems is complicated by p-elimination in the alkylmetal but procedures have been reported for cross-coupling of secondary and primary alkyl Grignard reagents and alkylzinc reagents with aryl or alkenyl halides [120].
R C H 2 C H 2 G X
A G G C S i M e a
(i). .BuLi, B(O€H&: H 2 4 (ii)...alkylatwn.see scheme 6 (iii)...BuLi; RCHO ( i ) ..P2&. sclvent; PdM2 (v) ...RCSZnCI, W(PPh3), (vi)...H;JPd (vii)...M-SiCSZnCI, Pd(PPh& (viii). .KOH,MeOH (k)..CIZnC.CH.H2NCH2CHflH2, Pd(PPh& (x).. 3-methylbut-1-ynQ-ol, Pd(PPh&. Cul. 'Pr2NH (xi)...KOH. toluene
Scheme 8. Alternative ways of obtaining alkyl and alkoxy groups
Isothiocyanates are readily made by reaction of a primary aromatic amine with carbon disulfide/triethylamine followed by ethyl chloroformate/triethylamine and by treatment of the amine either with thiophosgene, calcium carbonate, chloroform, water [138, 1391 or with carbon disulfide, N,N'dicyclohexylcarbodiimide, pyridine [ 140, 1411. Compounds with alkenyl terminal groups have been extensively studied ([ 142- 1441 and references therein) and their synthesis is quite varied, depending upon the position of the double bond and its stereochemistry, but Wittig-based routes are generally used.
1.15 References [ l ] D. Demus, Liq. Cryst. 1989, 5, 75- 110. [2] J. Barbera, M. Marcos, M. B . Ros, J. L. Serrano, Mol. Cryst. Liq. Cryst. 1988,163, 139-155.
1. I5
[31 A. I. Pavluchenko, N. I. Smirnova, V. F. Petrov, Y. A. Fialkov, S . V. Shelyazhenko, L. M. Yagupolsky, Mol. Cryst. Liq. Cryst. 1991, 209, 225235. 141 E. Bartmann, D. Dorsch, U. Finkenzeller, Mid. Cryst. Liq. Cryst. 1991. 204, 77 - 89. [ S ] H. Kelker, B. Scheurle, Angew Chem., Int. Ed. Engl. 1969, 8, 884-885. [6] H. Kelker, B. Scheurle, R. Hatz, W. Bartsch, Angew. Chem., Int. Ed. Engl. 1970, 9, 962-963. 171 G. W. Gray, Phil. Trans. R. Sor. Lond. 1990, 330A, 73-94. [8] C. Hilsum in The Anatomy of a Discovery Biphenyl Liquid Crystals (Ed. C. Hilsum), Ellis Horwood Ltd., Chichester, UK, 1984, pp. 43-58. [9] G. W. Gray (Ed.), Thermotropic Liquid Crystals, Critical Reports on Applied Chemistry, Vol. 22. J. Wiley and Sons, Chichester, UK, 1987 [ 101 B. Bahadur in Liquid Crystals, Applications and Uses Vol. 1 and Vol. 2. (Ed. B. Bahadur) World Scientific: Singapore. 1990 and 1991. 11 13 G. W. Gray, Phil. Trans. R. Soc. Lond. 1983, 309A, 77-92. [I21 D. Demus, H. Demus. H. Zaschke, Fliissige Kristalle in Tabellen, Vol I ; VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig, Germany, 1974. [ 131 D. Demus, H. Zaschke, Fliissige Kristalle in Tabellen, Vol I!; VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig, Germany, 1984. [I41 E. Poetsch, Kontakte (Darmstadt) 1988, 2, 15-28, [IS] G. W. Gray, M. Hird, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1991, 204, 91 - 110. [I61 M. Hird, G. W. Gray, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1991,206, 187-204. [I71 G. W. Gray, K. J. Harrison, 1972, UK Parent 1433 130. [I81 G. W. Gray, K. J. Harrison, 1973, US Parent 3 947 375. 1191 C. T. West, S . J. Donnelly, D. A. Kooistra, M. P. Doyle, J. Org. Chem. 1973, 38, 2675 -2681. 1201 N. Miyaura, T. Yanagi, A. Suzuki, Synth. Comniun. 1981, 11, 513. [21] A. Suzuki, Some Aspects of Organic Synthesis using Organoborates, Vol. 112 (Ed. A. Suzuki) Springer-Verlag, Heidelberg, 1983, pp. 67 - 1 15. [22] T. I. Wallow, B. M. Novak, J. Org. Chem. 1994, 59,5034-5037. 1231 T. Watanabe, N. Miyaura, A. Suzuki, Svnlett 1992,207-210. 1241 E. Negishi, A. 0. King, N. Okukado, J . Org. Chem. 1977,42, 1821-1823. [25] R. B. Miller, S. Dugar, Organomelallics 1984, 3, 1261. [26] M. Hird, K. J. Toyne, G. W. Gray, Liq. Cryst. 1993,14,741-761. [27] R. F. Heck, Organic Reactions 1982, 27, 345 - 390.
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Synthesis of Nematic Liquid Crystals
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[83] U. Lauk, P. Skrabal, H. Zollinger, Helv. Chim. Actu 1981,64, 1847-1848. [84] G. W. Gray, D. Lacey, Mol. Cryst. Liq. Cryst. 1983,99, 123- 138. [85] U. Lauk, P. Skrabal, H. Zollinger, Helv. Chim. Acta 1983,66, 1574-1575. [86] U. Lauk, D. Diirst, F. Valeri, Chimia 1989, 43, 382-385. [87] U. H. Lauk, P. Skrabal, H. Zollinger, Helv. Chim. Actu 1985,68, 1406- 1426. [88] M. Cereghetti, R. Marbet, K. Schleich, Helv. Chim. Actu 1982,65, 1318- 1330. [89] G. W. Gray, N. A. Langley, K. J. Toyne, Mol. Cryst. Liq. Cryst. Lett. 1981, 64, 239-245. [90] G. W. Gray, N. A. Langley, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1983, 98,425 -43 1. [91] P. Kaszynski, A. C. Friedli, J. Michl, Mol. Cryst. Liq. Cryst. Lett. 1988, 6, 27-33. [92] P. Kaszynski, A. C. Friedli, N. D. McMurdie, J. Michl, Mol. Cryst. Liq. Cryst. 1990, 191, 193- 197. [93] R. C. Geivandov, S. 0. Lastochkina, I. V. Goncharova, B. M. Bolotin, L. A. Karamysheva, T. A. Geivandova, A. V. Ivashchenko, V. V. Titov, Liq. Cryst. 1987,2, 235 -239. [94] L. K. M. Chan, P. A. Gemmell, G. W. Gray, D. Lacey, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1987,147,113-139. [95] L. K. M. Chan, P. A. Gemmell, G. W. Gray, D. Lacey, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1989,168, 229-245. [96] W. Binder, J. Krause, E. Poetsch, K. Tarumi, The Mesogenicity of Cyclobutune Modules in Different Liquid Crystal Structures, Vol. BOral 5 (15th International Liquid Crystal Conference), Budapest, Hungary, 1994, p. 124. [97] B. M. Fung, C. W. Cross, C. Poon, Mol. Cryst. Liq. Cryst. Lett. 1989, 6, 191 - 196. [98] V. S. Bezborodov, V. A. Konovalov, V. I. Lapanik, A. A. Min’ko, Liq. Cryst. 1989, 4, 209 - 2 15. 1991 R. Steinstrasser, Z. Nuturforsch. 1972, 27B, 774-779. [I001 M. E. Neubert, T. T. Blair, Y. Dixon-Polverine, M. Tsai, C.-C. Tsai, Mol. Cryst. Liq. Cryst. l990,182B, 269-286. [lo11 J. D.Margerum,S.-M. Wong, J. E. Jensen,C. I. v. Ast, A. M. Lackner, Mol. Cryst. Liq. Cryst. 1985,122,97- 109. 11021 M. A. Osman, L. Revesz, Mol. Cryst. Liq. Cryst. Lett. 1979,56, 105- 109. [lo31 C. J. Booth, J. W. Goodby, J. P. Hardy, 0. C. Lettington, K. J. Toyne, J. Muter. Chern. 1993, 3,935-941. [lo41 M. F.Hawthorne,J. Org. Chem. 1957,22,1001. [lo51 R. L. Kidwell, M. Murphy, S. D. Darling, Org. Synth. 1969,49, 90-93. [lo61 K. B. Sharpless, A. 0. Chong, J. A. Scott, J. Org. Chem. 1975,40, 1252-1257.
1.15 References 11071 A. Hassner, V. Alexanian, Tetrahedron Lett. 1978,4475-4478. [ 1081 G. W. Gray, M. Hird, D. Lacey, K. J. Toyne, J. Chem. Soc., Perkin Trans. 2 1989,2041 -2053. [I091 C. J. Booth, G. W. Gray, K. J. Toyne, J. Hardy, Mol. Cryst. Liq. Cryst. 1992, 210, 31 -57. [ 1101 E. Chin, J. W. Goodby, Mol. Cryst. Liq. Cryst. 1986,141,311-320. [ I l l ] K. Tamao, K. Sumitani, Y. Kiso, M. Zembayashi, A. Fujioka, S. Kodama, I. Nakajima, A. Minato, M. Kumada, Bull. Chem. Soc. Jpn. 1976,49, 1958- 1969. [ 1121 G . Fouquet, M. Schlosser, Angew. Chem. lnt. Ed. Engl. 1974, 13, 82-83. [ 11 31 A. 0 . King, E. Negishi, F. J. Villani, A. Silveira, J. Org. Chem. 1978, 43, 358-360. [ 1141 W. J. Scott, J. K. Stille,J. Am. Chem. Soc. 1986, 108,3033-3040. [115] A. M. Echavarren, J. K. Stille, J. Am. Chem. SOC. 1987,109,5478-5486. 11161 T. N. Mitchell, Synthesis 1992, 803-815. [117] V. Farina, B. Krishnan, D. R. Marshall, G. P. Roth, J. Org. Chem. 1993, 58, 5434-5444. [ 1IS] V. Snieckus, Pure Appl. Chem. 1990,62,671680. [ 1191 V. Snieckus, Pure Appl. Chem. 1990,62,20472056. [ 1201 T. Hayashi, M. Konishi, Y. Kobori, M. Kumdda, T. Higuchi, K. Hirotsu, J. Am. Chem. Soc. 1984,106, 158- 163. [ 1211 W. Weissflog, D. Demus, Cryst. Res. Technol. 1983,18,21-24. 11221 W. Weissflog, D. Demus, Cryst. Res. Technol. 1984,19,55-64. [123] W. Weissflog, D. Demus, S. Diele, P. Nitschke, W. Wedler, Liq. Cryst. 1989, 5 , 1 11 - 122. [124] S . Berg, V. Krone, H. Ringsdorf, U. Quotschalla, H. Paulus, Liq. Cryst. 1991, 9, 151-163. [125] W. D. J. A. Norbert, J. W. Goodby, M. Hird, K. J. Toyne, J. C. Jones, J. S. Patel, Mol. Cryst. Liq. Cryst. 1995, 260, 339-350. [126] W. Weissflog, G. Pelzl, H. Kresse, D. Demus, Cryst. Res. Technol. 1988, 23, 1259- 1265.
59
11271 J. W. Emsley, G. R.Luckhurst, G. N. Shilstone, 1. C. Sage, Mol. Cryst. Liq. Cryst. Lett. 1984. 102,223-233. [128] A. C. Griffin, S . R. Vaidya, R. S . L. Hung, S. Gorman, Mol. Cryst. Liq. Cryst. Lett. 1985, I , 13 1 - 138. [129 P. J. Barnes, A. G. Douglass, S. K. Heeks, G. R. Luckhurst, Liq. Cryst. 1993, 13, 603-613. [130] M. A. Osman, T. Huynh-Ba, Mol. Cryst. Liq. Cryst. Lett. 1983, 92, 57-62. 11311 S. M. Kelly, T. Huynh-Ba, Helv. Chim. Actu 1983,66, 1850-1859. 11321 M. A. Osman, Mol. Cryst. Liq. Cryst. 1985, 128,45-63. 11331 R. Eidenschink, G. Haas, M. Romer, B. S . Scheuble, Angew. Chem., lnt. Ed. Engl. 1984, 23, 147. [I341 R. Eidenschink, Mol. Cryst. Liq. Cryst. 1985, 123,57-75. 11351 R. Eidenschink, B. S. Scheuble, Mol. Cryst. Liq. Cryst. Lett. 1986, 3, 33-36. [I361 C. Tschierske, H.-M. Vorbrodt, H. Kresse, H. Zaschke, Mol. Cryst. Liq. Cryst. 1989, 177, 113-121. 113’71 C. Tschierske, H. Kresse, H. Zaschke, D. Demus, Mol. Crysr. Liq. Cryst. 1990, 188, 1 - 12. 11381 R. Dabrowski, J. Dziaduszek, T. Szczucinski, Mol. Cryst. Liq. Cryst. 1985, 124, 241 -257. [139] R. Dabrowski, J. Dziadusek, T. Szczucinski, Mol. Cryst. Liq. Cryst. 1984, 102, 155-160. 11401 J . C . Jochims, Chem. Ber. 1968, 101, 17461752. [141] A. J. Seed, K. J. Toyne, J. W. Goodby, D. G. McDonnell, J. Mater. Chem. 1995,5, 1 - 1 1. [ 1421 M. Schadt, R. Buchecker, F. Leenhouts, A. Boller, A. Villiger, M. Petrzilka, Mol. Cryst. Liq. Cryst. 1986, 139, 1-25. [ 1431 M. Petrzilka, R. Buchecker, S . Lee-Schmiederer, M. Schadt, A. Germann, Mol. Cryst. Liq. Cryst. 1987, 148, 123- 143. [ 1441 M. Schadt. R. Buchecker, A. Villiger, F. Leenhouts, J. Fromm, Proc. o f t h e SlD 1986, 27, 203 -210.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
2.1 Elastic Properties of Nematic Liquid Crystals Ralf Stannarius
2.1.1 Introduction to Elastic Theory This section contains an outline of the theory and results of experimental studies of the elastic properties of nematics. First, a short introduction of the standard theories is given and the characteristic quantities, used to describe nematic phase elasticity are introduced. After an overview of the standard methods of measuring elastic constants, a summary of the experimental results is given. In particular, we list a collection of papers dealing with the extensively explored cyanobiphenyls and the standard substance 4-methyloxy-4’-butylbenzylideneaniline (MBBA). The next part is devoted to the less-common surface-like elastic constants, and this is followed by a sketch of the theoretical approaches to the microscopic interpretation of elastic constants and the Landau-de Gennes expansion. The section . is concluded by a brief discussion of elastic theory for biaxial nematic phases. Spatial elastic distortions of the nematic director field change the free energy of the mesophase. The relations between the spatial derivatives of the director field and the free energy density of the nematic phase are described by the elastic moduli. In de-
veloping an elastic theory of the nematic mesophase, two different approaches were chosen. The phenomenological theory starts from phase symmetry considerations. The free energy is expanded in terms of combinations of director derivatives, which leave the free energy invariant under the symmetry operations of the phase. For each independent term in this expansion, an elastic modulus is introduced. The molecular theory is similar to Cauchy’s description of the elastic theory of solids [ 11 and utilizes additive local molecular pair interactions to describe elasticity. The latter approach was taken by Oseen [2], who was the first to establish an elastic theory of anisotropic fluids. Oseen assumed short-range intermolecular forces to be the reason for the elastic properties, and he derived eight elastic constants in the expression for the elastic free energy density of uniaxial nematic phases. Finally, he retained only five of them, which enter the EulerLagrange equations describing equilibrium deformation states of the nematic mesophase, and omitted the other three. Oseen’s elastic theory was developed further by Zocher [3] and re-examined by Frank [4] in a phenomenological approach.
2.1.1
Frank reinstalled two terms omitted by Oseen and dropped two 'surface-like' contributions instead, which do not affect the director field in the bulk mesophase. In 1971, Nehring and Saupe [ 5 ] presented a generalized derivation of the elastic free energy and they compared the phenomenological and the molecular theories. They reintroduced the surface elastic terms neglected by Frank. In their phenomenological approach, they expanded the free energy for weak deformations of the director field n ( r ) into a series in first and second spatial derivatives n I J=&,/a5 and n,,Jk=a2n,ia+bk of the director. Table 1 shows the total number of elastic coefficients that enter expansions up to fourth order. As can be seen from the table, there are no nonzero first- and third-order coefficients for ordinary nonpolar achiral nematics. The elastic theory of nematics is usually restricted to secondorder expansion of the free energy, Frank and many successors also neglected the terms containing second derivatives of the director field. For mesophases with only rotational symmetry about one axis (C, symmetry), one can form nine independent invariant combinations out of the total num-
Table 1. Number of elastic constants in different orders of approximation (from Nehring and Saupe [ 5 ] ) . Order Typeofterms
C,
Introduction to Elastic Theory
61
ber of first-order (ni,;) and second-order ( ~ , , ; T zand ~ , ~ n,,J terms. The general expression for the elastic part of the free energy density for a mesophase with C, symmetry is [ 5 ]
Equation (1) must be positive definite, which adds some restrictions to the elastic moduli [ 1981: KlI
2 0, K22 2 0, K3, 2 0,
lK241s
K229 K 2 2 +
K2452K11
All the elastic moduli K j j have the dimension of a force (N) except for the first two coefficients K , and K2 which have the dimension of a force per length (N m-'). The results obtained phenomenologically agree with those obtained using the molecular theory [ 5 ] ,except for an additional relation
D, Dm h (cholesteric) (nematic)
in the molecular approach, which reduces the number of independent parameters to eight. The phenomenological theory considers the invariance of the free energy under symmetry aspects, and should therefore be more general than the molecular approach, which deals with molecular interactions only and disregards entropy effects [ 5 ] .A decision about the validity of Eq. ( 2 )
62
2.1 Elastic Properties of Nematic Liquid Crystals
and a justification of the molecular approach in this respect would require very accurate measurements of K24that have yet to be reported. Frank’s theory differs from the NehringSaupe approach in that it considers only first derivatives of the director field in first and second order, and therefore does not include the last two terms in Eq. (l),which contain second derivatives also. In all other respects, it is equivalent to Eq. (1). The K24 term of Eq. (1) apparently contains second derivatives of the director field as well, but it can be rewritten in a form where it is expressed completely in terms of first derivatives [5]:
(K22+K24)
i< j
(3)
(ni,jEj,i -%,inj,j)
In Eq. (l), only the relatively low C, phase symmetry has been assumed. This is a very general requirement, which does not account for the nonpolarity and non-enantiomorphy of nematic phases. If the mesophase contains more symmetry elements, fewer invariants remain and the number of elastic parameters is reduced. In nonpolar systems such as cholesterics (D,), which are characterized by an additional two-fold symmetry axis perpendicular to the C, axis, K,, K,, and K23 vanish identically. In nonchiral phases (C,,), the coefficients K,, K,, and K23 are zero, and in the nonpolar nonchiral uniaxial nematic (Dmh)K,, K,, K,, and K23 are zero and five elastic moduli remain in Eq. (1). In enantiomorphic phases (cholesterics), the nonzero K2 term leads to a spontaneous equilibrium twist q=- K2/K22. There, the unbiased director field forms a helix of pitch length p=2n/q. The sign of K2 gives the handedness of the helix. In the case of a hypothetical polar nematic phase (which has not yet been found experimentally), a nonzero K , term would lead to spontaneous permanent splay s =K,/K, Like-
,.
wise, K,,#O leads to a deformed ground state of polar enantiomorphic phases. Regarding the remaining coefficients in Eq. (l),we consider the integral Fe= jvfedv over the volume V of the phase that makes the contributions to the total free energy of the system. The volume integrals of the K13 and K24 terms contain complete divergences and can be transformed in surface integrals over the volume boundaries by means of Gauss’ theorem (this also holds for the K , and K23 terms). As these surface integrals are given solely by the director field at the boundaries, the integral free energy contributions of these elastic terms do not depend upon the nematic director field in the volume. The corresponding elastic constants KI3 and K24are therefore often denoted as surface or surface-like elastic constants. They can be neglected in many situations where only the nematic director field in the bulk phase is regarded. The elastic deformations in the bulk can be described by just three coefficients K , KZ2and K33. However, this complicates the straightforward determination of K, , and KZ4and the experimental verification of Eq. (2). In practice, the weak influences of the surfacelike coefficients on bulk director deformations makes their measurement difficult. This topic is discussed in more detail below. The remaining three terms in Eq. (1) correspond to three basic types of bulk nematic director distortion - twist, splay and bend which give the bulk free energy density of a nematic (q=O) or cholesteric (q#O) sample:
,,
L=,( K11
+&2
[n.( vxn)+ q]
+ q n x ( v x n ) 2] 2
2
(4)
The notation used for these three coefficients varies in the literature. For conven-
2.1.2.
ience, K , is sometimes abbreviated to K , , K, (splay) or K , (Querverbiegung),K22 to K 2 , KT (twist) or KD (Drehung), and K,, to K,, KB (bend) or KL (Langsverbiegung). Figure 1 illustrates the three types of director deformation connected with these bulk elastic constants. The pictures show the geometry of an electrically or magnetically driven thin planar cell under rigid boundary conditions, where the corresponding types of deformation can be generated and measured. The elastic moduli Kii, i = { 1 , 2 , 31 of low molecular mass nematics are typically of the order of several piconewton. The splay and bend constants K , I and K,3 are often of comparable magnitude, and their ratio is often
electrode
glass substrate
alrgnn,ent layer gl- substrate
Figure 1. Cell geometries for the determination of splay (top), twist (middle) and bend (bottom) elastic constants from the FrCedericksz threshold. The corresponding types of director deformation are sketched on the right.
Measurement of Elastic Constants
63
close to 1 at TN-I. The twist constant K22 is usually smaller (see below).
2.1.2 Measurement of Elastic Constants This section covers the experimental methods used to measure the bulk elastic constants K , K22 and K3,. As these constants play an essential role in all types of bulk deformation of the nematic director field, access to the bulk elastic constants can be gained from many conceivable experiments, in fact, most macroscopic observables related to some anisotropic property of the nematic phase can be utilized to monitor director deformations and subsequently to draw conclusions on elastic constants or ratios of elastic constants. Although a large variety of experiments provide data that are in some way related to the elastic properties of nematics, we concentrate here on a few direct methods of particular importance. These methods yield elastic constants directly, without the need to know too many additional parameters. In practice, to measure elastic constants one chooses director deformations generated either by external electromagnetic fields in a suitable simple geometry or director deformations imposed by the surface anchoring conditions in nontrivial geometries such as droplets, cylindrical cavities or hybrid aligned films. The analysis of the director field deformations can be done in many ways; for example, by optic, by capacitance, by thermal or electric conductivity measurements or by magnetic resonance methods. Instead inducing static or dynamic director deformations by means of external forces, the study of thermal fluctuations can be used to provide information on the elastic moduli. These orientational fluctuations of the director field are detected using conventional scattering tech-
,,
64
2.1 Elastic Properties of Nematic Liquid Crystals
niques, or sometimes by means of nuclear magnetic resonance (NMR) [6]. Measurements of surface-like elastic constants are particularly difficult, and these are dealt with in Sec. 2.1.5.
2.1.2.1 FrCedericksz Transition The standard method for measuring elastic constants in nematics is the analysis of onedimensional director deformations in thin planar cells with defined anchoring conditions. This approach allows separate study of splay, twist or bend deformations in a pure form at the onset of the transition. The experiment is based on an effect first described more than 60 years ago by FrCedericksz and Zolina [7]. A nematic substance is sandwiched between two parallel plates, which fix the director orientation at their surfaces. The initially homogeneous director field in the sample is deflected by an external electric or magnetic field only above a certain threshold field strength (FrCedericksz threshold), which depends upon the elastic properties of the substance. The director response to the electromagnetic field is usually detected optically or by means of capacitance measurements. Reviews of the different methods of measuring elastic constants from such electromagnetically driven elastic deflections have been given by, for example, Gerber and Schadt [S], Bradshaw et al. [9] and Scharkowski and co-workers [lo, 111. It has been known since FrCedericksz’s work in the 1930s [7, 121 that the threshold field for director deformations in planar cells can be used to determine the elastic coefficients of nematic liquid crystals. Saupe [ 131was the first to describe analytically the static director field in planar cells under the action of an external magnetic field in terms of Frank’s elastic theory, and not only did he derive expressions for the threshold mag-
netic field H,, but he also gave analytic expressions for small director deformations and the optical birefringence of the cell as a function of the applied magnetic field in the vicinity of H,. He discussed the three geometries for the magneto-optic measurement of splay, twist and bend constants. The cell geometries for the direct determination of K,,, KZ2 and K33 from the FrCedericksz threshold are shown in Fig. 1. Rigid planar or homeotropic anchoring is required. At the onset of the deformation above the threshold field, pure splay, twist or bend is generated in the corresponding geometry, and therefore one particular elastic constant is effective for each threshold. The moduli Kii (i = 1, 2, 3) are found from the magnetic FrCedericksz field B, =AH, K.. = 2
&(?)
z1
Po
Ax=xII-xL
where is the magnetic anisotropy ( A x >O is required), po is the vacuum permeability and d is the cell thickness. In a number of publications (see, for example, the pioneering papers of FrCedericksz and Zwetkoff [14]) only the critical fields have been exploited to determine the elastic coefficients. In twist geometry, the deformation stays pure twist, even at high external fields. In the other two geometries splay and bend deformations mix with increasing director deformation. In addition to the elastic modulus that defines the threshold field, a second elastic constant can therefore be extracted in splay or bend geometry if more than only the threshold is analyzed. Saupe noted that the steepness of the deformation versus magnetic field curve above B, can be used to determine the splayhend elastic ratio in experiments utilizing either splay or bend geometry. In the vicinity of the threshold field, the director deflection angle 0, in the cell midplane with respect to the surface
2.1.2 Measurement of Elastic Constants
orientation in splay geometry is given by
For the bend transition in homeotropic cells this holds analogously, but K , , and K,, change their roles. In these geometries, the sample cell is usually observed in the transmitted light with crossed polarizers inserted in 45" orientation to the director tilt plane. While the ordinary polarized light in the birefringent medium always experiences the ordinary index of refraction n, and is unaffected by the deformation, the optical path of the extraordinary wave is sensitive to the director tilt. Both waves are brought to interference at the analyser and the optical interference can be related in a direct way to the director deflection. Saupe first used this magneto-optical method with splay geometry to determine the splay and bend constants of p-azoxyanisol (PAA) [13]. Oldano et al. [ 151 have proposed that, instead of varying the field strength, one can vary the magnetic field orientation. If the magnetic field is rotated stepwise from the normal to a planar orientation in the director tilt plane, magnetic fields of less than B, are sufficient, and exact angular adjustment is less critical than for the pure splay experiment. The resulting interference fringes are monitored optically. in twist geomeThe measurement of try is not as straightforward as the splay and bend experiments described above. The optical waves of transmitted light are guided with the slowly changing director twist through the cell (Mauguin effect), and pass the cell uninfluenced, at least for small twist deformations. In order to study the twist deformation, Frkedericksz and Zwetkoff [ 121 chose a total reflection method. The cell was studied under obliquely incident light. The critical angle of total reflection is very sen-
65
sitive to small twist deformations and allows for the detection of the threshold field. In order to determine the twist Frkedericksz threshold, the sample can also be observed conoscopically [ 161. A prerequisite for the magneto-optical experiments is a knowledge of the diamagnetic anisotropy A x and the cell thickness, in order to determine the elastic constants from the threshold fields, and the refractive indices, in order to fit the complete transmission characteristics. .4s an alternative to magnetic fields, electric fields can be used to drive the director deflection. As the electric field is conventionally applied between two electrodes at the upper and lower plates, respectively, of a planarly oriented nematic cell, the splay transition is generated. Gruler and co-workers [ 171 and Deuling [ 181 extended Saupe's calculations to the electrically driven FrCedericksz transition. The modulus K , , is found from the threshold voltage U,:
where A&= q1- &I(> 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,<,- I, ...}). The optical transmission of the planar cell with crossed polarizers in 45"orientation is
neff = n,
nf2 0
Fv d q / F-1 Fv
n12 0
-3 dq
F-1
in the electric and magnetic cases, respectively. Likewise, the cell capacitance C can be calculated from the director profile by
where A is the effective area of the cell. A fit of the full transmission or capacitance versus driving field strength curve increases the reliability of the experimental measurement of the ratio K 3 3 / K l l .Such a procedure has been applied for example in [ 1 1, 17, 19, 71, 104, 318-3231. The one-dimensional deformations in Frkedericksz cells and their optical characteristics are now well understood. A comprehensive theoretical treatment of the onedimensional director patterns in electromagnetically driven cells can be found in publications by Thurston [25], who has also considered the stability of configurations in pretilted cells. Ong [26] has calculated the optical properties when the splay/
68
2.1 Elastic Properties of Nematic Liquid Crystals
bend transition is observed using obliquely incident light.
2.1.2.2 Light Scattering Measurements The intense light scattering of nematics is due to thermally induced orientational fluctuations of the nematic director field. These orientational fluctuation modes are related to the viscous and elastic properties of the nematic (see, for example, Litster [27]). The de Gennes formulae [28, 291 establish a relation between the elastic coefficients and the scattering intensities. Small thermal director fluctuations can be expressed in terms of two eigenmodes, the splay-bend mode 6nl and the twist-bend mode 6n2.The equipartition theorem gives the intensities
(6.:) =
kB T K33qi + K,, q f + A x H 2 + A&E~ E2
(a= {1,21) for a sample in an electric field E and a magnetic field H along the director; qI1and q1 are the components of the scattering vector with respect to the director. The differential scattering cross-sections are proportional to (fin;), with the proportionality factor depending on sample and geometrical properties such as the polarization directions chosen for incident and observed scattered light. Usually, it is not the absolute scattering intensity that is determined in the experiment, but rather its angular or field strength dependence is investigated. By varying the scattering angle in zero field, one can determine the K , l/K33and K22/K33 ratios. When the electric or magnetic field strength is varied, one can relate Ki, to the corresponding field term and determine the absolute elastic constants. A comparison of four different light scattering techniques used to determine KZ2can be found in, for example, Toyooka [30].
The de Gennes equations have been reexamined by Chen et al. [311,who discussed experimental limitations as boundary influences and finite sample dimensions. Possible error sources are stray light in the detector and inaccurate adjustment of the sample cell, which may lead to systematic errors in the scattering angle. An advantage of measuring elastic constants by study of such fluctuation modes with light scattering is that the experiment requires considerably less time that it takes to record the voltage or magnetic field characteristics of a FrCedericksz cell. Moreover, dynamic light scattering can be used to study the frequency spectrum of the director fluctuation modes from the temporal autocorrelation function of the scattered light. The time constants of these correlation functions provide ratios of elastic constants and viscosity coefficients [32]. Less common is the determination of elastic coefficients from Raman scattering measurements of liquid crystals [33, 341.
2.1.2.3 Other Experiments Among the many other methods of measuring the elastic constants of nematics, the studies of deformed director fields in nonplanar geometries are of particular importance. Nematics confined in cylindrical cavities with homeotropic surface treatment form a number of complex deformed director configurations. The theoretical description of non-planar (escaped radial) director fields in cyclindrical geometry has been given by Cladis and KlCman [35]. Cladis and co-workers [36, 371, Meyer [38] and Saupe [39] studied the escaped radial structure by means of polarizing microscopy. The stability analysis of the escaped director configurations was used to investigate the divergence of the bend constant K33 near the nematic-smectic transition [37]. The
2.1.3 Experimental Elastic Data
method was refined by Scudiery [40] and Scharkowski et al. 1411, by the inclusion of weak surface anchoring 1421 and surfacelike elastic constants [43, 441. The experiment is simple and requires knowledge only of the diameter of the cylindrical container and refractive index data. It yields reliable K 3 J K 1 , data even though the exact calculation of the optics in this experiment has not yet been achieved. Studies of the director fields in other cylindrical geometries [45,46] can, in principle, also provide elastic ratios. Of particular interest are nematic droplets with spherical geometry, such as, for example, polymer dispersed liquid crystals. Their director configurations depend strongly on the elastic properties of the nematic (see, for example, Kralj and Zumer [47]). These systems may be of some importance in the study of surfacelike elastic terms. For investigating bulk elastic constants, however, other methods are useful. Several types of spontaneous periodic director pattern yield information about elastic coefficients. Static stripe textures, as described by Lonberg and Meyer [45], appear in polymer nematics if the twisthplay ratio K2,1K,, falls below the critical value of 0.303. Calculations of director fields and the influence of elastic constants and external fields on the appearance of these periodic patterns have been performed by several authors (e.g. 149-5 11).In nematic cells with different anchoring conditions at the upper and lower cell plates (hybrid cells), other types of striped texture appear; these are similar in nature, but involve different director deformations and elastic coefficients. For a description of various types of static periodic texture and their relationship to elastic coefficients see, for example, Lavrentovich and Pergamenshchik [52]. In thin hybrid aligned films, a critical thickness is observed below which the director align-
69
ment at the surface of weaker anchoring is abandoned. This critical thickness has been shown to depend on the splay/bend elastic ratio of the nematic [53]. As in the case of static patterns, the analysis of spontaneously formed dissipative director patterns yields the elastic ratios [20, 54, 551. Deformations of the director field can also be generated optically. Periodic gratings in the nematic liquid crystalline sample are produced by means of short, high-intensity laser pulses. The gratings are formed either from thermal heating (amplitude grating) or due to reorientation of the nematic director (phase grating) in the electric field of the laser beam. Such experiments were first proposed by Herman and Seriko [56] and were demonstrated by Khoo [57]. The refraction of a low-intensity laser beam at these gratings provides the elastic constants and viscosity coefficients 158-601. The spontaneous twist in the cholesteric phase, in particular the field-induced nematic-cholesteric transition, can be exploited for the experimental determination of the twist constant K2, 161, 621. Finally, there are some unique measurements of the mechanical torque connected with an elastic deformation of the nematic. Faetti et al. [63] determined the splay and bend elastic constants by means of such torsion measurements, and Grupp [ I391 made measurements of the twist elastic constant K22.
2.1.3 Experimental Elastic Data As a consequence of the complexity of molecular interactions in the nematic phase, there are no general quantitative relations between the elastic constants and molecular structure. However, several general rules have been extracted empirically from a large
70
2.1
Elastic Properties of Nematic Liquid Crystals
number of experiments performed in recent years [ l l , 20,22,23,30,41,62-1801. Such empirical structure/elasticity relations were established early on by several authors (e.g., 23, 64, 65, 67, 68, 1661) on the basis of experimental data. De Jeu et al. [70] have discussed the influence of molecular geometry on the elastic constant ratio. From simple geometrical considerations they stated that the splay/ bend ratio should correlate with the molecular length/width ratio for rigid molecules, i.e. K33:K11=L2:W2with K33>K,,. (Pretransitional effects of smectic-like ordering are discussed below.) This view has been confirmed by some experimental data [66]. If long, flexible alkyl chains are incorporated in the molecular model structure, the trend is reversed (K33< K , 1). In practice, both cases are observed. For example, the 4’-n-alkyl-4-cyanobiphenyls (nCB) are characterized by K33> K , the bend/splay ratio gradually decreases with increasing alkyl chain length starting with = 1.5 for the pentyl homologue (e.g. [104, 1661). For 4-cyanophenyl-4-n-alkyloxy c yclohexanoates the K33/K11 ratio decreases from about 1.8 for the propyl homologue to about 1.15 for the octyl homologue (at T/TN_,=0.96)[ 101. PCH-5 (5-cyano-l-(4-npentylcyc1ohexane)-benzene) even has a K33/K,, ratio of =2, whereas for some 5-nhexyl-2- [4-n-alkyloxyphenyl] -pyrimidines this ratio is inversed, K3,/Kl1=0.6 at temperatures well below the clearing point [ 10, 111. Exceptionally low K33/K1 ratios of about 0.4 have been found by Schadt et al. [69] in non-polar alkenyl compounds. Within homologous series, there is a pronounced oddleven alternation of the K33/K1 ratio with the number of chain segments [72]. As a general trend, the elastic ratio is closer to 1 near the nematic-isotropic transition (at low order parameters) than deeper in the higher ordered nematic phase. This
,,
,
,
is consistent with the theoretical predictions of Landau-de Gennes expansions of the free energy where the splay-bend degeneracy is raised only by a term of third power in the order parameter. Such a term becomes more dominant far from the isotropic phase. In 1983, Gramsbergen and de Jeu [73] conjectured that nematics consisting of molecules of curved shape should have a lower bend constant because they might adjust a bend deformation by redistribution of the molecules, but they failed to demonstrate this experimentally. Later, the influence of the shape of dimers on the elastic splay/bend ratio was investigated with more success by DiLisi et al. [74]. Bent and straight dimers have been constructed by using spacers of odd and even lengths, respectively. Compared to the monomer, their splay and twist coefficients are lower, and in general the bent dimer exhibits lower elastic constants than the straight dimer. In accordance with the prediction of Gramsbergen and Jeu [73], the bend/splay ratio K33/K1 of the bent dimer is found to be considerably smaller than that of the straight dimer. In discotic systems, the roles of K,, and K33are reversed, because in such phases the bend deformations require the lowest energy [ 1811. Measurements of splay and bend constants in a homologuous series of discotic n-hexa(alkanoy1ox)truxenes [76] revealed that K33is always smaller than K,,. The splay/bend ratio approached unity at the high temperature transition to the columnar phase. Qualitatively different results have been obtained, however, by Raghunathan et al. [75], who found K33> K , in a discotic nematic phase enclosed between two columnar phases. The authors interpreted this unexpected result as being a consequence of short-range columnar order. For many nematogenic compounds, the twist/splay ratio is found to be quite constant (except for pretransitional effects in
,
,
2.1.4
the vicinity of smectic phases). Although the value of 113 derived in several theoretical approaches (e.g. [182, 1831) is not obtained experimentally, it is well established that K22is always the smallest constant, with K2,/K1 typically being of the order of 1/2. The measurement of elastic constants is of particular interest near the nematic-smectic A (TN.SmA)transition. The bend and twist elastic constants contain terms that diverge at TN.SmAaccording to a power law in reduced temperature [329]: K,, = (7'-7'N-smA)p'. Critical exponents have been measured for the twist [77-79, 81-87, 1711 and bend [77-79,81,82,85,88-91,93-97, 168, 171, 1721 constants. X-ray diffraction measurements made by Bradshaw et al. [98] indicate a correlation between short-range smecticlike order and the K,,IK, ratio, even for nonsmectogenic substances. Critical exponents measured for K2, are p,=0.66 [77] and p,=0.66 [87], and for K,, are p3= 1 (octylcyanobiphenyl [SS]), p,=0.66 [77], p3=0.62+0.03 (octylcyanobiphenyl [ 168]), p,=0.68 20.04 (diheptylazoxybenzene [96]), p3 = 0.84 2 0.03 (4-nhexyloxyphenyl-4-n-nonylbenzoate [95]) and p3=0.825 20.008, p3=0.8 15 20.03 (dihexylazoxybenzene [95]), from FrCedericksz transition and light scattering experiments, respectively. (See also the data on critical exponents collected in Garland et al. [90].) Almost all the critical exponents determined experimentally are in the range 0.66-0.85. The coefficient K3, may reach values of lo-' N near the transition [95]. The practical importance of the 'anisotropic' elastic ratio K,,IK, for display applications has been pointed out by Pohl et al. [ 1121. Small values of K,, increase the steepness of the deformationholtage characteristic, which is desirable in multiplexed nematic displays. An increasing K3,/K1 ratio also favours the inset of striped instabilities in a homeotropic geometry [96].
MBBA and n-CB
71
Some investigations have been devoted to the behaviour of elastic constants in particular regions of the mesophase diagram; for example, studies near the N-SmA-SmC tricritical point [86,89,93,94] and studies of elasticity in a re-entrant nematic phase [ 1131. In general, in comparison with low molecular weight nematics, polymeric nematics show higher elastic constants. Solutions of low molecular weight fractions of polymers in monomeric nematic liquid crystals are of practical interest, because viscoelastic coefficients can be tailored in this way. Investigations of the viscoelastic characteristics have been reported, e.g. for side-chain [99] and main-chain polymers [ 100-102, 1601. In the side-chain mixtures, K , , has been found to remain constant in mixtures containing up to 20% of added polymer. For main-chain additives, the bend and splay constants both increase moderately with polymer concentration (measurements up to 5% [l02]). The twist constant seems to be uninfluenced [ 1601.
2.1.4
MBBA and n-CB
A substance that has been studied extensively by means in elastic coefficient measurements is MBBA. Elastic data on MBBA have been obtained using various techniques [22, 23, 62, 119-1411, and these allow methodological comparisons. In particular, elastic coefficients or ratios of elastic coefficients have been reported for
0
K , , [22, 120-123, 125, 126, 128-130, 133, 134, 136-138, 1401 K,, [22,62, 119, 126, 129, 131, 133, 134, 136-1401 K33 [22, 119-130, 133-138, 1401 K , , 11841
The experiments can be subdivided into, for example, magneto-optical methods [22,119,
72
2.1
Elastic Properties of Nematic Liquid Crystals
1201, electo-optical methods [127, 1321 (in mixtures), capacitive methods [ 1301, light scattering [ 129,137, 1381,Rayleigh scattering [133, 1361, absorption measurements [ 1261, mechancial torque measurements [ 1391, electrical conductivity [122, 1281, thermal conductivity anisotropy measurements in FrCedericksz cells [121], shear flow alignment [123, 1641 and electrical reorientation with infrared absorption detection [ 1351. The most frequently studied homologuous series of nematic liquid crystals with regard to the measurement of elastic constants is the n-alkylcyanobiphenyls (n-CB, n=5 to 8) [20, 30, 41, 63, 142-1801. In particular, data have been reported for [41, 143-146, 149, 150, 153, 156, 162, 166,169, 170, 172-1781 K.-~[20,30,145,146,148,150,154-156, 161, 162,166, 170, 171, 174, 176-1781 K33 [41, 142-146, 150, 153, 156, 160, 162, 166, 169-172, 175-1781
20
0
I0 lTNl-TioC
K11
Experiments on the determination of surface-like coefficients, K I 3 [147] and K24 [163, 1781, have been reported, although they give only rough estimates or lower limits for these coefficients (K24 > K , in 8-cyanobiphenyl [ 1781). The variety of data on this homologuous series allows for a comparison of the reliability of different methods. Moreover, the octyl homologue (8-CB) [ 165- 1801 exhibits a nematic phase followed by a SmA phase and is therefore particularly interesting for the study of the critical divergence of the K33and elastic coefficients on approaching the transition from the nematic to the SmA phase. Elastic coefficient measurements show that short-range pretransitional smectic-like order is found more or less in all n-CB homologues [98]. In Fig. 2a-c the elastic constants of the cyanobiphenyl series, as determined by Karat and Madhusu-
20
20
0
10
TNI
[
I
15
- T 1°C
I
10 ITNL-T)’C
I
5
I
0
Figure 2. Elastic constants of 4’-n-alkyl-4-cyanobiphenyls as functions of the relative temperature (1 dyne=10-5 N): (a) K , , , (b) K 2 2 ,(c) K33.Results of different experiments are marked separately. (Reproduced from Karat and Madhusudana [166], Part 11, with permission of Gordon & Breach publishers.)
2.1.5
dana [ 1661 from the Frkedericksz transition are depicted. One can easily see the divergence of K22and K,, at the N-SmA transition.
2.1.5 ‘Surface-like’ Elastic Constants The K , and K23 terms, which vanish identically in the apolar nematic and cholesteric phases, are not considered here. As discussed above, the volume integrals of the free energy terms containing the splaybend elastic constant K,, and the saddlesplay elastic constant K2, can be transformed into integrals over the nematic surface s:
&3=Kl3
[n’(v‘n)]ds S
(8)
Therefore their contributions to the total free energy can be expressed in terms of the nematic director field at the boundaries only. The variation in the free energy density in the bulk, and thus also the equations describing equilibrium bulk deformations of the sample with a given director field at the surface, are independent of K13 and K24. Note, however, that both coefficients represent bulk properties of the nematic. The name ‘surface elastic constant’, which is sometimes used for these coefficients, is therefore misleading; they might be more appropriately called ‘surface-like elastic constants’. Schmidt [ 1851has proposed that the contributions to bulk elastic deformations be regrouped in order to include the saddle-splay term KZ4.While his arguments have been rejected on the basis of simple mathematical considerations [ 1861, the idea
73
‘Surface-like’ Elastic Constants
behind the proposal, that although the influence of the ‘surface-like’ coefficients K,, and K,, are manifest only at the boundaries of the liquid crystal volume, their physical origin lies in the nematic bulk, is still correct. It goes without saying that these coefficients, as well as the bulk coefficients, depend only on the nematic substance and not on the surrounding medium. Elastic bulk forces connected with the K , , and K24 free energy terms are neutralized in the volume, as long as the elastic coefficients are homogeneous in space throughout the sample volume. In such a case, the free energy contributions of these terms can be written as complete divergence terms. If, however, the nematic order parameter changes within the sample, then K , and K2, themselves may vary locally, and the simple transformation of the corresponding integrals over the elastic free energy density into surface integrals can no longer be performed. In particular, if the order in the bulk and at the surface are different, the elastic energy is not determined by the value of the surface-like constants in the liquid crystal surface layer only. If K13and Kz4can be considered constant within the sample, their influence on the bulk elastic deformations under fixed boundary conditions of the directorfield can indeed be neglected, and the bulk deformations are described exclusively by K , K2, and K,,. Then, the influence of the surface-like elastic terms is often masked by the anchoring energy of the nematic phase at the substrate. The K , , and K24 terms have thus been dropped by many authors when calculating bulk distortions, although the values of these constants have been estimated from microscopic calculations [ 187- 1891and experiments [44, 178, 190-1941 to be of the same order of magnitude as the bulk constants. Part of the considerations that lead to the neglect of surface terms may well be the
,
,,
74
2.1 Elastic Properties of Nematic Liquid Crystals
difficulties involved in their mathematical treatment. The neglect of the surface-like elastic constants in the calculation of equilibrium director configurations is, however, only justified in cases of strong homeotropic or planar anchoring at the surfaces [195]. Under weak surface anchoring or oblique anchoring angles, the surface-like constants can take effect, and they can modify the equilibrium director orientation and gradients at the surface. Under strong anchoring, the director orientation is fixed at the boundaries, irrespective of surface-like elastic terms. However, as discussed below, K , , and K 2 4 effects may still be observed. We will now discuss the physical relevance of the two surface-like terms separately. The coefficient KZ4 was considered by Oseen [2] and Zocher [3] in their early work on elastic theory. First, we introduce for convenience the substitution k24= K 2 4 + K22. The use of k,, is not uniform in the literature, and sometimes one must check the definition when comparing different sources (e.g. [43, 187, 196, 1971). Our k24 corresponds to the coefficient K 2 4 in Allender et al. [43]; the definition of K 2 4 here coincides with that of Nehring and Saupe [ 1871 and Chandrasekhar [ 1981, while it differs from that of Faetti [ 1971 and Pergamenshchik [ 1991. Although the elastic term connected with k24 itself is not positive definite, it poses no mathematical problems with regard to the free energy minimization, as the free energy functional remains positive definite (bound from below) as long as 0 5 k24 I 2 m i n ( K , K22) (In contrast, the introduction of K,, leads to mathematical problems, as discussed below.) In a large number of geometries of practical relevance, the k24 term can be shown to vanish completely. Written in the form of Eq. ( 3 ) , the k24 term consists of
products of director derivatives with respect to different coordinates ri#rj. If the director field depends upon one Cartesian coordinate only, these products are identical zero. Therefore, the k24 contribution vanishes in all director fields with only one-dimensional inhomogeneity. It can therefore be neglected in all types of planar or non-planar director field within planar cells, as long as the deformation is homogeneous in the cell plane (in the absence of disclination walls). The k24 contributions also average out in director configurations of planar cells that are symmetrical with respect to the cell midplane, including for example walls separating oppositely reorienting twist or splay-bend domains in the FrCedericksz transition. Moreover, when the nematic director field is planar in any geometry, i.e. the director is perpendicular to a certain direction everywhere in the volume, we can write Eq. ( 3 ) in the following form (assuming n ( r )le,) (%,y n y , x - n x , x n y , y )
which is zero due to the conditions ( T Z ~ ) , ~ = 2 (n, nx,x+ ny n,,,) so, and (n2),,=2 (n, n,,y + nyn,,,)=O, and the k24 term in Eq. (3) vanishes identically. Thus, k24 will only be effective in non-planar director fields. In addition, Pergamenshchik [200] has shown that a non-zero k24 term will only induce director derivatives at the boundaries perpendicular to the surface normal. However, there is no physical reason why the coefficient k24 itself should be exactly zero, and therefore in special geometries the saddle-splay contribution must be taken into consideration. The k24 term is nonzero for director configurations containing stable point defects [52]. For example, it influences the director fields in cylindrical [43, 44, 178, 194, 201-2031 and spherical [47,204,205]cavities, in nematics confined between concentric cylinders in bend geom-
2.1.5
etry [206], in periodically deformed ground states of the nematic director field of hybrid aligned planar cells [192, 207, 2081, topological defects in hybrid aligned cells [209, 2101, and the curvature of fluid membranes [211]. Klkman has suggested that k24 may also be essential in the stabilization of blue phases [212]. Experimentally, access may be gained to k24 by studying director configurations in stripe textures (e.g. [ 196]), or in the non-planar geometries cited above (e.g. [43, 471). As an example, we discuss the saddle-splay term in nematics confined to cylindrical cavities. A means of measuring k24, on the basis of an analysis of the nematic director field, has been proposed and performed by Allender et al. [43]. The director configuration in the cylinders is monitored by deuterium NMR lineshape analysis [44, 1911 or polarizing microscopy [ 1941. The submicrometer cylindrical pores of a nuclepore filter are treated such that the director is anchored perpendicular to the pore walls everywhere. The nematic liquid crystal 4n-pentyl-4'-cyanobiphenyl (5-CB) is adsorbed to the filter pores. There are several possible different stable director configurations in cylindrical geometry. The planar configuration with a strictly radial director field (PR) leads to pure splay with a defect line along the cylinder axis. The planar, polar (PP) configuration exhibits two defect lines at the cylinder walls. Both planar configurations are independent of k24. However, the director can escape the plane of the pore cross-section to form the non-planar escaped radial (ER) configuration, in which the director is oriented axially in the pore centres and which has no defect line. Above a certain critical pore radius, this configuration is energetically favoured over the PP structure. The influence of k24 on the director field in the cylinder pores is manifested in two
'Surface-like' Elastic Constants
75
ways. First, the elastic energy of the nonplanar ER conformation depends upon k24, while the PP and PR energies are independent of k24. The ER total free energy per unit pore length is n(3K-k24) [43], whereas for the PP configuration it is n Kln [Rl(2p)], where R is the pore radius and p is the radius of the defect line. A structural transition from PP to the ER configuration at some critical pore radius occurs at the intersection of the free energy graphs (Fig. 3). Thus, if director fields in different pore sizes are analysed, one can estimate k24 from the critical radius for the range of stability of PP director configurations. Figure 3 shows the results of free energy calculations and Fig. 4 gives the computed range of stability of the PP structure. Note that the surface-like elastic term is effective here, even at strong anchoring. Evidently, both the PP and the ER configuration represent equilibrium states of the director field, one of which is metastable with a corresponding higher free energy. Although k24 does not enter the Euler-Lagrange equations for the bulk, and therefore does not affect the director profile in the ER configuration, it is still effective
Figure 3. Free energy per unit length in terms of anchoring strength for the planar polar (PP) and non-planar escaped radial (ER) structures (one-constant approximation, K;,= K ) . The critical radius for the structural transition is given by the intersection points of the energy graphs. (Reproduced from Crawford et al. [1911.)
76
2.1 Elastic Properties of Nematic Liquid Crystals
in determining the absolutely stable director configuration. Of course this is not unusual in elastic theory; for example, the coefficient K2 does not enter the EulerLagrange equations describing a homogeneously twisted planar cell either, but selects stable twist configurations that satisfy the boundary conditions. The second effect of k24 is its indirect influence on the radial director profile in the ER configuration at weak anchoring. The director angle at the pore walls depends on the quantity o = ( R W0+k2,)lK-l, where Wo is the anchoring strength, and thus the bulk distortion changes with k24. This is reflected in, for example, the NMR lineshape. From the determination of for different pore sizes R , Crawford et al. [191] determined the value k,,lK= 1 for 5-CB. Investigations of the octyl homologue (8-CB), which exhibits a N-SmA transition, have been reported by Ondris-Crawford et al. [ 1781. From the absence of stable PR structures, they give an estimate of k24>K1,. Polak et al. [194] have studied optically the director field in glass capillaries, and derived a lower limit of k24> 1.2 K , , for 5CB and k24 > 1.6K , for the nematic mixture
E 7 Merck. Analysis of the ER stability seems to provide more accurate kZ4values than does monitoring the director deformation. The elastic constant K,, introduced by Nehring and Saupe [5] is the only coefficient in the second-order elastic theory of ordinary nematics that involves explicitly second derivatives of the director field. Apart from its practical consequences, K13 is of some theoretical significance because of the relations K;, =K , ] + 2 K 1 3 and K j , =K33- 2 K,, between the Oseen-Nehring-Saupe coefficients K , 1, K33 and K13 and Frank's elastic constants K;, and K j , . The introduction of K13 is not as straightforward as that of K24,and causes serious mathematical problems. The free energy contribution corresponding to the K,, term is not bound from below, and the simple application of the variational principle with a nonzero K13 coefficient may lead to discontinuities in the director field at the boundaries. This problem is known as the Oldano-Barbero paradox [213, 3251. Consider the simple one-dimensional splay geometry having the director field n = [sin O(z),0, cos O(z)] in one constant approximation K , =K33=K . The free energy density is
,
1 Ke,2 - 1 K13d (sin (20) 6,) f =2 2 dz
(O,=JO/&). Together with the surface energy terms Fo (Oo) and F1(el),where Oo= O(0) and O1 = O(d) are the tilt angles at the boundaries z = 0, d, the total free energy per unit area
+ 21 K I 3[sin(20)Oz -
2 1.5 ‘Surface-like’ Elastic Constants
is minimized by the bulk equation O,,=O. In addition, if 19(0),8(d) and e,(O), OZ(d)are considered independent variables, the four boundary conditions
[ K - K~~C O S ( ~ O ) ] ~aeo , / ~ = ~ ~ - [ K - K~~cOs(2e)l e,~= a4 ae, K I 3sin(28)io= 0 K13sin(28)jd = 0 must be obeyed. For K,,#O this is, in general, impossible in the class of continuous functions [213]. The Euler-Lagrange equation for the bulk solution in this case is a second-order differential equation containing only two free parameters. It can be seen that the linear dependence of the last two terms in Eq. (9) on the director derivatives 0, at the boundary lead to an unbound free energy contribution. This is in conflict with the assumptions of elastic theory, which presupposes weak deformations of the director field. In their first explanation, Oldano and Barbero suggested that changes in K13 on approaching the phase boundary and the appearance of additional elastic coefficients in the subsurface layer could remove the paradox. This explanation is, however, unsatisfactory in a physical sense. To bypass the mathematical difficulties associated with the K13term, two new approaches were proposed. Hinov [ 184, 214, 2151 and Pergamenshchik [199] state that the solutions of the Euler-Lagrange variational problem must be sought in the class of continuous functions. That is, the first derivatives of the director field at the boundaries are not free parameters [ 1841but have to be taken from the bulk solutions of the Euler-Lagrange equations. The free energy is formally expanded to an infinite sum of higher order director derivatives, which poses a lower bound on the total free energy. As a consequence, the mathematical problem becomes well posed and the
77
higher order terms in the expansion give rise to apparent derivative-dependent terms in the anchoring energy. However, these terms are considered to be small [ 1991 compared to the well-established Rapini-Papoular 12161 terms. Faetti 12171 has shown that this approach, while circumventing the OldanoBarbero paradox, gives rise to another problem. In the case of an oblique surface orientation ofthe director (sin (20) z = O , d # O ) , the torque balance, which is indeed a fundamental physical quantity, is violated at the surface. An alternative interpretation has been proposed by Barbero and co-workers [195, 2 181. These authors expand the free energy to fourth order in the director derivatives. This increases the number of elastic terms by 35 and makes a general application of this so-called ‘second-order elastic theory’ rather complicated. While this approach provides the correct torque balances, it results in large subsurface director deformations on a molecular length scale which are not consistent with the ideas of Frank’s theory, which is based on the assumption of weak director gradients. Yokohama et al. [219], Barbero et al. [220, 3271 and Faetti [221] have proposed interpreting the strong surface deformations as apparent surface energy terms. According to Faetti’s [221] formulation, such shortrange sub-surface distortions can, in general, be treated as an apparent contribution to the anchoring energy. The main difference from Pergamenshchik’s approach is that, with Faetti’s assumptions, principally all physical effects of nematic surface-like elasticity should be explainable by proper scaling of the anchoring strengths, thus setting K , , equivalent to zero. It seems that, until now, no final decision has been made concerning the validation of these two interprei ations. There is, however, evidence that some experimental findings are consistent-
I
78
2.1 Elastic Properties of Nematic Liquid Crystals
ly described only by setting Kl3+O (e.g. [190, 217, 222, 2231) and even non-zero numerical values have been reported [ 190, 2241. This would strongly support Pergamenshchik’s theory in favour over Faetti’s. On the other hand, Stalinga [225] has reported experiments in the splay Frkedericksz geometry that yielded results consistent with Kl3 -- 0. Finally, we will discuss some consequences of the Kl3 term on elastic deformations in nematic phases. First, if K13is of the same order as other elastic constants, it will be effective in much more situations than will K 2 4 .In fact, in most cases where KZ4is effective, Kl3 will have to be considered as well. This has been pointed out for stripe domains in hybrid aligned films [ 1901, surface transitions in nematics on solid surfaces [224], nematic droplets [47] and cylindrically confined nematics [214]. Many authors have emphasized the modification of the apparent surface anchoring energy by the K,, term (see above). The influence of Kl3 on director fluctuations in nematics has been discussed by Shalaginov [226]. He gives an explicit expression for the correlation function in homeotropically aligned cells, where the apparent anchoring energy W:pp=K33 W01(K3,- K l , ) is a function of the surface elastic coefficient and raises the possibility of measuring Kl3 by means of light scattering experiments. In free standing nematic films, nonzero K13 may lead to a deformed ground state [188]. Derzhanski and Hinov [227] have pointed out theoretically that a non-zero splay-bend term may lead to a first-order Frkedericksz transition in homeotropic, planar or twisted cells; that is, the induced tilt angle at the critical threshold field does not vary continuously but may jump on passing the threshold and show hysteresis effects. A spontaneous polarization at the surface between a nematic and a solid substrate due
to a non-zero K,, term has been predicted by Barber0 and Kosevich [228]. This surface polarization is proportional to the surface order parameter. It is effective only at oblique surface alignment; that is, it vanishes for homeotropic or planar samples. Alexe-Ionescu and co-workers [229,230] have analysed the temperature dependence of K,, by theoretical considerations. They introduced a term that is proportional to S and which is not present in the other elastic constants. At small S in the vicinity of TN-I, the linear order parameter term should dominate the temperature dependance of the splay-bend elastic constant, and the ratio to the bulk elastic constant K131K should be proportional to US. Probably the most direct method of measuring Kl3 to investigate the critical thickness of hybrid aligned nematic (HAN) cells [231, 2321. The nematic is anchored at different preferred polar angles at its parallel opposite interfaces. The interfaces may be isotropic with degenerate azimuthal orientation, as for example in Langmuir liquid crystals [233, 2341, or homeotropically at one surface and planar at the other (e.g. solid substrate). If the anchoring is weak at one substrate and strong at the other, then the film exhibits a critical thickness phenomenon. The director field is homogeneous below a critical film thickness which depends on the anchoring strength as well as on Kl,. A wedge cell method for measuring Kl3 has been proposed on this basis by Strigazzi [232]. Other methods of determining K,, have been proposed by Chang et al. [236] and Sparavigna and Strigazzi [222, 2351 and Kiselev [328]. However, few experimental data are available. Faetti and Palleschi [237] have given an upper limit for K13. The only numerical values reported so far are K I 3= cgs units (lo-” N) for 4n-heptyl4’-cyanophenylcyclohexane (PCH7), by
2.1.6 Theory of Elastic Constants
Madhusudana and Prathiba [238], later corrected to cgs units ( lo-', N) by Barbero and Durand [224] and KI3=0.2K, for 5-CB by Lavrentovich and Pergamenshchik [190]. However, in view of the mathematical difficulties discussed above, one has to treat these quantitative data with proper care. Finally, it should be noted that surface effects on nematic elasticity do not amount only to the appearance of the K I 3 and K,, elastic terms. Changes in the order parameter in a surface layer (see Barber0 and Durand [239]) and references 1-6 therein), as well as unbalanced molecular interaction forces due to the broken symmetry of the nematic interaction potential at the surface [240], may lead to a spatial variation in the bulk elastic constants and the emergence of new elastic terms near the surface.
'
2.1.6 Theory of Elastic Constants The first theoretical dicussion of the temperature dependence of elastic constants within the framework of the molecular-statistical Maier-Saupe theory was given by Saupe [241]. He attributed their temperature dependence to changes in the order parameter S and the molar volume Vmol with temperature, and he introduced reduced elastic constants
The C, should be practically temperature independent according to this theory, and the Frank elastic constants scale with the square of the nematic order parameter, while their ratios should be constant material parameters. In his first qualitative estimation of their relative quantities Saupe [241] derived a K,,:K,,:K33 ratio of -7:11:17. This non-
79
physical result (the predicted K, I < O is in conflict with the well-established stability of the undeformed free nematic phase) is explained by the author as being due to oversimplified assumptions about the molecular shape and interactions. These calculations have been extended to surface elastic constants and later corrected for the effective splay and bend constants (second-order elasticity correction) by Nehring and Saupe [187]. The Kil:K;2:Ki3:K13:K,4 ratio of 5: I1:5:-6:-9 reflects correctly the rough approximation K; = Ki3 established experimentally for a large number of nematics (far from smectic phases). The surfacelike coefficient K24is not independent in this microscopic treatment (see Eq. 2). The model fails to predict the experimental finding that the twist constant K2, is, in general, smaller than the splay and bend constants. Moreover, the elastic constant ratios obtained experimentally are temperature independent only to a very rough approximation. It is necessary that anisotropic molecular shapes and short-range order be included in a more elaborate microscopic description of nematic elasticity. In view of the desirable molecular design of liquid crystalline phases, the final goal of microscopic theories is not only to predict the temperature dependence of elastic coefficients, but also to reveal relations between the molecular and elastic properties of the mesophases. Since the original work of Saupe in 1960 [241], a large number of microscopic theories have been developed [181-183, 242-2701. The first molecular statistical theories of the Frank elastic constants were formulated by Priest [242] and Straley [243], and a significant step was made by Poniewierski and Stecki [244,245] who applied density-functional theory in order to relate in a direct quantitative way the elastic constants to characteristic properties of a statistical ensemble of molecules with
80
2.1
Elastic Properties of Nematic Liquid Crystals
given nematic interaction potential. The widely used formulae given by Poniewierski and Stecki correlate the Kii with the direct pair correlation function c (r, O,, n,) and the orientational distribution p (cos 0):
P Kll = P JdrdL2dOid o j c ( r ,i21, 0 2 )
12
. p’(cosO1) ~ ’ ( 0 I,r) r: el, P K Z 2=
$ jdrd12dL2i dQj c ( r ,Ql,
. P’(COS@l) P’(@2 1 1 r l 2
e2
(10) Q,)
2 ely e2 (11)
P K23= fj d r dDdDi dfij c ( r ,Q1,Q2) . p’(cosO1
I ,1
~ ‘ ( 0 2 r)
r: el, e2
(12) where P= l/KBT, r is the molecular separation vector, a is the Euler angle, Qi are the molecular axis orientations, Oiis the angle between the axis of molecule i and the director (along e,), p’(cos0) is the derivative of p with respect to its argument, and e l jand e2j represent the j = {x,y , z } component of the molecular orientation. Each equation is built up of a seven-fold integral over the distance r and the Euler angles 0, Oi and Oj describing the relative positions and orientations of molecules 1 and 2. These expressions were later re-derived by, for example, Singh [255], Lipkin et al. [256] and Somoza and Tarazona [271]. A transparent description of the approach is given by Lipkin et al. [256]. An expression similar to Eq. (10) for the surface-like constant K,, has been derived by Teixeira et al. [ 1891. The calculation of the orientational distributions and two- or multiple-particle correlation functions is not straightforward even for the simplest potentials, and commonly involves proper simplifications and truncations. An alternative approach is to perform molecular dynamical simulations
of a statistical ensemble of particles (e.g. [273-2761) in which the classical equations of motion are solved for the multiple-particle system. Using the structural properties of the statistical ensemble in these molecular dynamical simulations, the elastic constants can be obtained in one of two ways. The first approach directly utilizes the Poniewierski-Stecki relations to calculate the direct correlation functions. The second method follows closely experimental situations such as, for example, the FrCedericksz transition [272], orientational fluctuations [273] or the induction of twist in a nematic sample [277], and the elastic constants are determined from an analysis of experimental macroscopic observables. In all molecular statistical calculations, the choice of a proper interaction potential is of crucial importance. Hard-core simulations [242-244,274,278,279,3301 assume only repulsive forces between ellipsoidal particles, and fail to reflect realistic properties of the nematic phase [264, 269, 280, 28 11. Therefore, attractive intermolecular potentials must be added. In most cases, an additive superposition of pair potentials is assumed in the calculations. Hybrid models use hard core repulsive potentials plus some attractive anisotropic potentials, for example, modified van der Waals models (e.g. [282]). Poniewierski and Stecki [245] combined hard Onsager spherocylinders with an attractive Maier-Saupe type quadrupolar potential. The Lenard-Jones interaction potential often used in isotropic phases with a repulsive term proportional to r-’, and an attractive part proportional to rP6depends only on the intermolecular distances r, and is therefore not suited to the description of anisotropic fluids. A modification of this isotropic potential that accounts for the relative orientations of anisotropic particles has been proposed by Berne and Pechukas [283]. The further improved Gay-Berne
2.1.6
(GB) potential [284] considers, in addition, the orientation of the molecules with respect to their interdistance vector. Sometimes, the repulsive part is replaced by a hard core [189, 2851. The Gay-Berne model forms nematic and SmA and SmB phases [189, 2861 and, although far from being a realistic microscopic description of a nematic phase, currently represents the most appropriate model for the simulation of liquid crystalline states. In a recent publication Stelzer et al. [276] reported the calculation of the three bulk and two surface-like elastic constants of a GB fluid. In the molecular dynamics simulations the bulk coefficients K , K2* and K,, were all of the same order of magnitude, while K , , and K24 were smaller by one order of magnitude. The reported K , , values were negative for all temperatures. Although not stated explicitly, the surface-like constants given by Stelzer [275, 2761 indicate a much weaker temperature dependence than do the bulk constants. Teixeira and co-workers [ 1891 reported qualitatively different results from their investigations of an almost identical system. They found that K , , for the GB fluid was always positive and of the order of the value of the bulk constants. Obviously, in their calculations K , , also contains a term that is linear in the order parameter. A quantitative comparison of different theoretical approaches in the study of a hard spherocylindrical system [265,273,279] has been reported by Poniewierski and Holyst [279]. While the order parameters obtained using the different models coincide fairly well, the agreement between values of the elastic constants is rather poor. In general, because of the complexity of the assumptions and approximations and the sensitivity of elastic coefficients to details of the orientational distribution and correlation functions [279], quantitative and even qualitative compari-
,,
Theory of Elastic Constants
81
sons of molecular statistical approaches and experiment are unsatisfactory. At present it seems that all such theories, while giving insight into the properties of GB and other model fluids, are far from reaching the goal of providing a microscopic understanding of nematic elasticity. A theoretical relation between the nematic elastic constants and the order parameter, without the need for a molecular interpretation, can be established by a Landau-de Gennes expansion of the free energy and comparison with the Frank-Oseen elastic energy expression. While the Frank theory describes the free energy in terms of derivatives of the director field in terms of symmetries and completely disregards the nematic order parameter. The Landau-de Gennes expansion expresses the free energy in terms of the tensor order parameter Q , and its derivatives (see e.g. [287,288]). For uniaxial nematics, this spatially dependent tensor order parameter is QlJ
[
( r )= S ( r ) n, ( r )nJ ( r )- 3v'
]
(13)
2 S (Y) is the largest eigenvalue, and has the 3 corresponding eigenvector n ( r ) .In its principal axis system, the order tensor has the form -
If spatial variations in the order parameter S are small, Q , can be taken as a tensor of fixed eigenvalues with a spatially varying principal axis system. An expansion of the free energy density up to quadratic order in the first spatial derivatives of the order tensor, Q,.,k, as originally introduced by de Gennes [288], yields three invariants
82
2.1
Elastic Properties of Nematic Liquid Crystals
Qij,k Qij,k, Q i k , i Q j k , j a n d Q i j , k Q i k , j [2871, the second and third differing only by a surface term. Hence the bulk term is described by two invariants with coefficients L, and L,:
51 {LIQij,k
fe =
Qij,k
+L2 Qik,i
Qjk,jI
Inserting Q from Eq. (13) into this equation and comparing the result with the Frank elastic energy expression, one obtains the relations
(14)
K l l = K33= S2(2L1+ L2) and K2, = 2S2L1 between the elastic constants and the expansion parameters L, and L,. Since in second-order expansion all terms are preceded by the constant factor S2, the Li are order-parameter independent, and all elastic constants are proportional to the square of the order parameter. There are only two invariants in this expansion, and hence this approximation cannot describe correctly the physical situation K , # K33, but leads to equal values for the splay and bend constants. An expansion of the free energy to higher order terms in first derivatives has been performed by, among others, Schiele and Trimper [289], Berreman and Meiboom [290], Poniewierski and Sluckin [291] and Monselesan and Trebin [292]. We give here the expansion derived by Poniewierski truncated to fourth order, with 11 independent achiral terms:
,
fe =
~
[
1 (2) 2 L1 Qij,k L(:) Qij + LY’ Qij
‘(5)
h2’Qik,i Qjk, j Qij,k Qkl,l + h3) Qik, j Qkl,l
Qij,k
+
Qij
Qij Qik,l Qkl, j
+ L(P)Qij
Li3’ Qij + Ld3’ Qij
Qik,k Q j l , l +
Qkl Qij,m Qij,m
+ L‘24’ Qij Qkl Qim, j Qkm,l + LY)Qij Qkl Qim,j Qkl,m}
Qik,l Qjk,l Qkl,i Qkl,,j
In this approximation, K , # K33, and thirdand fourth-order terms in S enter the expression for elastic constants. Chiral terms and invariants that differ from others only by surface terms have been dropped from this expansion. Further steps in the generalization of the Landau-de Gennes expansion have been the introduction of chiral terms (e.g. [293]) and second-order derivatives (e.g. [47, 2941). Kralj and Zumer [47], in their derivation, have re-expressed of Eqs. (14)-(16). In addition, they included expressions for the surface-like elastic coefficients. In a one-constant approximation (only L‘,~)+o),all constants are equal except for K,,=O; in a second-order approximation (only L(i2)# 0), there is still a splay-bend degeneracy, K 1 =K33# K2,# K24 and K13 remains zero. K13#O and K l 1 # K 3 , requires inclusion o f third-order terms. However, from the expansion given by Barber0 [294] it seems that the expression has to be completed by a term Q,,,, which has a linear order parameter dependence and influences the surface-like elastic constants. Alexe-Ionescu et al. 12291 have pointed out that K13 might therefore have a different (weaker) temperature de-
2.1.7
pendence than the bulk constants near the nematic-isotropic transition. The coefficients in the Landau-de Gennes expansion are in first-line formal parameters, and the theory does not require assumptions in the microscopic interpretation of these parameters. The main impact of the Landau-de Gennes expansion on elastic theory is the well-founded explanation of the S 2 leading term in the bulk elastic constants, and the prediction of a linear term in K13. A number of publications deal explicitly with the theory of elastic constants at phase transitions. The behaviour of nematic elastic constants in the vicinity of the nematicsmectic transition has been analysed by means of the Ginzburg-Landau Hamiltonian [295]. At the transition to the smectic A phase, a critical divergence of K22 and K33 is predicted. Simple mean field theory yields a divergence of the form Kf)(T-TN.s)-1‘2 in the vicinity of the phase transition temperature TN-S. De Gennes argued that mean field results might not be very appropriate, and corrected the critical exponent p to 0.66. Further theories and Monte Carlo simulation studies of the N- transitions have been published since (e.g. [279, 296-3021. Few theoretical studies have been done on the nematic-columnar phase transition [303, 3041. At the transition to the columnar phase, K , and K2, are predicted to diverge, while K33 should behave normally [3041.
,
In biaxial nematic mesophases, the rotational symmetry of the phase around its director n is broken. It is commonly understood that the term ‘biaxial nematic’ refers to an orthorhombic nematic phase. With respect
83
to uniaxial nematics, their phase symmetry reduces from Dh, to &. The orientationa1 state can be described by two director fields Z(r)and m ( r ) .The number of invariant terms in an expansion of the free energy to second order of the director derivatives increases to 12 bulk elastic constants and three additional surface-like coefficients [305-3091. Three of the bulk elastic constants describe twist deformations, six of them refer to splay and bend deformations, and the remaining three refer to the coupling of bend and twist deformations. A derivation of the elastic coefficients of chiral biaxial phases (D2 symmetry) has been given by Govers and Vertogen [3 101who reported three chiral terms [311, 3121 in addition to the 12 achiral bulk coefficients. When the nematic orientation is described by the orthonormal tripod { I , m ,n ) , n (r)= Z(r)x m ( r ) ,the elastic free energy has the form [292, 310, 31 I ]
fi= k / ( z . V x z ) + k , ( m .V x m )
1 + k , ( n . VXn)+-K[I(V.Z)* 2
+-21 Ki2 ( 1 . VXZ)*+-21 Kl-j (1 x VXZ)’ + I2K I , V.[(ZV)Z-(V.Z)Z] 1 +;K,,( L
V . m ) 2+; 1 Km2( m .V X ~ ) ~ L
+ -1K m 3 ( m xV ~ r n ) ~ 2 1 K , 4 V .[(mV )m - ( V .m ) m] +5
+ 21 K,I -
2.1.7 Biaxial Nematics
Biaxial Nematics
( V .n ) 2+
1 Kn2 (n . V Xt ~ ) ~ 2
-
+ -1K n 3 ( n x V x n ) * 2
+-Kn4 21 V.[(nV)n-(V.n)n] 1 1 +-Kim ( I . V X ~+- )K,, ~ ( m .V X ~ ) ~ 2 2 + 21 Knl(n. V x Z)2 -
84
2.1 Elastic Properties of Nematic Liquid Crystals
In achiral nematic phases the first three terms vanish (k,=k,=k,=O). The Ki4 (i= {I, m, n } )terms can be transformed into surface integrals and, therefore, do not contribute to the equilibrium bulk free energy. The remaining 12 terms correspond to the 12 basic types of bulk elastic deformation of an orthorhombic biaxial non-chiral nematic. Monselesan and Trebin [292] have made an attempt to predict theoretically the temperature dependence of the elastic constants of orthorhombic nematics on the basis of an extension of the Landau-Ginzburg-de Gennes theory, where the free energy : f is minimized by the order parameter:
They calculated the coefficients of an expansion of the KV(S,T) up to fourth order in the order parameter S and the degree of biaxiality T. In case of weak biaxiality T + S , the elastic moduli Kni (i= { 1, m, n } )are predominant and the deformation state may be described satisfactorily with three bulk and one surface elastic constant, as in the uniaxial case. Recently, these three quasi-uniaxial bulk elastic constants of slightly biaxial nematic copolyesteramide have been determined by De’Neve et al. 13131 from an optical observation of the Frkedericksz transition in different geometries. Liu [3 141has pointed out that a more general concept of biaxial nematics should include triclinic, hexagonal, cubic and even quasi-isotropic symmetry. He gives the number of independent elastic constants for triclinic systems as 36 and that for quasiisotropic systems as 2. A discussion of elastic theory for nematics having arbitrary point symmetry groups has also been given by Fel [324].
Kini 1315, 3161 and Fel 13171 have discussed the influence of elastic constants of biaxial nematics in several experimental situations. They examined the feasibility of their experimental determinations by means of the simultaneous application of electric and magnetic fields in different geometries. Until now, however, no measurements have been report.ed that go beyond uniaxial elastic theory; that is, there has yet to be an experimental demonstration of elastic deformations connected with the second director in biaxial nematics.
2.1.8 References A. C. Cauchy, Mem. Acad. Sci. Paris 1850, 22, 615. C. W. Oseen, Arkiv Mat. Astron. Fysik 1924,19, I ; Fortschr. Chem. Phys. Phys. Chem. 1929,20, 1; Trans. Faraday SOC.1933, 29, 883. H. Zocher, Trans. Faraday SOC.1933,29,945. F. C. Frank, Discuss. Faraday SOC.1958,25, 19. J. Nehring, A. Saupe, J. Chem. Phys. 1971, 54, 337. P. Esnault, J. P. Casquilho, F. Volino, Liq. Cryst. 1988, 3, 1425. V. FrCedericksz, V. Zolina, Z. Kristallogr. 1931, 79, 225. P. R. Gerber, M. Schadt, Z. Naturforsch., Teil a 1980,35, 1036. M. J. Bradshaw, E. P. Raynes, J. D. Bunning, T. E. Faber, J. Phys. 1985,46, 1513. A. Scharkowski, Dissertation, Leipzig 1991. A. Scharkowski, H. Schmiedel, R. Stannarius, E. Weisshuhn, Z. Naturforsch., Teil a 1990, 45, 37. V. FrCedericksz, V. Zwetkoff, Phys. Z. Sowjet. 1934, 6,490. A. Saupe, Z. Naturforsch., Teil a 1960, 15, 815. V. FrCedericksz, V. Zwetkoff, Acta Physicochim. URSS1933,3,895.V. Zwetkoff,Acta Physicochim. URSS 1937,6, 865. C. Oldano, E. Miraldi, A. Strigazzi, P. TavernaValabrega, L. Trossi, J. Phys. 1984,45, 355. P. E. Cladis, Phys. Rev. Lett. 1972,28, 1629. H. Gruler, G. Meier, Mol. Cryst. Liq. Cryst. 1972,16,299. H. Gruler, T. J. Scheffer, G. Meier, Z. Naturforsch., Teil a 1972,27, 966. H. Deuling, Mol. Cryst. Liq. Cryst. 1972, 19, 123. C. Maze, Mol. Cryst. Liq. Cryst. 1978,48, 273. E. E. Pashkovsky, W. Stille, G. Strobl, J. Phys. IZ 1995,5, 397.
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2.1 Elastic Properties of Nematic Liquid Crystals
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Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
2.2 Dielectric Properties of Nematic Liquid Crystals Horst Kresse
2.2.1 Rod-like Molecules in the Isotopic State Molecules consisting of atoms with different values of the electronegativity are polar. The dipole moment of a chemical bonding is a vector and therefore, a compensation or increase of the bond moments in a molecule can be observed [ 1, 21. Furthermore, the overall dipole moment of a molecule depends on the life time of different conformations. By the dielectric method, only a very small orientation of the molecular dipoles and the time for its reorientation can be measured as static dielectric constant E~ and relaxation time z,respectively. Thereby the static dielectric constant can be ‘produced’ by switching off an external electrical field in different steps as demonstrated in Fig. 1. It can be expected that the reorientation of the 0-CH, group (b) is faster than that of the whole molecule about the short mo-
(a)
(b)
Figure 1. Possibilities for the reorientation of a molecular dipole.
lecular axis (a). The resulting splitting of the relaxation frequencies for motions with different moments of inertia was investigated at first by Bud0 et al. [3] and Fischer and Frank [4] but it could not clearly be confirmed experimentally. The reason for it is the big half width of a dielectric absorption curve of more than 1.14 decades. The first clear experimental evidence was given by Parneix et al. on 4,4’-n-hepylazoxybenzene [5] and Bone et al. on monoesters [6]. More detailed investigations were carried out later [7 -91. It should be pointed out that the differences between the processes (a) and (b) given in Fig. 1 can be obtained also by increasing cooperativity of the motion (e.g. at the glass transition [ 10- 151) or in metastable solids [ 16- 2 l]) where mechanism (a) is frozen. As an example, experimental data for a relatively complicated terminally branched molecule H I , C s ~ ~ C ~ ~ cooc ~ ,OH21~~ ~~ , I
in the isotropic (is) and nematic phase (N) are presented in Fig. 2. The existence of two different relaxation ranges in the isotropic and liquid crystalline phases is evident. The low frequency mechanismfRllcould be observed in the nematic phase only if the measuring electrical field is parallel to the direc-
~
92
2.2 Dielectric Properties of Nematic Liquid Crystals
5.6 5 I
I
I
I
370
380
390
TIK-
Figure 3. Static dielectric constant of the above given swallow-tailed compound near to the I/N transition [261.
Figure 2. Relaxation frequencies of the main reorientation processes for the reorientation around the short (fRII) and long molecular axis fRL in different phases [7].
tor ( E ; , E ! ) or in other words, it is the reorientation mechanism around the short molecular axis designated with (a) in Fig. 1. This motion is influenced by the anisotropic surroundings ('nematic potential' in the theory by Maier and Saupe [22, 231) and is hindered by aretardation factor gllbelow the i s m transition. It should be mentioned here that during the experiments at higher temperatures the given sample shows a small tendency to decomposition. Therefore, no clear step infRl,at the phase transition was detected. For this reason, one can follow the change of fRll at the phase transition ism. This makes the designation of the mechanisms clear. The reorientation about the molecular long axis characterized by T, (b in Fig. 1) is practically not influenced by the transition in the isotropic phase.
A second effect of the same sample shown in Fig. 3 is also interesting. By cooling the isotropic liquid deviations of the static dielectric constant q,from the straight line by approaching the is/N transition were measured. Such behavior was at first detected by Bradshaw and Raynes [24], confirmed by Thoen and Menu [25] and explained as an antiparallel correlation of the strong dipoles in the nematic-like clusters formed in the isotropic phase. For less polar molecules the driving force for the antiparallel orientation can also be produced by a combination of the steric and dipolar forces as shown by Kresse and Kremer [26] and demonstrated in Fig. 3 .
2.2.2 Static Dielectric Constants of Nematic Samples Firstly the nematic phase and the theoretical description of its dielectric behavior will be discussed briefly. In the isotropic state anisotropic molecules are statistically dis-
2.2.2
Static Dielectric Constants of Nematic Samples
tributed and, therefore, only mean values of the respective physical properties can be measured. At the transition into the nematic phase the molecules become ordered with respect to their long axis (orientational order). With exception of a nematic glass both discussed main relaxation processes, the reorientation around the short and the long molecular axis, take place. Thereby, the reorientation around the short molecular axis is additionally hindered by the ‘nematic potential’ already mentioned [22] - an expression of the mean field theory for the description of the anisotropic surroundings. The external electrical field, necessary for dielectric measurements, is unable to destroy the nematic order. Only if the electrical voltage is higher than the threshold one can change the orientation of the sample. For this reason -
-
the static dielectric constants indicated by qlo(indirection of the nematic director 0 ) and (perpendicular to 0 )should reflect the single axis symmetry of the nematic phase. the mean value Eo = ( 2 + ~ ~ ~ ~should ~ ~) / be Eo = q,, where e0, is the static dielectric constant in the isotropic phase extrapolated to the same temperature.
For such a comparison one has to consider the step of the density at the phase transition. All the other relations which connect molecular parameters such as the molecular dipole moment p , the polarizability a and the angle between the molecular long axis and ,u with each other have a general problem: the calculation of the internal field and its anisotropy. Therefore, all the equations given in Vol. 1, Chap. VII.2 are necessary and useful but one has to take always into account the limitations of the models. Nevertheless, the Onsager theory [27] (basis for the Maier-Meier model [28]) and Kirkwood-Frohlich model [29] have been
93
very successful for the design of new liquid crystalline compounds. From the beginning of the 20th century to 1970 the dielectric behavior of liquid crystals was more of academic interest. Especially dielectric anisotropy at low frequencies, A E ~ = E ~ , was ~ - Eone ~ ~of many qualities for the characterization of liquid crystals. Results of 18 samples measured by Specht, Vaupel, Sulze, Errera, Jezewski, Schulwas-Sorokina, Maier and the respective coworkers are summarized in the tables by Landold-Bornstein [30]. Based on these data Maier and Meier could give a connection between the dielectric constants E ~ ~ .cl0 and molecular parameters [28]. In this model the dielectric anisotropy 1 N v FhS A E =~Er
LAa - F .
&
1
~ ) ,
-8
(1 - 3 cos2p)
(1)
where E = 8.85 x Fm-’ N , = number of molecules per unit volume E h = constants of the internal field [27] 3S = degree of order A a = anisotropy of polarizability, A a > 0 p = angle between the molecular long axis and the dipole moment ,u k = Boltzmann constant was explained as result of an overall dipole moment p acting parallel (A%> 1) or perpendicular (A%
-
E
94
t
0
2.2
Dielectric Properties of Nematic Liquid Crystals
- - - - - - - - ----
Eo,is
W
I
I
300 T-
Figure 4. The expected static dielectric behaviour of a nematic liquid crystal with A%>O according to frequency dielectric constant with Eq. (1). EllO2=high respect to the low frequency absorption (fRII, All)
310
TIK-
320
4
1.2
12.9
p, 14.1 10-30Cm p2=0 directly related to the component of dipole moment parallel to the molecular long axis. Figure 6. Static dielectric constants of 4-n-octylcyaAs it can be seen All should increase with nobiphenyl in different phases [25] and the group didecreasing temperature if there is no special pole moments. interactions. For a given dipole moment, the dipolar contribution to Aq, designated as depends on the angle between the dicases is presented in the Figs. 6 and 7. The pole moment and the molecular long axis. data shown in Fig. 6 are a very good examThis is illustrated in Fig. 5 where the A E ~ ( ~ ) ple for the stepwise change of q, at the i s m value for D (1 ,u was chosen to be + 1. A simtransition indicating that this one is of first ilar description was given by Tsvetkov [3 1 , order. On the other hand it also demonstrates 321 later. One example for each of these two that a well purified and chemically stable sample was investigated. In contradiction to this the substance with A%
2.2.2
390
400 TIK
-
410
Static Dielectric Constants of Nematic Samples
420
95
ed on oximesters [35]. With the substituents R r = C 7 H I s ,R,=CN and R,=CH, (A) the expected high positive dielectric anisotropy of 19 and 17 at T N I l s fK 5 were detected. If the lateral substituent R, is CN (R = C6H,, R2= OCIOH2,(B)) a relatively small negative value of A&,,=-0.031 and ~~,,,,=3.17were measured at the same temperature differences to the clearing point. In , ~ B illusparticular, the low value of E , ~for trates the strong compensation of the partial dipole moments in the middle part of the molecule. This results also in a small absolute value of A&,,. A second point should also be taken into consideration: the mutual influence of different partial dipole moments via a shift in the z-electron system [36a]. Such conjugated systems can be found in the stiff middle part of most of the liquid crystals consisting of aromatic building units. This effect can be used to increase the molecular dipole moment by a push-pull system [37,38]. Samples with extremely high positive dielectric anisotropies can be produced in this way, like:
Figure 7. Static dielectric constants of 2,6-bis-[4-nbutyloxybenzol]-cyclohexanone [33] together with the group dipole moments.
periments. Also the slopes of EO and &is,O are different indicating an interaction of the molecular dipole moments. Below the figures, the chemical formulas and the group dipole moments are also given [34]. The chosen samples practically exhibit only overall dipole moments of the above discussed boundary cases p=O and p=90°. This is a result of a compensation of longitudinal dipole components for the second sample. Such compensation effects can be very important as it was demonstrat-
* extrapolated from data of mixtures (see also discussion to Fig. 28). At about 1970 the interest in different liquid crystalline samples increased due to a possible technical application. Chemical firms, academy institutes and universities like: Hoffmann-La Roche, Base1 [41-471 Merck, Darmstadt [48 - 521 - Phillips Research Laboratory, Eindhoven [53 -601 - Brown-Boveri, Baden [61-671 - Chisso Corporation, Tokyo [68-7 11 - Royal Signal and Radar Institute, Malvern [72-761 -
-
96
2.2
Dielectric Properties of Nematic Liquid Crystals
I
- Military University of Technology, Warsaw [77-801
- State University St. Petersburg [81-841 Raman Research Institute, Bangalore [85-921 - Institute of Organic Intermediates and Dyes, Moscow [93-951 - Hungarian Academy of Science, Institute of Solid-state Physics, Budapest [96-981 - Institute of Molecular Physics, Poznan [99- 1041 - Edward Davies Chemical Laboratory, Aberyswyth, UK [ 105- 1091 - Meerut University [ l l O - 1141 - Sheffield University, UK [ 115- 1171 - Halle University [ 118 - 1311
3.6
-
were interested in the static dielectric constants and its relation to the chemical structure. They confirmed the general correctness of the Maier-Meier model as first approximation. Later the dielectric method was used to study special interactions in nematic phases. The first publication in this direction was related to the dipolar correlation. De Jeu and his coworkers discovered on 0
H & ~ N = ~ - @ C d h
a change in the sign of A% from positive to negative near to an expected N/S, transition [56]. behaves according to the MaierMeier relation [28] (see also Fig. 4) but surprisingly a decrease of E~~~ was measured (Fig. 8). From the experimental side one has to say that %-values measured parallel to the orienting field can decrease at least to the smaller data if the sample is not correctly oriented. That is why the static values never can cross the curve. Therefore, the authors considered a compensation of molecular dipoles especially in direction of the molecular long axis [ 1321. Such an abnormal dielectric behavior was also detected
W
3.5
3.4 390
-
41 0 TI K
430
4 50
Figure 8. Static dielectric constants of 4,4'-n-hexylazobenzene [56].
quite earlier on classical p-azoxyanisole (PAA). The experimental data of Maier and Meier [133] in Fig. 9 clearly show that both and are smaller than qs,oat the phase transition N/is. Taking into account the symmetry of the phase and the increasing density at this transition, one has to expect much higher cl0 values. Quite stronger dipolar correlation effects were found in swallow-tailed liquid crystals. Experimental data of the sample for which the chemical formula is given at the
"'"
I
390
-
4 00
TIK
41 0
Figure 9. Static dielectric constants of p-azoxyanisole 11331.
2.2.2
Static Dielectric Constants of Nematic Samples
beginning of Sec. 2.2.1 of this chapter are shown in Fig. 10 [134]. The static dielectric constant at 340 K is two &-unitssmaller than expected according to the MaierMeier model [28]. In this case also a clear decrease of the dielectric absorption intensity of E; couid be detected (Fig. 11). With
A
6.C
Ell0
t, "'
W
4.5 320
340
360
380
TIK-
Figure 10. Static dielectric constants of di-n-hexyl[4-n-octyloxybenzoyloxy)benzylidenemalonate
[134]. 1.0
368.5
97
respect to the data of PAA shown in Fig. 9 and its derivative [56] such effect cannot be explained only by the dipolar interactions. Therefore, the authors proposed a model in which the antiparallel order is mainly forced by steric reasons. Similar results were obtained on the 1,3,4-oxadiazole derivatives
[ 1351as demonstrated in Fig. 12. In this case the angular shape of the molecule can be responsible for the antiparallel packing. In this connection one remark is necessary. The given samples exhibit the relatively strong perpendicular dipole moment of the oxadiazole fragment but due to the positive anisotropy of polarizability it was measured that 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
Dielectric Properties of Nematic Liquid Crystals
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
2.2 Dielectric Properties of Nematic Liquid Crystals
-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
Dielectric Behavior of Nematic Mixtures
/
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
2.2 Dielectric Properties of Nematic Liquid Crystals
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
Dielectric Behavior of Nematic Mixtures
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
Dielectric Properties of Nematic Liquid Crystals
(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-
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109
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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
2.2 Dielectric Properties of Nematic Liquid Crystals
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Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
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. (In biaxial nematics, the diamagnetic susceptibility tensor is characterized by three different principal values x3<0.[ I l l
x27
x,,
114
2.3 Diamagnetic Properties of Nematic Liquid Crystals
The susceptibility tensor x can be split into an isotropic contribution
:I;
1 XIW X(iso)=jTr{X}=(2XL+ and the traceless anisotropic part x(a,.
(rt
X(a) = A X 0
-O+
0
Ax=(xll-xl.)
++
(2) In the isotropic state, the orientational anisotropy is zero and the susceptibility reduc~ ~mentioned ). es to its isotropic value x ( ~ As is weakly temperature depenabove, x(iso) dent, decreasing by approximately 0.1% K-' with increasing temperature. The molar and are and mass susceptibilities temperature invariant. The orientation-dependent part of the magnetic free energy density of a uniaxial nematic liquid crystal is found from Eqs. (1) and (2):
xl:)
1 /LO ( H .n)A x ( n . H ) Fmag= -2
xlEAb,
tically equal to the external field, and the molecular polarization is not influenced by the nematic dipolar moments of the surrounding molecules. The magnetic polarization of the sample is basically determined by the macroscopic order of the molecular polarizability tensors, and x ( ~is) therefore a measure of the order parameter of the nematic phase. A relation between the molecular diamagnetic polarizabilities xapin their molecular principal axes frame {a,p }= {{, q, [} and the susceptibility tensor of the nematic phase can be established. The isotropic average is given by X(iso)
= N Tr { K } 13
where N = N , p / M , is the number of mole' is Avogadro's cules per unit volume; N number. The anisotropy of the susceptibility tensor in the director frame {I, m }= [ x, y, z } can be related to K by the Saupe order matrix s ~ D=
~
(3)
and the torque exerted on the director by an external magnetic field is given by Dmag = PO(n X
H ) AX(^ . H )
(4)
The minimum magnetic free energy is reached when the nematic crystal aligns with the axis of the largest component of x parallel to the field H , i.e. nematic crystals with positive diamagnetic anisotropy (Ax > 0) align parallel to the field whereas in negatively anisotropic nematic crystals (Ax < 0) the director orientation is non-uniform in the plane perpendicular to H . In practice, fields of
x
+
+
e, e l .ep em e, e m .ep el
1
- sap 4 m where the ei are unit vectors and the overbar indicates ensemble averaging. X(a) In
=N
~2~cxb
In the nematic phase, only the two components S=SA
1 (2-5) + D N - ( K g- K q q ) 2 The quantity D is considered to be small compared to S , [2] and is often neglected in the interpretation of the magnetic anisotropy (see also the discussion by Korte [3]). Then, Eq. ( 5 ) reduces to
A x = SAx0
(2-6)
2.3.1
where
(2-7) is a function of the molecular diamagnetic polarizabilities only. The extraction of the order parameter from Eq. (6) requires knowledge to A x o . There are, in principle, three approaches to gauge A x o . In the first approach, an empirical method, the measured susceptibility anisotropies are fitted to the function
This is known as the Haller extrapolation method [4] and is based on the assumption that the order parameter depends on the temperature as
TNI is the clearing temperature, y< 1 is a fitting parameter. The absolute anisotropy Ax0 is found by extrapolation to T=O. In the vicinity of TNI, this approximation fails and a correction factor p has to be introduced. The fit of experimental data on low molecular weight nematic crystals to the generalized equation [ 5 ]
yields p close to 1 (0.994-0.999) and y in the range 0.134-0.217, which justifies the application of the Haller approach. Although this method has been widely used, it is not supported by theoretical studies. Indeed, it seems that the conclusions on molecular polarizabilities drawn from the Haller extrapolation should be treated cautiously. If the exponents yof two homologs differ only slightly, the extrapolation may
Magnetic Quantities
115
give considerably different A x o values despite the comparable A x values at equal reduced temperatures T/TNI in the nematic phase [6]. Alternatively, A x o may be determined if the order parameter S is known from independent measurements of a different physical quantity such as, for example, 'H NMR dipolar splitting, 13CNMR chemical shifts, or optical anisotropies [7]. In practice, however, the temperature curves of A x ( T ) and other anisotropies often cannot be brought to coincide over the whole temperature range (see e.g. [6]) which prevents an absolute scaling of the order parameter. Some authors have used the order parameter predicted using Mayer-Saupe theory to scale A x o . A third method is to calculate the molecular polarizabilities by means of increment systems. The concept of localized diamagnetic polarizabilities [8] proves very useful in the calculation of the average molecular polarizabilities. The method is based on the assumption that the diamagnetic shielding can be split into independent local contributions from the individual atoms, plus corrections for chemical bonds. The mean susceptibilites calculated with such increment systems usually differ from experimental values by no more than about 5%. It is therefore tempting to apply a similar concept of local anisotropic atom or bond polarizabilities to compose the anisotropic molecular polarizability. A tensor increment system may be established empirically from available experimental data (single crystal measurements or molecular beam techniques). Efforts have also been made to compute mean susceptibility ab initio (see e.g. [9]). Flygare and coworkers [lo-131 have proposed a tensor increment system for the magnetic polarizability from a number of organic molecular segments. The method is discussed in more detail below.
x(iso)
116
2.3 Diamagnetic Properties of Nematic Liquid Crystals
2.3.2 Measurement of Diamagnetic Properties Experimental methods can be subdivided into two classes. The first class determined the magnetic dipolar field induced in the nematic crystal, or the force on a nematic sample in an inhomogeneous magnetic field; these methods give absolute susceptibilities A second class of experiments measures the torque on nematic samples in magnetic fields; these experiments are sensitive The anisotropic properties are by far to more relevant to the characterization and application of nematic samples. Therefore the latter methods can be considered more direct, although they give no information on absolute susceptibilities.
x.
Ax.
where m is the sample mass. The force K is determined from the difference in the sample weight with and without a magnetic field. The field gradient is in the vertical; its magnitude is determined from gauge measurements. Alternatively, the magnetic force can be determined from the deflection of the sample in a field of horizontal gradient. The reproducibility of Faraday balance measurements is of the order of 1%, whereas the relative accuracy is slightly better. This method was first applied to susceptibility measurements in nematic crystals more than 60 years ago by Foex [ 141, since when it has become established as a standard method, (see e.g. [ 5 , 6, 16, 171). The magnetic field used in this method is strong enough to align the nematic crystal. Therefore, only the largest component of x can be determined. Nematics with > 0 orient parallel to the field and is measured, while for negatively anisotropic nematic crystals the effective susceptibility is The second independent component of x is found from the temperature dependence. The constant average magnetic susceptibilis measured in the isotropic liquid ity phase. As or is known from the measurements made in the nematic phase, the can be determagnetic anisotropy mined from the difference
x,,
2.3.2.1 Faraday-Curie Balance Method [8, 14, 151 The standard method for the determination of magnetic susceptibilities of diamagnetic samples is the Faraday-Curie method 181. The method is based on the measurement of the force K on a sample with susceptibility in an inhomogeneous magnetic field. For diamagnetic substances
x
Ax
xL.
xi:)
x,, xL
Ax'"'
x'
where is the difference between the volume susceptibility of the sample and that of the surrounding medium, V is the sample volume, and the last term is the gradient of H 2 averaged over the sample. If the external medium is a diamagnetic gas, one can replace by In practice it is more convenient to measure the mass susceptibility x(") from
x' x.
2.3.2.2 Supraconducting Quantum Interference Devices Measurements 118, 191 Supraconducting quantum interference devices (SQUIDS) provide very accurate tools for magnetic susceptibilities. The sample is inserted in the field of a supraconducting magnet and the magnetic flux quanta are counted as the sample is shifted through a
2.3.2 Measurement of Diamagnetic Properties
detector coil. SQUID devices measure the absolute susceptibility x("'). Despite the high accuracy of such devices, only a few measurements have been reported in literature so far [ 18, 191, presumably because the SQUID measurements represent a relatively new technique. The basic problem of SQUID susceptibility measurements in nematic lies in the fact that the sample is surrounded by a cryomagnet at liquid helium temperatures, and temperature control of the sample within the cryostat in the hole of the magnet is not easy to achieve.
2.3.2.3 NMR Measurements [20, 211 The NMR method based on the induction of a local dipole field in the sample by the external NMR magnetic field B,. The principle of the method was described by Zimmermann [20] and the method was first applied to liquid crystals by Rose [21]. The liquid crystal is put into a cylindrical sample tube which is then inserted into a second tube. The proton NMR signal of a liquid probe substance contained in the space between the two tubes is observed. The additional field arising from diamagnetic polarization of the nematic crystal adds to the external NMR spectrometer field and causes a splitting 6v of the NMR line of the probe liquid which is proportional to the difference between the volume susceptibilities of the liquid crystal sample and the liquid. The splitting can be calculated analytically, but in practice 6 v vs is gauged using substances of known susceptibilities. As in the two methods described above, A x has to be determined from difference measurements. A disadvantage is that the NMR method is sensitive to the volume susceptibility, and density corrections are necessary to yield the temperature independent ~221. value
x
&'~~,
117
2.3.2.4 Magneto-electric Method [23 - 251 If the electric anisotropy A& of the liquid crystal is known, the diamagnetic anisotropy of the volume susceptibility may be determined from the FrCedericksz threshold in thin cells of a defined geometry by means of the simultaneous or successive application of electric and magnetic fields. An appropriate geometry has to be chosen with respect to the sign of A& and A x such that at least one field destabilizes the initially undeformed state of the director field. If, for example, AE is positive, planar sample cells with strong anchoring can be used. The cells, are filled with the nematic sample and exposed to a magnetic field normal to the cell plane [25] with induction B . The critical electric field strength E ( B ) for splay deformation is measured. The equation
A E ~E 2) ( B )= A&lgE$ - A x B2/p0 defines a characteristic ellipse for A x > 0 or a hyperbola for negative susceptibility anisotropy, from which the value of A x can be extracted. EF is the critical electric field in absence of the magnetic field. As it is the critical voltage, and not the electric field strength, that is measured, the method requires exact knowledge of the cell thickness. The magneto-electric technique can be particularly important in the measurement of very small magnetic anisotropies [ 2 5 ] . Koyama et al. 1261proposed a similar method that is applicable to homogeneous cells. General expressions for the Frkedericksz threshold in crossed electric and magnetic fields have been derived by Barber0 [27]. The Frkedericksz threshold may be detected optically [28] or by means of capacitance measurements [29]. All magneto-electric methods provide only the anisotropic part of the diamagnetic susceptibility tensor; they provide no information about the absolute susceptibility values.
118
2.3 Diamagnetic Properties of Nematic Liquid Crystals
2.3.2.5 Mechanical Torque Measurements [30, 3 11 If a nematic liquid crystal is suspended in a magnetic field, the magnetic torque exerted on the nematic director by the external field can be measured from the mechanical torque exerted on the sample [30]. In the equilibrium state under a constant magnetic field, the nematic director aligns with the field such that the torque becomes zero. However, when a sample suspended on a torsion wire is slowly rotated in the field at constant speed, a resulting torque of the magnetic field on the sample can be determined from the torsion angle of the wire. Below some critical frequency w,, this torque is proportional to the angular velocity of the revolution. The constant relating the distortion angle of the torsion wire to the torque is determined from gauge experiments. This method can also be used to determine directly the susceptibility anisotropy. With a slight change in the experimental set-up, the susceptibility anisotropy can also be determined by means of an oscillatory method [31]. The sample is suspended in the magnetic field and excited to oscillations of small amplitudes. The oscillation frequency LL) depends on the ratio of the torque exerted on the sample and its moment of inertia. When sufficiently thin wires are used, the magnetic torque dominates and its value can be determined from a plot of cc)vs the magnetic field strength B2. The condition that the director has to stay fixed to the sample tube during the oscillations restricts the method to smectic, polymeric nematic and very viscous nematic samples. A way of measuring the anistropic susceptibility of low molecular mass nematic samples with the oscillation method has been proposed by Jakli et al. [32]. The nematic sample is mixed with a small portion of a photoreactive monomer. After polymerization in
ultraviolet light the system forms a gel the diamagnetic properties of which are practically the same as those of the pure nematic sample, but the director is mechanically fixed to the container.
2.3.3 Experimental Data Some experimentally determined values of the susceptibilities of low molecular mass nematic crystals are collected in Tables 1 and 2. For convenience, all data have been converted to molar SI susceptibilities. Experimental mass susceptibility data are multiplied by the molar mass given in the second column of the table. Values have been rounded to the same number of significant digits as raw data. Original cgs values are given in parentheses. Absolute susceptibilities are of minor importance in the characterization and application of liquid crystals and thus the discussion here is restricted to the susceptibility anisotropies Ax‘~’=x~~’-xI~’. In selecting the literature data we focused on substances where comparable absolute aniosotropies were given explicitly. More data have been published, for example, by Osman et al. [33], Schad and coworkers [34,35], Achard et al. [36], Ibrahim and Hasse [37], Haller et al. [4], Kiebs andEidner [38], Scharkowski and coworkers [25, 28, 391, Molchanov [40], Shin-Tson et al. et al. [24], Rao et al. [41], Gasparoux et al. [42], Burmistrov and Alexandriiskii [43] and Jakli et al. [32]. Measurements of PAA (para-azoxyanisole) have been performed by Gasparoux and Tsvetkov (see [30] and references therein). A discotic system has been investigated by Levelut et al. [44]. Also, a number of papers deal with the diamagnetic susceptibility of lyotropic nematics [45]. In order to establish structure-propertj relationships between the molecular com.
2.3.3 Experimental Data
Table 1. Experimental diamagnetic susceptibility anisotropies (1 Molar mass, M
mCN @) ecN @ eCN Q @ eCN
Compound C7HlS
C7H15
C7HlS
C7H15
C5Hll
C6H13 C6H13
cm3 mol-') of selected compounds.
(exp.)
Source
N I' I
277.4
363.2 (28.9)
0.9
~231
283.5
113.3 (9.01)
0.9
~231
289.5
- 106.5 (-8.48)
0.9
~ 3 1
28 1.4
321.8 (25.6)
0.95
WI
255.38
99.3 (7.9)
0.98
[61
259.3
92.5 (7.36)
0.98
[61
28 1.4
91.9 (7.31)
0.98
[61
aOC6H13
340.5
316
0.95
[281
eOC9Hl9
382.6
310
0.95
[281
267.4
507.4 (40.4)
0.9
[211
267.4
416.7 (33.15)
0.95
WI
O C N
a) a)
CH30 e C H N o C 4 H 9
position and diamagnetic characteristics, susceptibilities of different compounds have to be compared in a suitable way. When no additional information about the order parameter is available, it is reasonable to compare values measured at equal reduced temperatures. Table 1 gives a selection values measured at fixed reduced temperatures. The first four substances differ only in the composition of the core. The cyanobiphenyl shows the largest positive anisotropy. It is obvious that successive replacement of aromatic benzene by cyclohexane leads to a rapid decrease in Ax'M'. The bicyclohexane compound without aromatic rings in the core is negatively anisotropic. The substance with the aromatic pyrimidine ring shows an anisotropy comparable to the biphenyl (the reduced temperature is slightly higher). The substances in rows 5-7 show the effect of the substi-
119
tution of different non-aromatic rings. The diamagnetic anisotropy does not change noticeably. The bicyclooctane derivative shows the smallest anisotropy at the reduced temperature used, but the highest extrapolated Axo [6]. The last two rows give MBBA (4-methoxybenzylidene-4'-n-butylaniline) susceptibility anisotropies at two temperatures. The substitution of the negatively anisotropic cyano group by an alkoxy chain increases the diamagnetic anisotropy noticeably with respect to the cyanobiphenyl. More relevant to the prediction of the magnetic properties and for the determination of nematic order are the absolute anisotropies (see Eq. (6)). There are, however, only a few methods which provide correct absolute order parameters for liquid crystals. The comparison of the absolute anisotropies given in Table 2 may therefore not always
120
2.3 Diamagnetic Properties of Nematic Liquid Crystals
Table 2. Selected experimental absolute molar susceptibility anisotropies of nematic liquid crystals. Compound
=xfy’’-xiM’ (
Molar mass, M
AxAM)(exp)
Method a
289.5
-192 (-15.3)
MS
289.5
-163 (-13.0)
H0.114
255.4
188 (15.0)
H 0.165
283.5
215 (17.1)
MS
283.4
167 (13.3)
H 0.145
259.3
176 (14.0)
H 0.174
28 1
220 (17.5)
H 0.252
294.4
570 (45.3)
H
249.4
532 (42.3)
H 0.141
249.4
588.6
H 0.1413
263.4
572 (45.5)
H
277.4
554 (44.0)
H
277.4
655 (52.1)
MS
277.4
550 (43.8)
H 0.146
279.3
572 (45.5)
H 0.159
301.4
544 (43.3)
H 0.164
314.4
489 (38.9)
H 0.181
304.4
199.4 (15.87)
H
304.4
209.0 (16.63)
H
332.5
190.3 (15.14)
H
299.4
203.6 (16.20)
H
279.3
524 (41.7)
H
307.4
563 (44.8)
H
321.4
664 (52.8)
H
321.4
610 (48.5)
H 0.160
37 1.4
780
P
354.5
714 (56.8)
H
298.4 298.4
656 (52.2) 675 (53.7)
MS H
cm3mol-I) Source
2.3.3 Experimental Data
121
Table 2. (continued) Compound
C7H15
Molar mass, M
A x : ! ' (exp)
Method"
368.5 368.5 354.5 354.5 368.5 368.5
679 (54.0) 692 (55.1) 632 (50.3) 643 (51.2) 651 (51.8) 704 (56.0)
MS H MS H MS H
328.4
722
H 0.250
41 2.5
696
H 0.156
414.5
837 (66.6)
H
358.4
726 (57.9)
H
337.4
537 (42.7)
H 0.150
309.4 309.4 309.4 309.4
721 (57.4) 700 (55.7) 704 (56.0) 690 (54.9)
MS H MS H
236.2
596 (47.4)
H 0.1343
267.4
659 (52.4)
H
267.4
642 (51.1)
H 0.1737
351.5
698
P
269.3
717 (57.1)
H 0.1853
283.3
731 (58.2)
H 0.1944
297.4
751 (59.8)
H 0.1813
311.4
830 (66.0)
H 0.2173
325.4
804 (64.0)
H 0. I983
339.4
742 (59.0)
H 0.1928
353.5
772 (61.4)
H 0.1969
367.5
837 (66.6)
H 0.2018
38 1.5
795 (63.3)
H 0.1878
306.5
594 (47.3)
H 0.184
306.5
662 (57.2)
H
334.5
661 (52.6)
H
362.5
666 (53.0)
H
33 1.5
640 (50.9)
H
359.5
643 (5 1.2)
H
eCN
@0
Source
122
2.3 Diamagnetic Properties of Nematic Liquid Crystals
Table 2. (continued) Compound
Molar mass, M
A\xhMM' (exp)
Method a
324.5
557 (44.3)
H
342.0
568 (45.2)
H
[461
386.4
670 (53.3)
H
[461
382.5
1850 (147)
H
[731
Source
H, Haller extrapolation (with fit exponent); MS, Mayer-Saupe order parameter; P, 'HNMR order parameter data.
a
be more reliable than a comparison of data for different substances at equal reduced temperatures. Therefore the method of gauging AxAMM' is given in the fourth column of Table 2. One should be aware that the order parameters assumed in the determination of may be affected by systematic errors. It turns out, that in most experiments the decrease of A x near the phase transition TNJis much stronger than predicted from Mayer-Saupe theory and, therefore, the fit is rather poor. Some scalings have been performed using order parameters determined from 'HNMR. Anisotropies determined from the Haller fit are very sensitive to the fit exponent. Nevertheless, the Haller fit is well suited to describe the temperature ) most substances with two curve A x ' ~ ) ( Tof or three parameters. Therefore, the exponent y, when available, is given in column 4 of Table 2. We have not included the parameter p, which is usually close to 1 and influences A x only in the vicinity of TNI. Most of the compounds with two aromatic rings and lateral aliphatic chains exhibit susceptibility anisotropies between 600 and 800x cm3mol-'. This anisotropy can be attributed mainly to the benzene ring contributions of about 375 x for each ring this value being obtained from benzene single crystal data. The contributions of pyrimidine and benzene rings are comparable. A terminal cyano group reduc-
es this value by about lOOx cm3mol-' compared to alkyl or alkyloxy substituents. Likewise, a CEC-C-C core reduces Ax;MM'.For samples with one benzene ring substituted by an aliphatic ring, the anisotropy drops to 190- 220 x 1 0-6 cm3mol-'. Bicyclohexane compounds are characterized - 1 6 0 ~lop6cm3mol-', by negative but only few data [6, 231 are available. The influence of the central linkage groups between the rings is not significant. The main effect of terminal alkyl chains is to increase the molar mass while not noticeably contributing to the molar susceptibility anisotropy. Therefore, the molar anisotropy is relatively constant with increasing chain length, while the mass susceptibility anisotropy decreases (see the data on Schiff bases reported by Leenhouts et al. [5]). Three-ring compounds containing one cyclohexane and two benzene rings have been investigated by Buka and Jeu [6] and Muller and Hasse [46]. The anisotropy is slightly lower compared to compounds containing two aromatic ring. This may be attributed to a slight negative contribution by the cyclohexane (about -80 to -100 x lop6cm3mol-'), which is also in agreement with the data for bicyclohexane derivatives. The influence of a lateral substitution of ring hydrogen atoms in cyanophenyl esters has been studied in detail by Schad and
2.3.3
Kelly [35]. No significant changes in the magnetic anisotropy were detected if one or more ring hydrogen atoms were substituted by fluorine atoms. The presence of more than two aromatic rings in the molecular further increases A x above the biphenyl values. SQUID measurements of a four-component nematic mixture (E2) [47] containing naphthyl and phenyl groups have been performed by Turk [ 191. Figure 1 shows the composition of the sample, which provides an extended nematic range when supercooled in a glassy state. The mass susceptibility anisotropy of the mixture as a function of temperature is shown in Fig. 2 together with data on three cyano compounds
C3H~O-~-COO-~-COO-
I
Br
AxhM'=
OCH3
Figure 1. Composition of the four-compound nematic mixture E2 (TN,= 392-398.5 K).
..
-
- o - ~ ~ Q 8 9 o o o - -0 . - 0 . .
.....
............
......... .....
- ...............
O
o.5
..o -
.
o-...
.... ........
AXhM)(i)<(i)
i
The first component of E2 has three benzene rings; it contributes 70% of the value of
* - - . *oe--._
........................
....
.... ...
....
. . . . . . . . +.
1
t .......................
........ " = % "
U*X?
X
0.7
0.75
0.8
0.85
0.9
123
with none, one and two aromatic rings, respectively taken from reference [6]. The susceptibility curve for E2 can be used to compare the different methods for determining the molar diamagnetic anisotropy The Haller extrapolation gives cm3g-', the parameters Axhm)=2.18 x px0.996, ~ ~ 0 . 1 3 TN,=395 5, K. Adjustment of either TNIor p has equivalent influence. TN,=395 K is in the middle of the nematic-isotropic transition range. The order parameter curve S ( T )was determined independently from the NMR dipoledipole splitting of the benzene ring ortho protons [48]. The scaling of Ax'~'(T) with S ( T ) order parameters gives A$Y)=2.5 x lop6 cm3g-'; the corresponding molar ancm3mol-'. isotropy is 1.25 x For comparison, we estimated from tensor increments, considering only the aromatic molecular segments. The contributions Ax{Y)(i) of the different molecular species i with molar fractions <(i) in a mixture are additive:
9.0 mol%
I
Experimental Data
0.95
1
Figure 2. Mass susceptibility anisotropies of heptylcyanobiphenyl (a),heptylcyanophenylcyclohexane (+), heptylcyanobicyclohexane (x), and the mixture E2 (0).The data for the first three compounds were taken from reference [6] and converted to SI units. The lines indicate the Haller extrapolation curves with Ax;"' = 2.18 x 1 r 6 c m 3g-', 0= 0.996, and y= 0.135 for the mixture E2, and the parameters given in reference [6] for the three cyano compounds. Scaling the Ax'"') of E2 with 'H NMR order parameter data gives Ax;"') = 2.5 x 1 0-6 cm3g-' .
124
2.3 Diamagnetic Properties of Nematic Liquid Crystals
and its molar anisotropy is approximately 3 x 375 x lop6cm3 mol-'. The molecular anisotropies of the other three compounds are essentially equal. From single crystal data for naphthene [ 111 (see Table 4) one can estimate an increment of 750x lop6cm3mol-' for the naphthyl group, a value which is twice that of the benzene anisotropy. This gives a molar susceptibility anisotropy of 1.5x lop3cm3mol-' for each of the three naphthyl derivatives. The total of the mixture amounts of 1 . 2 4 ~ cm3mol-', which is in excellent agreement with the value calculated from the 'HNMR order parameter. The diamagnetic anisotropy of a discotic system has been reported by Levelut et al. [44]. Two homologs of triphenylene hexaalkoxybenzoate with hexyl (C6) and undecyl (C1 1) chains have been investigated in the N, phase. The observed anisotropies are negative, with about -88Ox cm3mol-' (C6) and - 5 0 0 ~ cm3mol-' ( C l l ) near the clearing point. Note that, by definition, the director (optical axis) is now perpendicular to the triphenylene plane. The negative diamagnetic anisotropy is due to contributions from the aromatic rings which lie with their ring planes normal to the director in this discotic system. As shown in these examples, the calculation of diamagnetic properties by simple additive rules yields promising results. The application of increment systems is discussed below.
2.3.4 Increment System for Diamagnetic Anisotropies Increment systems for the calculation of atom and bond contributions to the mean susceptibility have been proposed by several authors [& 10, 491. The systems are very useful in predicting isotropic averages x(iso). The susceptibility is calculated as a sum of
Table 3. Tensor increments of the molar susceptibilcm3mol-') 1131. ityX(M)
ka
a, b in plane
Atoms HC(H3)C(H2k O< >C = O= -C= N= - N< S< S= P=
Bonds C-H
c-c c=c c-0 c=o 0-H
c-s c=s c=c C=N C=P
-27.6 -95.9 -90.5 - 106.8 -57.8 -27.2 - 103.5 -77.5 -119.8 -214.5 -131.5 -250.9
2.5 -23.5 8.8 -8.8 21.4 26.0 -20.9 -41.9 -22.2 -20.5 190.6 -51.9
0.0 0.0 -11.3 - 16.3 49.0 77.9 0.0 0.0 - 154.6 13.8 124.4 0.0
-49.4 -34.8 -44.4 -74.1 -50.7 -73.3 - 137.4 - 142.4 - 176.3 - 166.3 -332.6
-20.9 -64.5 34.3 - 16.3 34.4 16.8 -20.9 215.3 4.2 -41.0 -49.4
0.0 0.0 223.7 -36.4 191.0 -25.1 -30.2 223.7 0.0 0.0 0.0
atom increments and bond contributions. The experimental susceptibility data for organic molecules given in reference [50]can be used to improve and complete the increments. These increment systems have been used successfully to calculate isotropic averages of the diamagnetic polarizability. A tensor increment system such as the one developed by Flygare allows the anisotropic properties to be predicted. The atom and bond increments are shown in Table 3 which is composed from reference [ 111. In contrast to Pascal's and Haberditzl's systems, where atom and bond contributions are superimposed, Flygare has proposed the use of two independent systems, where the anisotrop-
2.3.5 Application of Diamagnetic Properties
Table 4. Additional increments of the molar susceptibilityX(M) ~rn~mol-~).
0 00
a
34.3 a 33.5" -73.Ia -41.9b -4.1ab -36.9b -40.2b -33.5" -54.4"
-
125
molecular inertia tensor). The benzene para axis deviates from the long molecular axis (principal axis of inertia), which lowers the anisotropy measured in the director frame. In principle, segmental order parameters S'"' could be introduced and the susceptibility anisotropy is
-
-688.6
250.1
750.2
-1311.9
498.9'
-
-1176.6
-501.8
-
Calculated from anisotropies given by Ibrahim and Haase [52]. From experimental fits in the nematic phase (Buka and Jeu [6]). Calculated from single crystal data given by Flygare [ I 11.
ic polarizability has to be calculated using either the atom or the bond table. Several authors have applied the Flygare scheme to calculate Ax;MM'for nematic liquid crystals [51] and to modify increments or supplement additional data [6,52]. A collection of these empirical increments together with single crystal data is given in Table 4. For ease of comparison, the literature data have been converted to (M) - 2~ (M).
x ~ ~ ) - x ~ l s xo o)
agreement with the above discussion of the experimental data, the benzene ring concm3mol-' tribution to is 375 x along the para axis. The cyclohexane contribution calculated from bond increments is above -65 x lop6cm3mol-'. Alkyl and alkyloxy chains make very small contributions to the anisotropy. Difficulties arise from the determination of the realistic average molecular conformation and the average orientation of the local polarizability tensors with respect to the molecular principal axes frame (PAF of the
where dn) are the increments of individual segments. In practice, one has insufficient to apply Eq. (8). information on S'") and dn) Moreover, the increment system is incomplete, and is based on empirical value measured on a limited number of organic substances. The method is, however, suitable for providing reasonable estimates of the molecular polarizabilities, and reflects general properties such as chain length influences and odd-even effects. In conjugated systems, the major contributions to A x come from aromatic rings and multiple bonds, and A x is mainly determined by the order of the aromatic cores of the molecules.
2.3.5 Application of Diamagnetic Properties In a number of magneto-optical experiments, the ratio of the diamagnetic anisotropy to an elastic or viscous parameter is determined. The ratio KiilAx (i= 1, 2, 3 ) can bee found from the splay, twist or bend Frkedericksz thresholds, respectively, in magnetic fields [25,53,54], K,,IAxis measured from the cholesteric-to-nematic transition, [55] flip or rotation experiments in magnetic fields yield XIAX (see e.g. [48, 56-58]), and knowledge of A x is a prerequisite for the determination of the viscoelastic coefficients in these experiments. In conventional magnetic fields, the influence of diamagnetism on phase transitions and
126
2.3 Diamagnetic Properties of Nematic Liquid Crystals
nematic order is very weak. Pretransitional magnetic effects in the isotropic phase have been studied by Kumar et al. [59]. The influence of diamagnetic anisotropy on the nematic order is discussed by Palffy-Muhoray and Dunmur [60] and Hardouin et al. [61]. The latter considers a system that undergoes a change in sign of Ax. The transition from positive to negative A x is found in mixtures of nematogens with opposite diamagnetic anisotropies. It occurs as a function of the temperature and concentration of the mixture. The transition has been studied theoretically by Sinha and coworkers [62] and Kventsel et al. [63]. Such systems are of practical importance in the determination of the anisotropic properties of dissolved molecules oriented in the nematic host phase. NMR chemical shielding anisotropies, [64] direct and indirect dipolar couplings [65, 661 and quadrupolar coupling constants, [67] as well as spin-lattice relaxation times [68] can be determined. Systems with weak magnetic anisotropy have been studied, for example, by NMR. The orientation of the nematic director of a sample rotating in a magnetic field is no longer governed by diamagnetic anisotropy, but by inertia effects at the intersection with Ax=0 [69]; a change in the director orientation with respect to the field with a change in the spinning rate has been reported [70]. Brochard and de Gennes [71] have proposed a way to increase the magnetic torque on a nematic sample by means of the dispersion of ferromagnetic particles. The minimum number of ferromagnetic grains necessary to stabilize the nematic ferrofluid has been determined experimentally by Net0 and coworkers [72] in a lyotropic sample. The magnetic particles were Fe,O, grains of about 10 nm length coated with oleic acid to prevent aggregation. Net0 reported a critical concentration of lo9 grains ~rn-~.
2.3.6 References [ l ] L. J. Yu, A. Saupe, Phys. Rev. Lett. 1980, 45, 1000. [2] W. H. de Jeu, Mol. Cryst. Liq. Cryst. 1976, 37, 269. [3] E. H. Korte, Mol. Cryst. Liq. Cryst. Lett. 1983, 92, 69. [4] I. Haller, H. A. Huggins, H. R. Lilienthal, T. R. McGuire, J. Phys. Chem. 1973, 77, 950. [5] F. Leenhouts, W. H. de Jeu, A. J. Dekker, J. de Phys. 1979,40, 989. [6] A. Buka, W. H. de Jeu,J. de Phys. 1982,43,361. [7] St. Limmer, Fortschr. Phys. 1989, 37, 879. [8] W. Haberditzl, Magnetochemie, WTB, Berlin 1968. [9] M. Schindler, W. Kutzelnigg, J. Am. Chem. SOC. 1983,105, 1360; U. Fleischer, W. Kutzelnigg, P. Lazzeretti, V. Muhlenkamp, J. Am. Chem. SOC. 1994,116,5298;C. van Wullen, W. Kutzelnigg, Chem. Phys. Lett. 1993,205, 563. [lo] W. H. Flygare, R. C. Benson, Mol. Phys. 1971, 20, 225. [ l l ] W. H. Flygare, Chem. Rev. 1974, 74, 685. [12] T. D. Gierke, H. L. Tigelaar, W. H. Flygare, J. Am. Chem. SOC. 1972, 94, 330; T. D. Gierke, W. H. Flygare, J.Am. Chem. Soc. 1972,94,7277. [13] T. G. Schmalz, C. L. Norris, W. H. Flygare, J. Am. Chem. Soc. 1973,95,7961; 1983,105,1367. 1141 G. Foex, L. Royer, Compt. Rend. 1925, 180, 1912; G. Foex, J. Phys. Radium. 1929,10,421; Trans. Faraday SOC. 1933,29,958. [15] L. N. Mulay, I. L. Mulay, Anal. Chem. 1976,48, 3 14R. [16] Hp. Schad, G. Baur, G. Meier, J. Chem. Phys. 1979, 70, 2770. [I71 W. H. de Jeu, W. A. Claassen, J. Chem. Phys. 1978, 68, 101. [IS] B. J. Frisken, J. F. Carolan, P. Palffy-Muhoray, J. A. A. J. Perenboom, G. S. Bates, Mol. Cryst. Liq. Cryst. Lett. 1986, 3, 57. [ 191 St. Turk, personal communication, see reference ~481. [20] J. R. Zimmermann, M. R. Foster, J. Phys. Chem. 1957, 61, 282. [21] P. I. Rose, Mol. Cryst. Liq. Cryst. 1974, 26,75. [22] R. Stannarius, Thesis, Leipzig, 1982. [23] Hp. Schad, G. Baur, G. Meier, J. Chem. Phys. 1979, 71,3174. [24] Shin-Tson Wu, W. H. Smith, A.M. Lackner, Mol. Cryst. Liq. Cryst. 1986, 140, 83. [25] A. Scharkowski, Dissertation, Leipzig 1990. I261 K. Koyama, M. Kawaida, T. Akahane, Jpn. J. Appl. Phys., Part I 1989,28, 1412. [27] G. Barbero, E. Miraldi, C. Oldano, P. Taverna Valabrega, Z. Naturforsch., Teil a 1988,43,547. [28] A. Scharkowski, H. Schmiedel, R. Stannarius, E. WeiBhuhn, Z. Naturforsch., Teil a, 1989, 45, 37.
2.3.6 References [29] Z. Belarbi-Massouras, G. Guillaud, F. Tournilhac, H. Acourag, B. Khelifa, Jpn. J. Appl. Phys., Purt I 1991,30,711. [30] H. Gasparoux, J. Prost, J. dePhys. 1971,32,953. 1311 G. Ilian, H. Kneppe, F. Schneider, Z. Nuturforsch., Teil a, 1985,40,46. [32] A. Jakli, D. R. Kim, L. C. Chien, A. SaupC, J. Appl. Phys. 1992, 72, 3161. [33] M. A. Osman, Hp. Schad, H. R. Zeller, J. Chern. Phys. 1983, 78,906. [34] Hp. Schad, M. A. Osman, J. Chem. Phys. 1983, 79, 57 10. [35] Hp. Schad, S. M. Kelly, J. de Phys. 1985,46,1395. [36] M. F. Achard, G. Sigaud, F. Hardouin, C. Weill, H. Finkelmann, Mol. Cryst. Liq. Cryst. (Lett.) 1983, 92, 1 1 1. [37] I. H. Ibrahim, W. Haase, Z. Nuturforsch., Teil u 1976.31, 1644. [38] B. Kiebs, K. Eidner, Wiss. Z. KMU Math.-Nut. R 1981,30, 197. 1391 A. Scharkowski, H. Schmiedel, R. Stannarius, E. WeiRhuhn, Mol. Cryst. Liq. Cryst. 1991, 191, 419. [40] Yu. Molchanov, Fiz. Twj. Telu 1978, 1, 20; Yud. Mugn. Rezon. (USSR)1981,6, 113. [41] K. R. K. Rao, J. V. Rao, L. V. Choudary, P. Venkatacharyulu, Z. Phys. Chem. 1985, 146, 35. [42] H. Gasparoux, J. R. Lalanne, B. Martin, Mol. Cryst. Liq. Cryst. 1979, 51, 221. [43] V. A. Burmistrov, V. V. Alexandriiskii, Russ. J. Phys. Chem. 1988,62,962. [44] A. M. Levelut, F. Hardouin, H. Gasparoux, C. Destrade, N. H. Tinh, 1.de Phys. 1981, 42, 147. [45] M. E. Marcondes Helene, L. W. Reeves, Chem. Phps. Lett. 1982, 89, 519; L. Q. Amaral, Mol. Cryst. Liq. Cryst. 1983,100,85; M. Stefanov, A. Saupe. Mol. Cryst. Liq. Cryst. 1984, 108, 309; A. S. Sonin, Usp. Fiz. Nuuk. 1987, 153, 273. 1461 H. J. Muller, W. Haase, J. de Phys. 1983, 44, 1209. [47] W. Schafer, G. Uhlig, H. Zaschke, D. Demus, S. Diele, H. Kresse, S . Ernest, W. Wedler, Mol. Cryst. Liq. Cryst. 1990, 191, 269. 1481 R. Stannarius, W. Gunther, M. Grigutsch, A. Scharkowski, W. Wedler, D. Demus, Liq. Cryst. 1991, 9, 285. 1491 P. W. Selwood, Mugnetochemistry,Interscience, New York 1943. [SO] Handbook of Chemistry and Physics, 71 ed., CRC Press, Boca Raton, FL 1990. [SI] A. V. A. Pinto, I. Vencato, H. A. Gallardo, Y. P. Mascarenhas, M o l . Cryst. Liq. Cryst. 1987,149, 29. 1521 I. H. Ibrahim, W. Haase, J. de Phys. 1979, 40, Colloq. C3-164.
127
[53] T. Kroin, A. J. Palangana, A. M. Figueiredo Neto, Phys. Rev. A 1989, 39, 5373. [541 A. J. Palangana, A. M. Figueiredo Neto, Phys. Rev. A 1990,41, 7053. [55] H. Toriumi, K. Matsuzawa, J. Chern. Phys. 1985, 81, 6085. [56] F. Brochard, L. Leger, R. B. Meyer, J . de Phys. 1975, 36, Colloq. C1-209. [571 P. Braun, S. Grande, St. Limmer, B. Hillner,Ann. Phjs. Sex 8 1978,35,61. [58] A. S. Lagunov, A. N. Larionov, Russ. J. Phys. Chem. 1983,57, 1005. [59] S. Kumar, D. J. Litster, C. Rosenblatt, Phys. Rev. A 1983,28, 1890. [60] P. Palffy-Muhoray, D. A. Dunmur, Mol. Cryst. Liq. Cryst. 1983, 97, 337. (611 F. Hardouin, M. F. Achard, G. Sigaud, H. Gasparoux, J. Phys. Lett. 1984,45, L143. [62] K. P. Sinha, R. Subburam, C. L. Khetrapal, Mol. Cryst. Liq. Cryst. 1983, 94, 375; K. P. Sinha, R. Subbaram, A. C. Kunwar, C. L. Khetrapal, Mol. Cryst. Liq. Cryst. 1983, 101, 283. [631 G. F. Kventsel, J. Katriel, T. J. Sluckin, Mol. Cryst. Liq. Cryst. Lett. 1987,4, 147; Mol. Cryst. Liq. Cryst. 1987, 148, 225. [64] P. Diehl, J. Jokisaari, M. Moia, J. Mugn. Reson. 1982,49,498;A. Pulkkinen, Y. Hiltunen, J. Jokisaari, Liq. Cryst. 1988, 3, 737; S. Raghothama, J. Mugn. Reson. 1984, 57, 294; E. E. Burnell, C. A. de Lange, Chem. Phys. Lett. 1987,136,87. [65] S. Arumugam, A. C. Kunwar, C. L. Khetrapal, Mol. Cryst. Liq. Cryst. 1984, 109. 263. [66] J. Jokisaari, Y. Hiltunen, J. Lounila, J. Chem. Phys. 1986,85,3198. [67] J. Jokisaari, Y. Hiltunen, J. Mugn. Reson. 1984, 60, 307. [68] J. P.Jacobsen, P. Elmelund,J. Chem. Phys. 1985, 82, 2141. [69] J. P. Bayle, A. Khandar-Shababad, J. Courtieu, Liq. Cryst. 1986, I , 189; J. P. Bayle, F. Perez, J. Courtieu, Liq. Cryst. 1988, 3, 753. (701 B. S. Arun Kumar, N. Suryaprakash, K. V. Ramanathan, C. L. Khetrapal, Chem. Phys. Lett. 1987,136,227. [71] F. Brochard, P. G. de Gennes, J . de Phys. 1970, 31, 691. [72] A. M. Figueiredo Neto, M. M. F. Saba, Phvs. Rev. A 1986,34,3483. [73] P. L. Sherrell, D. A. Crellin, J. de Phys. 1979, 40, Colloq. C3-2 1 I . [74] M. Mitra, R. Paul; Mol. Cryst. Liq. Cryst. 1987, 148, 185. [75] I. P. Shuk, W. A. Karolik, Actu Phys. Pol. 1979, A55. 377.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
2.4 Optical Properties of Nematic Liquid Crystals Gerha rd Pelzl
2.4.1 Introduction
duced a new prism method for nematic liquid crystals that gave separate measureOne of the most striking anisotropic propments of n, and no. Chatelain was the first erties of nematic liquid crystals is their to correlate the birefringence and the orienoptical anisotropy, which is manifested as tational order of nematic liquid crystals birefringence. It was this property of liquid [5,61. Reliable data on the refractive indicrystals that led to their discovery about ces of liquid crystals known up to 1959 were 100 years ago, and early in the history of collected by Maier in Landolt -Bornstein ’s liquid crystals attempts were made to deTables [7]. In the following years the biretermine their birefringence. The first rough fringence of many nematic materials was estimation was made by Lehmann in 1905 measured using various different methods. [l], who placed the nematic phase of In most cases the molecular polarizability 4,4’-bis(methoxy)azoxybenzene between a anisotropy and the orientational order were plane glass plate and a lens with a large racalculated from the birefringence using difdius of curvature. The birefringence ferent local field approximations. However, it should be noted that the birefringence of An = n, - no nematic liquid crystals is a very important was determined from the polarization rings parameter with respect to their practical apin the light converged between crossed poplication, as in each type of nematic display larizers. (TN, STN, ECB, polymer dispersed liquid Dorn [2] performed the first precise crystal displays) an optimum birefringence measurements of the principal refractive invalue is required to obtain a maximum opdices n, and n, for the N and SmA phases tical contrast (see Sec. 3.1 of Chap. I11 of of ethyl-4-[4-ethoxybenzylideneamino]-a- this volume). methylcinnamate using Abbe’s total reflection method. Also later measurements on 2.4.2 Experimental Methods nematic liquid crystals by Gaubert [3] and Mauguin [4] were based on the determinaAn essential condition when measuring the tion of the boundary angle of total reflection. In 1950, Pellet and Chatelain [ 5 ] introbirefringence of nematic liquid crystals is
2.4.2
the homogenous alignment of the sample, which should behave like a ‘liquid monocrystal’. This alignment can be realized by surface forces or, in special cases, by applying a magnetic field of sufficient strength. In principle, the birefringence can be measured using any of the methods that are applicable to solid crystals. In the following a brief survey of the most important methods is given, together with some representative references.
Total Reflection Method
In Abbe’s double prism method a thin homeotropically oriented nematic film is placed between the hypotenuse faces of two rectangular prisms. Using light polarized parallel and perpendicular to the optical axis, respectively, the principal refractive indices n, and n, can be obtained directly from the critical angle of total reflection, provided that the refractive index of the prism is greater than that of the liquid crystal [2, 8- 101. In some cases the director of the nematic phase was oriented uniformly parallel to the prism planes [ l l - 141. Special variants of the total reflection method have been described [3, 4, 15, 161. A total reflection refractometer of the Abbe type has also been used to determine n,, no and An in the infrared region between 2.5 and 14 ym ~71.
Experimental Methods
129
which are polarized parallel and perpendicular to the optical axis. From the deflection angles a, and a, the corresponding refractive indices can be calculated according to h e l l s ’ law (Fig. 1):
where @ is the prism angle. In a modified variant of this method the perpendicularly incident beam is reflected onto the second face of the prism [27]. In the Leitz- Jelley microrefractometer the planar-oriented nematic liquid crystal is placed into a small hollow prism. The light passing through the prism is doubly refracted, and two images can be recorded on a scale. The two images are due to the ordinary and extraordinary rays [8, 28-31].
Interference Method for Wedge-shaped Nematic Samples This method was first described by Haller et al. [32, 331, and later was applied by Van Hecke et al. [34]. The nematic liquid is pot into a wedge formed by two glass plates, where the optical axis is parallel to the edge of the wedge.
Hollow Prism Method
A frequently applied method to determine n, and no was introduced by Chatelain [ 5 , 61 (see also refs. [18-261). The nematic liquid crystal is prepared inside a hollow, glass prism with a small refracting angle (210’). The nematic liquid is aligned with the director lying parallel to the edge of the wedge. The incident beam is perpendicular to the first face of the prism. In this geometry the beam splits into two components,
Figure 1. The paths of the light rays in Chatelain’s hollow prism method (the optical axis of the nematic liquid is parallel to the edge of the wedge).
130
Optical Properties of Nematic Liquid Crystals
2.4
The sample is observed using monochromatic light passed between crossed polarizers which make an angle of 45" with the optical axis. Because of the interference between the ordinary and extraordinary rays, equidistant fringes arise parallel to the edge of the wedge. Each of the fringes reflects the matching of the condition
(n,-no)d = k A where k is an integer, ilis the wavelength and d is the maximum wedge thickness. From the distance between two consecutive fringes Ax, the birefringence An =n, -no can be calculated for a given wavelength Aif the length of the side of the wedge xo and dare known (Fig. 2):
An = n, - no =
XO ~
d Ax
optical axis, the absolute values of n, and no can be deduced from the Fizeau interference fringes in the liquid crystal as well as in the air region [37, 381.
Interference Methods f o r Plane-parallel Nematic Cells Several methods to determine An in nematic liquid crystals are based on the interference of the ordinary and extraordinary ray in plane-parallel nematic cells. The uniform planar oriented nematic layer is observed in a monochromatic light beam between crossed polarizers, where the optical axis and the polarizers enclose an angle of 45 In this case the intensity of the transmitted light ,Z is given by Fresnel's law: O.
11 = 10
In order to determine the absolute values of the refractive indices, no is measured using an independent method, such as Abbe's double prism method. In a modified variant, the wedge is only partially filled with nematic liquid crystal. On viewing the portion of the wedge with the air gap, equidistant Fizeau interference fringes are seen, the spacing of which in the reflection condition is Ax'. As shown elsewhere [35, 361, An follows immediately from An=Ax'lAx, where Ax is the distance between two consecutive birefringence fringes in the part of the wedge filled with liquid crystal. In transmission geometry, An=2Ax'lAx is valid. If for the same geometry the incident light is polarized parallel or perpendicular to the
2
sin
nAnd (T)
When the transmitted monochromatic light is recorded as a function of the temperature, the intensity has a minimum value if An d= k A is satisfied (where k is an integer and d is the thickness of the cell) [39]. The number k can be determined by applying a variable magnetic field, which reorients the planar into a homeotropic alignment for which k=O [ 4 0 ] .In a similar way, the birefringence for a given temperature can be measured by recording the transmission maxima and minima that occur on applying a magnetic field to the original planar oriented sample [ 4 1 ] . The same geometry was used in the interference method proposed by Chang [42] (see also [ 4 3 - 4 5 ] ) , but in this case the tem....
L ............_.. .........................
x, ......................................
(3)
Figure 2. Wedge parameters no and d.
2.4.2
perature is kept constant and the wavelength is varied. Between crossed polarizers and an angle of 45" between the optical axis and the polarizers the intensity of light is minimal at those wavelengths for which the conditions (An)*,d = k , Al and (An)*,d = k, & are fulfilled ( k , and k, are integer numbers). For (An)*,=(An)*,and k , = k , + 1, An =
412 -
4)
(4)
In this method the wavelength is changed continuously by using a spectrophotometer. From the wavelengths of consecutive minima (or maxima) the birefringence can be calculated according to Eq. (4). To achieve higher accuracy the dispersion of An has to be considered [45 -501. An improvement of Chang's method, presented by Wu et al. [5 11, allows the measurement of birefringence at discrete wavelengths or as a continuous function of the wavelength up to the infrared (IR) region (2- 16 pm). This technique is based on transmission measurements as a function of the voltage. If the planar oriented nematic sample is enclosed between two plane-parallel pieces of semitransmitting glass, the perpendicularly incident rays multireflected at the inner surfaces interfere mutually. When the light intensity is recorded as a function of the wavelength, maxima and minima occur because of the multiple beam interference. For light polarized parallel and perpendicular to the optical axis, respectively, the refractive indices n, and no can be obtained separately according to [ 5 2 ] : ne,o =
A1 a2
(5)
A,1 where ill and & are the wavelengths of two consecutive maxima (or minima): 4 >ill. 2d(&
-
Experimental Methods
131
Other Interference Methods In the shearing method [ 5 3 ] ,the nematic liquid crystal is placed between a glass support with a trapezoid-like groove and an optically flat cover glass. Before filling, the glass substrates are rubbed in one direction so that planar alignment results. When a linearly polarized beam (ordinary or extraordinary ray) is transmitted, whereby half passes through the groove containing the nematic liquid, an interference fringence pattern can be observed using an interference microscope. The refractive indices (n,, n,) can be calculated from the refractive index of the glass, the depth of the groove and the displacement of the interference fringes in the groove region. The modified Rayleigh interferometer [54] is based on the same principle. Half of the beam (ordinary or extraordinary) is passed through the planar-oriented nematic cell and the other half transverses to the empty part of the cell. When the two beams are mixed an interference pattern results, from which the refractive indices n, and rz, can be determined separately. In particular, changes in the refractive indices can be measured with high accuracy, using this method. In the Talbot -Rayleigh interferometer developed by Warenghemet al. [ 5 5 , 561, the planar-oriented nematic cell is inserted in the focal plane of an ordinary spectroscope that covers only half of the field of polychromatic light. In this way dark bands (Talbot bands) appear due to the interference between the upper and the lower part of the beam. The position of the bands is correlated with the phase retardation (and, therefore, with the refractive index) induced by the nematic layer. By means of a proper spectrum analysis, dispersion curves of n, and n, can also be determined. It should be noted that the birefringence in the millimeter wavelength region has
132
2.4
Optical Properties of Nematic Liquid Crystals
been measured using a Mach-Zehnder interferometer [57]. Lim and Ho [58] and Gasparoux et al. 1591 have described an interference method that was inspired by the rotating analyser technique used in ellipsometry. The incident light is divided into two beams. The main beam passes successively through the sample, a quarter-wave plate and a rotating analyser before reaching the photodiode, which detects the light intensity. The optical axis of the planar-oriented nematic sample is oriented in an angle of 45" to the direction of polarization of the light. This modulated interference method can be used to measure changes in the birefringence with high sensitivity ( 4 x For this reason the method was applied to measure the change in birefringence at TN-SmA in order to distinguish between phase transitions of first and second order [60,61]. Bruce et al. [62] have used this method to determine the birefringence of metallomesogens.
1,80
1-
1,70
t
C
nematic isotropic
'r
I
30
I
I
I
40
50
60
I
70
I
80
9/"C+ Figure 3. Temperature dependence of the refractive indices in the nematic (ae, no) and isotropic (n,) phases of 4-n-propyloxybenzylidene-4-n-heptylaniline at different wavelengths (509,546,589,644 nm). (Adapted from Pelzl et al. [lo]).
The principal refractive indices n, and no have different temperature dependences. Whereas n, strongly decreases with increasing temperature, for no there is a weak increase with temperature. The refractive in2.4.3 Temperature Dependence dex of the isotropic phase nI decreases linof Birefringence and Refractive early with rising temperature. As shown in Indices Fig. 4, there are cases where the temperature dependence of the birefringence is less For 4-n-propyloxybenzylidene-4-n-heptyl- pronounced and the no curve goes through aniline the temperature dependence of the a flat minimum [63]. principal refractive indices n, and no and the The birefringence of nematics containing refractive index in the isotropic nI liquid at calamitic metal has been measured [ 16, 621. different wavelengths (509, 546, 589, For palladium complexes of 4,4'-bis(hepty644 nm) is shown in Fig. 3 [lo]. It can be 1oxy)azoxybenzene it was found that comseen that the birefringence is positive plexation increases n, and no but decreases (ne-no > 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
2.4 Optical Properties of Nematic Liquid Crystals
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
2.4 Optical Properties of Nematic Liquid Crystals
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
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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.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
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,
2.5.2 Determination of Shear Viscosity Coefficients
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
Determination of Shear Viscosity Coefficients
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
Determination of Shear Viscosity Coefficients
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.
2.5.2 Determination of Shear Viscosity Coefficients
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-
Determination of Rotational Viscosity
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
Determination of Rotational Viscosity
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.
Determination of Rotational Viscosity
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.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
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 Dynamic Properties of Nematic Liquid Crystals
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
2.6 Dynamic Properties of Nematic Liquid Crystals
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
178
2.6 Dynamic Properties of Nematic Liquid Crystals
of the local nematic order. The fluctuations which are most important for nuclear spin relaxation are those which have correlation times of the order of the inverse Larmor period, m i ’ . The corresponding wavelengths of these modes is of the order of 10-100 nm. At the transition from the isotropic to the nematic phase in 5CB the proton TI drops discontinionly at low Larmor frequencies (e.g. 8.9 MHz) as observed by Koellner et al. [94]. The same effect has been seen in PAA (Fig. 8) by Woelfel [92]. This effect demonstrates that a new powerful relaxation mechanism appears in the nematic phase at low frequencies below 1 MHz which does not exist in the isotropic phase. The characteristic m i l l 2 Larmor frequency dependence of TI shows that this new mechanism is given by nematic director orientational fluctuations, as first suggested in 1969 by Pincus 1341 and Blinc et al. [35]. For the description of the long-wavelength elastic excitations in liquid crystals, we introduce a director field n (t,t), which describes the local orientation of the long axes of liquid crystalline molecules. For finite temperatures, this director field will fluctuate because of thermal excitations
n (t,t ) = n,(r) + 6n (r,t )
(17)
This will not only give rise to the strong scattering of light (see Eq. (l), Sec. 2.6.1), but also strongly influence the spin-lattice relaxation rate, It should be noted that in contrast to the fluctuation rate for the magnitude of the nematic order parameter in the isotropic phase (see Eq. (12)) the two angular fluctuations rates of the nematic director go to zero in the long wavelength limit ( q-0). The two director modes responsible for the spin-lattice relaxation in the nematic phase at low Larmor frequencies are thus the Goldstone modes of the isotropic-nematic transition and have been discussed in Sec. 2.6.1. When the nematic director in parallel to the external field, no IIHo, the spin-lattice relaxation rate induced by the director fluctuations is
Here C is a numerical factor of the order of unity and (Av), 17 and K denote the average splitting of the corresponding NMR line in the nematic phase, the average viscosity and the average elastic modulus in the one elastic constant approximation [43, 1341, respectively. Taking the dipolar splitting of the proton pair in 5CB at room temperature as (Av)=16 kHz, 17 =6.3 . lop2Nsmp2 and K = 1.3 . lo-” N one finds = 5 150 sP3l2 in good agreement with the experimental value A=5290 sp312+ 10% [94]. In 5CB, deuterated at the chain sites, where the deuteron quadrupole splitting of the NMR line amounts to (Av)=30 kHz, one similarly gets an estimate of as 18000 sp312 which is somewhat smaller than the experimental value [94]. This is not too surprising in view of the scatter of the viscosity and Frank elastic constant data. The proton spin-lattice relaxation dispersion data (Fig. 9) in MBBA at 18°C [ 1351obtained by the field cycling technique clear-
A
A
100 lo-‘
loo
101
102
lo3
lo4
105
vlkH7-
Figure 8. Frequency dependence of proton T , of 5CB phases [94]. in the nematic (m) and isotropic (0)
L-
179
2.6.6 Nuclear Magnetic Resonance and Orientational Fluctuations below T,
103
104
105
106
o 125'C
107 108 v /Hz
Figure 9. Dispersion of the proton T , in the nematic phase of MBBA. The solid line is the fit to Eq. 10 where DF denotes the contribution of director fluctuations, SD the contribution of translational self-diffusion, and R the contribution of molecular reorientations about the short axis [135].
ly show that director fluctuations dominate T r l in the nematic phase below 105-106 Hz. Above a few MHz, director fluctuations become less effective and are masked by larger contributions due to translational self-diffusion ( TGkiff,))and molecular rotation (TGbot)).A similar result has been obtained in deuterated PAA, MBBA and 5CB [40,94] except that here instead of self-diffusion, the molecular rotational term becomes dominant at higher frequencies. The nematic director fluctuation contribution to the deuteron T,' at 30 MHz in PAA-d, and PAA-d8 amounts to 30% for the chain deuterons and only about 3% for the ring deuterons, respectively [ 1361. The total dispersion in the deuteron TI is quite large as T,(6.8 MHz)IT,(IO kHz)= 10 for 5CB-d,,. Since director fluctuations are specific for the orientationally ordered nematic phase it is particularly useful to compare the Tl dispersion in the nematic and isotropic phases. Such a comparison is shown for the dispersion of the proton TIin PAA (Fig. 10, [ 1351). T , is nearly frequency independent in the isotropic phase at 135 "C, whereas a strong mil2 dispersion is seen in the nematic phase, characteristic of director fluctuations.
0
I I
I
103
102
I 104
135.t'C
I
1
I
I
105
106
107
108
v/Hz
Figure 10. Proton T , dispersion in PAA in the nematic and isotropic phases. The solid lines are model fits [135].
There is a cross-over point in the two T , dispersion curves. At this frequency there is no discontinuity in T , at the isotropic-nematic transition. The temperature dependence of the director fluctuation induced T,' is given by ( S 2 T I K ) ( q l K ) 1 /and 2 should be weak because K K S 2 ,where Sis the magnitude of the nematic order parameter S = (3 cos2B- 1). This has been indeed observed (Fig. 11) in the proton TI in 5CB at 20 kHz [94]. It should be noted that the T , ' ~ m , 1 " ~ dispersion law cannot hold for arbitrary low Larmor frequencies as we get a singularity 500
2
\
F 50
I
nemaf IC
5
25
lsotroplc
' ' ~ ~ ~ ' ' ' ' 1 ' ' ' ' ' ' ' ' ' 40 30 35
T/"C
Figure 11. Temperature dependence of the proton T , at 20 kHz in 5CB at the nematic-isotropic transition 1941.
180
2.6
Dynamic Properties of Nematic Liquid Crystals
T,' -+ 00 for mL-+ 0. This singularity disappears if one takes into account that the nematic correlation length 5 is finite because of boundary effects, disclinations and other defects. In fact coherent angular reorientational fluctuations can only take place for wavelengths longer than the molecular dimension Z and smaller than 5. This introduces an upper, u ) ~ ,and ~ a~ lower, ~ , m,,MIN, cut-off frequency into the spectrum of director fluctuations [51, 57, 1371. The nematic director fluctuation mechanism becomes ineffective when mL%-mc,MAxwhereas TG&) approaches a constant value for WLQ mc MIN . Only for mc, MIN < OL < mc, MAX the mili2 dispersion law holds. The nematic director fluctuation contribution to T;' also depends on the angle between the nematic director no and the external fieldHo (Fig. 12, [137-1391).
For a nuclear probe consisting of two protons with a fixed separation distance r, the dipole-dipole interactions of which are modulated by fluctuations in the orientation of internuclear vector r with respect to the external magnetic field H due to nematic order director fluctuations, the spin-lattice relaxation rate is
and in the rotating frame r
Here C is a constant independent of the Larmor frequencies in the laboratory ( mL= yHo) and rotating ( m1= yHl) frames; fo(A), fi(A) andf2(A) are functions of the angle A between the molecular director and magnetic field, f o (A) = 18 (COS~A - cos4A) fi (A) = -1 (1 - 3cos2A + 4cos4A) 2 f2
w =Q3wc
l v w=wc
0
2
0
I
4
'
0
"
6
"
A [DEGREES]
0
8
0
Figure 12. Theoretical dependence of the proton T , on the angle between the nematic director and the direction of the external magnetic field for the nematic order director fluctuations for different ratio between the Larmor frequency and the cut-off frequency w, [137].
(A) = 2 (1 - COS~A)
(21) (22) (23)
1 u2+u\12+1 2 u2-uU+1 - arctan(u 4 + 1) - arctan ( u 42 - 1) (24)
g ( u ) = z - - In
and u1
= (m&Dc)1/2, u = (mlmc)1/2
(25)
The upper cut-off frequency mc is given by W, = K 4,2117
(26)
Here qcE zlZ, I is a distance of the order of the molecuar length, K is the elastic constant
2.6.7
Optical Kerr Effect and Transient Laser-Induced Molecular Reorientation
and q is the viscosity. For OGW,,g ( u ) is constant and T,&, is proportional to w-”*. Here the lower cut-off frequency was taken as zero. These theoretical predictions have been verified by experiments [140]. It should be noted that director fluctuations produced by undulation waves also represent an effective spin-lattice relaxation mechanism in the SmA phase. Here, however the relaxation rate is proportional to 1/0, [138, 1391. In contrast to nematics, a helical twist of the molecular director takes place in the chiral nematic phase. Studies of the spin-lattice relaxation in chiral nematics have shown that the relaxation mechanisms are essentially the same as in pure nematics [141, 1421. At high Larmor frequencies the relaxation is diminished by molecular self-diffusion and by local molecular rotations, whereas director fluctuations determine the relaxation rate at low Larmor frequencies. This can be easily understood because the spin-lattice relaxation rate in the MHz region is dominated by orientational fluctuations with wavelength much smaller than the period of the helix. The influence upon the rotating frame spin-lattice relaxation time TI,, of the rotation of the molecules due to diffusion along the helix, an effect specific for twisted structures, has not been observed in COC [ 1431.
181
duced birefringence of the isotropic phase was measured with a probing He-Ne laser beam. The observed temperature dependence of the order parameter relaxation rate (Fig. 5) and the nonlinear refractive index in MBBA (Fig. 13) and EBBA were in good agreement with the predictions of de Gennes theory and showed a clear pretransitional divergence at T,, as shown in Figs. 5 and 13. Prost and Lalanne [77] have performed similar experiment in MBBA. The molecular theory of orientational fluctuations and Kerr effect can be found in the work of Flytzanis and Shen [76]. The optical Kerr effect in 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 pretransitional dynamics of alkyl cyanobiphenyl homologs. In the nematic state, the optical field of the pump beam couples to the anisotropy of the index of refraction An and exerts a torque on the molecules. This results in several interesting nonlinear phenomena, such as the optically induced Fredericksz transition [ 144, 1451 and transient induced molecular reorientation [146]. The dynamics in the vi-
2.6.7 Optical Kerr Effect and Transient Laser-Induced Molecular Reorientation The first observation of optical-field induced ordering in the isotropic phase of a nematic liquid crystal was reported by Wong and Shen [74]. They have used a linearly polarized Q-switched, 50 kW ruby laser pulse to induce molecular ordering in the isotropic phase of a nematic liquid crystal. The in-
TEMPERATURE
(OC
1
>
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
2.6 Dynamic Properties of Nematic Liquid Crystals
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
2.6 Dynamic Properties of Nematic Liquid Crystals
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/<,< 4 from starlike into a structure with an equatorial line disclination [203-2051. NMR, and particularly deuterium NMR, are the best experimental techniques for the determination of the director field and the molecular dynamics in submicron nematic droplets. The theoretical static proton NMR spectra of the nematic micro-droplets for a bipolar and a radial configuration are shown in Fig. 17 a. The corresponding motionally averaged spectra are shown in Fig. 17b. Here the motional averaging is produced by translational diffusion which induces slow molecular rotations due to the non-uniform orientational ordering in the droplet [206]. The first study of the frequency and temperature dependence of the proton-spin lattice relaxation rate of micro-confined nematics has been reported by Vilfan et al. [202] for E7 nematic micro-droplets dispersed in an epoxy polymer. Here the bipolar molecular director configuration is expected and &, should be bigger then the radius of the droplets R. Instead of a doublet
186
2.6
Dynamic Properties of Nematic Liquid Crystals
Figure 17. (a) Simulated static
BIPOLAR
ii )
proton NMR spectra of nematic microdroplets for the bipolar (NoIIHo) and radial configurations. (b) Dynamic proton NMR spectra for (1) the bipolar (NollHo)and ( 2 ) the radial director configurations [206].For ~ = 5 the 0 diffusion is slow whereas for E = 0.05 the diffusion is fast. Here E = A PlD with 2 A being the static line splitting.
b)
splitting of =20 kHz at room temperature which is observed in nematic E7 in the bulk, the proton NMR spectrum of polymer dispersed E7 consists of a simple line with a half-width of = 7 kHz superposed on the much broader line (= 34 kHz) due to protons in the epoxy polymer material. The above measurements showed that four different spin-lattice relaxation mechanisms: director fluctuations, translational self-diffusion, local reorientations, and cross-relaxation, are present and that all of them are affected by the confinement. (1) Director fluctuations: In a droplet, the wavelengths of director fluctuations cannot be larger than the dimension of the droplet. This results in a cut-off frequency 2 wc,,in=Kqmin/q, where qmin=n / 2 R . This result has been derived previously for bulk nematics where qminwas introduced to take into account the finite dimension of the uniformly oriented domain [ 1401. The consequence of the small wave vector cut-off is a leveling-off of the .\lo, relaxation disper-
sion curve at frequencies smaller than qmin and consequently the frequency independence of TGbF, in the limit w,+O. In a droplet with a radius R = 0.1 pm the lower cut-off frequency is about 40 kHz for E7 [2021. ( 2 )Translational self-diffusion.Whereas in bulk nematics, translational self-diffusion modulates only the dipolar interactions between protons on different molecules (i.e. intermolecular interactions), in microdroplets it also modulates intra-molecular dipolar interactions because the director field in a confined geometry is non-uniform. This new relaxation mechanism is called translational diffusion induced rotation (TDIR). Since intramolecular dipolar interactions are generally stronger than intermolecular interactions, translational selfdiffusion represents a much more effective relaxation mechanism in micro-droplets than in bulk nematics. TDIR is also effective at much lower frequencies than diffusion induced modulation of inter-molecular
2.6.10
interactions. The TDIR correlation time s for is of the order of z=R2/6D = 3 . R=0.1 pm and D = 5 . lo-" m2 s-l [202]. (3) Local molecular reorientations.The frequency dependence of this relaxation mechanism is of the BPP type [ 3 3 ] . It is not affected by the confinement except for molecules anchored at the droplet boundary where their mobility is hindered. (4) Cross-relaxation at the nematicpolymer interface. The liquid crystal protons and the polymer protons constitute a two phase proton system. The cross-relaxation at the boundary leads to an exchange of Zeeman energy between the two phases and couples their spin-lattice relaxation rates [202]. Cross-relaxation affects all molecules in the droplet if the exchange of molecules at the surface is so fast that within the spin-lattice relaxation time each molecule in the droplet takes part in this process. For this to take place, both the time required for a molecule to diffuse from the inside of the droplet to the surface zDs, and the time z,for which the molecules remain anchored at the surface must be short compared to the spin-lattice relaxation time T I . In the limit of very rapid cross-relaxation ( k c $ ( T ; ' ) n , ( T c l ) p )both phases relax with the same relaxation rate which is an weighted average
T,' = Pa(T,')n + P p ( T c 9 p
(29)
of the rates of the liquid crystal ( T T 1 ) aand polymer (T;'& protons. Here p n and p p are the relative number of protons in the two phases. The effective cross-relaxation rate k, is smaller than the actual rate at which the bound fraction of the liquid crystal Nn,b transports spin energy to the polymer by the factor
k = k,/x
187
Dynamics of Nematics in Micro-Droplets and Micro-Cylinders
(30)
where x is the relative number of bound liq=: 3 d,lR uid crystal molecules, x =Nn,b/Nn
and d, is the thickness of the bound surface layer [202].At 46 MHz the temperature dependence of the proton T , of nematic E7 in droplets with R=0.25 pm is roughly given by a weighted average of the relaxation rates of the bulk nematic ( T c l ) b u l k , n and the pure polymer (TT1&[202]. In kHz region the situation is quite different and the droplet T;: is far from being a weighted average of (Tc$bulk,n and (T;;), . The dispersion of the rotating frame relaxation rate (Fig. 18) can be described by
T;d =
el
+ e2
(31)
The first term is the result of translational diffusion induced rotation in the limit w , $ 1 whereas the second term, which is frequency independent includes the contributions of both ( T ; d ) b u l k , n and of the crossrelaxation to the polymer. The time during which a liquid crystal molecule remains attached to the surface has been estimated as z,=: 8 . s [207].Deuteron NMR studies 450
-
-
-a ,-
1 = 22°C V,IH)
400
-
350
-
300
-
o
=31MH2
polymer
o o nem droplets Q25pm x x -1109pm bulk Oematic E7
b-
f
0
50
0
I
b C .
0.5
I
1
I
1.5
2
HI h T 1
Figure 18. Frequency dependence of the proton T I , for polymer dispersed nematic E7, bulk nematic E7 and the pure polymer [202].
188
2.6 Dynamic Properties of Nematic Liquid Crystals
[204,205] have been used to study director fields, surface order parameters and molecular dynamics. At a critical enclosure size the weakly first order isotropic-nematic transition has been found to be replaced by a continuous evolution of nematic order [208, 2091. The deuteron NMR work of Crawford et al. 1210-2121 on SCB-d, confined into cylindrical submicrometer channels of organic (Nucleopore) membranes, provided the first insight into the order and dynamics of liquid crystals in cylindrical micro-cavities. The 'H NMR pattern directly reflects the distribution of molecular directors in the cavity. According to theoretical predictions [213,214] the nematic director field can be here either:
planar-radial (Fig. 19a) with the directors lying in the plane perpendicular to the cylindrical axis and pointing in the radial direction, or - planar-polar (Fig. 19b) with a two pole structure in the plane perpendicular to the cylinder axis, or - escaped radial (Fig. 19c) where the director bends gradually towards the direction of the cylinder axis on going from the cavity walls to the center [215J. -
a
b
C
Figure 19. Schematic representation of nematic director configurations for the (a) planar radial, (b) planar polar, and (c) escaped radial nematic structures in microcylinders [215].
The three structures require that the molecules are anchored normally to the surface. For SCB-Pd, confined into cylindrical channels of 2 R = 2 pm [210-2121, the escaped radial configuration was detected. By changing the radius of the cylindrical cavities, the surface anchoring strength and the surface elastic constant K24 were determined [210-212, 2141. The surface of cylindrical cavities can be modified with a suitable surfactant (e.g. lecithin) before the filling with the liquid crystal. In this way the surface anchoring strength can be reduced so that the transition between the escaped radial and planar-polar structure was observed [214]. The possibility of rotating the cylinders with respect to the magnitude field allowed for a simple and direct measurement of the angular dependence of the deuteron spin-lattice relaxation rate in the nematic phase [216]. In the nematic phase the spin-lattice relaxation rate at high Larmor frequencies is determined by local reorientations of the molecule and internal molecular motions. The spin-spin relaxation rate, UT,, on the other hand, is determined by nematic order director fluctuations and rotations induced by translational diffusion [2 16J.
ed in a 17 K interval above the isotropic-nematic transition by 2H NMR in 5CB-d, confined to submicron cylindrical cavities [2 102121. The 'H-NMR spectra show a strong quadrupolar splitting in the isotropic phase of about 200 Hz (Fig. 20a) which reveals the presence of a weakly ordered ( S = 0.02) molecular layer at the cavity walls (Fig. 20b). The corresponding splitting in the nematic phase is of the order of 20 kHz. The or-
2.6.12 Dynamics of Randomly Constrained Nematics
a
189
Here r is the distance from the cylinder axis and 6 is the coherence length. The distance that the molecule migrates in the isotropic phase during a NMR measurement m i s in the above case of the order of the cylinder diameter R and the motional averaging by translational self-diffusion must be taken into account. The diffusion coefficient in the surface layer was estimated as D,-- lo-" cm2 s-l and is much smaller than the bulk value. The time a molecule resides s. In at the surface is then z,-- l,$D,yz the fast exchange regime the effective spinspin relaxation rate can be expressed as
(TF'Iconfined
= (TT')b",k ( 1 - 4
A
N
I
200
cn -
T - T *=1
S
m c ._
. ~ 8 ~
(34)
.- 175 a o, 150
<2 0
a
0
125 100 32
(33)
where 6 is the fraction of molecules in the partially ordered surface layer where the quadrupole interaction is finite, so that:
225
-
+ (TT1),",!6
X V
1 I I
-%7vv
I I!
k I
34
I
36
I
I
V I
I-v>
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)/<]
(32)
Here 6vBis the quadrupole splitting of the 2H NMR line in the bulk, S, is the corresponding bulk nematic order parameter and Sois the nematic order parameter in the surface layer.
2.6.12 Dynamics of Randomly Constrained Nematics Randomly constrained orientational order has been investigated by *H NMR in porous Vycor glass [217] and aerogels [218] of various pore size distributions. The isotropicnematic transition was found to be replaced by a continuous evolution of orientational order in the pores. The reason for this is that in contrast to classical liquids the surface effect on the orientational molecular order in liquid crystals is of long range. Critical dynamics of a nematic liquid crystal in silica gels, as observed by the
190
2.6 Dynamic Properties of Nematic Liquid Crystals
1 .o
0.8 0.6
0.4
Figure 21. Square root of the autocorrelation function in the nematic phase of 8CB in a silica gel [219] for different temperatures: 40 "C (squares), 38 "C (circles) and 36 "C (triangles).
0.2
0.0 10-5
10-3
10-1
103
x)'
t [msl
105
quasielastic light scattering was first reported by Wu et al. [219]. The observed intensity autocorrelation function in the nematic phase could be described by the form G2(x) (1 +x2)-' where x=ln(tlzo)lln(z/zO). Here z and zo are the adjustable parameters that are related to bulk properties (2) and to the constrained geometry (zo).The autocorrelation function has a characteristic "tail" extending to very long times (see Fig. 21), indicating very slow dynamics due to restricted geometry. The relaxation time z was observed to follow the Vogel-Fulcher law, indicating a glassy-like dynamics (see Fig. 22).
Light scattering and precision calorimetry have ben used by Bellini et al. [220,221] to study the ordering and dynamics of 8CB in silica aerogel. Instead of well defined phase transition, characteristic of bulk crystal, they observe a continuous evolution of nematic ordering, reflected in a broadening of a heat-capacity anomaly. Quasi-elastic light scattering of 8CB in silica aerogel shows the nematic-like dynamics [221], reflecting the distribution of the pore sizes and an additional, low-frequency, glassy-like relaxation. Recently, Schwalb and Deeg [222] have used the optical Kerr effect to study the pretransitional dynamics of 5CB in a porous silica glass matrix. Instead of nearly divergent pretransitional dynamical behavior, characterisic for the bulk, they observe quenching of a relaxation-time divergence due to constrained geometry.
2.6.13 I
OD
0.15
(T-T*)-'
I
I
0.20
0.25
Figure 22. Vogel-Fulcher plot of the relaxation time z of 8CB in a silica gel [219].
Other Observations
When an external, symmetry breaking field is applied perpendicular to the director of a nematic liquid crystal, confined between two orienting surfaces, the lowest order fluctuation mode undergoes a softening and
2.6.14
condensation at the critical field, i.e. at the Fredericksz transition point. The critical dynamics of this system were investigated by Arakelyan et al. [223], Pieranski et al. [224], Sefton et al. [112], Eidner et al. [225], Galatola (2261 and Galatola and Rajteri [227]. Because of micron wavelengths, the observed dynamics is extremely slow (1 Hz) and exhibits softening in the vicinity of a critical field. The finite size effets and the influence of K,, elastic constant on the director fluctuations of a nematic, confined in planparallel cell is discussed by Shalaginov [228,229]. Surface anchoring and nearsurface dynamics is discussed by Gharbi et al. [230], Lee et al. [231] and CopiEet al. [ 1201. The Fredericksz transition in a polymer dispersed nematic liquid crystal was discussed by Kralj and k m e r [232]. A very interesting neutron scattering and computer simulation study of the so-called fractional Brownian motion in the nematic crystalline phase has been reported by Otnes and Riste [233] and Zhang et al. [234]. They used the Hurst-exponent analysis of the (long term) temporal fluctuations of the intensity of the scattered neutron beam. For a given recorded signal Z ( t ) , the Hurst exponent H H connects the range R, and the standard deviation SH of the recorded signal via the equation RHISHK(zH/2)HH(for details, see [233]). Here zHis the time span of the recorded signal. For an independent process HH= 112, whereas HH# 112 indicates statistical dependence and has been associated with the fractional Brownian motion by Mandelbrot. Zhang et al. [234] have found H , = 1 for the recorded neutron intensity in zero external field, whereas for finite symmetry breaking field they observe a crossover to the value HH= 0.5, as shown in Fig. 23a and b. This was explained by the fact, that the Goldstone mode of the nematic phase, which is responsible for the longterm fluctuations of the scattered intensity
3.5 I
n
a)
05
lo
191
References
I
I
10
I 15
I
20 tog (T1
I
25
I
313
30
12
Figure 23. (a) Log-log plot of the RIS value vs time range 7" for the nematic director fluctuations, as observed in a neutron scattering experiment and different values of the external magnetic field 12341 and (b) plot of the Hurst exponent versus external magnetic field 12341.
is critical for all temperatures and is thus subject of power-law correlations. The Hurst exponent analysis of the Goldstone and massive-mode dynamics has been treated by Yeung et al. [235] and Zurcher [236].
2.6.14 References [ l ] R. Blinc, B. iekS, Soft modes in ferroelectrics and antiferroelectrics, North-Holland Publish-
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192
2.6 Dynamic Properties of Nematic Liquid Crystals
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[I511 I. C. Khoo, R. G. Lindquist, R. R. Michael, R. J. Mansfield, P. LoPresti, Dynamics of picosecond laser-induced density, temperature, and flow-reorientation effects in the mesophases of liquid crystals, J. Appl. Phys. 1991, 29, 29722976. [I521 I. C. Khoo, P. Zhou, Y. Liang, H. Li, Dynamics of transient probe beam amplification via coherent multiwave mixing in a local nonlinear medium-nematic liquid crystal, IEEE J. Quantum Electron, 1993, 29, 2972-2976. [I531 I. DrevenSek, M. CopiE, Properties of nematics studied by four wave mixing, Mol. Cryst. Liq. Cryst. 1991, 207, 241-250. [I541 A. J. Martin, G. Meier, A. Saupe, S-ymp.Faruday Soc. 1971,5, 119. [ 1551 H. Kresse, Dielectric behaviour of liquid crystals, Fortschr. Phys. 1992, 30, 507-582. [ 1561 W. Maier, G. Meier, Z. Nuturforsch. 1961,16u, 1200. 1.571 A. Axmann, Z. Naturforsch. 1965, 21a, 290. 1581 G. Meier, A. Saupe, Dielectric relaxation in nematic liquid crystals, Mol. Cryst. Liq. Cryst. 1966,1,515-525. 1591 A. Janik, S. Wrobel, J. M. Janik, A. Migdal, S . Urban, Rotational diffusion in PAA, Furuday Symp. Chem. Soc. 1972,3,48. 1601 J. A. Janik, J. M. Janik, T. T. Nguyen, K. Rosciszewski, S . Wrobel, Estimation of rotational correlation times for PAA and MBBA molecules, Phys. Stat. Sol. 1973, A19, K143. [I611 J. A. Janik, 1. M. Janik, K. Otnes, K. Rosciszewski, S . WrobeI, Estimation of rotational correlation times for PAA and MBBA by the dielectric relaxation and the neutron quasielastic scattering methods, Proc. Int. Conf. Bangalore, Liq. Cryst. 1973, 253. 621 S. Wrobel, J. A. Janik, J. Moscicki, S. Urban, Dielectric relaxation in the i, n, and k phases of PAA in the radio and microwave frequency range, Actu Phys. Pol. A 1975,48, 215. 631 V. K. Agarwal, A. H. Price, Dielectric measurements of MBBA in the frequency range 1 kHz to 120MHz, J. Chem. Sac., Faruday Trans. 2 1974, 70, 188. [ 1641 F. Rondelez, D. Diguets, G. Durand, Dielectric and resistivity measurements on nematic MBBA, Mol. Cryst. Liy. Cryst. 1971, I S , 183. [ 1651 F. Rondelez, A. Mircea-Roussel, Dielectric relaxation in the radio frequency range for nematic MBBA, Mol. Cryst. Liq. Cryst. 1974,28, 173. 661 J. K. Moscicki, X . P. Nguyen, S. Urban, S. Wrobel, M. Rachwalska, J. A. Janik, Calorimetric and dielectric investigations of MBBA and HAB. Mol. Cryst. Liq. Cryst. 1977, 40, 177. 671 R. A. Kashnow, Dielectric observations of nematic instabilities, Phys. Lett. A 1974,48, 163.
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[184] H. K. M. Vithana, G. Xu, D. L. Johnson, Dynamics of the lowest order bend-twist director mode near nematic-smectic-A criticality, Phys. Rev. E 1993,47,3441-3455. [185] C. W. Garland, G . Nounesis, Critical behavior at nematic-smectic-A phase transition, Phys. Rev. E 1994,49,2964. [186] P. G. de Gennes, Analogy between superconductors and smectics A, Sol. State Commun. 1972, 10,753. [ 1871 W. L. McMillan, Time-dependent Landau theory for the smectic-A-nematic phase transition, Phys. Rev. A 1974,9, 1720. [188] F. Brochard, Dynamique des fluctuations prks d’une transition smectique-A-nkmatique du 2“ ordre, J. Physique 1973,34,411-422. [ 189) F. Jahnig, F. Brochard, Critical elastic constants and viscosities above a nematic-smectic-A transition of second order, J. Physique 1974, 35,301-313. [190] H. Gruler, Elastic constants of nematic liquid crystals, Z. Naturforsch. 1973, 28, 474. 1911 L. Cheung, R. B. Meyer, H. Gruler, Measurements of nematic constants near a second order nematic-smectic-A phase change, Phys. Rev. Lett. 1973,31, 349. 1921 M. Delaye, R. Ribotta, G. Durand, Rayleigh scattering at a second order Nematic to Smectic-A phase transition, Phys. Rev. Lett. 1973, 31,443-445. [193] K. C. Chu, W. L. McMillan, Static and dynamic behavior near the second order Smectic-ANematic phase transition by light scattering, Phys. Rev. A 1975,11, 1059-1067. 11941 H. Birecki, J. D. Litster, Mol. Cryst. Liq. Cryst. 1977, 42, 33. 1951 H. Von Kanel, J. D. Litster, Light scattering studies on the single layer smectic p-butoxybenzilidene p-octylaniline, Phys. Rev. A 1981, 23,3251-3254. 1961 S. Sprunt, L. Solomon, J. D. Litster, Equality of X-ray and light scattering measurements of coherence lengths at the nematic-smectic-A phase transition, Phys. Rev. Lett. 1984, 53, 1923. [I971 R. Mahmood, D. Brisbin, I. Khan, C. Gooden, A.Baldwin, D.L. Johnson, M.E. Neubert, Light scattering study of the nematic twist constant near the smectic-A transition, Phys. Rev. Lett. 1985, 54, 1031-1034. [198] R. Mahmood, I. Khan, C. Gooden, A. Baldwin, D. L. Johnson, M. E. Neubert, Light-scattering study of director dynamics above the nematic-smectic-A transition, Phys. Rev. A 1985, 32, 1286. [199] C. Gooden, R. Mahmood, D. Brisbin, A. Baldwin, D. L. Johnson, M. E. Neubert, Simultaneous magnetic deformation and light scattering study of bend and twist elastic constant diver-
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[222] G. Schwalb, F. W. Deeg, Pore-size-dependent orientational dynamics of a liquid crystal confined in a porous glass, Phys. Rev. Lett. 1995, 74, 1383. [2231 S . M. Arakelyan, L. E. Arushanian, Yu. S. Chiligaryan, Sov. Phys. Tech. Phys. 1986, 31. 1165. [224] P. Pieranski, F. Brochard, E. Guyon, Static and dynamic behavior of a nematic liquid crystal in a magnetic field. Part 11: dynamics, J. Physique 1973,34,35-48. [225] K.Eidner, M. Lewis, H. K. Vithana, D. L. Johnson, Nematic liquid crystal light scattering i n a symmetry breaking external field, Phys. Rev. A 1989,40,6388-6394. [226] P. Galatola, Light scattering study of Freedericksz transition in nematic liquid crystal, J . Phys. I / (France) 1992, 2, 1995-2010. [227] P. Galatola, M. Rajteri, Critical-noise measurement near Freedericksz transition in nematic liquid crystal, Phys. Rev. E 1994,49,623. [228] A . N. Shalaginov, Finite-size effects in fluctuations and light scattering in liquid crystals, Mol. C ~ s tLiq. . Cryst. 1994, 251, 1-5. 12291 A. N. Shalaginov, Influence of the liquid crystal splay-bend surface elastic constant on director fluctuations and light scattering, Phys. Rev. E 1994,2472-2475. [230] A. Gharbi, F. R. Fekih, G. Durand, Dynamics of surface anchoring breaking in a nematic liquid crystal, Liq. Cryst. 1992, 12, 515-520. 12311 S . D. Lee, B. K. Rhee, Y. J. Jeon, Dynamics of polar electro-optic effect in surface states in nematic liquid crystals. J. Appl. Phys. 1993, 73, 480-4 82. [232] S. Kralj, S . h m e r . Fredericksz transition in supra-pm nematic droplets, Phys. Rev. A 1992, 45, 2461. [233] K. Otnes, T. Riste, An experimental study of fractional Brownian motion, Physica Scriptu 1992, T44,77-79. 12341 Z. Zhang, 0. G. Mouritsen, K. Otnes, T. Riste, M. J. Zuckermann, Fractional Brownian motion of director fluctuations in nematic ordering, Phys. Rev. Lett. 1993, 70, 1834. [235] C. Yeung, M. Rao, R. Desai, Temporal fluctuations and Hurst exponents of Goldstone and massivemodes, Phys. Rev. Lett. 1994,73,1813. [236] U. Zurcher, Scaling behavior of fluctuations in systems with continuous symmetry, Phys. Rev. Lett. 1994, 72, 3367.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
3 Applications 3.1 TN, STN Displays Harald Hirschmann and Volker Reiffenrath
3.1.1 Introduction Soon after the production of twisted nematic (TN) liquid crystals by Schadt and Helfrich in 1971 [l], commercialization of low information content liquid crystal displays (LCDs) for watches and calculators began. However, passive matrix addressing of TN cells did not satisfy the requirements for contrast ratio and viewing angle in high information content displays in laptop computers. These problems could potentially be overcome by the introduction of the active matrix addressing (TFT technology) [2], but this is more expensive and suffered from only small yields. In 1985 the first prototype supertwisted nematic (STN) displays, driven by a passive matrix, were demonstrated by Scheffer, Nehring et al. [3]. These offered substantial improvements of viewing angle and contrast ratio over the high information content passive matrix TN displays. Commercialization of STN displays for laptop computers and wordprocessors started in 1987. Compensation techniques, necessary for producing colored displays with RGB filter technology, came into produc-
tion by the end of the 1980s.Today the range of STN display applications spans from automotive uses, through mobile telephones, personal digital assistants (PDA) and wordprocessors to color displays in laptop computers and reflective color LCDs [4]. The disadvantages of STN LCDs are the low response speed, not suitable for video applications, and the limited viewing angle compared to TFT technology. There is strong competition from improved TFT displays [5-71 and prototypes of in-plane switching (IPS) [8, 91, vertically aligned TN (VANTN) [ 10, 1 11 and electrically controlled birefringence (ECB) modes offering video operation and minimum viewing angle dependence. However, STN displays are still cheaper in price and even though the costs for TFT displays have decreased there is still a price factor of about two between these technologies. It can be expected that STN displays will enter the monitor marked soon. At the Japan electronics show in 1996 several prototypes of 17.7 inch STN monitors were presented. The largest display prototype shown so far is a 21.4 inch XGA-format STN-LCD.
200
3
Applications
In the following text the operational principles of TN and STN displays will be reviewed and details of liquid crystal materials for these technologies will be presented.
3.1.2 Twisted Nematic Displays 3.1.2.1 Configuration and Operation Principles of Twisted Nematic Displays The configuration and the operation principle of a twisted nematic (TN) cell are shown in Fig. 1. The cell consists of two transparent glass plates coated with thin layers of indiumtin - oxide (ITO) and polyimide on their inner surfaces. The polyimide layer is unidirectionally rubbed to achieve a macroscopic orientation of the liquid crystal director. The two glass plates are held apart at a distance 6- 10 pm by spacers with the rubbing directions of the polyimide layers perpendicular to each other. Owing to the boundary conditions a nematic liquid crystal will become orientated parallel to the rubbing direction of each glass plate and consequently the director will undergo a twist of 90"
u Off
on
Figure 1. Configuration and off- and on-state of a normally white mode operated twisted nematic (TN) cell.
over the layer distance. Reversed twist defects and reversed tilt defects can be avoided by adding a small amount of cholesteric dopant and by applying a pretilt angle of about 1O at the boundaries. Polarizer sheets are attached to the outer surfaces of each glass plate with their axis of vibration (polarizing axis) parallel to the rubbing directions. Unpolarized light is transformed into linearly polarized light by the entrance polarizer. In the so-called Mauguin limit [ 121 (see Sec. 3.1.2.2) the polarization axis of lights is rotated by 90" on propagating through the twisted liquid crystalline structure and can pass the second polarizer. In this configuration, the so-called normally white (NW) mode, the display appears bright in the unactivated (no applied voltage) state. A NW mode with enhanced viewing angle can be achieved by setting the polarizers with their polarization axis perpendicular to the rubbing directions. The NW mode is used as a transmissive mode with additional backlight in TFT displays or as a reflective mode, by using a reflective sheet at the back of the cell, in calculators and watches. The application of an electric field orients the liquid crystal molecules with their long axis towards the layer normal. In this so-called activated state the polarization axis of light is not rotated by the liquid crystalline medium and the display appears black. Orientation of one polarizer parallel and the second polarizer perpendicular to the rubbing directions results in a black appearance in the unactivated state and a bright appearance in the activated state. This so-called normally black (NB) mode is mostly used in automotive applications.
3.1.2.2 Optical Properties of the Unactivated State The principles of operation described in above are only valid in the so-called Mau-
3.1
guin limit [ 121.
1 st, 2nd and 3rd minimum condition according to the Gooch and Tarry curve for layer thickness d = 6 pm and d = 8 pm.
2
Where d is the layer t k k n e s s , An the birefringence of the liquid-crystal and il the wavelength of light. For typical liquid crystal mixtures with An=0.07-0.25 and d = 6 - 10 pm the Mauguin limit can hardly be fulfilled and the linearly polarized light becomes elliptically polarized on propagating through the twisted structure. For a cell operated in the NB mode this would cause light leakage and coloration in the unactivated stable. An increase of the layer thickness, d, to fulfill the Mauguin limit results in impractically slow displays, as the switching speed of LC displays is proportional to the square of d (see Sec. 3.1.4.4). According to the calculations of Gooch and Tarry the transmitted intensity T ( u ) as a function of the parameter u = 2 d A n l a for a 90" twisted structure operated in the NB mode is given by [13, 141.
Figure 2 shows the plot of T(u) as a function of u , the so-called Gooch and Tarry curve. For large values of u , the transmitted intensity T ( u ) drops to zero and the Mauguin limit is fulfilled. Additional intensity
Minima of the Gooch and Tarry curve for NB-mode
1 st minimum 2nd minimum 3rd minimum
-
-
4
6
u = 2dm I
8
10
i
Figure 2. Gooch and Tarry curve for a normally black mode operated TN display.
12
Birefringence, An d = 6 pm
d = 8 pm
0.0837 0.187 0.286
0.0628 0.1404 0.2145
minima can be achieved by setting u = 2'3, t'l5,\135, which are the so-called Ist, 2nd and 3rd minima values. For operation of a TN display under these minima conditions the polarization state of light is not changed by the twisted structure. For the peak maximum of the spectral eye sensitivity (A=0.555 pm) the necessary An values for layer thicknesses of d = 6 pm and d = 8 pm to fulfill the lst, 2nd and 3rd minimum conditions are given in Table 1. The Gooch and Tarry curve for the NW mode shows intensity maxima for values of u = 2 d Anla corresponding to those of the intensity minima of the NB mode. The human eye detects the transmitted luminance, which is an integral over the visible spectrum of the product of
-
2
20 1
Table 1. Necessary birefringence values to fulfill the
dAn%-a
0
TN, STN Displays
the wavelength distribution of the illuminating light source, the Gooch and Tarry transmitted intensity as a function of ~ = 2 d A n l A(Eq. 2), the spectral eye sensitivity curve.
For the NB mode, intensity minima of the transmitted luminance are calculated for dAn=0.48 pm, 1.09 pm and 1.68 pm which correspond to the minima of the Gooch and Tarry transmitted intensity for a wavelength ;1=0.55 pm. Operation in the 1 st minimum is mostly used in TFT displays as it offers a wider viewing angle [15, 161. The 2nd minimum condition is used in watches and calculators.
202
3 Applications
3.1.2.3 Optical Properties of the Activated State Distribution of the Optical Axis In the following it is always assumed that the liquid crystal is characterized by a positive dielectric anisotropy, A&.In a nontwisted structure with zero pretilt a reorientation from a planar to a homeotropic alignment takes place above the Freedericksz threshold voltage
where K , is the splay elastic coefficient and .q,= 8.854 x C V-' m-'. In a TN cell with zero pretilt the corresponding threshold voltage for the transition from the twisted to the nontwisted structure is given by [l]
Relative distance z/d
Figure 3. Tilt and twist distribution as a function of the relative distance, z/d (0
IL I L 90%F................................. 7
1W%
C
L
/
.........................
I .
g9% ..........................
9 c
.......................
10% 0%
...................
Voltage
(4) where KZ2is the twist- and K33the bend elastic coefficient. The reduced threshold voltage Vth, defined by the ratio UthlUo,is given by
The application of an electric field results in a change of the tilt and twist distribution within the cell. Figure 3 shows calculated curves of the tilt and twist distribution as a function of the reduced distance z/d through the layer, with 0 < z < d , for different values of the reduced voltage v t h [ 171. The change of tilt is strongest in the middle of the cell and changes from the value of the pretilt in the unactivated state to a maximum value of 90" in the fully activated state. The tilt distribution is symmetrical around the cell cen-
Figure 4. Electro-optical curve for a normally black operated TN display.
ter and approaches the value of the pretilt angle at the boundaries. The twist distribution remains uniform for a midlayer tilt angle below 30".
Transmission and Viewing Angle Dependence The transmission as a function of the reduced voltage, the so-called electro-optical curve is shown in Fig. 4 for the NB mode. For the NW mode the complementary curve is achieved. Gray levels can be obtained by applying a voltage corresponding to a transmission value between 0% and 100%. The electro-optical curve strongly depends on the viewing angle and the operating temperature. The viewing angle is characterized by an azimuthal angle 8 and an a polar angle
3.1 Viewinq direction
\
TN, STN Displays
203
/
80 -
0
l
"
2
3
4
5
Reduced voltage F
40
-
Figure 7. Influence of operation in the 1st and 2nd minimum condition and different viewings angles on the relative contrast.
30 -
10 -
0
1
2
3
4
Reduced voltage
Figure 5. Influence of different azimuthal angles 8 and polar angles (b on the electrooptical curve of a normally white mode operated TN display for fixed temperature.
The electro-optical curve is different for a display operated in the 1st or 2nd minimum condition. This is shown in Fig. 7 for azimuthal angles O=O" and 45". Influence of Material Parameters on the Slope of the Electro-optical Curve
I
400c
20oc
Iooc
-
Reduced voltage
Figure 6. Influence of operating temperatures 0 " C , 20 "C and 40 "C on the electro-optical curve of a normally white mode operated TN display.
Cp. The influence of different viewing angles
on the electro-opical curve for fixed temperature is shown in Fig. 5. Increasing temperature results in a shift of the electro-optical curve to lower reduced voltages. This is shown in Fig. 6 for direct view (azimuthal angle O=Oo) and three different temperatures T=O "C, 20 "C and 40 " C .
One possible definition to characterize the slope of the electro-optical curve of a NB mode operated cell is the ratio of the voltages V90/V10. The voltage values V90 and Vlo correspond to those where 90% transmission and 10% transmission are achieved. Accordingly for a NW mode operated cell the slope is characterized by V10/V90. In the following discussion only operation of the NB mode is considered. Decreasing values of V,,/V,, result in a steeper electrooptical curve which becomes infinite for V9,/Vl,= 1. For TN-cells the ratio V90/V10 is about 1.4- 1.6. The slope can be increased by decreasing the ratios K3,/Kl I and [ 181. is the dielectric constant perpendicular to the principal axis of polarizability. In Fig. 8 calculated electro-optical curves for different values K 3 , / K l for a display operated in the 2nd minimum condition are shown. It is obvious that a steep electrooptical curve should be obtained for values of K,,/K, much smaller than 1 . However,
,
204
3 Applications
_ _,- . .- - -
10.
02
- I.__
1 1 ,
," I
I
,I ,
,
,
. .
,
.
the minimum achievable experimental K,,/K,, for TN mixtures is about 1, which results in a slope V90/Vlo= 1.35 of the electro-optical curve. The influence of the slope of the electro-optical curve on the resolution limit of passive matrix addressed displays will be discussed below. Contrast Ratio of the Normally Black and Normally White Mode The contrast ratio, defined as the ratio of transmitted luminance of the bright state to the dark state, is different for a NB-mode and a NW-mode display. In the NB-mode, ellipticity of the propagating light caused by a deviation from the optimized values of the Gooch and Tarry curve may cause light leakage in the unactivated black state, resulting in reduced contrast. Increasing temperature shifts An to smaller values and the effect becomes even more pronounced. Maximum contrast ratios of 100 : 1 can be achieved. In the NW-mode the influence of ellipticity of the propagating light in the unactivated bright state is less severe than for the NB-mode. In the fully turned on dark state the only limiting factors are the alignment and the efficiency of the polarizers. Maximum contrast ratios of 1OOO:l can be achieved. The advantage of the NB-mode is that the maximum contrast ratio is achieved at lower voltages than for the NW-mode [ 191.
Dye Doped Twisted Nematic Displays An improvement of both contrast ratio and viewing angle can be achieved by doping a TN-cell with a small concentration of a dye. This type of cell is called dye-doped TN display [20]. The dye concentration is typically about 1% and consequently the threshold characteristics and the switching speed of dye-doped TN-cells are comparable with standard TN-cells. The incorporation of a dye broadens the Gooch and Tarry minima, which disappear at larger dye concentration. Increasing temperature generally results in a deviation of the retardation d An from the optimized value. Consequently a NB mode operated cell with additional backlight will show a finite transmission at elevated temperatures in the unactivated state. This effect can be effectively suppressed in dye doped TN-cells by use of a blue dye. Other dichroic display types to improve the viewing angle of standard TN-cells can be found in the literature. The most popular are dichroic phase change effect displays or White-Taylor mode displays [21] and Heilmeier type dichroic LCDs [20, 22, 231.
3.1.3 Addressing of Liquid Crystal Displays The I T 0 layers on both glass substrates are patterned to generate conductive areas in which the liquid crystal orientation can be modified by an applied electric field. These active areas are separated by nonconductive areas. Low information content displays for watches and calculators are typically addressed by the so-called direct-addressing method. Higher information content displays for PDAs, mobile telephones, laptops and monitors require matrix addressing. In TFT displays an active matrix is used to drive the pixels while in STN displays ad-
3. I
dressing is performed by a passive matrix. In the following text the principles of direct addressing and passive matrix addressing will be discussed.
3.1.3.1 Direct Addressing Each pixel is addressed by an individual connection on one electrode side and a common backplane on the other side. The addressing of a display with P pixels thus requires P + 1 connections to the driving source. The nonactivated state is generated by applying voltage pulses of strength Vand same sign (phase difference zero) to both electrodes resulting in an overall voltage of zero. The activated state is achieved by applying voltage pulses of strength V, but opposite sign (Phase difference of n), which results in a total voltage of 2 V across the pixel. Direct addressing is used for low information content displays, such as a 3.5 digit watch display requiring 24 connections. However a black and white VGA display (640 x 480 pixels) driven by direct addressing would need 307201 connections. The number of connections can be reduced dramatically by matrix addressing.
3.1.3.2 Passive Matrix Addressing The electrodes are patterned to form a number of parallel conductive lines. Both electrodes are oriented at right angles to form a set of N row electrodes and M column electrodes. This is shown schematically in Fig. 9 for a display consisting with N=M=2. The number of active areas or pixels P = N x M can be addressed by P/N + N individual connections. The addressing of a black and white VGA display thus requires 1120 connections. Each pixel of the matrix is addressed by applying voltage pulses to row and column electrodes. The N rows are sequentially addressed by voltage pulses of
TN, STN Displays
205
Column electrodes
1
i
3
Figure 9. Principle of a matrix array consisting of two row electrodes and two column electrodes. The overlapping four areas define the pixels.
strength S during the selection interval At. N rows are addressed in a time T= N x At, the so-called frame time. This means that within the frame time each row receives a voltage pulse of strength S for a period At and a voltage pulse of zero for the remaining period ( N - l ) x A t . The columns are addressed by voltage pulses of strength and polarity +D or -D. The voltage for one line during one frame period consists of voltage pulses + D for the period ( N - 1) x A t and a voltage pulse of strength S + D or S - D for the time period At. A liquid crystal responds to the root-mean-square (r.m.s.) voltage across each pixel [24]. RMS behavior is obtained if the following two conditions are fulfilled: the response time of the liquid crystal mixture in the display must be many times larger than the period of the driving waveform; and the interaction between the applied electric field and the liquid crystal must purely be due to induced polarization. The corresonding r.m.s. voltage across one pixel in the on or off state is given by
--
--
\I(S+D)~+(N-~)D~ (Van) = N
,(S
r--
(Kff) =
-
- D)*
(6)
-
+ ( N - 1)D2 N
(7)
206
3 Applications
In contrast to direct addressing, the off-voltage (V,,) is not zero, but has a finite value. As discussed above, the threshold voltage depends on the angle of viewing and the operation temperature. Assuming that (Voff) was optimized for a special viewing angle and temperature it becomes obvious that a change of these parameters might cause a finite transmission of the display if (V,,) is fixed (see Figs. 5 to 7). The ratio (Von)/(Voff) is given by
10
100
1000
Number of matrix rows N
Figure 10. Dependence of the selection ratio, (Van)/ (Voff), on the number of matrix rows, N , according to Eq. (10).
(8) This ratio is optimized by differenting Eq. (8) with respect to S/D and setting this equation equal to zero. This results in
-=JN S D
(9)
Inserting Eq. (9) in Eq. (8) yields
This is the Alt-Pleshko law of multiplexing relating the number of matrix rows N(or the multiplex ratio N) to the required ratio of (Vo,)/(Vo,), the so-called selection ratio, to achieve an optimum contrast ratio [25, 261. The r.m.s. voltages (V,,) and (VoE) are also referred to as the select- and nonselectvoltages. The corresponding optical states are the select-state respectively the nonselect-state. In Fig. 10 the ratio (Vo,)/(Voff) is plotted versus the number of matrix rows N . The selection ratio (V,,)/(Voff) decreases with increasing matrix row numbers N and tends to 1 for an infinite number of N . For a dual-scan VGA display (N=240) the value of (V0J is only 6.7% higher than (V,,). For dual-scan XGA resolution (N=384) the selection ratio decreases to 1.052. This requires a steep electro-optical curve to obtain a large contrast ratio. As discussed above,
the slope of the electro-optical curve of a TN-cell can be increased by a decrease of . the the ratios K3,/K, and A E I E ~However, required selection ratio for high information content displays can not be achieved with a TN display. Typical TN mixtures are operated at multiplex ratios of up to 16 and 32. A reasonable contrast ratio at higher multiplex ratios can be achieved by increasing the twist angle of a standard TN cell to achieve a steeper electro-optical curve. For middleinformation content displays the twist angle is typically increased to 110". A disadvantage of this higher twist angle compared to a cell wih 90" twist is a worse viewing angle dependence. A steep electro-optical curve to satisfy the required selection ratios for at least dual-scan VGA resolution can be achieved by increasing the twist angle to values between 180" and 270" [27, 281. These types of cell are the so-called supertwisted nematic (STN) displays, which will be discussed in detail in Sec. 3.1.4. Matrix addressing causes certain requirements with respect to the frequency dependence of the liquid crystal mixture. For a display with N rows and frame frequency f the time interval, At, for addressing one line corresponds to a frequency of Nf.Decreasing tempera-
3.1
tures results in a shift of the liquid crystalline mixtures relaxation frequency, f R , which is mostly due to the increased rotational viscosity, yl. Operation of the display is possible if the conditionf,> Nfis fulfilled. If the relaxation frequency is close or smaller than the product Nf, the dielectric anisotropy tends to zero and the switching process either requires a higher operating voltage or can not be performed at all. The problem of frequency dependence at low temperatures becomes even more severe with increasing multiplex ratio and decreasing threshold voltage of the liquid crystal mixture. A further disadvantage of matrixaddressing is that the voltage at one pixel may influence other pixels. This effect is called crosstalk and depends on several parameters such as electrode-conductivity, capacitance, output impedance of IC drivers etc. [29-321.
3.1.3.3 The Improved Alt-Pleshko Addressing Technique The addressing scheme described in above would not be suitable for practical application, because it involves a net d.c. component resulting in an electrochemical decomposition of the liquid crystal. A net d.c.-free addressing requires modifications of the standard Alt -Pleshko addressing scheme. One possibility is to reverse the row and column voltages during alternate frames. This, however, requires an enhancement of the row voltages from S to 2S and is only used in displays where the numer of columns is much larger than the number of rows. In many applications the described voltage reversal during alternate frames is combined with an offset of both row and column voltages by D in one frame and by S in the reversed frame. This requires a maximum driving voltage of S + D for both row and column signals. This addressing method is
TN, STN Displays
207
referred to as DF switching or improved Alt -Pleshko addressing technique (IAPT) [33]. Typically the DF switching for a display with 240 rows is performed every 27 lines instead of only once per frame to reduce crosstalk effects.
3.1.3.4
Generation of Gray Levels
Techniques to achieve gray levels are frame modulation or frame rate control (FRC) [34], pulse width modulations (PWM) [35] and pulse height modulation (PHM) [36, 371. Gray Levels with Frame Rate Control In FRC a pixel is switched on during certain frames of a so-called superframe, consisting of up to 16 frames. This is schematically illustrated in Fig. 11 for the case of five pixels and a superframe consisting of four frames resulting in five different gray levels. In STN displays 64 gray levels can be achieved. A necessary condition for flickerfree images is that the relaxation period of the liquid crystal be many times larger than the superframe period [34]. Gray Levels with Pulse WidthModulation The r.m.s. voltage (Von,of+)can be generally described by (see Eqs. 6 and 7)
d ( S + kD)2 + ( N - 1) D2 (1 1) (Con,off) = N k = l refers to the on state and k=-1 to the off state. In PWM the column voltage is held at +D ( k = l), corresponding to the on-state, for a time periodf’At, where 0 At the column voltage is changed to -D ( k = - 1 ) , corresponding to the off state. This results in a r.m.s. voltage ( Vgray), which is intermediate - 1
~
~~-~ -~ ~
208
3
Applications
interval resulting in a r.m.s. voltage across a pixel given by
42S2 - 4 k S D + 2 N 9 (Vpixel) = N
(14)
PHM allows the generation of a larger number of gray levels than FRC and PWM and can also be used in fast responding STN displays [36, 371.
Figure 11. Schematic illustration of frame rate control (FRC) for the case of five pixels and a superframe consisting of four frames resulting in five different gray levels.
between those given by Eq. (1 1)
i
f(S +
(%ray) =
m2+ (1- f )
(s - D ) +~(N - 1) D* N
(12)
The voltage reversal of the column voltages requires higher operation frequencies and limits the number of gray levels to 16 due to the low-pass filtering action of the panel [351. Gray Levels with Pulse Height Modulation In PHM gray levels are achieved by setting the column voltage to an intermediate value between + D and -D. With respect to Eq. (1 1) this mean that the parameter k is set of values -1 < k < + l to achieve a voltage between (V0J and (V&. However the r.m.s. voltages across the other pixels in the same column (Vpixel) are changed to J(S (Vpixel) =
+ D)2+ (kD)2+ (N - 2) 02 N
3.1.4 Supertwisted Nematic Displays As described above, the slope of TN displays, described by the ratio V,,/V,, for a NB mode operated cell, is in the range of 1.4- 1.6, which is only sufficient for displays with a maximum number of multiplexedrows N= 16-32. Forhigherinformation content displays an increase of the slope is necessary to achieve a reasonable contrast ratio. In this subsection the influence of a twist angle >90° and other cell and material parameters on the midlayer tilt angle as a function of the reduced voltage, the socalled electrodistortional curve, is considered.
3.1.4.1 Influence of Device and Material Parameters Figure 12 shows calculated curves of the midlayer tilt angle as a function of the reduced voltage, for different twist angles, @ from 90"-360" [17, 28, 38, 391. Increasing twist angle, @, results in
- an increase of the reduced threshold voltage
(13)
This can be avoided by choosing the column voltage to be (k+(l-k2)) D in one time interval and (k-(1-k2)) D in another time
- an increase of the slope of the electrodis-
tortional curve an infinite slope for a twist angle of 270" a bistable region for twist angles above 270"
3.1 90
n
0
05
10
15
20
25
30
Reduced voltage
Figure 12. Influence of different twist angles from 90" to 360" on the electrodistortional curve.
A twist angle @>90" can be achieved by doping the nematic liquid crystal mixture with a cholesteric liquid crystal. For a cell with zero pretilt the twist angle @ depends on the ratio of the cell-thickness d to the pitch p of the doped liquid-crystal mixture:
The reduced threshold voltage V,, for a cell with arbitrary twist angle @and zero pretilt is given by [40]
TN, STN Displays
209
slope of the electrodistortional curve and the threshold voltage is shown in Fig. 13. The standard condition, common to all figures, refers to the parameter set consisting of a twist angle @=210", a pretilt angle 8=5", K,,IK, I = 1.5, K2,IK1 =0.6 and y=2.5 [ 171. The curves of Fig. 13 were calculated assuming that an applied electric field only results in a reorientation of the local optical axis perpendicular to the layer (Freedericksz configuration). However, in a highly twisted structure an applied electric field may also lead to an additional reorientation of the local optical axis parallel to the layer, which was first described by Chigrinov [4 11. This additional reorientation causes the occurrence of striped domains resulting in a destabilization of the twisted structure [42-441. In Fig. 14 microscopic photographs of a domain-free STN cell and a STN cell with striped domains are shown. Table 2 summarizes the influence of increasing twist angle @, pretilt angle 6, d/p ratio, K,,IK,,, K221K,l and y o n the slope of the electrodistortional curve and the stability of the Freedericksz configuration. From Table 2 it follows that a variation of twist angle 0, K,,/K, K2,/K, I and A€/&, towards a steeper electrodistortional curve will result in a destabilization of the Freedericksz configuration. A simultaneous increase of the slope and the stability of the Freedericksz configuration can only be achieved by an increase of the pretilt angle [451 and a decrease of the d/p ratio. Decreasing the d/p ratio below a certain value however results in the formation of a twisted structure with a twist angle @- 180". In the following typical values for the different parameters will be given:
,,
For a TN-cell with twist angle @=90" and d/p=O, Eq. (16) reduces to Eq. ( 5 ) . The stabilization of a twisted structure with twist angle d b 9 0 " requires a finite pretilt angle at the boundaries. Pretilt angles from 2" to 10" can be achieved using commercially available polyimides. An increasing pretilt angle results in a shift of the threshold voltage to values which are smaller than given by Eq. (16). The influence of different values of the pretilt angle, the d/p ratio, the ratios of the elastic constants K,,IK, and K2,1Kl and the dielectric parameter y=A&/E, on the
,
(a) For a twist angle of 180" a pretilt angle of about 2" is necessary. Typical STN displays with twist angle of 240" require pretilt angles in the range of 5". Pretilt
210
3 Applications
mj
0
p
?
90
80 70
0.5
1.5 2.0 Reduced voltage
10
25
3.0
dlp = 0 33
0
05
10
15
20
25
90
80
.
U
70
10
/
0
05
10
15
20
25
Reduced voltage
10
15
20
25
30
Reduced voltage
Figure 13. Influence of different values of (a) the pretilt angle, (b) the d p ratio, (c) the ratio of the elastic constants K3,IK1I , (d) the ratio of the elastic constants K22/K1 and (e) the dielectric parameter, y= on the electrodistortional curve. The standard condition, common to all figures, refers to the parameter set consistingof a twist angle @=210", apretilt angle 8=5", K 3 3 / K 1=1 1.5, K22/K11=0.6 and y=2.5.
Table 2. Influence of increasing parameters of twist angle, @, pretilt angle, 8, d/p ratio, elastic constant ratios K3,IK1 and K2,IK1 and dielectric parameter y=A&I% on the slope of the electrodistortional curve and the stability of the Freedericksz configuration. Increase of parameter ~~~~
K33/K1 = 0 5
05
30
Reduced voltage
g
0
30
Twist, @ Pretilt, 8 dP K331K1 I
K22IKI 1 y= A&/%
Slope of the electrodistortional curve
Stability of the Freedericksz configuration
Increasing Increasing Decreasing Increasing Decreasing Decreasing
Destabilizing Stabilizing Destabilizing Destabilizing Stabilizing Stabilizing
~
K z z / K i i = 0 T4-
o, 60
5 % L
50
:
30
20 10
0
0
05
10
15
20
25
30
Reduced voltage
angles of 2" to 10" are achieved using adequate polyimides [46 -481. Increasing temperature will result in a decrease of the pretilt angle.
(b) The d/p ratio for twist angles ranging from 180" to 270" is between 0.35 and 0.55. Increasing temperature results in a decrease of the upper limit of the d p value, defining the transition from the Freedericksz configuration to the formation of striped domains. The lower limit of the d/p value corresponding to a transition to a twist of a- 180" remains relatively unchanged with increasing temperature.
3.1 TN, STN Displays
12
F
11
~
I
I ~~
10 -~
a"
9
-
I
-
~~
+Lob&
I
: * *! - .
. . + *. . .,. . '+*
~~
8 7
iI
-
1
'c
*.
1
+
*+'***
-,
'&&a +*.
2.- *
-
6
(c) The elastic ratio K33/K11an be influenced in the range 1-2.5 by the mixture composition. Polar compounds display higher K33/K11values than neutral singles. The introduction of double bonds in the core structure or the side chains results in a further increase of K 3 J K I 1 [49,50] (see also Sec. 3.1.5). Increasing temperature results in a slight decrease of K d K ,1 . (d) The elastic ratio K2,1K, is typically about 0.5-0.6 and the temperature dependence is rather weak. The dielectric parameter y=A&kI as a function of A& at room temperature for mixtures with similar clearing point is plotted in Fig. - 15. It becomes obvious that the problem of the destabilization of the Freedericksz configuration is more severe in mixtures with large threshold voltages (smaller A&values). Increasing temperature decreases AE due to the decrease of the nematic order parameter
1
21 1
Figure 14. Microscopic photographs of (a) a domain-free STN-cell and (b) an STN-cell with striped domains.
I
Figure 15. Dielectric anisotropy A& as a function of the dielectric parameter at room temperature of liquid crystal mixtures with similar clearing point
while the changes of &Iare rather weak. Consequently the probability for the formation of striped domains is higher for increasing temperature. Summarizing these facts it follows that the different parameters need to be optimized to obtain a required slope of the electrodistortional curve for a certain application and avoid the occurrence of striped domains or the formation of a twisted structure with a twist of @-180" for the temperature regime of operation.
3.1.4.2 Configuration and Transmission of a Supertwisted Nematic Display A typical STN configuration with orientations of rubbing directions and polarizer directions for a cell with a twist angle of 240", dAn=0.85 and d/p=0.53 is shown in Fig. 16. The orientation of the rubbing directions of the polyimide layers of front and
212
3 Applications rear polarizer , 1 , , 1 p ) C
rear glass plate
front glass plate
,/*
/
rubbing direction
front polarizer
-/'
Figure 16. Typical STN-configuration consisting of front and rear polarizers and front and rear glass plate with orientations of rubbing directions and polarizer directions for a cell with twist angle 240°, dAn=0.85 and dlp=0.53.
A'
rear substrate depend on the twist angle @. The contrast ratio and the brightness are optimized by setting polarization axis of front and rear polarizers at an angle of (30-60)" with respect to the rubbing directions [5 11. For a cell with zero pretilt and an orientation of both polarizers at 45" to the rubbing directions the transmission of a STN-LCD is given by [52]
In Fig. 17 the transmission is plotted as a function of dAnlA for different twist angles @= 180"-270". The positions of the transmission minima are given by
Regarding the maximum of the spectral eye sensitivity curve (A=0.555 pm) this results in a retardation value q=dAn = 1.1-0.73 for twist angles @= 180"-270". The retardation value is about twice as large as for the 1st minimum condition of a TN-display. For a display with layer thickness d = 6 pm
a liquid crystal mixture with An=0.14 would be required for a STN display with twist angle @=240" while An=0.088 would be requested for a TN display operated in the 1st minimum condition. For general STN applications liquid crystal mixtures with An in the range 0.12-0.2 are necessary. As described in Sec. 3.1.2.2 the orientations of the front and rear polarizers of a TNcell are either parallel or perpendicular to the rubbing direction. For operation in a minimum condition, according to the Gooch and Tarry curve, the outcoming light is linearly polarized. Due to the off-axis orientation of polarizers and rubbing directions in a STN-cell, necessary to optimize the contrast ratio, the outcoming light is elliptically polarized. In combination with the large retardation values d An this leads to strong interference colors. The complementary color state can be achieved by turning one polarizer by 90". The STN-configuration shown in Fig. 16 appears yellow in the unactivated state and dark blue in the activated state. Black and white operation necessary to produce a colored STN display with RGB filter technology can not be achieved
3.1
TN, STN Displays
213
08
32
0
0
05
1
15
2
u = din//
in the standard STN-configuration and requires additional compensation techniques (see Sec. 3.1.4.5). Noncompensated STN displays are normally optimized for operation in yellow mode or the complementary blue mode. The designations yellow mode and blue mode correspond to the nonselect state. Different operating temperatures will change the product d A n due to a change of A n which is proportional to the nematic order parameter S. This causes coloration of the display which becomes more dominant with increasing operation temperature. The effect of unwanted coloration can be reduced by using a liquid crystalline mixture with a clearing point at least (30-40) K higher than the maximum operation temperature.
3.1.4.3 Electro-optical Performance of Supertwisted Nematic Displays According to Scheffer and Nehring the transmission spectra of the nonselected and select states of the yellow mode and the complementary blue mode for twist angles @=210" and @=270" show the following characteristics [ 171: -
The transmission spectra of the nonselect state of the yellow mode (blue mode) show a broad peak with a maximum (minimum) for wavelength A=(SOO-
2 5
Figure 17. Transmission as a function of u = 2 d A n l L for different twist angles @= 180" - 270" calculated according to Eq. 17.
550) nm. For twist angle @=270" the yellow mode is greenish-yellow and the blue mode shows a dark, purplish-blue colour. The yellow mode for a twist angle of 210" is greener than for 270". - The wavelength dependence of the select state is nearly constant in the visible range above A = SO0 nm. For wavelengths below A=SOO nm an increase (decrease) of the transmission spectra for the yellow mode (blue mode) is observed. For twist angle @=270" the yellow mode appears black and the blue mode is bright and colorless. The yellow mode for a twist angle @=210" is dark purple. - The application of a voltage intermediate between the nonselect and the select state also changes the wavelength of the peak maximum (minimum) for the yellow mode (blue mode) of operation. The increase of the twist angle @ from 210" to 270" results in an increase of the range of viewing directions with high contrast and a decrease of the areas showing contrast reversal at large viewing angles.
3.1.4.4 Dynamical Behavior of Twisted Nematic and Supertwisted Nematic Displays Equations for the switching on time z,, and the switching off time zoffunder static driv-
214
3
Applications 1000
ing conditions for a cell with arbitrary twist angle and zero pretilt angle were calculated by Tarumi et al. [53]: v)
a"
.-
E 100 L
yl is the rotational viscosity, U,,, the oper-
ating voltage and U, the Freedericksz threshold voltage. The denominator of Eq. (20) is related to the elastic constants K , K22and K33,the d/p value and the twist angle @by the following equation [53]: EO A&U i
=
The switching time, z, can be decreased by decreasing the rotational viscosity, yl, the layer thickness, d, and by an optimized balance of elastic constants and dielectric anisotropy, A&.Polar materials generally show higher rotational viscosities than neutral substances of similar clearing point. Consequently mixtures with lower threshold voltage will show a higher rotational viscosity yl due to the larger percentage of polar materials. The rotational viscosity of neutral increases with increasing clearing point, TN. I (see Fig. 18). Consequently an increase of TN-Iof a mixture without affecting the polarity will in a first approximation result in an increase of the total rotational viscosity and the switching time. The product dAn has to be kept constant for an optimum contrast ratio. Consequently for a decrease of the cell thickness, d, to achieve a smaller switching time, liquid crystal mixtures with increased birefringence An are necessary.
10 0
' ' ' ' 50I " ' '
100
150
T, I O C
200
250
Figure 18. Rotational viscosity, y,, as a function of the clearing point TN.Iof different neutral single materials.
For STN laptop and monitor applications showing switching speeds of (250- 300) ms, liquid crystal mixtures with An = (0.12 0.14) are used according to a layer thickness of (6-7) pm. For fast switching STN displays, liquid crystal mixtures with An = (0.17 -0.21) are required. This increase in An and subsequent decrease of d results in a switching time reduction by a factor of about three. However, even switching speeds of (80- 100) ms are still two slow for video presentation. Figure 19 shows the contrast as a function of time for the switching on process, corresponding to an increase of the contrast ratio from 0% to 100% followed by the switching off process. The switching onprocess consists of a so-called turn on delay and the rise time characterized by a change of the contrast from 10% to 90%. The switching off process consists of a turn-off delay and the decay time for the change of the contrast from 90% to 10%. The rise time and the decay time are generally not identical. The rise time is determined by an interaction of elastic constants and the dielectric anisotoropy while the decay time only depends on the elastic constants. The response
3.1
time strongly increases with decreasing temperature as shown in Fig. 20 for the rise time, the decay time and the delay time. This
TN, STN Displays
215
effect is mostly due to the quasi exponential increase of the rotational viscosity, y,, of liquid crystal mixtures with decreasing operation temperature (see Fig. 21). Under multiplex operation increasing operating voltage results in a decrease of the switching on time zOnand an increase of the switching off time zOff.The crossover condition Ton
(22)
=
can be fulfilled for a defined operating voltage which is smaller than for achieving an optimum of the contrast ratio.
3.1.4.5 Color Compensation of STN Displays Figure 19. Contrast as a function of time for the switching-on and the switching-off process.
Black and white operation of STN displays, necessary to produce a color display with the typical color filter technology, requires a compensation of the interference colors of a standard STN device. In this subsection several compensation techniques will be described.
Black and White Operation by Decreasing the Product d An I
I 0
1 1
- 50
1 100
50
Temperature I
O C
Figure 20. Dependence of the rise-time, the decaytime and the delay-time on the operation temperature.
The transmission spectra of the nonselect state for the yellow mode (and the complementary blue mode) are characterized by a broad interference peak with a maxi-
100000 I
10000 v,
-I
~
-
.
a E
'
1 100 230
240
250
270
260
TIK
280
290
300
Figure 21. Dependence of the rotational viscosity, yi, of a liquid crystal mixture on the operation temperature, T.
216
3 Applications
mum (respectively minimum) for wavelength of about 500-550nm. Black and white operation can be achieved by shifting this interference peak to shorter wavelengths. This requires a shift from the optimized retardation value d An - 0.9 pm to d A n -(0.4-0.6) pm [54, 551. The remaining transmission spectra is relatively flat. However this results in a reduction of the luminance by 50% and the brightness by 75%. The transmission can be enhanced by the so-called extended viewing angle (EVA) cell requiring a twist of 270' and a pretilt angle of (12-15)'. For a cell with layer spacing d=4 pm, a large viewing angle and switching time in the range of 10 ms were reported [56].
phase compensating element restores the linear polarized state. The principle of phase-compensation is to use a retarder foil placed between the STN-layer and the polarizer, with the same absolute value of the phase retardation A q but with its optical axis perpendicular to the optical axis of the STN layer. This implies an additional phase retardation A 9 of
Supertwisted Nematic Cell with Dichroic Color Sensitive Polarizer
Double Layer Compensated Supertwisted Nematic Displays
In this technique one standard polarizer is replaced by a dichroic color sensitive polarizer. For the yellow mode this results in a compensation of the off state and only slight influence on the on state. This mode of operation is called the neutral STN-mode (NSTN). For the complementary blue mode a compensation of the on state is achieved. A disadvantage of this technique is the low polarization efficiency of only (50-75)%. This limits its use to low-multiplexed displays with moderate requirements of contrast and viewing angle.
The double layer compensated configuration [57], (DSTN) shown in Fig. 22, consists of a stack of two STN-cells with identical values of d A n , but opposite handedness of the helices. At the interface between both cells the directors must meet at right angles. In the bright off state the polarizers are oriented parallel to each other. In the dark off state the orientation of polarizer and analyzer is perpendicular. The angle between rubbing direction and polarization axis is about (30-60)'. Assuming that both cells contain the same liquid crystal mixture the DSTN configuration has the following advantages:
Phase- Compensation Light propagating through a STN-cell will undergo a phase retardation A q given by
This phase retardation results in a transformation of the incoming linear polarized light into elliptically polarized light. A
Consequently the overall retardation is zero (Soleil- Babinet compensator) resulting in a black and white operating LCD configuration.
-
-
LC mixture parameters such as clearing point, birefringence, rotational viscosity, dielectric anisotropy and elastic constants can be optimized for a special applications without affecting the compensation effect. The compensation effect should be wavelength independent owing to the same dispersion in both cells.
3.1
n i
\
1" STN layer
polarizer
-
2 ~ STN 4
I
layer
i n
I
............._.._,, ..__
..',._....-
"..._ h
polarizer
light propagation
Figure 22. Principal configuration of a double layer compensated STN (DSTN) display. The 1st STN layer is an active layer, the 2nd STN layer is a passive layer.
-
U
217
90
. 0-J
TN, STN Displays
The temperature dependence of the birefringence, An, is the same in both cells resulting in a temperature independent compensation. Due to this effect DSTN displays are mostly used in automotive applications where a maximum operating temperature of up to 85 "C is necessary.
The compensation becomes nonperfect if the products d A n of both layers are different due to deviations of the layer thickness. These deviations should be less than 50 nm [58]. Generally the second STN layer is a so-called passive layer, as it is not addressed. As can be seen from Fig. 23 the deformation profile in the nonselected state and the field free state is rather similar. The birefringence of the active layer is smaller in the nonselected state than in the field free state. Consequently the retardation value d A n of the passive layer, which is held in a field free state, should be adjusted to the retardation value of the active layer in the nonselected state to optimize the contrast ratio. This requires a liquid crystal mixture for the passive layer with a retardation value about (2- lo)% smaller than for the active layer in the field free state [59-611. The range of viewing directions of a DSTN cell with a twist angle of 210" is similar to a noncompensated cell with twist angle of 270". A DSTN cell offers higher
Relative distance dd
Figure 23. Tilt angle as a function of the reduced distance d d (O
contrast, black and white operation and is about 50% brighter than an conventional STN cell. Disadvantages of the DSTN configuration are the increased thickness, weight and cost compared to the standard STN cell. The replacement of the second passive STN layer by a cholesteric polymer film with the same value of d A n and twist was described and commercialized [62,63].
Film Compensated Supertwisted Nematic Displays Compensation can be achieved by replacing the second passive STN cell of a DSTN display by an anisotropic, nonliquid crystalline polymer film made of polycarbonate (PC), polypropylene (PP) or polyvinyl alcohol (PVA). This type of compensated STN cell is the so-called film compensated STN (FSTN) cell [64]. The films of about 0.1 mm thickness are uniaxially stretched to obtain a retardation value of (200 - 800) nm. The configuration of a stretched film with refractive indices n, (parallel to the stretching direction) and n y , n, is shown in Fig. 24. Generally the films are slightly biaxial with n,>ny>n,. An even higher viewing angle can be achieved if n, > 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 , <:ecN -
C 71 N (53) I
36
0.228
171
1.73
0.194
126
(1.82)
0.182
237
(1.78)
No. 2.1 2.2
Structure c
5
,
w
c
N
-
C3H7=CN
2.3 W 2.4
H
C
N
C,H7 C -N
C5Hl
2.5 2.6
Ref.
3.1
223
TN, STN Displays
Table 5. Commercially used three-ring materials with high positive dielectric anisotropy. No.
Structure
yl [mPasJ K,,IK,,
Mesophases ["C]
A&
An
C45N242I
15
0.122
C53 N2041
20
0.123
C96N2191
17
0.210
C 131 N 240 I
Ref
1.95
[lo51
859
1.89
[I061
1338
1.92
[107, 1081
0.324
[931
C lllN226I
25
0.162
1227
C 9 1 N 1931
36
0.161
1424
[108, 1091
1.95
[110]
Table 6. Commercially used fluoro-aromatic materials with moderate dielectric anisotropy. No.
4.1
4.3
Structure C
7
H
i
w
Mesophases ["C]
A&
An
y, [mPas]
Ref.
C 36 N [-561 I
4
0.07
27
( 1 111
C 9 0 N 1581
3
0.08
156
11121
C 4 6 N 1241
6
0.08
160
[I131
C 25 SmB (51) N 119 I
5
0.08
229
(1141
C 3 9 S m B 7 0 N IS51
7
0.09
142
[115]
C 6 6 N 1021
8
0.14
194
[116]
F
C3H7+-J-o-QF
F
4.5
C3H7 3O C F*
-
F
4.7
C
,
H
7
W
:
OF
C 71 SmB (51) N I83 I
is a function of temperature and depends on the composition of the LC mixture. This fact often leads to a deterioration of the temperature dependence of LC mixtures. A predominantly parallel ordering of the molec-
ular dipoles and further increase of A& is possible with the introduction of ortho-fluorinated benzonitrile moieties [88] (Structures 2.4, 2.8 and 3.6).
224
3 Applications
Table 7. Influence of double-bonds on the elastic constant ratio K33/Kll. No
5.1 5.2 5.3
5.4
5.5
Mesophases ["C]
x KmPas1
C -3 SmB 68 I [N 17 I]
23
1.47
~901
C 23 SmB 33 N 34 I
34
1.59
[901
C 33 SmB (20) N 46 I
32
1.65
[901
C 29 N 44 I
26
1.68
~901
C 52 N 63 I
32
1.79
POI
Structure
%
% %
K33fKll
Ref.
Table 8. Commercially used materials with large elastic constant ratio K33/Kll. No
Structure
6.1
% -H I
6.2
m/
6.3
m\
6.4
F*/
6.5
F*
C C
H-
3
H -
-
3
C -9 SmB 52 N 63 I
39
1.53
[I181
C 66 N 162 I
118
1.72
[I 191
C 54 SmB 104 N 177 I
159
1.65
[1181
C 85 N 145 I
101
1.99
11181
C 47 N 109 I
115
1.95
[1181
F
Compared with the corresponding neutral structures the rotational viscosity, yl, of polar substituted LC - structures is increased (compare Structures 2.2/7.4, 3.3/8.3 and 3 3 8 . 6 ) . As given in Eqs. (19) and (20) this leads to an unwanted increase of the switching time. Therefore it is practice [89] in the design of mixtures for TN cells to include compounds with both large and small positive A&. The use of polar three ring materi-
als (Tables 5 and 6) in mixtures for multiplexed TN devices is restricted due to a deterioration of the frequency dependence of A&. Fluoroaromatic polar LC-materials (Table 6) with low to moderate A&show a better ratio of yl to clearing point. Owing to their high resistivity even at higher temperature these materials are especially useful in active matrix devices (TFT).
3.1
225
TN, STN Displays
Table 9. Commercially used basic two-ring materials. ~
No.
Structure
~~~
K,,IK,,
Mesophases ["C]
An
'/1 [mPas]
7.1
C -5 SmB 97 I
0.04
34
1.47
[I201
7.2
C 49 N 50 I
0.05
46
1.59
[121]
7.3
C 3 N [-751 I
0.08
14
1.47
[122, 1231
7.4
C 42 N (38) I
0.10
44
1.4
~1231
7.5
C 53 N [7] I
0.19
31
1.24
[I241
7.6
C 14 SmB 22 N 36 I
0.04
7.7
C 34 N (31) I
0.08
58
1.46
[I261
7.8
C 48 N 78 I
0.09
84
1.64
[I261
7.9
C 35 N (12) I
0. I5
58
7.10
C 32 N 42 I
0.15
3.1.5.3 Materials for the Adjustment of the Elastic Constant Ratio K33/KI1 All deformations in LCs can be expressed as a combination of the basic operations of splay, twist and bend of the director, mediated by elastic constants K,,, K22 and K33. As indicated in above it is particularly the elastic constants ratio K3,1K,,, that has received most attention because of its effect on the shape of the electro-optical switching curve in TN and STN cells. In TN devices it is essential to optimize the ratio of K,,IK, to low values, while for STN devices high values of K,,IK, are required to
Ref.
~251
~
7
11281
achieve a steep electro-optical contrast curve. A low value of K33IK11 can best be obtained by using heteroaromatic ring systems (structure 7.5). Compared with the neutral alkyl-chain substituted structures the introduction of a nitrile moiety leads to an increase of K,,IK, In general, a variation of K,,IK, can be obtained by the introduction of double bonds into the alkyl chain of LC-basic structures [49]. In Table 7 it is demonstrated that K,,/K, increases with the increasing number of double bonds introduced in basic structure 5.1 [90]. In addition the ratio of y,
,
1
226
3 Applications
Table 10. Commercially used basic three-ring materials. No.
Mesophases ["C]
An
fi [mPas]
C 62 SmB 109N 178 I
0.08
141
~ 9 1
C 51 SmB 129 N 157 I
0.08
275
[ 1301
C 66 SmB 134 N 166 I
0.16
100
[131,1081
0.15
154
11321
C 59 SmB 154 N 190I
0.04
313
[108, 1091
C 64 SmB 150 N 199 I
0.07
231
[log, 1091
0.12
274
[log, 1091
Structure
8.1 3C3H7 HC*
-
-
8.3 C53HH 2C 7*
\ /
-
8.5 1-7H3C 8.6 C
3
H
7
W
,
Ref.
Table 11. Commercially used materials with extreme high clearing point. Structure
No.
C,H,
Mesophases ["C]
"/1 .. [mPasl
Ref.
C 158 SmB 212 SmA 223 N 327 I
491
[133,134]
C 133 N 302 I
651
~1321
C 110 SmB 212 N 325 I
911
[I351
F
9.3
C
3
H
7
W
I
to clearing point is improved. Commercially available materials used for STN devices are presented in Table 8.
3.1.5.4 Dielectric Neutral Basic Materials Tables 9 and 10 give an overview of basic materials used in TN and STN mixtures. The
choice is largely dictated by a compromise between clearing point and viscosity even at low temperatures, but other factors such as birefringence, elastic behavior or volatility play an important role. Structure 7.1 combines a low optical anisotropy with an excellent ratio of "/1 to clearing point. Structures 7.3 and 7.4 are very effective to suppress the formation of smectic phases at low
3.1 TN, STN Displays
temperatures. Table 11 shows effective basic materials for the increase and the adjustment of the clearing point of the nematic liquid crystal mixture. As an example the mixtures clearing point is enhanced by 3 K by adding only 1 % of Structure 9.1. Acknowledgements The authors wish to express their appreciation to T. J. Scheffer and J. Nehring for permission to reproduce figures from their publications [17, 191.
3.1.6 References (11 M. Schadt, W. Helfrich, Appl. Phys. Lett. 1971, 18, 127-128. [2] R. G. Stewart, SlD Seminar Lecture Notes 1996, M-5. [3] T. J. Scheffer, J . Nehring, M. Kaufmann, H. Amstutz, D. Heimgartner, P. Eglin, SID Digest of Technical Papers 1985, XVI, 120- 123. [4] T. Geelhaar, D. Pauluth, Nachr. Chem. Tech. Lab. 1997,45,9- 15. [ 5 ] M. Hirata, N. Watanahe, T. Shimada, M. Okamoto, S. Mizushima, H. Take, M. Hijikigawa, AM-LCD1996,1, 193-196. [6] T. Yamada, M. Okazaki, Y. Shinagawa, lnternational display works IDW 1996, I , 349-352. [7] H. Mori, Y. Itoh, Y. Nishiura, T. Nakamura, Y. Shinagawa, AM-LCD 1996,2, 189- 192. [8] R. Kiefer, G. Weher, F. Winscheid, G. Bauer, Japan Display 1995, 547. [9] M. Oh-e, M. Ohta, S . Aratani, K. Kondo, Asia Display 1955, 577-580. [lo] S. Yamauchi, M. Aizawa, J. F. Clerc, T. Uchida, J. Duchene, SlD Digest 1989, X X , 378 -38 1. [ I 11 H. Hirai, Y. Kinoshita, K. Shohara, A. Murayama, H. Hatoh, S . Matsumoto, Japan Display 1989, 184-187. 1121 C. Mauguin, Bull. SOC.Franc. Mineral. 1911, 34, 71 - 117. [13] C. H. Gooch, H. A. Tarry, J. Phys. D.: Apply Phys. 1975,8, 1575-1584. [I41 C. H. Gooch, H. A. Tarry, Electron Lett. 1974, 10, 2-4. [ 151 L. Pohl, R. Eidenschink, F. del Pino, G. Weber, US Patent4,298,803 (15.6. 1981),MerckPatent GmbH. [16] L. Pohl, G. Weber, R. Eidenschink, G. Baur, W. Fehrenbach, Appl. Phys. 'Lett. 1981, 38, 497 -499. [17] T. J. Scheffer, J . Nehring, SlD Seminar Lecture Notes 1996, M-2. [18] I. Sage in Thermotropic Liquid Crystals, (Ed.: G. W. Gray), John Wiley & Sons, Chichester, 1987,64-97.
227
[ 191 T. J. Scheffer, J. Nehring in Liquid crystals: Ap-
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3.1 TN, STN Displays
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Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
3.2 Active Matrix Addressed Displays Eiji Kaneko
3.2.1 Thin Film Diode and Metal-Insulator-Metal Matrix Address [1 -201 The simplest way to overcome the scanning limitations encountered in passive matrix liquid crystal display panels is to provide one or more nonlinear circuit elements at the intersection of the gate and data electrodes, thus producing sharper threshold characteristics for each pixel. Presently, diodes and intrinsic nonlinear devices are used for these nonlinear circuit elements.
3.2.1.2 Back-to-back Diode Matrix Address [S- 101 Double threshold characteristics using two diodes which are connected, in series in opposite directions, can be constructed on a planar a-Si layer. Zener breakdown characteristics are used in this connection which is referred to as the back-to-back diode configuration. This connection provides larger threshold voltages in comparison with the diode ring connection. However, it is very difficult to control the Zener breakdown voltage of the diodes precisely.
3.2.1.1 Diode Ring Matrix Address [3-71 The double threshold addressed matrix liquid crystal display panel uses a two-terminal device that accomplished both set and reset functions for each pixel with appropriate signal pulses from the gate electrode drivers. To realize this panel, an amorphous silicon (a-Si) PIN thin film diode (TFD) matrix construction is used. The circuit diagram of a matrix panel addressed by these diodes is shown in Fig. 1 [4]. Each pixel is composed of a pair of diodes and one liquid crystal cell connected in series between a gate electrode bus and a data electrode bus. The diode pair is referred to as a diode ring, because the connection is a ring.
VI
In
I 3 )
w
7J
e
-Pixel <
+ m
-
Diode
...
ring
W
m
0
c7
YI
Y2
Data
Ya
electrode
---
YM
buses
Figure 1. Circuit diagram of diode ring matrix addressed liquid crystal display panel.
3.2.1 Thin Film Diode and Metal-Insulator-Metal Matrix Address
23 1
3.2.1.3 Two Branch Diode Matrix Address [l,2, 11-13]
3.2.1.4 SiN, Thin Film Diode Matrix Address [14-691
In the two-branch configuration of Fig. 2, the liquid crystal pixel is charged when the diode is forward biased during the select period. Leakage from the pixel through the diode during the nonselected period is prevented by keeping both diodes reverse biased. One disadvantage of this configuration is that areas of the gate electrode buses are large on the substrate, and as a consequence, the pixel aperture ratio decreases greatly as compared with other diode addressing configurations.
Nonlinear current-voltage (I-V) characteristics can be obtained with a silicon nitride (SIN,) layer. Figure 3 shows across sectional view of a system which consists of metalloff-stoichiometric-SiN,/ITO formed on a glass substrate. The transparent electrode (ITO) film is deposited on the lower glass and photo-etched to form a separate pixel electrode. Afterwards, a SIN, layer is deposited by RF-plasma CVD (chemical vapor deposition). I-V characteristics for a conventional TFD are not completely polarity-symmetric due to differences between the upper and lower SIN, interface barriers. In order to cancel these differences and to obtain symmetric I-V characteristics, the
'
Aperture ratio: the ratio of the actual display area to the occupied area of one pixel in a matrix liquid crystal display panel.
Data v o l t a g e
-Lr
n_._ -u-
Figure 2. Circuit diagram of two-branch diode matrix addressed liquid crystal display panel.
c Upper glass substrate
M e t a l electrode
( C r : 150nrn)
( D a t a electrode bus)
SiN,
layer
( IOOnrn)
- - - - - - - - - - -
- - -
-
-
(Gate electrode bus) Liquid crystal layer
Transparent p i x e l electrode Lower g l a s s substrate
Figure 3. Cross-section of an SIN, ma. trix addressed liquid crystal display panel.
232
3.2 Active Matrix Displays
Figure 4. An image displayed with the thin film diode switch matrix addressed liquid crystal display panel. (Courtesy of Philips Research Laboratories).
bridge structure TFD was developed. This structure consists of two conventional SiN,TFDs, connected to each other in back-toback series. Figure 4 shows an example of a displayed image obtained on an SiN,-TFD matrix drive liquid crystal display panel. The actual display are has a 10.4 inch diagonal and there are 480 x 1920 pixels.
3.2.1.5 Metal-Insulator-Metal Matrix Address [21-361 Highly nonlinear current-voltage characteristics can be obtained with an anodically formed tantalum pentaoxide (Ta,O,) layer. These characteristics result from the PooleFrenkel conduction mechanism [21, 221.
The characteristics of this layer can be used to drive matrix liquid crystal display panels instead of the SIN, diode device. It is called a metal-insulator-metal (MIM) diode. A serious problem in fabricating the MIM diode addressed matrix liquid crystal display panel which has a large number of gate electrodes is to reduce stray capacitances which are parallel to the MIM diodes. An ingeneously designed lateral MIM diode device which reduces the parallel capcitance is shown in Fig. 5 [27]. This MIM diode is constructed along the fringe of a thin tantalum (Ta) layer. The isolating layer is converted with a chromium (Cr) conducting layer. The obtained lateral sandwich construction of (Ta layer/Ta,O5 isolating layer/Cr) layer shows bidirectional non-
Figure 5. Diagram of lateral metal-insulator-metal diode device.
3.2.2
CdSe Thin Film Transistor Switch Matrix Address
233
Figure 6. An image displayed with the metal-insulator-metal switch matrix addressed liquid crystal display panel. (Courtesy of Seiko-Epson Co. Ltd.).
linear characteristics. The current flowing through this MIM diode flows primarily through the Ta,O, layer, if the polyimide insulator is sufficiently thicker than the Ta,O, layer. An example image displayed on the MIM diode addressed matrix liquid crystal display panel is shown in Fig. 6 [27]. The actual display area is 100x 96 mm. There are 240 gate and 250 data electrodes which provide a resolution of 25 lines cm-'. The contrast ratio obtainable is very high.
3.2.2 CdSe Thin Film Transistor Switch Matrix Address [37-561 Figure 7 (a) shows a top view of a matrix liquid crystal display panel which is addressed with thin film transistor (TFT) switches.
The gate and data electrode buses are located on a glass substrate and separated by a thin isolating layer inserted at their intersection. The rectangular shaped transparent pixel electrode is surrounded by the gate and data electrode buses. A tiny TFT is placed at each intersection of the gate and data electrode buses. Its drain and source electrodes are connected to the data electrode bus and the pixel electrode, respectively. The TFT gate electrode is connected to the gate electrode bus. Thus, each TFT is used to control the optical characteristics of the associated liquid crystal pixel of the matrix. A glass substrate, which has a transparent common electrode on its inner surface, is placed facing this matrix pixel substrate as shown in Fig. 7 (b). A liquid crystal molecular alignment layer is provided on the Glass s u b s t r a t e
Sate electrode
DU
TFT D a t a electrooe
DU
Srorclge capacitor
FTand pixel m a t r i x
loss substrate (a)
Top v i e w of p i x e l p o r t
( b l Cross sectional view of panel
Figure 7. Construction of thin film transistor switch matrix addressed liquid crystal display panel.
234
3.2 Active Matrix Displays Insulating layer
Gate electrode bus Source electrode and p i x e l e l e c t r o d e
D a t a electrode bus and d r a i n electrode
Gate e l e c t r o d e
Semiconductor (Cd S e )
( a ) Top view Semiconductor ( Cd Se 1
-,
Y
G
a
t
e
e lectrode
D o t o electrode bus
a n d d r a i n electrode
Source electrode and p i x e l e l e c t r o d e
Gate electrode bus
Glass substrate
I n s u l a t i n g layer
2 ( b ) Cross s e c t i o n a l view of
A-A'
inner surface of these two substrates. The liquid crystal material is introduced into the space between these glass substrate. Figure 8 shows the construction of an original TFT for the matrix liquid crystal display panel in which a cadmium-selenium (CdSe) TFT is used as the switch. Figure 8 (a) is a top view of the switch structure and its accompanying liquid crystal pixel electrode. Figure 8 (b) shows a cross-sectional view of the switch and pixel electrode. The CdSe semiconductor layer is used as a channel between the drain and source of the TFT.
Figure 9. An image displayed with the CdSe-thin film transistor switch matrix addressed liquid crystal display panel. (Courtesy of Stuttgart University).
Figure 8. Construction of CdSe thin film transistor for addressing a matrix liquid crystal display panel.
Figure 9 shows a black and white image displayed with a CdSe TFT switch matrix addressed liquid crystal display panel [56]. There are 128 gate and 192 data electrodes on this panel.
3.2.3 a-Si Thin Film Transistor Switch Matrix Address The field effect mobility of carriers in the a-Si thin film is very low, owing to many dangling bonds on the surfaces of silicon grains which constitute the film. This problem is significantly lessened by hydrogenization of the a-Si film which decreases the density of dangling bonds from about lo2' cmP3to about 1015cm-3 [57-581. There are two major types of a-Si TFT structures used in matrix liquid crystal display panels presently [59-721. One is a bottom-gate staggered structure and the other is top-gate staggered structure, with the former being more popular. The bottom gate structure is shown in Fig. 10. Several steps are needed for layer deposition and etching to fabricate the bottom-gate staggered structure. They are outlined as follows. First, a metal (sch as Cr) layer is sputtered onto a glass substrate and etched to form a
3.2.3
D a t a e l e c t r o d e bus-
Drain
3N
-
a-Si Thin Film Transistor Matrix Address
235
Gate e t e c t r o d e b u s
I T 0 pixel electrode Source Light s h i e l d l a y e r ( i s not shown
( a ) Top v i e w
Light s h i e t d Layer
D a t a electrode bus n+. 0 - S i l a y e r
i .a-Si layer
1
G a t e e l e c t r o d e Aw/
.”””
IT0 layer %SiNx layer -Glass substrate
( b ) A-n’ c r o s s - s e c t i o n a l view
rectangular gate electrode. To prepare the TFT array, a nondoped a-Si(i . a-Si) layer is deposited as an active layer by a glow discharge technique. Then, a phosphorus doped n+ . a-Si is deposited successively by plasma enhanced CVD. The i . a-Si layer and the n + . a-Si layer are etched into islands. The n+ . a-Si layer is used to prevent holes from being injected. Another metal layer is deposited and etched to form the data electrode bus and pixel contact. After that, an I T 0 layer is deposited and etched to form the pixel electrode. Finally, a passivation layer is deposited onto the layers to protect them. Figure 11 shows the structure of the topgate staggered TFT. Although the top gate
a-Si thin film transistor and pixel in a matrix liquid crystal display panel.
type TFT has many advantages, its application to active matrix liquid crystal displays has been limited for a long time, because of difficulties in making uniform ohmic contacts between a channel and two electrodes. As explained above, the present TFT fabrication requires may complicated steps with many photolithographic processes. To simplify fabrication and increase process yields, a fabrication with fewer mask processes are being developed [73-831. Figure 12 shows the fabrication flow for the two-mask-step a-Si TFT. DC sputtered Cr is deposited onto a substrate glass and patterned to form gate electrodes (a). SIN,, intrinsic amorphour Si (i . a-Si) and phosphorus doped n+ . a-Si are deposited succes,D a t a
( a ) C u t a w a y view ( A -A‘)
Figure 10. Construction of bottom-gate staggered
( b ) Top v i e w
e l e c t r o d e bus
lectrode bus
Figure 11. Construction of top-gate staggered a-Si thin film transistor and pixel in a matrix liquid crystal display panel.
236
3.2 Active Matrix Displays
n m ~ Deposition
(0)
Patterning Cr: Gate metal Deposition SIN,: Insulator Deposition 1.a- Si/nta-Si : c hannel
Developing OFPR-800 Patterning a-Si layer
(d 1
Deposition Patterning ITO: Source : Drain : Pixel
(e)
Spin coating photo resist :OFPR-800
Etching (nfa-Si remove) :channel
(f
(
Photo mask is used i n s t e p ( a ) and ( e l
sively by plasma enhanced CVD (b). The photoresist is spin coated and exposed to UV light from the back side of the substrate glass (c). After development of the photoresist, the n+ . a-Si and the i - a-Si are etched away except for the semiconductor layers on the gate electrodes (d). An I T 0 layer is deposited and patterned to form drain, source and pixel electrodes (e). The n+ . a-Si and a part of the i . a-Si are etched by the reactive ion etching method (f). In this way, the twomask-step TFTs is obtained. The SiN, on the gate electrodes to be connected to peripheral driver ICs is etched away after the liquid crystal cell assembly process. In this fabrication flow, the gate electrode is used as a mask for back side exposing light. This method is referred to as a self aligned method and it has been widely investigated as a way to reduce number of masks needed in photolithographic processes. To reduce the TFT area, the self-aligned method is probably the most suitable means of fabricating a large number of TFTs uniformly on a large substrate. And reducing the gate length, which is equal to the channel length, will keep the drain current high even in a small TFT.
)
Figure 12. Fabrication flow for the twomask step a-Si thin film transistor.
Typical values for field effect electron mobility and threshold voltage obtainable with the a-Si TFTs are around 0.6 cm2 V-' s-l and 2-4 V, respectively. The TFT area is usually covered with a black layer mounted on the opposite glass substrate of the liquid crystal panel to shield light, since an a-Si layer is a photosensitive material and a large off leak current flows under the illuminated condition [84-861. Sometimes, a light shield layer is mounted on the TFT as shown in Fig. lO(b). Figure 13 shows an example image displayed with an a-Si TFT addressed liquid
Figure 13. An image displayed with the a-Si thin film transistor switch matrix addressed liquid crystal display panel. (Courtesy of Hitachi Ltd.).
3.2.4
p-Si Thin Film Transistor Switch Matrix Address
237
aV= C G S . 2 V D
c,,+y
CLC
VO
I
Figure 14. Change in source voltage while the gate and drain (data) voltage are being ON/OFF driven.
crystal matrix display panel. There are 640x(480x3) pixels on this 10.4 inch diagonal panel. Figure 14 shows the change in source voltage (V,) while the gate voltage (V,) and drain (data) voltage (V,) are switched [87-891. The pixel must be charged to the drain voltage in a very short gated period of z ~ if ~the ,maximum contrast ratio is required in a displayed image. In order to obtain this condition, resistance of the drain electrode bus must be reduced as low as possible. To reduce the transient voltage drop AV, gate-source capacitance (C,,) must be small enough as compared with pixel capacitance and storage capacitance (CLC+C,). Off resistance of the TFT must be high enough in order to reduce the pixel voltage drop owing to leakage current during the unselected period of z ~ ~ ~ . Sometimes pixels are divided into two domains in which liquid crystal molecules are aligned differently [90-931. This divided domain TN mode can offer symmetric viewing-angle characteristics, since the two domains mutually compensate for the asymmetric viewing characteristics in the vertical direction. Thus, very wide viewing angles can be obtained for the image displayed with this panel. A huge number of TFTs must be mounted on high definition, large area liquid crys-
tal display panels. Many defective TFTs are apt to be present among them, which causes faults in the image on the panel. To prevent the faults, two TFTs are sometimes used for driving one pixel to increase redundancy [94]. For the same purpose, a butterfly drains architecture have been examined [95,96].
3.2.4 p-Si Thin Film Transistor Switch Matrix Address Field effect mobility of carriers in an a-Si layer is not high enough to apply a-Si TFTs as the gate and data electrode bus drivers for matrix liquid crystal display panels on which quick moving images are displayed. The field effect mobility can be increased if the a-Si layer is changed into a polycrystalline silicon (p-Si) layer, because the mean free path of the carriers can be increased in the latter. Furthermore, photo current of the p-Si TFT is lower than that of the a-Si TFTs, but it requires a quartz or high temperature glass substrate because of its high temperature fabrication processes [97, 981. There are two major methods which are presently -being used to producq the p-Si layer.
238
3.2
Active Matrix Displays
3.2.4.1 Solid Phase Crystallization Method [99-1191
Electron mobility of more than 100 cm2 V-' sC1 can be obtained with this method. Figure 16 shows an example displayed image on the p-Si TFT addressed matrix liquid crystal display panel. There are 6 4 0 x 4 8 0 ~ 3pixels on this panel. The display area is 5 inches diagonal.
A schematic cross-sectional view of the TFT and associated pixel electrode structure is shown in Fig. 15, which employs a conventional coplanar structure TFT with a double gate. Fabrication is done by the following procedure. First, the a-Si layer is deposited by low pressure chemical vapor deposition (LPCVD) on a substrate. Following photolithographic formation of the a-Si channel, the substrate is furnace annealed to convert the a-Si to p-Si through solid phase crystallization. An SiOz layer is deposited by atmospheric pressure chemical vapor deposition (APCVD). Chromium is then deposited and patterned to form the gate electrodes. After insulator deposition of SiO,, contact holes are opened photolithographically. Finally, TFT fabrication is completed by deposition and patterning of the I T 0 pixel electrode and the aluminum data electrode bus. The fabrication process required no hydrogenization step and has a maximum temperature of 600 "C which makes it ideal for low cost glass substrates.
I n s u La tins
Layer (Si 0,)
-,
3.2.4.2 Laser Recrystallization Method [120-1331 Figure 17 shows a cross-sectional view of the pixel constructed from a laser recrystallized p-Si TFT and I T 0 electrode. The fabrication process is as follows. After deposition of polysilicon by LPCVD, phosphorus ions are implanted in order to determine the threshold voltage. A finely focused CW argon laser beam was scanned on the layer. Successive fabrication steps are carried out by the standard N-channel MOS LSI technology. The pixel electrode is formed with the I T 0 layer. Usually, the gate and data driver circuits are mounted on the periphery of the p-Si TFT switch matrix addressed liquid crystal display panel.
G -/a et
electrodes
Dota electrode b u s
P i x e l electrode (IT01
p-Si layer
Lass substrate
( a ) C r o s s sectional view
/////////,-
Gate eiectrode bus
Drain contoctSource c o n t a c t
-Pixel e l e c t r o d e
Data e l e c t r o d e
(b)
Top view
Figure 15. Construction of a solid phase recrystallized p-Si thin film transistor and pixel for matrix liquid crystal display panel.
3.2.5 G l a s s substrate
Metal-oxide Semiconductor Transistor Switch Matrix Address
A
L i a h t schield /
:TO
.ayer
239
-Color ,~
\
\
~
’
,
-/--
.
\
- --
filter
A . anment .ayer
-Liquid
crystal
I gnment
“‘!‘~ITo
//
Glass substrate
”‘p-si
ibyer
Electron mobility of 320 cm2 V-‘ s-l is obtained, and the ON-OFF current ratio is about 10’. An XeCl excimer laser crystallization method is also very effective for field effect mobility enhancement of TFTs.
3.2.5 Metal-oxide Semiconductor Transistor Switch Matrix Address For driving matrix liquid crystal display panels, the silicon metal-oxide semiconductor field effect transistor (MOSFET) fabricated on a silicon monolithic wafer has been investigated by several groups [134-1501. The MOS transistor circuit fabrication techniques are well developed and have been used to produce various LSI devices. A dynamic scattering mode, a planar type GH mode or a polymer dispersed (PD) mode are used in these displays because the silicon wafer is intrinsically opaque. The circuit configuration of the panel is essentially the same as that of the p-Si TFT switch matrix addressed liquid crystal display panel as shown its equivalent circuit in Fig. 18(a). The physical arrangement of a prototype matrix liquid crystal display panel is shown in Fig. 18(b). Within the square area formed
//
layer
Layer
Figure 17. Construction of a laser recrystallized p-Si thin film transistor addressed liquid crystal pixel.
by the intersections of two adjacent gate electrode buses and two adjacent data electrode buses, there is an MOS transistor and a pixel. The MOS transistor source electrodes also serve as the pixel electrode. The pixel parts are usually sputtered with a white metal layer in order to obtain good diffused reflection of light. Reflective type MOS transistor drive liquid crystal display is being studied as an image mirror-cell of the liquid crystal projection TV display. In this cell, a PD mode is adapted to change cell light reflectivity. Figure 19 shows a projected picture on a 75 inch screen using the PD mode MOS transistor addressed liquid crystal display cell. The display area of the cell is 2.0 inch diagonal and the number of pixels is 640 x 480 x 3 [ 1501.
240
3.2 Active Matrix Displays
Figure 16. An image displayed with the solid phase recrystallized p-Si thin film transistor switch matrix addressed liquid crystal display panel. (Courtesy of SeikoEpson Co. Ltd.).
MOS transistor
Storage capacitor
Data electrode bus Gate electrode b u s
(a)
Equivalent
circuit
(b) M a t r i x MOS t r a n s i s t o r chip
3.2.6
Figure 19. An image displayed with the metal-oxide semiconductor thin film transistor switch matrix addressed liquid crystal display panel. (Courtesy of Hitachi Ltd.).
Figure 18. Metal-oxide semiconductor transistor switch matrix addressed liquid crystal display panel and its equivalent circuit.
References
[l] J. A. van Raalte, Proc. IEEE 1968, 56, 21462149. [2] G. J. Lechner et al., Proc. IEEE 1971,59, 15661579. [3] D. G. Ast, IEEE Trans. Electr. Dev. 1983, ED-30,532-539. [4] S. Togashi et al., SID 84 Digest 1984,324-325. [5] S. Togashi et al., Eurodisplay '84 1984, 141144. [6] S. Togashi et al., Proc. SID 26 1985,9-15. [7] K. H. Nicholas et al., Eurodisplay '90 1990, 170-173. [8] N. Szydlo et al., J. Appl. Phys. 1982, 53, 5044-505 1. [91 N. Szydloet al.,jpn. ~ i'83 1983,416418. ~ ~ [lo] T. Sat0 et al., SID 87 Digest 1987, 59-62. [l 11 Z. Yaniv et al., SID 86 Digest 1986, 278-280.
l
3.2.6 I121 K. E. Kuijk, Eurodisplay '90 1990, 174-177. [13] R. Hartman et al., SID 91 Digest 1991,240-243. [ 141 M. Suzuki et al., Japan Display '86 1986, 7274. [I51 J. W. Osenback, W. B. Knolle, J. Appl. Phys. 1986,60, 1408-1416. [16] K. Ohira et al., Japan Display '89 1989, 452455. [ 171 Y. Hirai et al, SID 90 Digest 1990, 522-525. [18] E. Mizobata et al., SID 91 Digest 1991, 226229. [19] A. G. Knapp IDRC Rec. '94 1994, 14-19. [20] J. M. Shannon et al., IDRC Rec. '94 1994, 373-376. [21] J. G. Simmons, Phys. Rev. 1967,155, 657-666. [22] H. Matsumoto et al., Jpn. J. Appl. Phys. 1980, 19,71-77. [23] D. R. Baraffet al.,SID80Digest1980,200-201. [24] D. R. Baraff et al., Tech. Dig. Int. Electron Devices Meeting 1980, 707-710. [25] D. B. Baraff et al., IEEE Trans. Electr. Dev. 1981, ED-28,736-739. [26] R. W. Streater et al., SID 82 Digest 1982, 248-249. [27] S. Morozumi et al., Japan Display '83 1983, 404-407. [28] K. Niwa et al., SID 84 Digest 1984, 304-307. [29] R. L. Wisnieff, IDRC Rec. '88 1988, 226-229. [30] H. Aruga et al., Japan Display '89 1989, 168171. [31] V. Hochholzer et al., SlD 90 Digest 1990, 526529. [32] V. Hochholzer et al., Eurodisplay '90 1990, 1 82- 1 85. [33] K. Aota et al., SID 91 Digest 1991, 219-222. [34] K. Takahashi et al., IDRC Rec. '91 1991, 247250. [35] V. Hochholzer et al., SID 92 Digest 1992,5 1-54. [36] V. Hochholzer et al., SID 94 Digest 1994, 423425. [37] A. G. Fischer et al., IEEE Conf. Record of 1972 Conf. on Display Devices 1972,64-65. [38] T. P. Brody et al., IEEE Trans. Electr. Dev. 1973, ED-20,995-1001. [39] T. P. Brody, F. C. Luo, SID Intr. Symp. Tech. Papers 1974, 166-167. [40] T. P. Brody et al., IEEE Trans. Electr. Dev. 1974, ED-22,739-749. [41] A. G. Fischer, Electr. Lett. 1976, 12, 30-31. [42] F. C. Luo et al., SID 78 Digest 1978, 94-95; Proc. SID 1978, 19,63-67. [43] J. C. Ershine, P. A. Snopko, IEEE Trans. Electr. Dev. 1979, ED-26, 802-806. [44] A. Van Calster, Solid State Electr. 1979, 22, 77-80. [45] T. P. Brody, P. R. Malmberg, Inr. J. Hybrid Microelectron. 1979, 2, 29-38. [46] W. Frash et al., Freiburger Arbeitstagung Flussigkristalle 1980, 20, 1-9.
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24 1
[47] F. C. LUO,W. A. Hester, IEEE Trans. Electr. Dev. 1980, ED-27,223-230. [48] F. C . Luo et al., IEEE Trans. Electr. Dev. 1981, ED-28,740-743. [49] F. C. Luo, D. Hoesly, SID 82 Digest 1982, 46-47. [50] A. G. Fischer et al., IDRC Rec. '82 1982, 161165. [ S I ] F. C. Luo, SZD 83 Digest 1983, 184-185. [52] T. P. Brody, IEEE Trans. Electr. Dev. 1984, ED-31, 16 14-1 628. [53] P. R. Malmber et al., SID 86 Digest 1986, 281284. [54] A. Van Calster et al., Japan Display '89 1989, 408-4 11. [55] J. De Baets et al., IDRC Rec. '91 1991, 215218. [56] D. Lueder, IDRC Rec. '94 1994, 30-38. [57] M. Milleville, W. Fuhs, Appl. Phys. Lett. 1979, 34, 173-174. [58] P. G. Le Comber et al., Electron. Lett. 1979, 15, 179-1 8 1. [59] H. Hayama, M. Matsumura, Appl. Phys. Lett. 1980,36,754-755. [60] A. J. Snell et al.,Appl. Phys. 1981,24,357-362. [61] A. I. Lakatos, IDRC Rec. '82, 1982, 146-151; Proc. SID 1983,24, 185-192. [62] D. G. Ast, IDRCRec. '82 1982,152-160; Proc. SID 1983,24, 192-198. [63] Y. Ugai et al., SID 84 Digest 1984, 308-3 1 1. [64] T. Snata et al., Proc. SZD 1986,27, 235-238. [65] S. Hotta et al., SID 88 Digest 1986, 296-297. [66] T. Ukawa et al., Japan Display '89 1989, 506-509. [67] Y.Nanno et al., SID 90 Digest 1990,404407. [68] T. Wada et al., Eurodisplay '90 1990, 370-373. [69] T. Yanagisawa, SID 93 Digest 1993,735-738. [70] A. Lewis et al., SID 94 Digest 1994, 251-254. [71] F. R. Libsch, H. Abe, SID 94 Digest 1994, 255-258. [72] W. E. Howard, IDRC Rec. '94 1994, 6-10. [73] S. Kawai et al., Proc. SID 1984, 25, 21-24. [74] Y. Nasu et al., SID 86 Digest 1986, 289-292. [75] Y. Lebosq et al., IDRC Rec. '85 1985, 34-35. [76] H. Tanaka et al., SID 87 Digest 1987, 140-142. [77] Y. Miyata et al., SID 89 Digest 1989, 155-158. [78] M. Akiyama et al., SlD 91 Digest 1991, 10-13. [79] N. Hirano et al., Japan Display '92 1992, 213216. [80] J. Gluck et al., Eurodisplay '93 1993, 203-206. [ 8 1 ] Y. Chouan et al., Eurodispluy '93 1993, 207-2 14. [82] J. Glueck et al., SZD 94 Digest 1994, 263-266. [83] N. Hirano et al., IDRC Rec. '94 1994, 369372. [84] S . Kawai et al., SID 82 Digest 1982, 42-43; Proc. SID 1982,23,219-222. [85] K. Suzuki et al., SID 83 Digest 1983, 146147.
242
3.2 Active Matrix Displays
[86] M. Ikeda et al., Japan Display '83 1983, 352354. [87] Y. Miyataet al., SID 88 Digest 1988,314-317. 1881 K. Suzuki, SID 92 Digest 1992, 39-42. [89] N. Nakagawa et al., SID 92 Digest 1992,781784. [90] K. H Yang, IDRC Rec. '91 1991,68-79. [91] Y. Tanaka et al., SID 92 Digest 1992,43-46. [92] Y. Koike et al., SID 92 Digest 1992,798-801. [93] T. Suzuki et al., SID 94 Digest 1994,267-270. [94] Y. Matsueda et al., SID 89 Digest 1989, 238241. [95] N. Bryeret al., JapanDispluy '86 1986,80-83. [96] J. F. Clerc et al., Japan Display '86 1986, 84-87. [97] M. Matsui et al., Appl. Phys. Lett. 1980, 37, 936-937. [98] F. Morin et al., Eurodisplay '81 1981,206-208. [99] A. Juliana et al., SID 82 Digest 1982, 38-39. [loo] T. Nishimuraet al.,SID82 Digest 1982,36-37; Proc. SZD 1982,23,209-213. [loll M. Matsui et al., J. Appl. Phys. 1982,53,995998. [lo21 S. Morozumi et al., SID 83 Digest 1983, 156157. [I031 M. Matsui et al., Jpn. J. Appl. Phys. 1983, 22 (Suppl. I), 497-500. [lo41 S. Morozumi et al., SID 84 Digest 1984, 316319. [lo51 S. Morozumi et al., SID 85 Digest 1985, 278281. [ 1061 N. Bryeret al.,Japan Display '86,1986,80-83. [lo71 S. Morozumi et al., Japan Display '86, 1986, 196- 199. [108] J. Ohwada et al., SZD 87 Digest 1987, 55-58. [lo91 S. Aruga et al., SID 87 Digest 1987, 75-78. [110] H. Ohshima et al., SID 88 Digest 1988, 408411. [ l l l ] J. Ohwada et al., IDRC Rec. '88 1988, 215219. [112] M. Takabatake et al., Japan Display '89,1989, 156-159. [113] K. Nakazawa et al., SID 90 Digest 1990,311313. [114] R. G. Stewart et al., SID 90 Digest 1990, 3 19-322. [115] U. Mitra et al., IDRC Rec. '91 1991,207-210. [116] T. W. Little et al., IDRC Rec. '91 1991, 219222. 11171 Y. Matsueda et al., Japan Display '92 1992, 56 1-5 64. [I 181 H. Ohshima et al., SID 93 Digest 1993, 387390.
[119] S. Chenet al., Eurodisplay '93 1993, 195-198. [120] A. F. Tasch Jun et al., Electron. Lett. 1979,15, 435-437. [121] T. I. Kanins et al., IEEE Trans. Electr. Dev. 1980, ED-27, 290. [I221 A. Ishizu et al., SID 85 Digest 1985, 282-285; Proc. SID 1985,26,249-253. [I231 E.Kaneko, Ext. Abs. of 1990 Int. Conf. on SSDM 1990,937-940. [I241 Y. Mori et al., SID 91 Digest 1991, 561-562. [125] S. Okazaki et al., SID 91 Digest 1991, 563564. [126] H. Hayama et al., SID 91 Digest 1991, 565566. [ 1271 H. Asada et al., IDRC Rec. '91 1991,227-230. [128] M. Kobayshi et al., SID 94 Digest 1994, 7578. [129] M. Matsuo et al., SID 94 Digest 1994, 87-90. [I301 H. Ohshima, IDRC Rec. '94 1994,26-29. [131] T. Hashizume et al., IDRC Rec. '94 1994,418421. [I321 A. Lewis et al., SID 94 Digest 1994,251-254. [133] K. Suzuki, SID 92 Digest 1992,3042. [I341 L. T. Lipton, SID 73 Digest 1973,44117. [135] M. N. Ernstoff, SID Technical Meeting Paper 1975, 1-9. [136] C. P. Stephens, L. T. Lipton, SID 76 Digest 1976,44-45. [137] L. T. Lipton et al., SID 77 Digest 1977,6445. [I381 L. T. Lipton et al., SID 78 Digest 1978,96-97. [139] M. N. Ernstoff, Proc. SID 1978, 19, 169-179. [140] K. Kasahara et al., 1980 Biennial Display Research Conf. Rec. 1980, 96-101; Proc. SID 1981,22,318-322. [141] M. Pomper et al., IEEE J. Solid-State Circuits 1980, SC-15,328-330. [142] T. Yanagisawa et al., SID 81 Digest, 1981, 110-112. [143] W. A. Crossland, P. J. Ayliffe, SID 81 Digest 1981, 112-113; Proc. SID 1982,23, 15-22. [144] M. Hosokawa et al., SID 81 Digest 1981, 114115. [145] K. Kasahara et al., SID 83 Digest 1983, 150151. [146] S. E. Shield et al., SID 83 Digest 1983, 179179. [147] K. Kasahara et al., Japan Display '83 1983, 408-411. [148] J. P. Salemo, SID 92 Digest 1992,63-66. [I491 J. P. Salemo, IDRC Rec. '94 1994, 39-44. [I501 T. Nagata et al., Tech. Rep. of IEICE, EID 9477,1994,97-101.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
3.3 Dynamic Scattering Birendra Bahadur
3.3.1 Introduction and Cell Designing The dynamic scattering effect is observed in nematic liquid crystals having low to moderate conductivity (resistivity < 10" ohms cm) and with mainly negative dielectric anisotropy. In the off mode and below a threshold voltage Vthw, the cells remains clear. When the voltage is increased beyond Vthw, striped patterns [ 1, 21 called Williams domains appear. On further increasing the voltage, these regularly shaped patterns are destroyed, giving way to a turbulent state called dynamic scattering [3, 41. Although the credit for discovering the dynamic scattering mode (DSM) and conceiving its electrooptical applications goes to Heilmeier et al. in 1968 [3, 41, a similar effect was reported much earlier in 1918 by Bjornstahl [ 5 ] . The dynamic scattering mode resulted in the first successful commercial application of liquid crystals in emerging flat panel display technology [6]. This in turn revitalized the scientific and technical interest in liquid crystals. The DSM effect and Williams domains are part of electrohydrodynamic instability, as these involve fluid motion. The physics of the DSM is still not fully understood because of its complex nature, and many of its effects are explained
on the basis of Williams domains, which are very well understood. The dynamic scattering effect is a classic example of chaos [7]. Electrohydrodynamic effects and DSM are summarized briefly here due to a shortage of space. For a detailed description, the reader is advised to read the review articles by Goossens [8], Dubois-Violette et al. [9] Bahadur [lo], Chandrasekhar [ l I ] and de Gennes and Prost [12]. In DSM cells, nematic liquid crystals of negative dielectric anisotropy with positive conductivity anisotropy are used. The LC (liquid crystal) mixture should have high birefringence, low viscosity, and a wide temperature range. The resistivity of the material should be about 10'- lo9 Ohms cm, which can be achieved intrinsically using materials such as Schiff bases or by doping the material with organic salts such as ternary amines, pyridinium salts, or HMAB (hexamethylaminobromide) [ 10, 131. The liquid crystal mixtures used were mainly composed of Schiff bases, azoxy, and esters [ 141. Dynamic scattering is usually not observed in very thin cells ( 4 5 pm). A cell gap of -10-30 pm is preferred. Cells are made with either homogeneous or homeotropic surface alignment [ 10, 151 for uniformity, although surface treatment is not essential to show DSM effects. For reflective mode,
244
3.3 Dynamic Scattering
Glass plates
Edge sealant
Tra nspa r e nt >conducting electrode pattern
Gasket
1 -
Liquid crystal
Reflector
a metallic reflector is used. Sometimes this reflector is put inside the cell to reduce double imaging and to form the back electrodes. The reactive nematic materials are separated from these electrodes by applying a nonconductive alumina or Si02 coating. A dynamic scattering mode cell is shown in Fig. 1.
3.3.2 Experimental Observations at DC (Direct Current) and Low Frequency AC (Alternating Current) Fields DSM cells exhibit the following sequence of regimes with an increasing DC or low frequency AC voltage. For simplicity, let us assume that glass plates were treated for unidirectional homogeneous alignment in the x direction.
3.3.2.1 Homogeneously Aligned Nematic Regime At low voltages (-1 V), the molecules are aligned normal to the electric field and therefore parallel to the glass plates, as expected for a material of negative dielectric anisotropy. In this regime we have a nematic single crystal.
3.3.2.2 Williams Domains When the rms (root mean square) voltage reaches a critical threshold Vthw ( - 5 V), a periodic distortion of nematic alignment is
Figure 1. Schematic diagram of a dynamic scattering mode LCD.
observed [S-12, 16-29]. Usually it is a simple one-dimensional type of distortion, as was.first observed by Williams [l]. A similar phenomenon was also independently reported by Kapustin and Larionova [2]. This perturbed state, observed only above a at low frewell-defined threshold, V,, quencies, is optically characterized by regular parallel striations perpendicular to the original direction of the director. The separation between the parallel strips is approximately equal to the thickness of the liquid crystal layer, d, or cell gap. This domainpattern (Fig. 2) is known as the Williams domain mode (WDM). The visible domain pattern is closely connected with the existence of a regular pattern of cellular or vortex fluid motion that can be observed by means of tracer dust particles. A schematic drawing of the flow pattern is given in Fig. 3a. Vortices extend in the y direction and the fluid motion is antiparallel in adjacent cells. The periodicity of motion, A,, is roughly equal to 2 d. The hydrodynamic motion is not visible directly, but becomes manifest due to the anisotropy in the refractive indices of the liquid crystal. When the sample is illuminated from the bottom, an observer above the sample sees a series of bright domain lines extending in they direction. Two sets of domain lines can be observed by focusing the microscope on the top and bottom of the cell, respectively. The lines are shifted over about half of their spacing when the focal plane is moved down to the bottom of the surface plane. The pattern is only visible for light polarized in the
3.3.2
Experimental Observations at DC and Low Frequency AC Fields
245
Figure 2. Domain pattern in p-azoxyanisole (PAA) observed in transmission. A 38 pm sample has been subjected to a 7.8 V driving voltage at 130"C.The rubbing direction (x) is horizontal and the voltage is applied perpendicular ( z ) to the page. The microscope is focused near the top electrode and has a & 10 pm depth of focus. The top set of bright domain lines are visible and have a spacing of 31 pm or 4 1 2 . When the microscope is focused at the bottom of the sample, another set of bright domain lines are visible. Several dislocations are visible in the domain patterns, as are many particles of dust, some badly out of focus. After Penz [19].
( C )
Figure 3. (a) Flow and (b) orientational patterns of Williams domain [ I I , 191; (c) light focusing by the periodic orientational pattern of a nematic liquid crystal. The molecular arrangement in mid layer is represented by line MM'. Plane parallel light is sent through the bottom plate. The initial wave front S is flat [12].
246
3.3 Dynamic Scattering
x direction, which is perpendicular to the domain walls, implying that the director is located in the plane xz, perpendicular to the wall. The director pattern, as deduced from the domain lines, is given in Fig. 3 b. The domain lines above the sample are the real images of the light source below the sample [ 191. The bottom lines are the virtual images. Figure 3 c shows the light focusing and formation of Williams domains strips. With light polarized in the x direction, the sample may be used as a periodic grating. At low frequency, the distortion in molecular alignment is static, the pattern remaining the same with the field reversal. The threshold voltage is usually a few volts and is practically independent of the sample thickness. However, it is strongly dependent on the frequency. There is a cutoff frequency f,(=0,/2n) above which Williams domains do not appear. The cutoff frequency,
f,, increases with the conductivity of the sample. The regions below and above the f, are called the conduction and dielectric regimes, respectively. Below f,, i. e., in the conduction regime, the regular Williams domain pattern becomes unstable at about twice the threshold voltage, Vth,and the medium goes over to dynamic scattering mode. Abovef,, i. e., in the dielectric regime, another type of instability called the chevron pattern is observed. Figure 4 shows the conduction and dielectric regime for p-methoxybenzylidene-p-n-butylaniline (MBBA).
3.3.2.3 Dynamic Scattering When the voltage V is increased above Vt, in the conduction regime, the distortion amplitudes and the associated flow velocities increase. Finally, at some higher voltage, Vthd, which is roughly 2 Vthwf a new regime
/*'
200
400
Frequency ( Hz )
("')
600 -3
Figure 4. Threshold voltage V,, of the AC instabilities for MBBA. Region I conduction regime (Williams domains); Region I1 - dielectric regime (chevrons). Full line from DuboisViolette, de Gennes, and Parodi model. After Orsay Liquid Crystal Group [17,23].
3.3.4 Theoretical Explanations
247
is observed [lo-12, 25-29] with the following characteristics: The Williams domains become completely disordered and mobile - the flow is turbulent - the long range nematic alignment is completely upset, and - the nematic layer scatters the light very strongly -
This new fluctuating disordered state can be observed in normal light without any specific polarization, implying that the molecules are no longer confined to the xz plane. Microscopic observations also show a number of disclination loops nucleating near the limiting surface. In this mode, the molecular motions are turbulent and the light is scattered strongly. The turbulent liquid crystal contains violently moving birefringent regimes several micrometers in size, and the diffuse optical scattering comes from the irregular refractive index gradients that are present. In a display, the activated areas look milky white on a clear, nonactivated background. DSM mode also depolarizes the polarized light.
3.3.3 Observations at High Frequency AC Field The optical pattern of the perturbed state in the high frequency ( f > 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)
<
and is a dimensionless quantity called the Helfrich parameter [ 10, 11, 231 given by
and ol,, 0, are the dielectric where ql, constants and electrical conductivity (11, I) respectively, Al and ;tZ are the shear coefficients, A& is the dielectric anisotropy, and qois a function of the viscosity coefficients. The quantity (C2-1)A& is also called the Helfrich parameter by some authors. This equation shows that the threshold of Williams domains is independent of the thickness. must be more than 1 in order to obtain an instability. The results of the Helfrich theory have been verified experimentally by several workers [ l 1,12,28,33, 341. Earlier it was thought that Williams domains could only be observed in materials
<’
Figure 6. Charge segregation in the applied field E, as caused by a bend fluctuation in a nematic of positive conductivity anisotropy. The resulting transverse field is Ex.
(z)
(=)
where V t= - 4 7c3
249
3.3.4 Theoretical Explanations
having negative dielectric anisotropy. However, Blinov [28] and de Jeu et al. [35-381 showed that Williams domains can also be observed in materials having positive dielectric anisotropy. They showed that the Carr-Helfrich theory is capable of explaining this fact. In calculating the threshold voltage, Helfrich assumed that the spatial periodicity of the fluid deformation was proportional to the thickness of the cell. Penz and Ford [ 19 - 2 1] solved the boundary value problem associated with the electrohydrodynamic flow process. They reproduced Helfrich’s results and showed several other possible solutions that may account for the higher order instabilities causing turbulent fluid flow.
3.3.4.2 Dubois-Violette, de Gennes, and Parodi Model
Low Frequency or Conduction Regime The Helfrich theory was extended by Dubois-Violette, de Gennes, and Parodi [ 171 to cover the AC field. The geometrical conditions are still the same. In the distorted state, the molecules are deflected by a small angle @ in the xz plane. The most important parameter from the point of view of charge accumulation is not exactly @, but rather the curvature ty=d$/dx of the molecular pattern; ty and the charge density, q , are used as fundamental variables. Their calculation yielded the threshold voltage Vthw
17, 181. The equation also shows that the threshold voltage is independent of the thickness of the cell and increases with an increase in the frequency, finally becoming very large on approaching the cut-off frequency, oc, where
The theoretical curve using Eq. ( 3 ) is in good agreement with the experimental results on MBBA. Williams domains are stable below o,and are not observed above 0,. From Eq. (3) we find that the relaxation frequency (l/z) increases linearly with the conductivity, which agrees with the experiments. In the low frequency regime (a5 o,), charges oscillate but domains or molecular patterns remain stationary. Therefore, this regime is also called the conduction regime.
High Frequency or Dielectric Regime When o reaches the cut-off frequency the threshold field becomes very large, oT reaches -1 and the curvature ty becomes time dependent; hence the low frequency calculations are not valid
where E and q are a suitable combination of the dielectric and viscosity coefficients, K,, is the bend elastic constant, and T is the decay or relaxation time of the curvature ty. Equation ( 5 ) concludes that the threshold field, E,, -o”* E, is thickness-independent, i. e., the phenomenon is field-dependent rather than voltage-dependent - the spatial period of striations .n/k 1 / 6 -
(3) with zthe dielectric relaxation time and w the angular frequency. With very low frequency or oz=O, Eq. ( 3 ) reduces to Helfrich Eq. ( 1 ) [8- 12,
-
In the high frequency regime (a> a,), the molecular pattern oscillates while the charges are static; for this reason, the regime
250
3.3
Dynamic Scattering
is often called a dielectric regime. It is also called the fast turn off, i. e., if AC voltage is turned off from slightly above V, to 0, the striation pattern disappears rapidly. A simple explanation is that the relaxation time in zero field ( T =q/K,, k 2 ) in the Dubois-Violette et al. model is very small due to the large value of the wave vector k. The Carr-Helfrich theory and its extension to AC field by the Orsay group have been verified experimentally by several workers and they found good agreement with the theory [8-12, 16-28, 33, 34, 39 -411. Besides the above-mentioned theories, attempts have been made by other workers [41-431. Some of these are beautifully reviewed by Goosen [8], DuboisViolette et al. [9], Chandrasekhar [ l 11, and Blinov [28].
3.3.5 Dynamic Scattering in Smectic A and Cholesteric Phases It has been observed that a homeotropically aligned appropriate SmA material with +A& exhibits dynamic scattering on the application of a suitable voltage [44-471. In Carr - Helfrich nematic electrohydrodynamic instability, the conduction and dielectric forces are usually required to be orthogonal to each other and the usual nematic materials exhibiting dynamic scattering are of -A& and +AD. Therefore, for SmA material with +A&, we require -AD. Fortunately, the smectic geometry provides this configuration as, contrary to nematics, the ions would move faster in the direction of the smectic layer compared to that perpendicular to it. A net negative conductive anisotropy is achieved either by doping SmA with ions or electric field dissociation of impurities. In the homeotropically aligned SmA state, the cell is clear in the quiescent mode. On application of a low frequency electric
field, it is converted to a turbulent light scattering state. When the field is removed, the scattering texture persists for a long period, but the intensity decreases slightly. By applying a high frequency electric field or a low frequency rms voltage less than the threshold voltage for scattering, the scattering can be erased. The cell becomes clear as the molecules adopt homeotropic texture due to dielectric orientation. The initial and final stages consist of homeotropically arranged molecules, whereas the scattering state consists of small focal conic groups (scattering centers) which are continuously agitating in the presence of a field. These displays have a very long memory and a wide viewing angle. However, they did not become popular due to high voltage (-100- 150 V) addressing, the need of special drivers, and the advent of supertwisted nematic and ferroelectric LCDs. A scattering effect similar to dynamic scattering has been observed in long pitch cholesterics with negative dielectric anisotropy [48]. Electrohydrodynamic instabilities in planar cholesteric texture leading to periodic grid type patterns have been reported in both negative and positive dielectric anisotropy materials [36, 49-53]. On further increasing the voltage, the grid structure is distorted to form a strong scattering state, which persists long enough even after the removal of the field. The scattering texture is approximately the same, i.e., focal conic texture with randomly distributed helix axes, as observed in the field-induced nematic -cholesteric transition of a long pitch cholesteric with positive dielectric anisotropy, although the mechanism for producing the scattering state is quite different. In this mode, randomly oriented focal conic textures are created due to the turbulent motion of the fluid, similar to dynamic scattering. The effect is used in storage mode devices [24, 48, 54, 551. The light scattered in stor-
3.3.6
25 1
Electrooptical Characteristics and Limitations
age mode is relatively independent of the cholesteric concentration, the direction of ambient light, and the cell gap. The scattering state can be erased by the application of an AC voltage having a frequency greater than the cut-off frequency. The cut-off frequency is proportional to the conductivity of the material. Helfrich [49] was first to propose electrohydrodynamic instability in cholesterics with negative dielectric anisotropy. Harault [S6], combining Helfrich theory with timedependent formalism, calculated a voltage frequency relationship similar to that observed for Williams domains. The existence of conduction and dielectric regimes was experimentally verified. The domain periodicity is proportional to ( pod)”2, where po is the quiescent pitch and d is the cell gap. The threshold voltage in the conduction regime is proportional to (d/p,)”2.
3.3.6 Electrooptical Characteristics and Limitations Recent studies by Japanese workers indicate that on increasing the voltage, the Williams domains do not pass directly to dynamic scattering mode but go through a succession of transitions [8, 24-29,57-751. The flow pattern passes from Williams domains (WD), a two-dimensional roll flow, to the grid pattern (GP), a three-dimensional conductive flow, to the quasi grid pattern, a three-dimensional time dependent flow, and finally to dynamic scattering mode (DSM), the turbulent flow mode [S7-591. These workers have also found that there are three types of turbulent flow: DSM-like, DSM1, and DSM2 [57-591.
3.3.6.1 Contrast Ratio Versus Voltage, Viewing Angle, Cell Gap, Wavelength, and Temperature Figure 7 shows the threshold characteristic of a dynamic scattering mode display for a material (N-014) for various cell gaps (6- 127 pm) [60]. With increasing voltage above the threshold v t h d , the transmission drops and scattering increases. The scattering starts to saturate at about 2 Vthd. Thinner cells are found to have higher contrast ratios, especially in reflective mode LCDs. The numerical value of the contrast ratio is found to be strongly dependent on measurement conditions, i. e., the angle of the light source and detector with respect to the display, the acceptance angle of the detector, the nature of the light (specular or diffuse), etc. The threshold voltage was found to have almost no thickness dependence, as predicted by the theory. The contrast ratio increases steeply above the threshold voltage (-7.5 V for N-014), but saturates above 20 V for a cell thicker than 12 pm. Unlike a twisted nematic (TN) display, scattering in a DSM LCD is symmetrical in a cone normal to the display. However, it decreases with increasing cone angles. Both
z401 1 N-014
25.C
I-
2
60
2 0
50pm
20
5W.n
l27pm
0
0
10
20
30
00
50
60
70
VOLTAGE
Figure 7. Contrast ratio of transmissive N-014 cells at 25°C vs. the applied DC voltage. After Creagh et al. [60].
252
3.3 Dynamic Scattering
the scattering and threshold characteristics are viewing angle dependent, and consequently the contrast ratio of a DSM display shows strong angular dependence. At a higher operating voltage, the viewing angle dependence of the light scattering is reduced. The contrast increases with voltage at higher angles due to an increase in the scattering. DSM displays have much higher brightness compared to standard TN displays, as they do not use polarizers. As dynamic scattering is a forward scattering phenomenon, a specularly reflective reflector or mirror has to be used to reflect the scattered light back to the observer for a reflective mode display. In this mode, glare is a major problem. Antiglare coatings have to be used to minimize this effect. The threshold characteristic of dynamic scattering mode displays satisfies the requirements to display some gray scale and intrinsic multiplexing [6, 10, 621. Intrinsically multiplexed calculator displays were made using dynamic scattering LCDs in the 1970s [63]. Studies of spectral transmission of a dynamic scattering display in off mode showed nearly the same transmission through the entire visible region, except for the region below 420 nm [lo, 611. The decrease in transmission below 420 nm is due to strong absorption of near ultraviolet light by the organic liquid crystal molecules and glass. Dynamic scattering itself is more or less achromatic, [ 101. Detailed investigations of scattering versus applied voltage, wavelength, viewing angle, and light polarization have been reported by Wiegeleben and Demus [71]. The threshold voltage of the dynamic scattering mode is nearly independent of temperature, except for the close vicinity of solid - nematic and nematic - isotropic transitions. However, the contrast ratio of DSM shows a significant decrease with an increase in temperature.
3.3.6.2 Display Current Versus Voltage, Cell Gap, and Temperature Current in a DSM display is mainly resistive. The minimum current density should be about 0.1-0.5 pA/cm2 for the scattering to occur. Figure 8 shows the current density ( j ) vs. the applied voltage (V) for N-014 at 25°C for the cells with cell gaps ranging from 6- 127 pm [60]. Only a small deviation from ohmic behavior is observed. These data can be quite accurately described by the relation j = V” with n = 1.2. Current decreases with increasing thickness for the same applied voltage. The current and hence the power consumption increase drastically with an increase in temperature [lo, 601. A plot of l o g j vs. 1/T is not linear, so the temperature dependence of the current density cannot be described by j = e-A/j-. I 10 -
u
-
N v)
-
a
I-
I
I
l
l
I
I
I
*/ N-OIe
I
i
CELL THICKNESS:
.
N
E u
-
-
U
t ln
l -
w
-
-.2
-
z
0
t-
z
611m
12pm
25pm
-
W
a a u 3
50 pm
0.1
10
100
VOLTAGE (dc)
Figure 8. Current density ( j ) as a function of applied voltage (V) at 25 “C for DSM cells filled with N-014. After Creagh et al. [60].
3.3.6 Electrooptical Characteristics and Limitations
3.3.6.3 Switching Time The time for complete relaxation of the cell is much longer than the apparent decay time for scattering centers [lo, 29, 60, 61, 64671. If a display is operated repeatedly so that it does not reach a fully relaxed state, the measured delay time in rise, td,, and rise time, t,, are shorter. However, the decay time, t d , is not affected. This is sometimes useful, as it gives a shorter switching time. It has been found that the switching time can be expressed by the following relationship
where 17 is the viscosity, A& is the dielectric anisotropy, V is the applied voltage, cl, c2 are constants, and K is the elastic constant. As is evident from the equation, both the on and off switching times can be reduced drastically by reducing the cell gap. Moreover, a reduction in the viscosity also helps in producing faster switching. The time can be further reduced by operating the cell at a higher voltage. However, this increase the current consumption and requires higher voltage drive electronics. The typical turn on times is -10-50 ms, while turn off time is 100-200 ms. To achieve the faster turn off ( - 5 ms), a dynamic scattering mode display is sometimes operated in fast turn off mode, i.e., after removal of the operating signal, a high frequency (more than the cutoff frequency) voltage signal is used [28,29, 64, 651. Both the rise and decay times of a homeotropic DSM cell are - 5 times slower than those of a homogeneous display (all other factors such as the cell gap, LC mixture, etc., being the same) [29]. This is due to the fact that a homogeneous or quasi-homogeneous state is necessary for the onset of turbulence. In a homeotropically aligned cell, this state
-
253
has to be induced momentarily by an electric field each time the display is turned on, while with homogeneous alignment this state exists already. The decay time of a homogeneous display is also smaller because the elastic realignment force exerted by the undisturbed layer of the NLC (nematic liquid crystal) molecules adjacent to the cell walls is larger for homogeneous alignment. The response time of a DSM display is also dependent on its conductivity. t d , and t, are inversely proportional to both the density and the mobility of charge carriers. The greater the ion density and the quicker they acquire momentum, the faster the turbulence appears. tdr and t, therefore decrease with an increase in the charge carrier density (e. g., by additional doping) or its mobility (e. g., by heating to reduce the viscosity or by increasing the voltage). Both the turn on and turn off times increase with a decrease in temperature. The main contribution to the decrease in switching speed comes from the increase in the viscosity at a lower temperature. Homogeneous alignment also produces faster switching, while initial homeotropic alignment produces greater circular symmetry in the scattering distribution. Homeotropic alignment also generates a better cosmetic appearance by minimizing the scattering in the off state.
3.3.6.4 Effect of Conductivity, Temperature and Frequency Margerum et al. [68] have reported that the threshold voltage decreases with increasing O,~/O,, and the optical density of scattering is directly proportional to ( ql/o,).They also found that V,, can be expressed as (Vth)-2 =A(O~,/O,)-' + B
(7)
where A and B are constants depending on liquid crystals. With increasing conductivity, t,, and t, become faster.
254
3.3 Dynamic Scattering
Dynamic scattering mode displays can be operated by AC as well as DC. However, a DC field generates electrochemical degradations, shortening the life of the display. Hence an AC field is preferred. It is found that an AC field enhances the life of the display almost >50 times compared to that of a DC field [60]. Dynamic scattering mode displays can be operated at any frequency below the cut-off frequency. However, the use of higher frequency increases the current consumption. With temperature, the resistance of the liquid crystal decreases and the conductivity increases. Although this does not affect the contrast ratio significantly, it increases the current consumption and the cut-off frequency (f,).Asf, is directly proportional to the conductivity, which increases exponentially with temperature, the following relationship between the cut-off frequency and the temperature [69] is possible
where E is the activation energy for conduction, b is the Boltzmann constant, and T is the absolute temperature.
3.3.6.5 Addressing of DSM (Dynamic Scattering Mode) LCDs (Liquid Crystal Displays) DSM displays show rms response. They can be driven directly for unmultiplexed uses, or using the Alt-Pleshko scheme for multiplexed applications [62]. The addressing methods for a dynamic scattering LCD are almost the same as those for a TN mode, although the DSM operates at a higher voltage and consumes more power [6, 10, 24, 251. The applied voltage for turning on the DSM display should have frequency below the cut-off frequency. DSM LCDs can be driven by CMOS (complementary metaloxide semiconductor) chips and have the
capability of some gray scale and intrinsic multiplexibility. Muliplexing schemes with drive signals, having frequency components both below and above the cut-off frequency, enhance multiplexibility and reduce switching times of DSM displays [24, 26, 27,651. DSM displays can also be addressed using active matrix addressing [76].
3.3,6.6 Limitations of DSM LCDs Dynamic scattering mode displays consume more power, operate at higher voltage, and are less legible compared to TN displays. Another problem with DSM displays is the limited operating temperature range due to the exponential increase in conductivity (and hence current) with temperature. If doping was adjusted for the high temperature end to give the required conductivity and hence current to suit the driver, the cell would not produce dynamic scattering at low temperatures due to a drastic increase in the resistance. If the current drainage is adjusted for the low temperature end, it becomes too much for the battery and the driver at the high temperature end. Moreover, DSM LCDs have a limited life. These limitations of dynamic scattering mode displays have made them obsolete. Acknowledgements Thanks are due to Shivendra Bahadur for his assistance in preparing this manuscript.
3.3.7 References [ l ] R. Williams, J. Chern. Phys. 1963,39, 384. 121 A. P. Kapustin, L. S. Larionova, Krystallographia (Moscow) 1964,9,297. [3] G. H. Heilmeier, L. A. Zanoni, L. A. Barton, Appl. Phys. Lett. 1968, 13,46. 141 G. H. Heilmeier, L. A. Zanoni, L. A. Barton, Proc. IEEE 1968,56, 1162. [5] Y. Bjornstahl, Ann. Physik 1918,56, 161. 161 B. Bahadur, Mol. Cryst. Liq. Cryst. 1983, 99, 345; B. Bahadur, Liquid. Crystal Displays: Gordon and Breach, N. Y. 1984 as a special issue of Mol. Cryst. Liq. Cryst. 1984, 109, 1-98.
3.3.7 References [7] J. Gleick, Chaos - Making a New Science, Viking Penguin, New York, 1987. [8] W. J. A. Goossens, in Advances in Liquid Ctystal Vol. 3 (Ed. G. H. Brown), Academic, N. Y. 1978. [9] E. Dubois-Violette, G. Durand, E. Guyon, P. Manneville, P. Pieranski, Solid State Phys. 1978, 14, 147. [lo] B. Bahadur in Liquid Crystals - Applications and Uses (Ed.: B. Bahadur) Vol I, World Scientific, Singapore, 1990. [ 1 I] S . Chandrasekhar, LiquidCrystals, 2nded. Cambridge University Press, Cambridge 1992. [12] P. G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd ed., Oxford University Press, Oxford 1993. [13] A. Sussman, Mol. Cryst. Liq. Cryst. 1971,14,183. [I41 Data Sheets on dynamic scattering mesogens and mixtures from E. Merck (Germany), Hoffman La Roche (Switzerland), American Liquid Crystal Company (Cleveland, U.S.A.), Chisso (Japan), etc.; A. M. Lackner, J. D. Margerum, Mol. Cryst. Liq. Cryst. 1985,122, 11 1; S. E. Petrie, H. K . Bucher, R. T. Klingbiel, P. I. Rose, Eastman Org. Chem. Bull. 1973,45, 2. [I51 J. Cognard, Mol. C y s t . Liq. Cryst., Suppl. 1 1981, 78, 1 . [16] W. Helfrich, J. Chern. Pkys. 1969, 51, 4092. [I71 E. Dubois-Violette, P. G. de Gennes, 0. Parodi, J . Physique 1971.32, 305. [IS] E. Dubois-Violette, J. Physique 1972, 33, 95. [I91 P. A. Penz, Phys. Rev. Lett. 1970,24, 1405;Mol. Cryst. Liq. Cryst. 1971, 1.5, 141. [20] P. A. Penz, G. W. Ford, Phys. Rev. A 1971, 6, 414; Appl. Phys. Lett. 1972,20,415. [21] P. A. Penz, Phys. Rev. A 1974, 10, 1300. [22] D. Meyerhofer, RCA Rev. 1974, 35, 433. (231 Orsay Liquid Crystal Group, Mol. C y s t . Liq. Cryst. 1971. 12, 251; Phys. Rev. Lett. 1970, 25, 1642. 1241 L. A. Goodman, J. Vac. Sci. Technol. 1973, 10, 804. [25] L. A. Goodman, RCA Rev. 1974,35,613. [26] A. Sussman, IEEE Trans. Parts, Hybrids Packuging 1972, PHP-8, 24. [27] R. A. Soref, Proc SID 1972, 13, 95. [28] L. M. Blinov, Electro-optical and Magnetooptical Properties of Liquid Crystals, Wiley, New York 1983. [29] M. Tobias, International Handbook of Liquid Crystal Displays, Ovum, London 1975. [30] G. H. Heilmeier, W. Helfrich, Appl. Phys. Lett. 1970, 16, 155. [31] E. F. Carr, J. Chem. Phys. 1963,38, 1536; 1963, 39, 1979; 1965, 42,738; Mol. Cryst. Liq. Cryst. 1969, 7, 253. 1321 N. Felici, Revue Gen. Electricite 1969, 78,717. [331 F. Gaspard, R. Herino, F. Mondon, Chem. Phys. Lett. 1974,25,449.
255
[34] M. 1. Barnik, L. M. Blinov, M. F. Grebenkin, S. A. Pikin, V. G. Chigrinov, Phis. Lett. 1975, S I A , 175. [ 3 5 ] W. H. de Jeu, C. J. Gerritsma, A. M. Van Boxtel, Phys. Lett. 1971, 34A, 203. [36] W. H. de Jeu, C. J. Gerritsma, P. Van Zanten, W. J. A . Goossens, Phys. Lett. 1972, 39A, 355. [37] W. H. de Jeu, C. J. Gerritsma, T. W. Lathouwers, Chem. Phys. Lett. 1972, 14, 503. [38] W. H. de Jeu, C. J. Gerritsma, J . Chem. Phjs. 1972,56,4752. [39] D. Meyerhofer, A. Sussman, Appl. Phys. Lett. 1972, 20, 337. [40] W. Greubel, U. Wolff, Appl. Phys. Lett. 1971,19, 213. [41] H. Gruler, Mol. Cryst. Liq. Cryst. 1973, 27, 31. [42] R. J. Turnbull, J . Phys. D. Appl. Phys. 1973, 6, 1745. [43] A. I. Derrhanski, A. I. Petrov, A. G. Khinov, B. L. Markovski, Bulq. Phys. J. 1974, 12, 165. [44] D. Coates, W. A. Crossland, J. H. Morrissy, B. Needham, J. Phys. 1978, D I I , 2025. [45] W. A. Crossland, S . Canter, SID Digest 1985, 124. [46] D. Coates, A. B. Davey, C. J. Walker, Eura Display Proc., London, 1987, p. 96. [47] D. Coates in Liquid Crystals Applications and Uses. (Ed.: B. Bahadur), World Scientific, Singapore 1990. [48] G. H. Heilmeier, J. E. Goldmacher, Proc. IEEE 1969, 57, 34. [49] W. Helfrich, 1.Chem. Phys. 1971, 55, 839. [50] F. Rondelez, H. Arnould, C. R. Acad. Sci. 1971, 273 B, 549. [51] C. J. Gerritsma, P. Van Zanten, Phys. Lett. 1971, 37A, 47. [52] H. Arnould-Netillard, F. Rondelez, Mol. Cryst. Liq. Cryst. 1974, 26, 11. [ 5 3 ] F. Rondelez, H. Arnould, C. J. Gerritsma, Phys. Rev. Lett. 1972, 28, 735. [54] W. E. Haas, J. E. Adams, et al., Proc. SID. 1973, 14, 121. [ 5 5 ) G. A. Dir, J. J. Wysocki, et al., Proc. SID 1972, 13, 105.
[56] P. J. Harault in Fourth In?. Liquid Crystal Conference, Kent, OH, 1972; J. Chern. Phys. 1975, 59, 2068. [57] H. Yamazaki, S. Kai, K. Hirakawa, J . Phys. Soc. Jpn 1983,52. 1878. [ S S ] H. Yamazaki, S . Kai, K. Hirakawa, Memoirs Fac. Eng. Kyushu Univ. 1984, 44, 317. 1591 H. Yamazaki, K. Hirakawa, S. Kai, Mol. Cryst. Liq. Cryst. 1985, 122, 41. [60] L. T. Creagh, A. R. Kmetz, R. A. Reynolds in IEEE Int. Conj: Digest, p. 630, N. Y. March 1971, IEEE Trans. Electron. Dev. 1971, ED-18, 672. [61] V. 1. Lebedev, V. I. Mordasov, M. G. Tomilin, Sov. J. Opt. Technol. 1976,43, 252.
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[62] P. M. Alt, P. Pleshko, IEEE Trans. Elect. Dev. 1974, ED21, 146; Proc. SID 1975,16,48. [63] K. Nakada, T. Ishibashi, K. Toriyama, IEEE Trans. Elect. Dev. 1975, ED-22, 725. [64] G. H. Heilmeier, L. A. Zanoni, L. A. Barton, IEEE Trans. Electron. Dev. 1970, ED1 7, 22. [65] P. J. Wild, J. Nehring, Appl. Phys. Lett. 1971,19, 335. [66] M. J. Little, H. S. Lim, J. D. Margerum, MoZ. Cryst. Liq. Cryst. 1977, 38, 207. [67] C. H. Gooch, H. A. Tarry, J. Phys. 1972, D5,
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[68] J. D. Margerum, H. S . Lim, P. 0. Braatz, A. M. Lackner, Mol. Cryst. Liq. Cryst. 1977, 38, 219. [69] S. Matsumoto, M. Kamamoto, T. Tsukada, J. Appl. Phys. 1975,14, 965.
[70] D. Jones, L. Creagh, S. Lu, AppZ. Phys. Lett. 1970, 16, 61. [71] A. Wiegeleben, D. Demus, Cryst. Res. Techn. 1981, 16, 109. [72] G. Elliott, D. Harvey, M. G. Williams, Electron Lett. 1973, 9, 399. [73] J. Nakauchi, M. Yokoyama, K. Kato, K. Okamoto, H. Mikawa, S . Kusabayashi, Chem. Lett. (Jpn) 1973, 313. [74] E. W. Aslaksen, Mol. Cryst. Liq. Cryst. 1971,15, 121. [75] NPL, New Delhi, India, Bulletin No. NPL-7401, 1974. [76] F. C. Luo in Liquid Crystals Applications and Uses (Ed.: B. Bahadur) World scientific, Singapore, 1990.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
3.4
Guest - Host Effect
Birendra Bahadur
3.4.1 Introduction The phenomenon of the alignment of dye molecules by liquid crystal molecules and its applications were first reported by Heilmeier et al. in 1968. They termed this phenomenon the guest-host effect [l-31. Liquid crystals are excellent solvents for organic and organometallic molecules. Nonmesomorphic molecules may be incorporated in liquid crystals up to a fairly high concentration without destruction of the long-range order of the liquid crystalline matrix. More generally, the phenomenon of dissolving and aligning of any molecule or a group of molecules, such as dyes, probes, impurities, or even mesogenic molecules, by a liquid crystal can be called the guest-host phenomenon. Elongated molecules are aligned better than are spherical molecules. The molecules behave as guest molecules in a liquid crystal host. The host liquid crystal can be a single compound or a multicomponent mixture. The guest molecules couple to the anisotropic intermolecular interaction field of the liquid crystal, but can diffuse rather freely within the host. The anisotropic guest - host interaction leads to a highly anisotropic tumbling motion of nonspherical guest molecules in the liquid crystal ma-
trix. In the time average this anisotropic tumbling leads to an appreciable orientation of the guest with respect to the local director of the liquid crystal. These liquid crystalline solutions can be easily oriented by electric, magnetic, surface, or mechanical forces, resulting in highly oriented solute molecules. The molecular properties of the guests are not altered appreciably by the weak intermolecular forces, and they behave as an ‘oriented gas.’ This finding provides the basis for the application of liquid crystals as anisotropic solvents for spectroscopic investigations of anisotropic molecular properties [4 - 71. The ordering of probe molecules i n liquid crystals was in fact known much earlier than 1968. It is widely used to determine various parameters of the solute and solvent liquid crystal using nuclear magnetic resonance (NMR), electron spin resonance (ESR), ultraviolet (UV), visible, and other spectroscopic techniques. After the pioneering work of Saupe and Englert in 1963 [8], the NMR spectroscopy of molecules oriented in liquid crystals became very important in structural chemistry, as it provides the only direct method for precise determination of the molecular geometries in liquid phase. In addition to structural and confor-
25 8
3.4 Guest-Host Effect
mational studies of the molecules, NMR has been used to determine the chemical shift anisotropies and the anisotropies of the indirect spin - spin coupling [4 - 71. The field has been reviewed by many authors [4-71 and is the subject of a separate chapter in this book. Paramagnetic probe molecules (guest) dissolved in liquid crystals are used for EPR studies. The first EPR studies on radical ions in liquid crystals were done in 1964 using diphenylpicrylhydrazyl and tetracyanoethylene anion dissolved in PAA [9]. The guest-host effect has also been used in measuring linear and circular dichroism [4], the Mossbauer effect [lo], and many other spectroscopic and electro-optical properties. It is also used as an indirect method to determine the order parameter of the liquid crystal. The guest-host effect is also used to alter the reactivity of the dissolved solute for desired chemical reactions [ 1 11. In a broad sense, most of the commercially available liquid crystal mixtures may be regarded as being based on the guest host effect, as they incorporate some nonmesomorphic molecules to generate the desired effect in liquid crystal mixtures. These broad topics are covered in other chapters of this book, and hence are not described here. The general perception of the guest host effect is a system composed of a dye and a liquid crystal. The most valuable commercial application of this effect has been in electro-optical devices [ 12- 171. Hence, this chapter is devoted to dichroic liquid crystal mixtures and dichroic liquid crystal displays (LCDs). The dyes used in dichroic LCDs normally absorb in the visible spectrum. The present market for dichroic LCDs, including drive electronics in some cases, is estimated to be US$ 35 million, and is mainly in avionics, military, sign board, and games markets. The dichroic market has been stagnant and declining during the last few years. However, there is a
new emerging interest in dichroic LCDs due to the demand for low power consumption, direct view LCDs for use in consumer electronics and lap-top computers. If a small amount of an elongated dye is mixed with a liquid crystal, the dye molecules become aligned with the liquid crystal matrix and hence can be oriented from one position to another along with the liquid crystal molecules by the application of an electric field. This dichroic mixture absorbs light selectively. With proper surface treatment, in one state (quiescent or activated) the dichroic mixture does not absorb light strongly, while in another state it does (Fig. 1). The application of an electric field results in a nonabsorbing state if the quiescent state is absorbing, or in an absorbing state if the quiescent state is clear. This is the basis of almost all dichroic displays [12-171. The absorption is usually increased by using a polarizer [1, 2, 15, 161, or by adding a suitable amount of a chiral dopant in the nematic host [15-171. The most popular dichroic displays are the dichroic phase change effect [3, 12- 171 (White-Taylor mode [ 171) and Heilmeier type dichroic LCDs [l -3, 12- 161. Besides these quarter wave plate dichroic [16, 18-201, double cell guest - host dichroic [16, 21 -241, dye doped twisted nematic [15, 16, 25-28], supertwisted dye effect [29-3 11, dichroic ferroelectric [32 - 351, polymer dispersed dichroic [36-391, and dichroic SmA [40, 411 LCDs are also known. The performance of a guest - host LCD is greatly dependent on the dye parameters (such as UV stability, solubility, order parameter, absorption, etc.), the host liquid crystal properties (such as viscosity, dielectric anisotropy, birefringence, order parameter, temperature range, stability, etc.), and the compatibility of the dye and the host [12- 17,42-581.
3.4.2 Dichroic Dyes
narrow absorption spectrum, the wavelength of maximum absorption being designated as Amax. The color seen is basically the light which is not absorbed by the dye. Fluorescent dichroic dyes are slightly different. They absorb at a given wavelength (UV, blue, green, etc.) and emit at a longer wavelength [59-611. This emitted radiation determines the color of the dye and display. To make a black mixture one has to use several dyes having different A,, [IS,16, 55-58]. The dyes used in textile and other industries normally cannot be used in LCDs, as non-ionic dyes are required in order to avoid electrochemical degradation and to reduce the current consumption. The usefulness of dichroic dyes in guest-host LCDs is determined by the following properties 115, 16,461:
100
80
z
P
sa
60
2 4 K !-
40
v,
259
v)
-
bp
10
0 380
460
540
610
700
780
WAVELENGTH (nm)
Figure 1. Operational principle of a dichroic display (Heilmeier display).
-
-
3.4.2 Dichroic Dyes Dichroic dyes absorb light more along one axis than the others. Usually, the major component of the transition moment of dyes is along the long molecular axis (pleochroic) or short molecular axis (negative dichroic). Pleochroic (positive dichroic) dyes [ 12- 16, 46, 541 absorb the E vector of light which is directed along the long molecular axis of the dye, while negative dichroic dyes absorb the E vector of light which is directed perpendicular to the long molecular axis [16, 46, 50-541. Normally, these dyes have a
-
The chemical and photochemical stability of the dye [15, 16, 46, 62-67]. Photochemical instability is also termed 'fading.' The color or hue (A,,,, wavelength of maximum absorption or emission). The spectral width (measured as the halfwidth). The extinction coefficient. The dichroic ratio [42]. The order parameter of the dye [421. The solubility of the dye in the host [ 16,46, 681. The influence of the dye on the viscosity of the host [ 16, 461. The nonionic nature. The purity and high resistivity. The compatibility of the dye with the host, which is usually determined by its order parameter, solubility, viscosity, and the absence of chemical reaction with the host.
260
3.4 Guest-Host Effect
3.4.2.1 Chemical Structure, Photostability, and Molecular Engineering The most widely used dichroic dyes in LCDs [16, 42-49] fall basically into two classes from a chemical structure point of view: azo [16,42-46,491 and anthraquinone [16, 42-48]. Besides these, methine [16,46], azomethine (Schiff base) [16,46], merocyanine [ 16, 44, 461, napthoquinone [ 16, 46, 56, 691, hydroxyquinophthalone [70], benzoquinone [46], tetrazine [52,53], perylene [70], azulene [46], and other types of dichroic dyes [ 16,461 have also been investigated. Fluorescent dyes are found to have many classes of chemical structures [59-611. Most of the dyes used are pleochroic dyes, as these exhibit a higher dichroic ratio and order parameter. Some of these dichroic dyes are listed in Table 1. Some good review articles on dichroic dyes have appeared recently [16,44-461, and these, especially the detailed articles by Bahadur [ 161 and Ivashchenko and Rumyantsev [46], should be consulted for more details on the chemical structures and physical properties of dichroic dyes and dichroic mixtures. Bahadur also provides extensive information about commercial dyes used in guest-host displays 1161. Attempts have been made to synthesize liquid crystalline dyes that exhibit both liquid crystalline and dichroic dye properties [46, 711. A few organometallic dichroic dyes have also been reported [72]. Some polymeric liquid crystals having light-absorbing groups have been reported [ 161. These can behave like a dichroic polymeric liquid crystal [ 161. Some dichroic dyes are also found to form a lyotropic liquid crystal phase [73]. However, they are not important for display applications. The vast majority of dichroic dyes used in LCDs are elongated in shape, and they more or less adopt the ordered arrangement of the host liquid crystal and exhibit
cylindrical symmetry. It is worth mentioning that many dichroic dyes, drastically differing from rod-like structure, have been synthesized, especially by Ivashchenko and Rumyantsev [4]. The color of the dye is basically dependent on the chromophoric and auxochromic groups present in the dye molecule. The angle of the transition moment of the dye determines whether the dye would be pleochroic or negative dichroic. Usually only one peak absorption wavelength (Amax) is observed. However, some dichroic dyes exhibit two or more peaks. Some of these dyes can exhibit both pleochroic and negative dichroic absorption bands [46]. Some prominent auxochromic groups are OH, NH,, NR,, NHR, NO,, C1, Br, F, -S-C,H4-R, and -S-C6H,,-R. To make a good black dichroic mixture, dichroic dyes in three colors (such as yellow, blue, and red; or magenta, cyan, and yellow; or violet, green-blue, and orange) with high order parameter, solubility, photostability, and absorption are required [ 161. Major efforts have been made in synthesizing these types of dichroic dye. Azo dyes with reasonable photostability can provide only red, orange, and yellow colors. Similarly, earlier anthraquinone dyes used to generate only blue, violet, or red colors. The photostability of dichroic dyes is one of the most important considerations for their use in LCDs [16,43-46,49, 62-67]. The photostability of many classes of dye is not sufficient for display applications [46, 64-66], this being particularly true for monoazo dyes with triazole and benztriazole rings, as well as bis(azo)dyes with theophelline and naphthalene fragments [46]. Monoazo and bis(azo) dyes without triazole and benztriazole rings have a sufficiently long lifetime [46]. Anthraquinone dyes are much more stabe than azo compounds. Naphthoquinone dyes have a photostability
Commercial Code
D35 D43 D46 D52 D54 D77
1.3 I .4 I .5 1.6 1.7 1.8 1.9 1.10
550 R, = ‘C,H~, R3= H, R, = tC4H9
R,=‘c,H~,
1.15
554 557 556 546 524 558
596 612
550
R=H Rxp-CH,
R=C,H, R=OC,Hl I R=OC,H,, R =N(CH3), R=N,C6HS R=CH(CH,), R = C6H, R =C,H,C,H,
R=OC,H,9 R=N(CH,),
L a x
(nm)
RI=H, R,=H, R3=H, R,=H
H2N 0 NH2
0 OH
drR
Structure
1.14
1.12 1.13
1.1 1
D16 D27
1.1 1.2
Antraquinone dyes
Dye No.
Table 1. Examples of various types of dichroic dyes and their physical parameters.
0.78
0.80
E43 (3.0%)
E43 (0.8%)
E7 E43 ZL1 1691 MBBA EN 24 ROTN 101 E 43 EN 24
0.7 1 0.76 0.78 0.31 0.52 0.56 0.68 0.65 0.79 0.80
E7 E7 E7 E7 E7 E7 ZLI 1132 ZLI I132
E7 E7
Host (solubility)
0.67 0.68 0.69 0.65 0.71 0.68 0.80 0.90
0.65 0.63
Order parameter
m
t 4
0
tl w
LCD 109
1.16
G 241
1.22
1.24
I .23
G 207
NC-@CH=N
C3H70-@
e
N= N*N=
CH3 CH3
N = N -@N
CH3
[email protected]~H~
N e C 4 H 9
N-
N = N*-N=
=N-@N<
1.20
1.21
& N = N * N = N e N = N G
1.19
N-@N
N = N+N=
1.18
@N=
@-N=
N-Q
Structure
1.17
Azo dyes
Commercial Code
Dye No.
Table 1. (continued)
n
L a x
455
566
39 1
500
400
359
450
(nm)
0.67
0.756
0.791
0.67 0.74 0.75 0.78
0.64
0.62
0.37
Order parameter
ROTN 101
ZLI 1840 (>3)
ZLI 1840 G-3)
E3 E7 E8 E9
E7
E7
E7
Host (solubility)
N Q\ N
3.4.2
263
Dichroic Dyes
r-
0 00
Y
8
r-
m
c?
N N
r-c: 0 0
c: 0
0
0 I
10
m
00
In
0
d
m
r-
+
-
I:
z 0
*i0 Q,
=* u
I
0 0 =v I
I
r -2
0
T
0
v =o
0
2
0 Q,
5 u
m N
-
0
-
3
-
c?'?
N
c?
264
3.4
Guest-Host Effect
0
zi m
m
vl
* c1
v, d
P
6
=4
€ Z = X
\?
"\
ir-n
r-n I
Q,
i-
(ri
r? 3
* r? 3
I
m r? 3
3.4.2
close to that of anthraquinone dyes [69]. Photostability of azo dyes depends on their La,,decreasing sharply with increasing Amax [49]. Only the yellow, orange, and red azo dyes have a satisfactory photostability, while the violet and dark blue mono and polyazo dyes seem to be unstable. The light degradation of azo dyes in the presence of oxygen and moisture is an oxidation reaction which generally proceeds by an attack on the azo group by a singlet oxygen molecule [64]. The singlet oxygen molecule is produced when the ground-state oxygen molecule receives the energy of the excited triplet state of the dye molecule. The photodecomposition of the dye is not only dependent on the intensity of the light source, but also on the spectral power distribution hitting the dye. Most of the photodecomposition is caused by the light with ;I< Lax of the dye. The deterioration can be reduced drastically by putting a UV cutt-off filter or just a UV barrier coating on the display [49]. Most dichroic LCDs involve glass substrates, which absorb most of the UV light. Glasses, films, and coatings having higher cut-off wavelengths (-400 nm) produce even better results. As this region has very low photopic response, the UV cut-off filters have no negative impact on the chromatic or electro-optical performance of the cell. Scheuble et al. [56] found a 20- to 30fold increase in the photostability of azo dyes by using a UV cut-off filter, giving a photostability comparable to that of stable anthraquinone dyes [56].Under this condition the photodecomposition of the dye basically takes place under the influence of visible light. The polarizers used in many dichroic LCDs also enhance the photostability, primarily due to its UV barrier coating, and secondly by reducing the transmitted light intensity to less than 50%. However, they would be effective only when the polarizer side faces the light before the di-
Dichroic Dyes
265
chroic mixture. The UV barrier coating increases the life of yellow to red azo dyes, but has little impact on the blue azo dye [49]. The photodecomposition of the dye is also dependent on the geometry and alignment in which the dichroic mixture is used. If the quiescent geometry is homeotropic with a pleochroic dye, the light absorption will be less, and consequently will lead to a longer lifetime. Although the light stability of dyes depends greatly on their structure, it is not an absolute property of the compound only [58]. It is also influenced by the compound’s environment and indeed it is a photoinduced reaction [ 5 8 ] . The lifetime of a dichroic mixture also depends on the host employed. In general, liquid crystals have an absorption edge lying above the glass cut-off which, in the absence of a dye, result in its photodecomposition [49]. A dye dissolved in a liquid crystal may be photosensitized as a result of the liquid crystal being excited. The effect of this process is to inhibit the degradation of the liquid crystal and to accelerate the decomposition of the dye. Liquid crystal mixtures exhibiting lower absorption above the glass cut-off generate longer lifetimes for dyes within them [491. In a mixture of dyes, the situation is more complex due to synergetic effects. This interaction may increase the light-fastness of the dyes, but may also have the opposite effect [ 5 8 ] . Since it is not easy to forecast how a photoinduced reactivity will develop, the correct photostability of the dye can be found only experimentally in the liquid crystal host. The excellent photostability of the anthraquinone dyestuffs are related to the introduction of a proton donor in the a-position of the anthraquinone molecule [58]. The anthraquinone molecule itself has no absorption band in the visible spectrum [46], so at least one of the 1 , 4 , 5 , or 8 (or 2,
266
3.4
Guest-Host Effect
3 , 6 , or 7) positions is occupied by a proper auxochromic group, such as OH, NH,, or NHR, to complete the chromophor system of the dye [45, 571. At the 1, 4, 5 , or 8 positions (i.e. a-positions) the introduction of two OH groups leads to a yellow dye, two amino groups generate red dyes, and two each of OH and NH, generate blue dyes [57]. These colors are affected by the bathochromic or hypsochromic elongated groups at a- or ppositions. The NH, substitutions are found to increase the order parameter, while OH substitutions decrease it. The substitution of all four a-positions by NH, group gives the highest order parameter, while substitution of all generate the lowest order parameter [58]. The order parameter drops from 0.69 to 0.53, and at the same time the hue changes from blue to red. In addition, the photostability decreases from excellent to poor [58]. The properties of the compounds between these two extremes correspond to those of their parent structures, depending on the permutations of the substituents [58].
served for some dyes. In the case of azo dyes, the long axis of the skeleton is usually the long axis of the molecule, and hence the transition moment making an angle with the skeleton usually reduces the order parameter of the dye. Before synthesis of a dichroic dye for display use, one should analyze the structure and estimate the order parameter (S), of the new dichroic dye, taking into consideration the bond lengths, valence angles, and transition moment direction. As the color of the dichroic dye is basically dependent on its auxochromic groups, proper auxochromic groups must be inserted into the molecule. Moreover, the structure has to be designed in such a way that for a pleochroic dye the transition moment should be more or less parallel to the long molecular axis of the dye. The solubility of the dye is also a critical parameter, so attempts should be made to insure that the dye chosen has good solubility in the liquid crystal. Moreover, the dye structure and the groups attached to it must have good photostability. It should be OH 0 NH,
Anthraquinone
S=0.69, blue
The auxochromic groups not only influence the color but also the angle of the transition moment in the dye molecule [46, 571. Whereas for a symmetrical substituted pattern the transition moment will be parallel (or perpendicular) to the long axis of the anthraquinone skeleton, the situation becomes quite complicated for an asymmetric substitution [74]. As the axis of alignment normally will not coincide with the axis of the skeleton, an oblique orientation of the transition moment with the skeleton axis may even be an advantage, and could provide an explanation for the high dichroic ratios ob-
S = 0.6 1, blue-violet
O H 0 OH
S=0.53, red
clearly understood that the change incorporated in the chemical structure of the dye to improve one property affects all the other properties simultaneously [ 16, 581. This is the reason why it is so difficult to produce a high-quality dichroic dye that satisfies most of the requirements.
3.4.3 Cell Preparation Cells are prepared by standard methods, as discussed by Bahadur [75, 761 and Morozumi [77]. For homogeneous alignment, poly-
3.4.3 Cell Preparation
vinyl alcohol, polyimide, obliquely evaporated SiO, and appropriate phenylsilane compounds are used [ 16,75-801. For homeotropic alignment, long-chain alkyl silane (such as steryltriethoxy silane), lecithin, specially formulated polyimide (such as RN-722 from Nissan Chemicals), or long-chain aliphatic chromium compounds, are used [ 16,75 - 79,8 1, 821. RN-722,being a polyimide material, provides a durable and strong homeotropic alignment. The homeotropic alignment achieved by silane compounds are not very stable, especially with regard to heat, humidity, and thermal cycling. After filling and end-plugging, the cell should be heated to the isotropic state and then cooled to room temperature to eliminate flow alignment defects. The structures of various dichroic cells are described in later sections. Most of the commercial dichroic displays use unidirectional homogeneous alignment produced by unidirectionally buffing the polyimide [ 16,75-80],as the latter is reliable, durable, low cost, and easy to apply. These displays include Heilmeier displays (negative mode), dye doped TN, ferroelectric dichroic, A/4dichroic, phase change dichroic, etc. For cases such as positive mode phase change dichroic displays using a dichroic mixture of negative dielectric anisotropy [12,13,15,161,homeotropic alignment [78,79,81,821 is required. For positive mode Heilmeier displays, which use homeotropic alignment and a pleochroic dye mixture in a negative dielectric anisotropy host, tilted homeotropic alignment [ 16,831 is usually preferred. Some supertwist dichroic effect displays may require highly tilted homogeneous alignment, which can be produced either by SiO coating or special polyimide [77,78,84,851. In normal phase change dichroic LCDs, some manufacturers prefer to use homeotropic alignment to reduce the memory effect. Occa-
267
sionally, hybrid alignment (i.e. homogeneous alignment on one plate and homeotropic on the other plate) is used in phase change displays [16,861.Homeotropic and hybrid alignments are also advantageous in the sense that they allow the dichroic mixture to retain its natural pitch in the cell and not to have a forced pitch as imposed by the homogeneous alignment on both plates [ 161. For ferroelectric dichroic displays, nylon and other polyamides are also being used [801. With regard to the dye-related parameter measurements, the dye concentration is usually kept at about 0.5-2%, depending on its absorption coefficient. For azo dyes the dye concentration is about 0.25-1% for dye doped TN, about 2-496 for Heilmeier displays, and about 2-5% for phase change displays. The cell thickness is usually about 5 pm for dye-doped TN at the first Gooch Tarryminimum[15,16,88],about7-10 pm for dye-doped TN at the second Gooch Tarry minimum [15,16,881, about 5-15 pm for Heilmeier, and about 10-20 pm for phase change dichroic displays. Usually, the dye concentration is increased by a factor of about 1.5-2 when anthraquinone dyes are used instead of azo dyes, as anthraquinone dyes have less absorbance than azo dyes. Sometimes combinations of azo and anthraquinone dyes are used [16,541. The cell spacing must be made uniform in the case of phase change displays with homogeneous alignment in order to avoid the Grandjean Cano disclination lines (also called pitch lines), which are quite visible because of the stepwise change in brightness appearing across them [16,75,891. These pitch lines are also visible in the case of homeotropically aligned cells, although to a lesser extent. Polarizers, color filters, and reflectors are usually mounted outside the cell, as dichroic displays do not have very high line reso-
268
3.4 Guest-Host Effect
lution. Color filters can be mounted inside the cell using normal materials (such as polyimide, acrylic, or gelatin-based color filter materials) and techniques used for TN LCDs [75 - 771. Efforts have also been made to develop internal reflectors [16, 901, but these are found to be inferior to external ones. For external reflectors in White-Taylor mode LCDs, BaSO,, Ti02,Melinex, and Valox (GE) films, etc., are used [91].
3.4.4 Dichroic Parameters and Their Measurement A dichroic mixture is basically a homogeneous mixture of dye(s) in a liquid crystal host. The various physical properties of dichroic mixtures are dependent on the physical properties of the dyes, the host, and their combination.
Figure 2. Geometrical relationship of a dye with its transition moment, the liquid crystal, and polarized light.
3.4.4.1 Order Parameter and Dichroic Ratio of Dyes The director of dyes in the host liquid crystal coincides with the director of the host, n. However, the direction of each dye molecule deviates from the director due to thermal fluctuations, in same way as individual liquid crystal molecules deviate from their own director [42,43]. The impact of thermal fluctuation may be different on dye and liquid crystal molecules, depending on their molecular lengths and geometries. The long molecular axes of the liquid crystal L, and the dye D , molecules make angles of 8 and @, respectively, with the director n,as shown in Fig. 2. The order parameters of the liquid crystal S, and dye S , molecules determined from the distribution of their long molecular axes are given by:
s, =
(3 COS2 8 - 1) 2
where (cos’8) and (cos2@)are the averages of cos28 and cos2@,respectively. The difference between 8 and @ is one of the reasons for the difference in the order parameters between the dye and the liquid crystal host. The main criterion for dichroic dye efficiency is the order parameter of the transition moment of the dye absorption S,, which is responsible for the color and absorption of the dye [14, 16,461. It must be clearly understood that the value of ST may differ from the order parameter of the long molecular axis of the dye SD. This is the case when the transition moment of the dye makes an angle with its long molecular axis. If the transition moment makes an angle & (not shown in Fig. 2) with the director of the liquid crystal, then by analogy with
3.4.4 Dichroic Parameters and Their Measurement
(2) If we assume that the direction of the transition moment, T, of the dye deviates from its long molecular axis D, by an angle p, the absorbance A of the incident polarized light, the electric vector P of which makes an angle ly with the director n, is given as [14,431 A ( P , l y ) = kcd [(?)sin'/i
+
(T) 1-s,
(3)
where k is the magnitude of the transition moment, and c and d are the concentration of the dye and the thickness of the liquid crystal layer, respectively. The dichroic ratio D is expressed as the ratio of the absorbance at y=O" and ly=90':
(4) The order parameter STof the transition moment is determined experimentally as:
269
ative dichroic dyes the transition moment order parameter is only half of that for a pleochroic dye. With OoIp<54'44'8'', S,>O and the dyes are pleochroic, while with p > 54"44'8", S, < 0 and dyes are negative dichroic dyes. The dyes with ST=O(p= 54'44'8" with $=Oo or p=0°1900 with $=54"44'8") are called 'phoney dyes,' because their optical densities A , , and A , are equal in magnitude [46]. For elongated pleochroic dyes, p is extremely small, or zero, making sinp almost negligible, and hence S,=S,. The order parameter measured by absorption measurements is always the order parameter of the transition moment of the dye, which is often referred to in the literature as the dye order parameter S. Hence, from here on we will use the symbol S for the dye order parameter or its transition moment order parameter ST. It is worth mentioning that Osman et al. [74] found theoretically that, in planar dyes, such as anthraquinone, the order tensor deviates strongly from cylindrical symmetry. The direction of the optical transition moment does not, in general, coincide with one of the principal axes of the order tensor. Based on their calculations they found that only those anthraquinone dyes that have a small angle between the transition moment and the molecular axis show a good dichroic ratio [74].
Using Eqs. (4) and ( 5 ) we get
3.4.4.2 Absorbance, Order Parameter, and Dichroic Ratio Measurement
From Eq. (6) it is clear that ST/SD decreases significantly as p increases, and hence p should be as low as possible in order to increase the dichroic ratio. One can also see that for p=Oo, ST=SD,while for p=9Oo, ST=-SD/2, which indicates that for the neg-
The dichroic mixture is put into cells having unidirectional homogenous alignment. A similar compensating cell is filled with the host liquid crystal. These cells are placed in a double-beam spectrophotometer and, by placing two identical high efficiency polarizers either parallel or perpendicular to the alignment direction, A , ,(absorption parallel to the long axis of the dye) and A , (ab-
270
3.4
Guest-Host Effect
the rub direction of the cell filled with pleochroic dye mixture having positive dielectric anisotropy, and then measuring the absorption in the quiescent (A,,)and fully excited (A,) state. However, A, obtained by this method results in a slightly higher value (Fig. 3) due to the absorption by the unoriented layers in the close vicinity of the glass surface. The order parameter Seffof a dye with a very wide absorption spectrum, or a black dye, can be calculated using Eq. ( 5 ) ,but the dichroic ratio is then evaluated over the whole visible spectrum:
sorption perpendicular to the long axis of the dye) are measured 1421. The reference cell compensates (and hence corrects for) the losses due to scattering, reflection, transmission, and polarization from the cell walls and host molecules [42]. The order parameter of the dye is calculated from the expression:
In the above expression the effect of the internal field is not taken into account. The correction to A,, and Al (or TI,and Tl) yields a slightly different value for the order parameter [42]:
andA,,(A)andA,(il) are the parallel and perpendicular absorbance of the dye at wavelength A. !A,,(A) dil and !A,(A) dA can be evaluated as the area under the absorbance curves in the 380-780 nm region; S,, and D,, provide the averaged values over the whole visible range. To account for the photopic response of the human eye for color [75], we may define the photopic order pa-
Usually the absorption (or transmission) spectrum is run and recorded in parallel or perpendicular geometry over the range 380-780 nm. From these measurements Amax,All, andA,aredetermined [42].A,,and A, are measured at A,, . Unless specified, the order parameter is usually calculated at Amax. A,,(A)and A,(& have also been calculated by keeping the polarizers parallel to
0.5 0.0
400
500
600 Wavelength (nm)
700
800
Figure 3. The absorption spectrum of a dichroic dye in a liquid crystal host.
3.4.6 Optical, Electro-Optical, and Life Parameters
rameter (S),
and the dichroic ratio (Dph)as:
and V ( A )is the value of photopic luminosity efficiency function at wavelength A. For these absorption and transmission measurements, polarizers must have extremely high polarization efficiency (as close as possible to loo%), otherwise the values of Seffand D,, will be too low, and even misleading in a few cases. Polarizers HN 32 or Sanritsu 9218 are good for this purpose [92]. Moreover, as the order parameter is temperature dependent, all measurements should be recorded at the same temperature. It is worth mentioning that, to obtain accurate results, the spectrometer beam should not carry any polarization. Unfortunately, however, most of them do. The absorbance measurement of a black dichroic liquid crystal mixture over the wavelength range 380-780 nm is shown in Fig. 3.
3.4.5 Impact of Dye Structure and Liquid Crystal Host on the Physical Properties of a Dichroic Mixture These parameters have been discussed in detail by the author and several other workers [14- 16, 42-49]. Studies have been done mostly on pleochroic dyes. In general, it has been found that the dye order parameter increases with increasing length of the dye, while it decreases with increasing breadth of the dye. The dye order parameter is heavily dependent on the host. Usually it increases with an increase in and decreases with a decrease in the host order parameter. Elongated dyes are found to have
27 1
higher order parameters, and shorter dyes lower order parameters than the host. Elongated dyes are also found to withstand thermal fluctuation better at higher temperature, and hence show less variation in order parameter compared to the host, with increase in temperature. The temperature range of a dichroic liquid crystal mixture is basically governed by the temperature range of the liquid crystal host. It has been noted that the addition of dichroic dyes increases or decreases the clearing point of the mixture slightly (-1 - 5 " C )depending on its compatibility with the host liquid crystal. The solubility of a dye depends greatly on its structure and host. In a multicomponent system (especially black dyes), the solubility of one dye is affected by the presence of others. Asymmetrically substituted dichroic dyes are found to have higher solubility than their symmetric analog [48]. The introduction of lateral alkyl substituents in dichroic dye molecules enhances their solubility in liquid crystals. An admixture of dichroic dyes absorbing in the same spectral range usually has higher solubility than does a single dye. The viscosity of host increases with increase in dye doping. The dielectric anisotropy, elastic constants, and refractive indices of dichroic mixtures are basically those of the liquid crystal host [ 161.
3.4.6 Optical, Electro-Optical, and Life Parameters As dichroic displays provide a man-machine interface through human eyes, their features and parameters must be optimized for human vision requirements [75]. For a clear understanding and detailed description of human vision, color and its measurement, visual requirements, and reliability issues of LCDs, the reader is referred to the article by Bahadur [75]. Some of the issues
27 2
3.4 Guest-Host Effect
related to dichroic displays are discussed very briefly here.
3.4.6.1 Luminance Luminance is the most important photometric quantity to define display performance. However, the perceived brightness does not bear a linear relationship with luminance, and depends also on the ambient lighting, the surroundings, etc. Luminance is usually measured with radiometric equipment using photopic filters or computer-controlled corrections for photopic response. The legibility of a character is not dependent entirely on contrast but also depends on luminance, the cone it forms on the retina, the color, background, etc. [75, 931. The sensitivity of the human eye to luminance discrimination (AL/L), and hence to the contrast between the pixel and the background, increases with increasing luminance level up to 100 Cd/m2 and then saturates [75]. Hence, for legibility of a display, luminance as well as contrast should be resonably high. A high luminance dichroic display with less contrast often looks better and more legible than a similar display with high contrast but very poor brightness or luminosity.
The background luminance can be taken to be either the luminance of the activated segment in its off mode or the luminance of the electro-optically inactive portion of the cell. Usually there is a small difference between the contrast in these two situations, which is neglected in most applications [75]. However, if the segment shows memory or reminiscent contrast (such as in the case of the phase change dichroic display) the value of the contrast calculated using these two procedures may be drastically different. The contrast ratio may be time dependent too. In the case of LCDs the contrast ratio is found to depend on the viewing angle and temperature. Dichroic LCDs exhibit a smaller reduction in contrast versus viewing angle compared to TN LCDs. In the case of dichroic (especially monochrome) displays, the contrast ratio is sometimes measured at Amax, which shows the maximum capability of the dye but does not correspond to the photopic response. The contrast ratios calculated using the radiometric equipment (or in arbitrary units of radiance) also differ from those evaluated using photometric equipment. Bloom and Priestly [94] therefore defined the perceived contrast ratio (PCR):
3.4.6.2 Contrast and Contrast Ratio The luminance contrast may be defined as the ratio of the difference between the symbol and background luminance, AL to the luminance of the symbol (or background, whichever is more luminous), i.e.
C=-AL L
The contrast ratio is defined as the ratio of greater luminance L,,, to lesser luminance Lminbetween the symbol and background. CR=- L a x Lin
where T'(A) and T,,(A)are the percentages of the light transmitted in the on and off states, respectively, and V(A) is the photopic luminous efficiency function. This equation is basically the same as Eq. (12) if the light intensities are measured in luminance (i. e. photopic response). Color is a combination of both chrominance and luminance, and hence to deter-
3.4.6 Optical, Electro-Optical, and Life Parameters
mine the contrast and contrast ratio of any colored pixel both these parameters must be used. However, there is no simple, exact, quantitative criterion for color that can be applied to color contrast in terms of legibility [75]. Some measurements have been reported in terms of color difference and color contrast [75].A more valuable approach would be to quantify the display’s visual performance with regard to its perception, from a human vision point of view [75].The threshold levels of luminance and chrominance detection are dependent on luminance level, target shape and size, search patterns, background, and other human vision parameters [75, 951.
3.4.6.3 Switching Speed The switching times of the LCDs are defined in the article by Bahadur [75].The rise and decay times Triseand Tdecayare given by the general equation [96]
T=
17
E~ A&E2 - kq2
where 17 is the viscosity, A& is the dielectric anisotropy, k is the appropriate elastic constant, E is the applied electric field, and q is the wave vector of the disturbance. The wave vector q can be expressed as q = -It
P where p is the pitch of the disturbance. In the case of cholesteric materials, q is the wave vector of the cholesteric helix and is also field dependent. Here p is the pitch of the material. In the absence of the field q=qo=n/po, where p o is the pitch in the quiescent state. In TN, dye-doped TN, and Heilmeier displays, where the decay time is determined by the propogation of the alignment from the cell walls, q will take the value of nld, where d is the cell
273
spacing. Hence,
Trise . =
17 d 2
E~ A&V 2- kIt2
and
where V is the applied voltage. Besides the rise and decay times, displays also exhibit turn-on and turn-off delays. The general equation (Eq. 15) becomes less accurate for the cholesteric -nematic transition, in as much as the reorientation to nematic is dependent upon the character of nucleation sites for the transition such that:
where B characterizes the nucleation sites, and is roughly a function of the inverse of the concentration of chiral material in the nematic host. Over a small range of pitch, the rise time is a relatively linear function of p-’ . Unlike the twisted nematic, the turnoff time of the cholesteric configuration becomes dominated by pitch rather than cell spacing as a result of the effect of the pitch on q . So phase change dichroic LCDs should have a much faster decay compared to TN displays. However, due to memory or reminiscent contrast the actual turn-off time perceived by the eye in the case of phase change dichroic LCDs is much slower than the predicted turn-off time. Cells having less memory, especially those formed with homeotropic or hybrid alignment, seem to have much faster turn off.
3.4.6.4 Life Parameters and Failure Modes As many of materials and processes are common to both dichroic and TN LCDs, most of the failure modes and defects observed in TN LCDs are also observed in
274
3.4 Guest-Host Effect
dichroic LCDs [16, 751. The defects and reliability issues in dichroic LCDs are basically related to the materials (such as dichroic mixture, glass, surface alignment, peripheral and end-seal, color filter, connectors, heater, polarizer, reflector, etc.) and their deterioration in adverse operating conditions (such as high temperature, intense light exposure, humidity, thermal shock, vibration, etc.). Even mild operating conditions over a period of time can have accumulated effects in certain types of defect. Some of these are blooming pixels, contrast loss due to dye bleaching, increase in power consumption, voids and air bubbles, and dye segregation. These, along with many others, have been discussed in the case of TN as well as dichroic LCDs by Bahadur (75) in an article that also includes a discussion of LCD failure modes, their causes, reliability, accelerated life testing and other life parameters of dichroic LCDs. The thickness nonuniformity, besides creating nonuniform contrast and switching, also creates annoying pitch lines, as discussed in Sec. 3.4.3. One noticeable defect in dichroic displays used in military and avionics applications, especially in deserts (high temperature, vibrations, and intense light) over a prolonged period is the development of gas bubbles in the displays [16]. This problem has been overcome to a great extent by cutting the light up to 400 nm by using appropriate glasses and filters. The problem of vacuum voids observed at low temperature is caused by the different coefficient of thermal expansion of liquid crystal and glass [75].
3.4.7 Dichroic Mixture Formulation Dichroic mixtures are usually formed in monochrome or black form. Dyes are mixed into the liquid crystal, and the mixture is
heated to about 10°C above its clearing point for sufficient time to dissolve the dyes completely. The dye concentration should be kept well below its solubility limit at the lowest required operating or storage temperature. If the dyes are near their saturation limit, their chromatographic separation during filling of the cell is observed more frequently. Usually the least soluble dye segregates first and acts as a nucleation center for further crystallization over time. The mixture should be degassed before use and should be kept under dry nitrogen or helium. A good method for degassing is a process where the surface area of the fluid is increased while applying ultrasonic agitation and heat simultaneously during degassing under high vacuum [97]. The absorption spectra of the dyes are found to be shifted when mixed in liquid crystals. The nature and the amount of the shift depends on the dye, its amount, and the liquid crystal mixture. Many monochrome and black dichroic mixtures are available commercially [54].
3.4.7.1 Monochrome Mixture Single dyes are usually used for forming monochrome mixtures. Sometimes it is necessary to mix two or more dyes to get a monochrome color if the color cannot be obtained with the desired properties by using a single dye. For example, a green dye can be obtained by mixing a yellow and a blue dye.
3.4.7.2 Black Mixture To make a black mixture, many dichroic dyes covering the whole visible spectrum are required [55-581. Besides the desired Amax and color, the three important criteria for choosing the dyes are their stability, solubility, and order parameter. Broad spectral band dyes are preferred over narrow band dyes.
3.4.8
Any given color can, in principle, be matched in two different ways: by spectral color matching or by metameric color matching [16, 5 5 , 931. In spectral color matching, colorants are mixed to reproduce the transmission (or reflection) spectrum of the given color. Spectrally matched colors have the advantage of staying matched under all conditions of illumination. However, they may require a large number of colorants to fit the spectrum. In the case of dichroic dyes the situation becomes a bit complicated as we require color matching in both quiescent and energized modes. In metameric color matching, dyes are mixed to achieve only the same sensation of the color to the human eye, and the resulting spectrum may be quite different than the original color [ 16, 55, 931. Any color can be matched metamerically using only three colorants. However, this color match is generally satisfactory only for one type of illumination. In dichroic display applications the color matching is usually done using 4-8 dyes. Efforts are made to achieve spectral matching of the colors as closely as possible in the quiescent state by using available dichroic dyes with high order parameter, photochemical stability, and solubility. Some tweaking is done to obtain finally the desired hue in the one state under given lighting conditions. It is extremely difficult to get exactly the same color matching in both the on and off states using different dyes from those contained in the specimen for all lighting conditions. For normal applications only two lighting conditions are required: one for daylight and one for nighttime applications. Usually incandescent lamps (source A) are used for phase-change type dichroic displays for night vision. For night vision goggle applications, commonly required in avionic displays, one has to filter out the infrared and most of the red light [98]. This can be done by using a fil-
Heilmeier Displays
275
ter. In large area displays the use of cold or hot cathode fluorescent lamps is becoming popular. Sometimes a minor correction for the desired chromaticity is done by using appropriate color filters behind the displays. To match the hue of a given dichroic mixture one can use a computer program [55, 561, or sometimes it can be achieved by 'tweaking' the existing mixture. In this case the absorption of both mixtures should be recorded using the same light source (or UVvisible spectrum) and the difference in the absorbance curves in various regions should be minimized by adjusting the dyes. The close spectral matching results in a close hue matching under various illuminations. Minor 'tweaking' may be required to match the on state chromaticities.
3.4.8
Heilmeier Displays
The Heilmeier display was the first dichroic display discovered [l-31 and can be made in transmissive, reflective, and transflective forms by appropriate choice of the reflector. However, these displays are used mostly in transmissive mode with a strong backlighting. Conventional Heilmeier displays use unidirectional homogeneous alignment and can be made with 0" or 90" twist [ 1, 2, 13- 161. The host liquid crystal has a positive dielectric anisotropy and the dyes are pleochroic. A Heilmeier display uses one polarizer mounted with its polarization axis along the long molecular axis of the dichroic mixture. The polarizer can be mounted on the front or the back of the display. The light, after passing through the polarizer, is polarized with its E vector along the long molecular axis of the dye and is absorbed. The cell looks dark colored or black depending on the dyes used. When the electric field is applied, the liquid crystal molecules, along with the dyes, become
276
20 l o0
3.4 Guest-Host Effect
c
TN display becomes saturated and achieves maximum contrast at lower voltage and its threshold characteristic is steeper compared to that of a Heilmeier display. In TN display the contrast ratio remains flat after saturation, while in Heilmeier displays the contrast ratio continues to increase with increasing voltage after becoming almost saturated. The reason for this is that TN LCDs are based on the capability to rotate plane polarized light and, once the central layer is aligned with the field, it is unable to rotate the plane of polarization of the light, and the display becomes full contrast. The contrast in a Heilmeier display is based on the alignment of more and more dichroic layers in the direction of the field. The central layer quickly becomes aligned after the threshold voltage, but layers in the vicinity of the glass plates are aligned more and more only with increasing field. Figure 4 also shows that for an optimized cell thickness both the contrast ratio and brightness are lower for Heilmeier displays than for TN displays. The contrast of a Heilmeier display can be made equal to or more than that of a TN display by increasing the amount of dyes in the mixture, but the transmission decreases drastically [ 15, 161. If transmission is matched, then the contrast ratio of the Heilmeier display decreases [ 15, 161. With increasing viewing angle both the contrast and transmission decrease drastically in TN displays, while these are little affected in Heilmeier displays (Fig. 5 and Table 2). Hence Heilmeier displays have a much wider viewing angle than do TN displays.
1
0
I
1
2
/
3
4
5
5
7
VOLTAGE ( V )
8
9
1
Figure 4. Threshold characteristic of Heilmeier display compared to those of a TN and a dye-doped TN display. The transmittance of the Heilmeier, dyedoped TN, and TN displays are 16.0%, 26.7%, and 35.5%, respectively. Operating voltage, 10 V.
aligned in the direction of the field. In this mode, the E vector of the light is perpendicular to the long molecular axis of the pleochroic dye, and light is not absorbed. The operational principle of Heilmeier displays is shown in Fig. 1. Although doping of the dichroic mixture with a chiral material is not necessary, occasionally (especially for 90" twist geometry) this is done. Heilmeier displays can also be made with (1) negative dichroic dyes in a liquid crystal host of positive dielectric anisotropy, or (2) pleochroic dyes in a host of negative dielectric anisotropy. These methods generate colored or black information on a clear background (see Sec. 13.1). The discussion below applies primarily to Heilmeier displays using pleochroic dyes in a host of positive dielectric anisotropy. The theoretical model for Heilmeier displays was proposed by many workers [16, 99, 1001.
3.4.8.1 Threshold Characteristic The threshold characteristic of Heilmeier displays and that of TN displays having the same polarizer and host liquid crystal are plotted in Fig. 4.The figure shows that the
0
3.4.8.2 Effects of Dye Concentration on Electro-optical Parameters With increasing dye concentration c , the contrast ratio of the Heilmeier display increases and its transmission decreases
3.4.8 Heilmeier Displays
277
Table 2. Contrast ratio and percent transmission of Heilmeier, dye doped TN, and TN displays versus viewing angle [16]. Viewing angle (")
TN
- 60 -54 -48 -42 -36 -30 - 24 -18 -12 -6 0 6 12 18 24 30 36 42 48 54
-60
-50
-40
Dye-doped TN
Heilmeier
T (70)
CR
T (%)
CR
T (%I
CR
24.2 27.2 30.1 32.8 35.1 36.8 37.7 38.6 38.9 39.1 38.8 38.7 37.6 37.1 35.1 33.6 31.4 28.5 25.3 21.5
14.8 19.8 27.9 33.8 43.5 51.7 73.9 77.5 73.2 69.6 66.6 63.3 57.1 50.3 43.2 34.7 27.8 22.1 17.4 13.6
20.9 26.6 29.4 31.7 33.6 35.3 35.8 36.8 36.5 36.8 36.8 36.4 35.6 34.2 33.2 31.4 29.7 27.1 24.0 20.0
24.8 35.7 49.0 67.0 91.9 109.0 110.8 108.0 99.1 88.9 82.7 74.8 66.9 58.1 50.4 42.5 35.3 29.2 23.4 19.1
13.0 13.0 14.8 16.3 17.2 17.7 17.7 17.8 17.6 17.6 16.9 16.9 16.5 15.8 15.3 14.6 13.8 13.8 11.2 9.6
67.2 75.5 75.6 75.7 72.9 68.9 66.4 63.6 60.4 62.5 59.0 60.8 62.7 62.9 63.9 69.0 69.0 70.3 68.1 63.1
-30
-20
-10
0
10
20
30
40
50
60
Figure 5. Contrast ratio versus viewing angle for Heilmeier, dye-doped TN (DDTN), first-minimum TN (FMTN), and second minimum TN (SMTN) LCDs.
Viewing Angle (degrees)
[ 15, 16, 1001. The switching time of the dis-
play also increases a little due to the increase in viscosity of the liquid crystal. This increase in switching time becomes more significant at lower temperatures and very often restricts the lower operating temperature of the display. The threshold voltage does not seem to be affected significantly by
an increase in dye concentration. Figure 6 shows the dependence of electro-optical parameters of a Heilmeier display on the dye concentration. It can be seen that the contrast ratio increases exponentially with increasing dye concentration, while the transmission shows a more or less linear decrease. This means that with a small increase
278
3.4 Guest-Host Effect 40
180
160
sH 4
U
5 U
8
140
g
8
30
120 100
20
80
P4 2
60 10
40
Figure 6. Dependence of the constrat ratio and the percent transmission of a Heilmeier display on the dye concentration.
20
0
1
2
3
4
5
DYE CONCENTRATION(%)
in dye concentration one can get a high contrast without a heavy loss in transmission.
3.4.8.3 Effect of Cholesteric Doping A doped dichroic mixture (0.15%cholesterylnonanoate) produces an esthetically better cell, especially with a 90" twist, as it is free from reverse twist patches. There is little change in contrast or transmission, but the turn-off time To, without cholesterylnonanoate was found to be about 15%shorter (-50 ms instead of 60 ms).
20
8 5
5
3 -1
r
18 -
16-
141
2
~
10-
8 6 -
C
2
4
6
8
10
12
14
16
VOLTAGE ( V )
Figure 7. Threshold characteristics of Heilmeier displays with 0" and 90" twisted homogeneous alignments.
3.4.8.4 Effect of Alignment The 90" twisted Heilmeier cells have sharper threshold characteristics and higher transmission than the parallel aligned versions (0" or 180") (Fig. 7). This can be explained by referring to Fig. 8 [13, 15, 161. In the field-off state the twisted layer absorbs nearly the same amount of light as the parallel aligned (or nontwisted) layer, as within the Mauguin limit the optically polarized mode propagating through the layer departs only very slightly from the linear polarized mode. The major axis of the ellipse follows very nearly in step with the twisted structure, and consequently remains more or less parallel to the optical (absorbing) axis. In the field-on state, however, the twisted layer
absorbs significantly less light than the nontwisted layer. The reason for this is that the orientation of the optic axis in the boundary region 2' on the lower substrate of the twisted cell is at right angles to the E vector of the polarized light and is, therefore, nonabsorbing. The transmission curve for the twisted Heilmeier display is much steeper at intermediate voltages than for the nontwisted layer, but the approach to saturation remains gradual at higher voltages because the upper boundary region 1' still absorbs the light. The threshold characteristic of 90" twisted Heilmeier cells is quite sharp from V,, to V,, (or V6& indicating that low-level multiplexing is possible. The nontwisted,
a)
-
-
-
-
Conventional Heilmeier
Incident Polarization
I---)
0
Transmitted Polarization Field Off
b)
Heilmeier Displays
279
Twisted Heilmeier
90"
0
0 0
3.4.8
Field On
II
0
-
0
U
0
Field Off
Field On
Figure 8. Molecular orientation in 0" and 90" twisted Heilmeier cells.
or 0" twisted, structure exhibits a higher contrast ratio compared to the 90" twisted structure, and is better suited for gray scale applications with TFTs. The isocontrast curves for 90" twisted and parallel aligned versions are shown in Fig. 9. The 180" twisted Heilmeier displays show switch-off behavior similar to n-cells. It takes a long relaxation time to return to the quiescent state after a very fast decay to an intermediate level. This long relaxation is undesirable, and a 180" Heilmeier shutter can function reasonably only after using a holding voltage similar to that of n-cells.
tioned earlier, due to strong surface anchoring, the molecules near the surface do not align with the field. So, even in an excited state, this layer d, is absorbing and therefore reduces the overall contrast of the display. The ratio of this inactive layer 2 d, to the active central layer d - 2 d S , which can be aligned by the field, should be kept small. The switching speed of the display is affected adversely with increase in thickness, as it is proportional to the square of the thickness (see Eq. 15).
3.4.8.5
As predicted from theory, the order parameter has a dramatic impact on the contrast ratio (Fig. 11). The order parameter of the dye is the only parameter that increases both the contrast ratio and the transmission simultaneously. Figure 11 shows that for a good Heilmeier display the dichroic order parameter should be as high as possible (preferably >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
3.4 Guest-Host Effect
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
3.4 Guest-Host Effect
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: AAln, ( 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
3.4 Guest-Host Effect
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/p<2), the departure of the experimental curve from the theoretical values for the threshold characteristic shows the impact of increasing surface alignment with larger pitch [12, 161. For a value of dlp below a critical value for homeotropically aligned sample, the effect of boundaries is so strong that the critical voltage is zero and a homeotropic nematic structure is obtained [ 1201.
3.4.11.2 Contrast Ratio, Transmission, Brightness, and Switching Speed The impact of the other parameter and pitch on To, is shown in Fig. 17 [108]. It can be seen that To, is less for dyes having higher order parameters. The impact of the order parameter on To, becomes very significant at smaller pitches. For a very large pitch the elliptical waves are converted into linear ones, thereby reducing the absorption of the o-wave, and consequently the contrast. When the pitch is small, the dyes absorb more, yielding a higher contrast. Whenp becomes equal to A/rze,the values of a,and oc, become equal, and light propagates in circularly polarized mode. However, this increases the operating voltage drastically.
S
0.70
0.75
0.80
n,, = 1.77 nL =1.53
0 . 0 1 ” I ’
0
2
I ’ I 4 6 PITCH (rm)
‘
I
0
”
10
Figure 17. Semilogarithmic plots of the transmission To, in Grandjean texture at 550 nm versus the pitch as a function of the order parameter for field-on transmission of 50% and nll and n, of I .77 and 1.53, respectively. (After Cole and Aftergut [ IOS]).
So, one has to make a compromise between contrast and operating voltage. The light is significantly elliptically polarized in normal White-Taylor mode LCDs, as p is kept moderately large (much more than Bn,) in order to reduce the operating voltage and memory. The impact of birefringence on the contrast ratio can be seen from Fig. 18 [ 12, 15, 1081. This figure also shows the impact of the number of turns of the pitch (d/p) on the contrast ratio. The curve shows that a low birefringence material attains saturation of the contrast ratio with a low number of turns or with a low cholesteric doping. Hence, a lower value of An would also be preferable from an operating voltage point of view. Figure 18 also shows that the contrast ratio increases with an increase in the number of
288
3.4 Guest-Host Effect
d
NEUTRAL DYE R 1 6 . 7
I
I
I
2
I
3
NUMBER OF TURNS
I
4
-
turns of the cholesteric in a fixed cell thickness. For practical devices, a thicknesdpitch ratio of 4-6 is found to be more than adequate for dichroic mixtures having a birefringence of about 0.13 in a cell gap of about 10- 15 pm. The contrast ratio of a dichroic display can be increased by putting more dyes in the mixture. However, this decreases the brightness of the display and it looks dull. With increasing concentration of a black dye, the contrast ratio increases while the brightness of the display is reduced [ 12, 161. However, for single dyes the contrast ratio increases and becomes saturated. In fact, with a dye concentration above this saturation point, the contrast ratio starts to decrease for monochrome dyes. This surprising behavior is a general phenomenon for a dye that has practically no absorption in a wavelength region where the eye is still sensitive [12, 161. An extremely high concentration of any such dye would give a contrast ratio near 1.O. The impact of host birefringence and the number of helical turns on the contrast ratio of the display is illustrated in Fig. 19. The fact that these curves are nearly straight
I
5
I
6
Figure 18. Dependence of the contrast ratio on the number of turns of the cholesteric helix in the layer for different host birefringence An. (After Scheffer and Nehring [12]).
u)
z a
3
I-
0.2
-
anO.3
Figure 19. Curves of equal perceived contrast ratio for different numbers of helical turns and different values of host birefringence An. (After Scheffer and Nehring [ 121).
lines passing through the origin indicates that for a given cell thickness and a small enough An the contrast ratio is inversely proportional to the product pAn. For the same contrast, the operating voltage can be reduced by increasing the pitch and reducing An, as the operating voltage is inversely proportional to the pitch.
3.4.11 Phase Change Effect Dichroic LCDs
-I
289
HOMOGENEOUS
II
HOMOGtNEOUS
IW
w 300 TlMElmrJ
ZM
z-
41
v)
2-
z
I--
I 0
0
\ ' -10
1
OFF STATE TRANSMISSION
I 20
0
I
I
1
40
Dichroic displays presently used in avionics have a reflective contrast ratio of >25 : 1 and a transmissive contrast of about 6: 1 with a brightness of over 18% at a 45" viewing angle. These displays operate from -30" to + 85 "C. The low-temperature operation is assisted by a heater. Scheffer and Nehring proposed a useful index f i for selecting a host material to give lower operating voltage by combining the linear relationship of p-l versus An for a fixed contrast and the threshold voltage relationship with material parameters. I--(-)
-
1
&,,A&
An
k22
1
where kZ2 is the twist elastic constant and c0 is the permittivity of free space (=8.85 x MKS). Asf l does not include the impact of the order parameter S , or the viscosity 17 of the host on the performance of the dichroic display [15, 161, we define another parameter [ 151.
Higher values offl and f 2 would be advantageous. Usually, liquid crystals having
I 60
I
801
Figure 20. Switching speeds and memory effects in phase change dichroic LCDs in transmissive mode. The inset figures show the switching speeds on a shorter time scale.
TIME (sec)
lower An also have lower 17. Sometimes, in very simplistic terms, SLcan be replaced by T,, as nematic materials of the same family with higher T, have higher S, and the order parameter of the dye follows the order parameter of the host. The brightness of the display is found to be dependent on the reflector also. A diffuse BaSO, reflector and Melinex and Valox (GE) plastic films are good Lambertian reflectors. It has been found that bonding these reflectors on the rear of displays reduces the brightness slightly. Sometimes it is preferable to put BaSO, on another glass plate, keeping it separate from the LCD. The switching speed on the phase change dichroic cell is discussed in Sec. 3.4.6.3 and 3.4.1 1.3 (see also Fig. 20).
3.4.11.3 Memory or Reminiscent Contrast As mentioned earlier, with a slow increase in voltage the phase change display goes from a planar texture to fingerprint cholesteric and then to homeotropic nematic [12, 13, 15, 16, 1121, and vice versa when the voltage is reduced slowly. However, the
290
3.4 Guest-Host Effect
actual operating or dynamic situation produces significantly different results, as the voltage is applied or removed quickly without giving time for equilibrium conditions. With quick application of the voltage, the transition from planar cholesteric to homeotropic nematic is very fast, and no unwanted electro-optical effects are observed. However, when the excited pixel is turned off it does not decay quickly and retains a significant contrast over a long time in a few geometries, the worst being the transmissive mode homogeneously aligned sample. In this geometry, contrast decays from 100% to about 10- 15% very quickly, but it takes a long time to decay from about 15% to 0% and to merge completely with the background contrast (Fig. 20). This is a very undesirable feature as it gives the impression that turned-off segments are still partially on. The fast decay in contrast from 100% to 15% is due to a nematic to focal conic cholesteric phase transition, and that from 15% to zero is basically due to a focal conic to planar transformation. Usually it takes a long time to relax from a fingerprint to a planar cholesteric texture, resulting in an unwanted memory effect. If the scattering is high, the pixel looks noticeably excited for a long time after the voltage has been turned off. In the case of homeotropically treated phase change dichroic LCDs, the contrast from 100% to <5% decay instantaneously and then merges from 5% to zero reasonably quickly, exhibiting almost no memory. In the case of a reflective mode homogeneously aligned sample the residual level is reasonably low (<4-5%), probably due to increased absorption. Similarly, memory is completely unnoticeable in the case of homeotropically treated reflected mode displays. Some people find that the parallel boundary configuration is unsuitable for display applications because the Grandjean
texture in deactivated regions of the display is full of metastable disclination lines [12, 13, 15, 171. These disclination lines strongly scatter the incident light and give the display an objectionable ‘after image’, which persists from several seconds to several minutes after the segment has been deactivated. The cholesteric texture obtained with perpendicular boundary conditions is not a uniform texture and scatters the light very slightly. Under the microscope the entire field of view is filled with right-handed and left-handed spirals. This cholesteric texture is termed the ‘scroll texture’ and appears very much like an end-view of a bundle of rolled-up scrolls [91, 104, 105, 1121. The helix axis in this texture is still predominantly perpendicular to the glass surface in the bulk of the layers, similar to the Grandjean texture. Only the layers in the close vicinity of the glass surfaces have their helix axes parallel to the glass surface. It is noteworthy from an application point of view that the scroll texture is adopted without any significant disclinations immediately after a display element is turned off, and this structure, essentially a nonscattering scroll texture, is quite different from the highly scattering cholesteric focal conic texture that occurs at intermediate voltages. In the focal conic texture the helix axis is essentially parallel to the glass. The dichroic dyes embedded in this geometry absorb less compared to the case when they are embedded in a planar texture. The transition from fingerprint or focal conic to scroll texture is much faster compared to that from focal conic to planar. However, it has been found that homogeneous alignment generates a higher contrast ratio and is also more durable. The memory with homogeneous alignment is found to exhibit a regular pattern of peaks with the pitch of the mixture in the cells. Smaller pitches have higher peaks. The memory is also found to be strongly de-
3.4.12
pendent on the viscosity of the mixture. Low viscosity mixtures have less memory. Highly absorbing cells also seem to have less noticeable memory, as do cells with larger pitch. With proper adjustments to the cell thickness, pitch, birefringence, and viscosity one can make a very good cell with low memory using homogeneous alignment.
3.4.11.4 Electro-optical Performance vs Temperature The contrast ratio of the phase change dichroic display is found to decrease with an increase in temperature (see Fig. 22). This decrease is basically caused by the reduced absorption in the quiescent state that results from the decrease in the order parameter and pitch of the dichroic mixture at higher temperatures. The cells show faster switching speed and lower memory at higher temperature. The switching becomes slow at lower temperature due to an increase in the viscosity of the mixture, and a heater is usually required for low temperature operation.
3.4.11.5 Multiplexing Phase Change Dichroic LCDs Phase change displays are basically operated in direct drive mode. Some efforts have been made to operate them, especially the longpitch White-Taylor mode [16, 110, 1131 and positive mode nematic cholesteric phase transition with negative dielectric anisotropy host [ 16, 1211 in multiplexed mode. Efforts have also been made to drive phase change displays for high information content using special drive schemes [ I 221. These approaches did not achieve much popularity but, due to their high reflectance, there seems to be some emerging interest for their application in AMLCDs [123, 1241.
29 1
Double Cell Dichroic LCDs
3.4.12 Double Cell Dichroic LCDs A single cell guest - host nematic (with infinite or very long pitch) dichroic LCD, unassisted by apolarizer or quarter wave plate, can have a maximum contrast ratio of 2: 1 , as it absorbs only the E vector of unpolarized light parallel to the long molecular axis of the dye [ 14- 161. Even in the case of phase change transflective dichroic LCDs with reasonable reflective brightness (15- 18% at a 45" angle) [114], transmissive contrast ratio (typically 5: I to 6: 1) falls short of the requirements for many applications. To increase the contrast ratio without greatly sacrificing brightness, double cell geometry has been used. Basically there are three categories of double cell dichroic LCDs [14- 16, 21 -24, 125, 1261, nematic dichroic, one pitch cholesteric, and phase change dichroic.
3.4.12.1 Double Cell Nematic Dichroic LCD The geometry of a double cell nematic dichroic LCD [13-16, 21, 1261 is shown in Fig. 21. The liquid crystal mixture generally used is composed of pleochroic dyes in a nematic host of positive dielectric anisotropy. The first cell has a unidirectional homogeneous alignment in one direction, while the second cell has a unidirectional homo-
'on +
SURFACE LAYERS
( a ) OFF-STATE
( b) ON-STATE
Figure 21. Geometry of a double cell nematic dichroic LCD. (After Seki, et al. [22]).
292
3.4 Guest-Host Effect
geneous alignment perpendicular to the first cell. Making the double cell, using only three pieces of glass including a thin middle plate, reduces the parallax. The component of the unpolarized light parallel to the pleochroic dyes in the first cell is absorbed by the first cell, while the component of the light perpendicular to it is absorbed by the second cell. Thus, the double cell absorbs the unpolarized light very effectively in its quiescent state. On application of the voltage the dye molecules align in the direction of the field along with the liquid crystal, and hence the light, is not absorbed. The cell has a very high contrast ratio and wide viewing angle. The mixture may be either pure nematic (infinite pitch) or slightly doped nematic with very long pitch (pS-44. The cell geometries could be made either unidirectional homogeneous or twisted nematic. In 90" twisted geometry the alignment on the first surface of the second cell should be perpendicular to the alignment on the surface of the first cells. Recently, Ong [ 1261proposed a Heilmeier display having two asymmetric cells. This display has a high contrast and wide viewing angles, but low transmission. One can also use two separate Heilmeier cells with different dyes to make acomposite cell, and by controlling voltage differently a set of colors can be obtained. Two cells with different dyes and one polarizer, can also be used.
3.4.12.2 Double Cell One Pitch Cholesteric LCD The geometry is very similar to that of the double cell nematic dichroic LCD, with each cell having a single turn of cholesteric dichroic mixture [23, 241.
3.4.12.3 Double Cell Phase Change Dichroic LCD In double cell geometry [ 16, 114, 1251 two identical cells are placed together with a transflector in the middle. In reflected light or daylight mode, the cell behaves as a normal reflective cell, as most of the light (-95%) is reflected by the transflector. In daylight mode the first cells only, or both cells, are excited, while in transmissive mode both cells have to be excited together. The background in the quiescent transmissive mode looks much darker as the light is absorbed by the two layers of the dichroic mixture. When the field is applied the pixels become transmissive due to the alignment of pleochroic dyes in the direction of the field. The transmissive contrast in the double cell mode is very high (>15:1), which is good enough for almost all applications. The temperature variation of the contrast ratio of the double cell dichroic display is shown in Fig. 22.
3.4.13 Positive Mode Dichroic LCDs Most of the LCDs discussed in the preceding sections are negative mode LCDs, that is displays exhibiting colorless or white digits on a colored or black background. In many applications colored or black digits on a colorless background are preferred - these are positive mode dichroic LCDs [ 13 - 161.
3.4.13.1
Positive Mode Heilmeier Cells
Using Pleochroic Dyes The geometry of Heilmeier cells was discussed in Sec. 3.4.8. Using a liquid crystal mixture of negative dielectric anisotropy mixed with pleochroic dye initially in homeotropic geometry, we can make a posi-
z5
I
REFLECTWE
20
2
'
3.4.13 Positive Mode Dichroic LCDs
0 d
0
293
viewing
6 R H / l 5 * V viewing
viewing
0
3
z
8
15
10
Figure 22. Temperature variation of the contrast ratio of a double cell phase chan ge dichroic LCD.
5
0
20
40
60
80
100
120
TEMPERATURE ( "C )
tive mode display. In the off state the cell would look clear, as the long axis of the pleochroic dye is in the direction of propagation of the light. On application of the field liquid crystal molecules will stand perpendicular to the electric field due to their negative dielectric anisotropy, and consequently the dyes become parallel to the E vector of the light. Hence, the light is absorbed and colored or black information is displayed on a colorless background. Originally, this approach required high driving voltage as the materials had small -A&values (--0.5). However, recent syntheses of materials of high-A& (--4.5), such as E. Merck's ZLI 2806 (A&=-4.8), Chisso's two-bottle miscible mixtures LIXON EN 24 (A&=-5.6) and N24 (A&=-l.l), have solved this problem, Many black and colored dichroic mixtures with high negative dielectric anisotropy and high order parameters are also available commercially [54]. The host material should be free of ionic impurities in order to prevent the occurrence of electrohydrodynamic effects in the display. To get the best results one requires unidirectional homogeneous alignment of the
REDUCED VOLTAGE
Figure 23. Threshold characteristic of a positive mode guest-host cell using a negative dielectric host and homeotropic alignment. (After Scheffer [ 131).
dichroic mixture in the direction of the polarizer in the field-on state, which is achieved by treating the glass plates with tilted homeotropic alignment [83]. The transmission characteristic of the display is found to be quite steep [13] (Fig. 23), which makes it a good candidate for high level multiplexing. This is reasonable because, just above the threshold, the axis of maximum absorption is perpendicular to the layer where it can produce a large change in absorption for a small change in the tilt angle. Saturation is only approached gradual-
294
3.4
Guest-Host Effect
ly, as higher voltages are required before the boundary layers start absorbing light. Introduction of a 90” twist in the layer does not improve the transmission characteristic. Scheffer [ 131 has reported computed isocontrast curves for both transmission and reflection. In transmission mode an acceptable contrast ratio was found over a wide range of viewing angles, but in reflection mode the viewing angle uniformity is spoiled by ‘holes’ where the contrast is reversed. The holes occur at the angle of incidence for which the homeotropic layer acts like a quarter wave plate. This effect is also present in the on state of Heilmeier-type displays, but is not apparent as it affects only the character segments and not the display background. Using Negative Dichroic Dyes
A dye of negative dichroism can be mixed into a liquid crystal mixture of positive dielectric anisotropy and put in a cell having unidirectional homogeneous alignment [ 13- 16,52,53].A single polarizer is oriented in front of the layer, with its transmission axis parallel to the rubbing direction of the adjacent cell. The cell does not absorb in the quiescent state, as the transition moment of
the dye is in the direction of propagation of the light. On application of the electric field the transition moment of the dye becomes parallel to the E vector of the light. In this case light is absorbed. The major problem for this type of display is the availability of high order parameter negative dichroic dyes covering the whole spectral range. The various geometries for Heilmeier displays are listed in Table 4 [16,53]. Using Dual Frequency Addressing These nematic mixtures [ 161 show positive dielectric anisotropy below a critical frequency f, and negative dielectric anisotropy abovef,. In a dichroic cell (Heilmeier type) using such a host, negative contrast results if a display with homogeneous alignment is driven by low frequency voltage VL (fL4 f,),whereas positive contrast results if a display having homeotropic alignment is driven by a high frequency voltage VH(fH@fc). By driving the same display having homeotropic alignment with VL and VH one can get a dual frequency addressable positive mode display. This dual frequency mode addressing provides a much sharper threshold characteristic and is a good candidate for multiplexing [75].
Table 4. Guest-host variants in nematic hosts. No.
Starting orientation
A&
Aa
Planar Planar Homeotropic’) Homeotropic’) Twisted by d 2 Twisted by d 2
>O >O O >O
>O O O
Theoretical contrast ratioa) ~~
1 2 3 4 5 6
Aa=q,-aL,dichroism of the dichroic dye.
~
~~
Sign of the contrast
~~~~
(1 +2S) / (1 4) (2+S) / (2-2s) (1+2S)/(I-S) (2+S) / ( 2 - 2 9 (1+2S)/(l-S) (2+S) / (2-2s)
-
+ + -
+
a) The contrast ratio is related to high voltages (V>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
3.4 Guest-Host Effect
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
3.4 Guest-Host Effect
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
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(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.
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3.4 Guest-Host Effect
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.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
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.
304
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
1 The Synthesis of Chiral Nematic Liquid Crystals
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
(3)
If a compound possesses an ee of 1, its entirely composed of one enantiomer and may be termed optically pure; similarly, an ee value of zero corresponds to a racemic mixture and would show no net optical activity. The optical purity of a sample will not only influence the optical properties, but also the transition temperatures; this will be apparent in certain examples given in this chapter, where the racemate [(R,S)-]often has noticeably higher clearing temperatures
3 10
1 The Synthesis of Chiral Nematic Liquid Crystals
that the enantiomers [(I?)- or (9-1 [37]. The enantiomeric purity of chiral materials will also depend a great deal on their source, their stability towards racemization (or decomposition) and on their chemical history. It may be appreciated that by careful consideration of these empirical rules in relation to the structure of any prospective target molecule, it is possible to “build-in” certain inherent physical or optical properties, leading to materials which may be more precisely tailored to given specifications. This is particularly important in the preparation of materials which may be used in thermochromic formulations with specific colour play characteristics or in the formulation of a mixture with a given pitch length or twist sense characteristic for use in a display device.
1.4 Cholesteryl and Related Esters The term cholesteryl ester is employed in this chapter loosely to describe any sterol based liquid-crystalline system. Cholesteryl esters (2) are historically unique in that they
(RCO),O, pyridine, 100 ‘C
or
RCOCI, N,N-dimethylmiline, 100°C
where R = akyl
were the first materials to be classified as being liquid-crystalline [ l , 2, 38, 391; since then hundreds of examples of these cholesterol derivatives have been studied or utilised for thermography during the 1960s and 1970s [6-9, 14, 40-43, represent just a few]. The structural nature of cholesterol (1) gives some indication of why its esters form mesophases; its seventeen carbon atoms form four fused rings (three six-membered rings plus one five-membered ring), which form a relatively linear and quasi-rigid lathlike structure which has no centre of symmetry and cannot be superimposed on itself. Furthermore, of these seventeen carbon centres, seven carbons are chiral or asymmetric; as a direct consequence of this, the optically active, quasi-rigid core, may technically be classified as belonging to the type I11 structural family. Synthesis of these types of material is usually achieved by esterification reactions of the 3-hydroxy group, often using a suitable acyl chloride (e.g. propionoyl chloride or myristoyl chloride) [41]; this is illustrated in Scheme 1. Cholesterol (1) is not the only naturally occuring precursor whose derivatives display cholesteric phases; for example the lau-
(i) RCOCI, pyridine, benzene; (ii) H,, RO,,EtOAc
Scheme 1. Cholesteryl esters: structures and synthesis.
1.5 Type I Chiral Nematic Liquid Crystals
311
Table 2. The transition temperatures of selected sterol based mesogens. Ester name Cholesteryl benzoate (5) Cholesteryl butyrate ( 6 ) Cholesteryl myristate (7) Cycloartenyl palmitate (8)
Transition temperatures ("C) Cr 145.5 N* 178.5 I Cr 96.4 N* 107.3 I Cr 72 Sm 78 N* 83 I Cr 55 (N* 53) I -
rate, myristate, and palmitate esters (3 b) of 24-methyl cycloartenol(3a) and the palmitate ester (4b) of 4 a , 14a, 245-trimethyl9,19-cyclocholestan-3~-ol(3 b); these triterpenoids were first isolated from banana peel (rnusa sapienturn) 144-461. Other examples include esters of p-sitosterins, stigmasterins, and cholestans [47]. The transition temperatures ("C) of typical cholesteric phases given by a variety of sterol esters ( 5 - 8 ) are listed in Table 2. However, the use of sterol-based materials in technological applications has several drawbacks, which may be briefly summarised as follows; firstly, they tend to be photochemically unstable [5], a process thought to be facilitated by the presence of oxygen [ 3 ] .Secondly, cholesterol is a natural product and will be of variable quality depending on the source used; this could manifest itself both in terms of chemical purity and optical purity (it would be highly impractical to resort to synthesizing the sterol unit using advanced stereospecific organic techniques on an industrial basis !). Thirdly, cholesteryl esters are frequently solids at or around room temperatures [ 3 ] ; this presents the problem of crystallization at low temperatures which could destroy, the integrity of microencapsulated material [48]. Although formulation of multi-component mixtures does depress this solidification/crystallization temperature it does not easily enable systems to be developed for use below temperatures of 0 "C. Similarly, formulation of high temperature mix-
Ref.
[I1 ~411 [411 [461
tures is difficult, despite the existence of individual esters which have clearing points in excess of 200°C. Fourthly, the fact that racemic modifications of cholesteryl esters are not available, means that the fine tuning of the colour play-temperature response is also not possible (211. Finally, comparatively thick films of cholesteryl based mesogens are necessary for acceptable colour play responses for a given application [ 5 , 2I ]. Despite these drawbacks cholesteryl esters still have a useful role to play commercially, particularly when precise temperature - colour play properties are not required, as for example in novelty applications.
1.5 Type I Chiral Nematic Liquid Crystals As the electro-optic display industry developed, great interest was centred on the development of suitable materials for use in twisted nematic or phase change displays, particularly as many of the first generation of materials frequently presented problems in practical usage. For instance, cholesteryl esters were deemed to be unsuitable for such applications for many of the reasons already outlined in Sec. 1.4 of this chapter, and also because of difficulties associated with optimising physical properties such as birefringence, viscosity, and dielectric anisotropy. Consequently, novel chiral materials based on known nematogenic materials
312
1 The Synthesis of Chiral Nematic Liquid Crystals
where X and Y = alkyl or alkoxy (chiral or racemic);
n and m = 1 or 2; A = -N=N-, -CH=N- or -CO2-.
Figure 6. The general structure of a non-sterol based chiral nematogen.
(hence the term chiral nematic liquid crystals) began to appear; these materials were not necessarily mesogenic, but because of their structural similarity to the host nematic mixtures of the time, this enabled formulation into suitable eutectic mixtures. These chiral nematogens may be divided into three kinds; the azobenzene derivatives, the azomethine materials (Schiff's bases), and the phenyl/biphenyl esters [18, 47, 491. All three classes may be represented by the general structure shown in Fig. 6. The central linking group (A) preserves the molecular linearity and increases both its polarisability (by allowing some degree of conjugation between the aromatic rings) and rigidity; however, as shall be seen, it can often be the weakest part of the mesogen [18, 491. The respective features of each of these three general classes of material will now be discussed with emphasis on the thermodynamic properties of the materials and the various synthetic routes employed.
1.5.1 Azobenzenes and Related Mesogens The use of the azo-linking group (- N = N -) in liquid crystal chemistry is now well documented, and hundreds of compounds of this class have been cited in the chemical literature [47]; the linkage is formed by an azo coupling reaction between a substituted aryl diazonium salt and a suitably activated substituted benzenoid compound [SO].
Typical examples of chiral azobenzenes are (R)-4-(2-methylbutyl)-4'-substituted azobenzenes (9- 13) which appeared with the emergence of synthetic methods which allowed the preparation of chiral precursors, such as (+)-2-methylbutylbenzene [5 1-54]. In the case of compound 12, the presence of two chiral terminal moieties was found to increase the helical twisting power (p) by a factor of two [51]. Both the compounds 9 and 10 show enantiotropic chiral nematic phases which have relatively low clearing points, unlike compounds 11 and 12 which are not liquid crystalline.
9;X=OC,H,,; Cr 31.8 N* 65.6 I ("C) [52] 10; X=OC,H,,; Cr 35.9 N* 58.2 I ("C) [52] l l ; X = C N ; C r 6 9 I ( " C ) ; p = l0.0[51]
12; Cr 112 I ("C);
fi = 4.7 [51]
13; n = 0, 1, 2 and 3 [54]
The azo group may be oxidized further, usually with a peracid such as 3-chloroperbenzoic acid to give azoxy linked materials; examples include compounds 14- 16 which are shown below [51, 54, 551, but only compounds 14 and 16 show chiral nematic phases.
14; X=OC,H,; Cr 4 N* 76 I ("C) [51] 15; X=CN; Cr 100 I ("C) [51]
16; Cr 24 SmB* 66 SmC* 79.3 N* 84.2 I ("C) [ 5 5 ]
313
1.5 Type I Chiral Nematic Liquid Crystals
Although early commercially available nematic mixtures for use in electro-optic displays were based on this class of material, they proved short lived because of their inherent strong yellow colour and because of their susceptibility to photochemical isomerization/degradation [IS].
1.5.2 Azomethine (Schiff 's Base) Mesogens The azomethine group (or Schiff's Base linkage), like the azo linking group, has been widely employed as a linking group in many forms of mesogen [47] and was employed in the synthesis of a variety of early chiral nematic materials [52, 53, 56-62]. During the early seventies, a variety of optically active Schiff's bases were developed from the now readily available chiral precursor (S)-(-)-2-methyl- 1-butanol (17),via a series of reactions which avoided inversion of the chiral centre or any appreciable degree of racemization [53]. The route used to manipulate (S)-(-)-2-methyl- 1-butanol is outlined in the synthetic Scheme 2 and is of importance as it shows the versatility of the synthetic methods used to manipulate the chiral alcohol (indeed many of the steps are directly applicable to later types of chiral mesogen, see Sec. 1.5.3 of this Chapter). The alcohol is converted to (S)-(+)-l-bromo-2-methylbutane (18)using phosphorus tribromide; subsequent conversion to its Grignard reagent followed by treatment with solid carbon dioxide gives (S)-3-methylpentanoic acid (19).The higher homologs (S)-(-)-3-methyl- 1-pentan01 (20),(S)-(-)5-methyl-I-heptanol(21),(S)-(-)-4-methyl1-hexanol (22),and (S)-(-)-6-methyloctano1 (23)may be obtained from the Grignard reagent of compound 18 via a series of homologation steps involving the addition of either formaldehyde or ethylene oxide.
-
repeat above steps-:
x i
i
OH
Scheme 2. Synthesis of optically active methyl branched primary alcohols.
The optically active alcohols (17,20-23) may then be brominated (PBr,) and used as alkylating agents for 4-hydroxybenzaldehyde. The resulting 4-alkoxybenzaldehydes (25)were then condensed with a variety of mono-substituted aromatic amines (26and 27) to give the two series of compounds shown in Scheme 3. These two ring azomethines gave chiral nematic phases which had relatively low thermal stabilities, but comparatively short phase ranges as demonstrated by compounds 28 and 29. The introduction of a third ring to give materials such as compound 30, led to markedly higher thermal stabilities. This compound is reported as having an optical rotation of 25000 degrees mm-' in its chiral nematic phase, further highlighting the extraordinary optical properties associated with the chiral nematic mesophase. However, despite showing promising thermal stability, this type of mesogen fell from widespread use simply because the azomethine linkage (- CH = N-) imparts colour to the material and proved too sus-
314
1 The Synthesis of Chiral Nematic Liquid Crystals PBr,
17,20-23
OHC
-W-
OH
24
where n = 1, 2, 3 or 4.
28; n = 1; (370.0 (N* 56.0) I ("C) [53]
29; n = 3;Cr 40.0 SmX*48.0 N* 66.0 I ("C) [531
1 1 ' 3
30; Cr 50 (SmX*43.5) N* 146 I ("C) [S3]
ceptible to water, making hydrolysis of the linkage and the subsequent degradation of the physical properties of the liquid crystal an ever present disadvantage during use U81.
1.5.3 Stable Phenyl, Biphenyl, Terphenyl and Phenylethylbiphenyl Mesogens During the early 1970s, the problem of manipulating a chiral substrate without adversely affecting the optical purity had largely been solved (in the main by use of readily available precursor (S)-(-)-2-methylbutan-1-01 17), but the problems associated with the poor chemical or photochemical stabilities and the inherently strong colours of the existing azo and azomethine derived materials were still to be addressed satisfactorily. The root of this problem lay with the linking group, which was recognised as being the weakest part of the liquid-crystalline molecule as a whole. The poor chemical
Scheme 3. Synthetic routes to optically active azomethine chiral nematogens.
stability and colouration of existing nematic materials was surmounted by elimination of the linkage, and resulted in the discovery of the now ubiquitous, stable, colourless nematic 4-alkyl- or 4-alkyloxy-4'-cyanobiphenyls, which are still the mainstay of many commercially based electro-optic mixtures [63]. It was subsequently discovered that chiral modifications of these materials, some of which had very low thermal phase stabilities, but had sufficient liquidcrystalline character, would be used successfully as reverse twist dopants in electrooptic mixtures for use in twisted nematic and later in supertwisted displays. Specific examples of such compounds are (S)-4-(2methylbutyl)-4'-cyanobiphenyl(31), which displays a N*-I transition at -30 "C and (S)-
4-(2-methylbutyloxy)-4'-cyanobiphenyl (32)which shows a monotropic phase at 9°C [64]; these materials are reported as having pitch lengths of 0.2 and 1.5 pm, respectively.
W
C
N
31; Cr 4 (SrnA* -54 N* -30) 1 ("C) [64]
*
O
W
C
N
32; Cr 53.5 (N* 9) I ("C) [64]
3 15
1.5 Type I Chiral Nematic Liquid Crystals
Whilst these chiral biphenyls fulfilled the needs of the display world, they were not immediately suitable for use in thermochromic applications, primarily because of their low N*-I transitions, which seriously restricted their use in higher temperature application environments. These low temperature restrictions were countered to some extent by the incorporation of either a further phenyl ring or by a CH,-CH, link between the existing rings, to give chiral terphenyl or phenylethylbiphenyl based structures [64]. In the case of the chiral terpheny 1, (S)-(+)-4 -(4-methylhexyl)-4”cyano-p-terphenyl (33), the clearing point of the the chiral nematic phase was raised to 186 “C; however, the material had a very high melting point of 120 “C, which again, not surprisingly, restricted its use. The use of the CH,-CH, link was much more successful in giving a compound with lower melting and clearing points; for example, ( S ) - ( + ) -1-[4’-(2-methylbutyl)biphenyl-4y1]-2-(4-~yanophenyl)ethane(34).
+ 33; Cr 120 SmA* 163 N* 186 I (“C) 1641
\ /
CN
34; Cr 91.6 N* 110.8 I (“C) [641
This class of chiral nematic materials clearly demonstrated their potential, as they
form the basis of a number of stable experimental thermochromic mixtures [64]. The synthesis of the compound (S)-(+)4-(2-methylbutyl)-4’-cyanobiphenyl (31), shown in Scheme 4, typifies the route used to obtain these types of materials. The first step involves the FeC1, catalysed coupling of the magnesium derivatives of (S)-(+)-2methylbutyl bromide (18) and bromobiphenyl to give the chiral biphenyl fragment (35); this was then brominated to give
(S)-(+)-4-(2-methylbutyl)-4’-bromobiphenyl(36) which was eventually cyanated us-
ing copper cyanide to give the chiral biphenyl (31). Although the above route differs slightly from the synthesis of the related chiral biphenyls [i.e. (S)-(+)-4-(3-methylpentyl)-4’cyanobiphenyl (41, n = 1 and m = l ) ] , the other chiral methyl substituted alkanoic acids (37) are obtained by various transformations from (S)-(+)-2-methylbutyl bromide (18);the acyl groups are introduced into the aromatic core by conversion of the acids to their acid chlorides (38) followed by Friedel -Craft’s acylation and subsequent Huang - Minlon reduction of the chiral methyl substituted alkanoylbromobiphenyls (40). This general approach is demonstrated in Scheme 5. The ability of the chiral 2-methylbutyl moiety to generate very short pitch chiral nematic phases was by now widely recognised. It was not therefore surprising that a number of research groups should attempt
wBr
(i) Mg, THF; (ii) Bromobiphenyl; (iii) FeCl,, THF;
18
Scheme 4. Synthesis of (S)-(+)-4-(2-Methylbutyl)-4’-cyanobiphenyl.
CuCN
31
-’cQQ
(iv) (+)-2-methylbutyl bromide, THF;
I
35
Br2,CHCl,, RT (in dark)
316
1 The Synthesis of Chiral Nematic Liquid Crystals
soc1, X n C O z H
38
37
H2NN2H.H20, KOH, diglyme.
H2S0,, AcOH, H,O.
where n = 1,2, or 3 and rn = 0 or 1.
to incorporate it into ester based structures, particularly as existing nematic esters were widely recognised as being both colourless and stable [65-671. The early materials (43-47) were relatively simple two ring materials often based on 4-substituted benzoic acids or trans-4-substituted cyclohexane- 1-carboxylic acids; the structures, relevant transition temperatures, and pitch lengths of a variety of such materials are given below.
w , 0
\ /
OCioHzi
43; Cr 36.0 (N* 32.0) I ("C); p = 0.23 pm [6S]
44; Cr 41.8 SmA* 42.2 N* 45.3 I ("C); p = 0.23 pm [66]
45;Cr 17 [N* -31 I ("C); p = 0.23 pm [66]
46; Cr 17.0 [N* 71 I ("C); p = 0.23 pm [66]
Scheme 5. Synthesis of higher homologues of chiral biphenyl mesogens.
0
mioHa
47; Cr 49.0 (SmA* 41.8 N* 45.41 I; p = 0.43 pm [66]
N.B. ( ) .. . denotes a monotropic transition, [ ] ... denotes a virtual transition SmA*
Cursory examination of the transition temperatures shown by these compounds, shows them to have rather low mesophase thermal stabilities; nevertheless, thermochromic mixtures composed of certain homologous of compounds 44 - 47 have been formulated, even if they have relatively low upper colour play limits which probably reduce practical applications. In most cases, the 2-methylbutyl group generates short pitch chiral nematic phases ( p = 0.23 pm), the only exception being the cyclohexyl compound 47 in which the pitch length is almost twice as long (p=0.43 pm). This loss of twisting power in this example is believed to be related to the fact that the chiral alkyl group is linked to a flexible moiety [66]. Vastly improved mesophase thermal stabilities were obtained on the introduction
1.5 Type I Chiral Nematic Liquid Crystals
317
Table 3. Transition temperatures and phase assignments for homologous (S)-4-(2-methylbutyl)phenyl4‘-alkoxybiphenyl-4-carboxylates.
Compound no.
n
Transition temperatures (“C)
Pitch lengths (km)
48 49 50
5 6 7
Cr 66 SmB* 77.3 SmA* 133.9 N* 156.0 I Cr 81 SmB* 71.0 SmA* 132.6 N* 146.2 I Cr 74.6 SmB* 75.0 SmA* 138.4 N* 147.6 I
0.23 0.23 0.23
of a third ring into these ester structures. This was achieved using a variety of chiral and achiral biaryl carboxylic acids and phenols, such as (S)-4’-(2-methylbutyl)biphenyl-4-carboxylic acid and 4-cyanophenol, many of which were by now readily available or were easily accessible from liquid crystal precursors (i.e. the hydrolysis of
(S)-4-(2-methylbutyl)-4’-cyanobiphenyl (31) to (S)-4’-(2-methylbutyl)biphenyl-4-
carboxylic acid). Generally, speaking it was found that materials containing a (S)-4’-(2methylbutyl)biphenyl-4-carboxylatemoiety gave slightly lower thermal stabilities and shorter phase sequences than the materials which contained the chiral group in the ester function in as an (S)-4-(2’-methylbuty1)phenyl moiety. It should also be noted that this difference in behaviour did not have a corresponding detrimental effect on the
Table 4. Transition temperatures and phase assignments for homologous 4-alkylphenyl (S)-4’-(2-methylbutyl)biphenyl-4-carboxylates.
Compound no.
n
Transition temperatures (“C)
Pitch length (vm)
5 6 7
Cr 63.6 N* 138.2 I Cr 60.3 N* 132.0 I Cr 61.0 N* 133.4 I
0.23 0.23 0.23
pitch length of the chiral nematic phases [66]. The difference in mesophase stability is highlighted in the following members of two homologous series: the (9-(+)-4(2-methylbuty1)phenyl 4’-alkylbiphenyl-4carboxylates (compounds 48-50, see Table 3 ) and the 4-alkylphenyl (S)-(+)-4’-
(2-methylbutyl)biphenyl-4-carboxylates
(compounds 51 -53, see Table 4). There are other differences between the series, notably that the (S)-(+)-4-(2’-methylbuty1)phenyl 4’-alkylbiphenyl-4-carboxylates (48-50) show smectic A* and smectic B* phases below the chiral nematic phases. The presence of an underlying smectic A* phase is advantageous, because it results in the startling pretransitional selective reflection effects as a selectively reflecting chiral nematic phase is cooled towards the smectic A* phase [ 5 , 171. Interestingly, the straight chain alkoxy analogues (compounds 54 and 55) of these materials, display chiral smectic C* phases which, although not iridescent, were successfully formulated into a number of broad range ( 1 13 “C) experimental thermochromic mixtures [64]. The nature of their N*-SmC* phase transition was to prove fascinating from the stand point of selective reflection.
~~
51 52 53
54; n = 8; Cr 78.0 Sm3 80.0 SmC* 128.3 SmA* 171.0 N* 173.2 I (“C): p = 0.23 l m [64]
318
1 The Synthesis of Chiral Nematic Liquid Crystals
55; n = 8; Cr 76.0 SmC* 88.6 N* 155.4 I (“C); p = 0.23 pm [64]
On cooling through the chiral nematic phase, the reflected colour of this mixture changes from blue through to red, then upon reaching and traversing the chiral nematic -chiral smectic C* phase transition, the reflected colour sequence reverses from red to blue (this corresponds to a shortening of pitch length of the smectic C* phase as the tilt angle increases [64]). Materials and mixtures which possess a chiral smectic C* phase as well as a chiral nematic phase, offer the opportunity for novel ‘reversed’ colour play of their thermochromic response (i.e., blue-redblue on cooling through a I-N*-SmC* sequence). The ready availability of the 2-methylbutyl and other related chiral alkyl or alkoxy substituted phenols and biphenyls resulting from this work made it possible to prepare esters which contained two chiral terminal chains easily [66]. Broadly speaking, providing the helical twist senses of both groups were identical, this had the effect of reinforcing the twisting influence of each group, often giving very highly twisted (short pitch) chiral nematic phases. Conversely, chiral groups with opposite helical twist senses, lead to compensation of the twisting influence of chiral nematic phases, giving longer pitch lengths. This may be illustrated using the following three compounds: (S)-4-(2-methylbutyl)phenyl (S)4’-(2-methylbutyl)biphenyl-4-carboxylate (56), (S)-4-(2’-methylbutyl)phenyl (S)-4’(2-methylbutoxy)biphenyl-4-carboxylate (57), and ( S ) -4 -(2’-methylbutyl)phenyl ( S ) 4’-(4-methylhexyl)biphenyl-4-carboxylate (58).
56; Cr 103 N* 115.5 I (“C) [66]; p = 0.10 pm [51
57; Cr 88 SmA* 124 N* 145 I (“C) [66]; p = 0.46 prn [ 5 ]
O
‘ /
58; Cr 83.4 (SmC* 74.3 SmA* 81.0) N* 113.5 I (“C); p = 0.23 prn [66]
Compounds 56 and 58, have chiral groups which may be described using Gray and McDonnell’s rules as ( S ) , e, d; therefore, the groups should reinforce one another. This is certainly the case with compound 56 ( p = 0.10 pm); the longer pitch of compound 58 ( p = 0.23 pm)is due to the increased distance between the chiral centre and the aromatic mesogenic core which effectively reduces any damping of rotation about the chiral centre [29]. On the other hand, the 2-methylbutoxy group of compound51 may be described by Gray and McDonnell’s rules ( S ) , 0,1, the opposite of the 2-methylbutyl group [ ( S ) , e, d], which leads to compensation and a longer pitch length (p=0.46 pm) [32]. It is worth drawing the reader’s attention to the elegant synthesis of the opposite enantiomer (i.e. the (R)-enantiomer) of (S)-(-)-4”-(2-methylbutylphenyl) 4’-(S)-2methylbutyl)biphenyl-4-carboxylate (56) (CE2); this was required for the detailed study of the Blue phase behaviour in binary mixtures [68, 691. The commercial unavailability of (R)-(+)-2-methylbu tan01 (or (R)-(+)-l-bromo-2-methylbutane) forced the authors to synthesize it from (S)-(+)methyl 3-hydroxy-2-methylpropionatevia
1.5 Type I Chiral Nematic Liquid Crystals
a five step route. The synthesis is also significant in that it successfully employed an efficient palladium (0) catalysed crosscoupling for the introduction of the valuable chiral side chain onto both the phenyl and biphenyl ring systems; this contrasts to the use of the inefficient ferric chloride catalysed cross coupling used 10 years earlier in the original synthetic route to this fragment of the molecule (see Scheme 4) [64]. In addition to these, a number of three ring esters which contained the more polar cyano group as a terminal group were prepared and evaluated (compounds 59 and 60); the thermodynamic properties of a selection of these materials is shown below ~641.
319
cially important, as many of these materials were very effective as reversed twist dopants for electro-optic devices, and also as the constituents of numerous thermochromic mixtures. A large range of mixtures is commercially available either in their neat forms or as microencapsulated inks or slurries, for a wide variety of different colour play ranges. It is also possible to obtain a particular set of mixtures and a partially racemized set of mixtures, the idea being to enable tailoring of the precise colour play properties to a specific requirement by the careful addition of a small quantity of the partially racemized mixtures in accordance with a specific set of temperature-composition directions [21].
(R)-2-(4-Hydroxyphenoxy)propanoic Acid Derivatives 1.5.4
59;Cr 96 N" 210 I ("C); p = 1.6 pm [64]
L
C
O
C
O
-
Q
-
Q
C
N
60; Cr 77.6 SmA* 138 N" 190.4 I ("C); p = 4.7 prn 1641
These materials show very much higher melting points and thermal stabilities of their chiral nematic phases than their tworing equivalents as a direct result of the increased polarisability of the liquid-crystalline core. The 2-methylbutyl group attached to the cyclohexyl ring is again notable in that this chiral moiety fails to give a tight pitch chiral nematic phase; indeed various studies performed on a variety of esters containing different ring systems has revealed that there is a marked order of twisting efficiency which is dependent on the nature of the ring system to which the chiral chain is attached. This may be summarised as follows, in descreasing order of twisting power: phenyl> 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
1 The Synthesis of Chiral Nematic Liquid Crystals
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
1 The Synthesis of Chiral Nematic Liquid Crystals
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
1 The Synthesis of Chiral Nematic Liquid Crystals
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
1 The Synthesis of Chiral Nematic Liquid Crystals
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
Transition temperatures ("C)
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
1 The Synthesis of Chiral Nematic Liquid Crystals
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
1 The Synthesis of Chiral Nematic Liquid Crystals
(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
Transition temperatures ("C)
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
1 The Synthesis of Chiral Nematic Liquid Crystals
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.
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Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
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.
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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
2 Chiral Nematics: Physical Properties and Applications
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
Introduction to Chiral Nematics: General Properties
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<
340
2
Chiral Nematics: Physical Properties and Applications
Figure 4. Schematic diagram of (a) the optical rotatory power and (b) the reflection spectrum from a planar chiral nematic texture.
RED
ROTARY DISPERSION
Figure 5. Schematic diagram of the rotatory power and dispersion of linearly polarized light incident on a chiral nematic along the helix axis.
cularly polarized light of opposite handedness but of the same frequency traversing the N* material. The right- and left-handed waves will travel with different velocities on passing through the material and there will then be a phase shift between the two components. If we now consider linearly polarized light as the superposition of two circular waves of opposite handedness then, after passage through the N* material, the two components are recombined to give linearly polarized light, but with its plane of
polarization rotated relative to the incident light due to the phase shift. Since different wavelengths will travel with different velocities, the different spectral components will show different rotations, i.e., dispersion (see Figs. 4 and 5). Thus a chiral nematic sample in the planar configuration will show different colors on transmission if placed between a crossed polarizer and analyzer using a white light source. If the analyzer is then rotated, there will be a shift in the transmitted color. As shown in Fig. 4,the specular reflection band separates the two regimes of opposite sign of rotatory power. On either side of the selective reflection band centered at & there are regions of strong rotation of the plane-polarized light. The optical rotation per unit length ty/d can be written [26] as
where A is the wavelength inside the medium and the condition that I A- &I > > AA/2
2.1
Introduction to Chiral Nematics: General Properties
applies. This equation also shows that the polarization plane rotates in the same sense as the helix for Ap. 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.
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2 Chiral Nematics: Physical Properties and Applications
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
2 Chiral Nematics: Physical Properties and Applications
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.
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2 Chiral Nematics: Physical Properties and Applications
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
Static Properties of Chiral Nematics
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
DISCLINATION LmE
h
Figure 8. Schematic diagram of the Cano-wedge technique for measuring the pitch, where p = 2 1x a=2 1hlL, in a chiral nematic (see text).
348
2 Chiral Nematics: Physical Properties and Applications
Figure 9. Typical Cano-wedge textures for a chiral nematic. The Grandjean-Can0 disclination lines occur at the blue-yellow interface. The slightly curved distortion shows how sensitive the technique is to undulations in the glass of the wedge cell used here.
local director inside the liquid crystal. Macroscopically the ordinary (no)and extraordinary (n,) indices are measured, averaged in a chiral nematic over several turns or partial turns of the helicoidal distribution of n. This is contrary to the simple case of 'planar' nematics where no=nl and n,=nll. The case of the chiral nematic has been analyzed [52] for a planar texture with obliquely incident light which is necessary if using an AbbC refractometer to measure n, and no [53]. This analysis, under the condition of critical angles for internal reflection at the glasslchiral nematic interface, gives
n,=nl
and
ni= '2( n i +n:)
where n, is the refractive index in the direction of the helix axis and no is normal to this helical or optic axis. With an AbbC refractometer (as manufactured by Bellingham and Stanley [54]) it is possible to measure straightforwardly refractive indices between 1.3594 and 1.8559 (+O.OOOl) well within the range of most chiral nematics. Using planar alignment and a polarizer adapted into the eyepiece of the refractometer, n, and no are readily determined [53] over a temperature range of -10°C up to
80°C (kO.1 "C) using a circulating water system. This range may be extended by using dibutyl phthalate as the circulating fluid up to the softening temperature of the optical cements used in the prism optics, and down to below 0°C. The refractometer may readily be adapted to work at different monochromatic wavelengths, using mercury lamps or tunable He-Ne lasers to determine refractive index dispersions. Thus nI1 and nl may be determined from no and n, as a function of temperature and wavelength, from which the pitch may be determined, the relation Aillil=AnlE verified, and the diffraction analysis from focal conic textures carried out. A method using selective and total reflections with rotating cylindrical prisms has also been presented [55], which allows A n andp to be measured. Using this technique, p may be readily measured down to 400 nm. The refractive index data for all and nI, calculated from no and n, (Eq. 1 l), may also be used to calculate the order parameter (S) in the chiral nematic phase using the Haller [56] technique with the Vuks' local field correction factor [57] from
2.2 Static Properties of Chiral Nematics
where f (a) is the molecular polarizability correction factor, rill and nL are the local refractive indices parallel and perpendicular to the director (as before), and E is a mean refractive index given in this notation as X(n ;+2n:). The temperature dependence of S used in the Haller curve fitting technique is given by S=(l-$)p where all temperatures are in Kelvin, T* is the critical temperature for a second order chiral nematic to isotropic phase transition (note T* is normally 1-2 K above the clearing temperature T J , and p is used as a fitting parameter. From the techniques outlined above, it is possible to determine the optical textures (using a polarizing microscope), the specular reflection maximum (&),and the bandwidth (AA), the helical pitch @), the refractive indices (ne,no, nl, rill), the order parameter (S), and the temperature dependence of S(T). An optical polarimeter may be used to measure the optical rotation or, given the high rotatory powers, i.e., lo3 degreedmm or 1 degree/pm, this can readily be done using a planar texture and a polarizing microscope with monochromatic light and sample cells -10-50 pm thick. Thus we are in a good experimental position to measure all of the relevant optical properties of chiral nematic liquid crystals as a function of temperature and for a variety of textures. As discussed in the Sec. 2.1, it is the helicoidal twist structure of the director n that dominates the optical properties and makes for their use in a growing number of optically related applications (see Sec. 2.5 of this Chapter). It is useful to summarize 19, 58, 591 these unique optical properties, again assuming planar alignment:
349
1. For light of wavelength A, incident on a planar chiral nematic texture of pitch p, the optical rotatory power is extremely high (i.e., lo3 degreedmm) outside the specular reflection band, i.e., a,K~3 2. If the incident wavelength A, is of the same order as the chiral pitch p , then the light is selectively reflected. 3. The selectively polarized light (for A, - p ) is circularly polarized with the same handedness as the chiral nematic helix. The other circular polarization is almost totally transmitted. 4. The spectral bandwidth (Ail) back-reflected has a narrow bandwidth defined by the materials birefringence ( A n ) . AA is typically of the order of 10 nm. 5. In the region of the selective reflection, the optical rotatory dispersion is anomalous and changes sign approximately at the peak wavelength of the reflection band. 6. The wavelength of the reflected maximum & varies with the angle of incidence 8 approximately as d cos 8, if the length scale d ( = p 2 ) is comparable with the helix pitch p. This corresponds to a Bragg-like reflection.
a,.
These optical properties of chiral nematic materials have all been observed experimentally. There have been quite extensive theoretical studies carried out by Mauguin [60], Oseen [61], and de Vries 1261 to explain how these properties arise from the helicoidal structure. Kats [62] and Nityananda [63] have derived exact wave equations to explain the propagation of light along the optic axis and Friedel [32] has reviewed the main textures observed with chiral nematics. We will outline the important elements of these studies in the next sections (Secs. 2.2.1.1 -2.2.1.3). In Sec. 2.2.1.4 we will consider how the helicoidal pitch, and
350
2
Chiral Nematics: Physical Properties and Applications
therefore the optical properties, depend on external factors such as temperature, pressure, and chemical composition. The influence of an external electrical and magnetic field on the pitch will be discussed in Sec. 2.4, since this influence will depend greatly on the dielectric and diamagnetic anisotropies as well as the flexoelectric behavior. These discussions will then lead on to consideration of the device implications (Sec. 2.5).
2.2.1.1 Textures and Defects The basic textures observed in chiral nematics were introduced in 2.2.1 ;namely (a) planar or Grandjean, (b) focal conic, and (c) fingerprint. Typical textures are shown in Fig. 6 and the seminal review by Friedel [32] gives a lucid account of how these textures arise. Associated with these textures are a number of singular lines and defects, as observed using a polarizing microscope. It is useful here to recall the terminology used when observing such lines and defects in a thin (5-50 pm) layer. In classical nematics, in a schlieren texture, black or dark brushes are observed originating from point defects (see, for example, Fig. 1.16b in [59] due to Sackmann and Demus [64]). The points are due to line singularities perpendicular to the layer. In a modified form of Frank's [65] original notation, these defects are now referred to as disclinations, defined as a discontinuity in orientation or rotation. The dark brushes (Fig. 6d) are then due to regions where the optical axis, due to the director n, is either parallel or perpendicular to the polarization of the incident light, i.e., in these regions the polarization only interacts with n, or n,,. In nematics we observe either two or four brushes; in chiral nematics, because of the helical structure, the structure of the lines is often far more complex. For the moment it is useful to con-
tinue with the brief discussion of nonchiral nematics. If we rotate the crossed polarizers, the end of line disclinations or points remain unaltered; however, the brushes rotate. If the brush rotation follows the polarizer rotation direction, we have positive disclinations. If, however, the brush rotation is in the opposite direction, we have negative disclinations. The strength of a disclination is defined as s = !4 (x the number of brushes), and only disclinations of strengths s =f % and 21 are generally observed in nematics. These are depicted in Fig. 10 after Frank [65]. In this notation, if we assume an elastically isotropic material (i.e., k , =k,, =k,, =k and k=O, i.e., achiral) and a planar nematic structure in the x y plane with the line disclination along z, then in the plan view we can define the director orientation @ relative to x along any polar line radiating at an angle a to x from the point defect as
,
@=sa+c
(14)
where a=tan-' ( y l x ) and c is a constant for nx=cos @, ny=sin @, and n,=O. Equation (14) describes the director configuration around the point defect or disclination line L along z , and the director orientation changes by 27cs on rotation around this line. It is also interesting to note that neighboring disclinations joined by such brushes are of opposite sign, and that the sum of the strengths of all disclinations in the sample layer tends to zero. Further, if we rotate the polarizers, as described earlier, the two brush patterns will therefore rotate with twice the rate of the four brush patterns. These in turn have approximately the same rate as the rotation rate of the polarizers. In the so-called Volterra process [ 6 5 ] ,the topological defects of these disclinations can be visualized as follows: If the nematic material is cut by a plane parallel to the di-
2.2
Static Properties of Chiral Nematics
s=-l
s=-j
(@ s=
I , c=o
35 I
s= I , c= Rl4
rector n, then the limit of the cut is at the disclination line L. One face of the imaginary cut is then rotated with respect to the other about an axis perpendicular to the director by an angle 2 n s. Material is then removed from the overlapping regions or added to fill in voids and allowed to relax. If the axis of rotation is parallel to L, as is true here, then the disclinations are called wedge disclinations [66]. The textures for achiral nematics have been treated in great detail by Nehring and Saupe [68], following the pioneering theoretical work of Oseen [61] and Frank [65], and more recently comprehensive reviews have been presented [69, 701. We are now in a position to consider the more complex case of chiral nematics.
a) Planar or Grandjean textures: As discussed in Sec. 2.2.1, in a planar texture the director at the interfaces is constrained to be parallel with the alignment layers and an orthogonal helix axis. A typical planar texture is shown in Fig. 6a. In this figure the relatively braod lines between the apparent
s=
I , c= X I 2
Figure 10. Lines of equivalent director orientation in the neighborhood of s = + % and + I disclinations, where c is a constant (see Eq. 14).
platelets are known as oily streaks formed by focal conic bands, which correspond to regions of defects and poor planar alignment. These disappear if we use a Canowedge cell of the type depicted in Fig. 8 with the observed texture shown in Fig. 9. Here the thin disclination lines of strength s = !4 are clearly visible. The gradual variation in color from yellow to blue is due to distortion of the helix as it accommodates the wedge angle between disclinations. As discussed earlier, these textures allow us to determine the pitch via Eq. (10). To return to the parallel plate situation, if we make a contact preparation between a chiral and a nonchiral mesogen we form quite readily a concentration in the gradient along one axis, say x. The pitch p o of the chiral compound is then ‘diluted’ as a function of x towards the achiral compound. The real pitch is again quantized but tries very hard to stay close to the varying function p , ( x ) . This leads to a succession of similar domains (see Fig. I I a), separated by sharp discontinuities [71]. We will return to concentration gradients below.
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2 Chiral Nematics: Physical Properties and Applications
Figure 11. Photomicrographs of concentration gradients with (a) planar and (b) fingerprint textures in chiral nematics. In both plates the high concentration of chiral compound is at the top left with the achiral compound at the bottom right.
b) Focal-conic texture: If a chiral nematic is cooled from the isotropic phase reasonably rapidly between the parallel glass plates, the bulk of the system does not have time to align in the planar texture and the helix axis is curved away from its direction at the surface interface to give the so-called focal-conic texture, where the director profile of any given repeat unit (i.e., any uniaxial direction at p / 2 ) orthogonally follows the same curvature. Since such directors are separated by p / 2 , this gives (macroscopically) a lamellar appearance which resembles a smectic A texture (Fig. 6 b). Microscopically the structure is still nematic (as discussed earlier) and Bouligand [72] has
discussed these similarities in detail. With good aligning agents, slow cooling, and, if necessary, a slight shear field, it is possible to align the texture into planar (with uniformly rubbed polymers) or fingerprint (with a homeotropic surface agent such as lecithin). c) Fingerprint texture: As discussed previously with respect to Fig. 6c, it is usually possible to obtain a fingerprint texture, in which the helix axis lies parallel to the substrates, using homeotropic surface alignment agents. In order to remove the degeneracy, a slight shear field is applied, in which case the helix axis aligns orthogonal to the
2.2
shear direction. This method is applicable tolong pitch systems (i.e.,p>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-
Static Properties of Chiral Nematics
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.
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2 Chiral Nematics: Physical Properties and Applications
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
Static Properties of Chiral Nematics
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
2 Chiral Nematics: Physical Properties and Applications
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,<<E), and (4) that the wave vector of the incident light has the same direction as that of the helix axis (i.e., z ) . Finally, we will outline the main theoretical predictions for light incident at oblique angles and normal to the optic (helix) axis. These three directions of the incident light are of interest experimentally for the behav-. ior of, for example, (1) planar films leading to optical transmissive and reflective filters or mirrors, (2) polydomain samples as used in microencapsulated thermometry devices, and ( 3 ) diffractive elements and flexoelectric displays. The incident electromagnetic lightwave represented by
where o is the angular frequency and c the velocity, interacts with the chiral nematic material via its dielectric permittivity tensor. Here, clearly, we are interested in optical frequencies, where ~ ~ ~ , ,211,1, = n and we represent this tensor by a 'spiraling ellipsoid' with its major axis parallel to the local director n and of principal value ql, with its minor axis perpendicular to the director and of value E ~ We . ignore any biaxiality as negligible for these systems (since E~-E lop4, ~if, E,; I is in the z direction) and we assume E,, and E, are in the x, y plane. Using the form of the director given in Eq. (l), the dielectric indicatrix spirals around the z axis through the medium. For
357
Static Properties of Chiral Nematics
convenience we take the major axis of the ellipsoid as parallel to x at the origin, which then defines the dielectric tensor E for any value of z as coskx -sinkz][~ll sinkz coskz 0 coskz sinkz -sink2 coskz
=[
1
E~ 0
]
]
E+(8~)cos2kz (6~)sin2kz (&)sin2kz 2 - (6e)cos2kz (19)
where E = X (E~~+ E ~ ) , (6 E ) = !4 (E~~- E ~ =) X(n;-n:)=EAn, assuming &=n2 at optical frequencies. Maxwell's equations then reduce to
If we introduce the variables E+= 2-'/* ( E + i E, ) and E-= 2-1/2(Ex-i E,), then E + is right circular and E- is left circular for a wave propagating along +z, and vice versa for propagation along -z (i.e., if E-=O then E , = i E, and Ex lags behind E ) by d 2 ) . The inverse of this transformation may then be represented in matrix form by
Equations (21) and (19) are then substituted into the wave equation for propagation (Eq. 20) to give
it["+] az3 E-
which has a solution of the form
358
2
Chiral Nematics: Physical Properties and Applications
and this is a superposition of two waves of opposite circular polarizations with wave vectors differing by 2 k. If the (k’+ k) component of Eq. (23) is substituted into Eq. (22),then this component experiences a wave vector shift of 2 k and it is converted into a (k’-k) wave and vice versa for the (k’- k ) component. Thus, due to the dependence of &onz, a right circular wave generates a left circular wave (and vice versa) with a wave vector shifted by -2 k (and +2 k), so that the two components form a closed set. Equation (23) therefore represents a true normal wave which, with a proper choice of A+ and A-, can satisfy the wave equation (Eq. 22). Substituting u (see Eq. 23) into Eq. (22) then gives
waves corresponding to the roots k, and k2, where each is dominated by one of the opposite circularly polarized components. Further, the mixing of these two components with wave vectors differing by 2 k is a consequence of the Bragg-like reflection. This equation may then be rewritten as
[
]
bei(K2+2k)z
u2 = eiK,z
1
(k’ + k)2- Zw2/c2 - ( & ) 0 2 / c 2 -(d€)02/C2 ( k ’ - k)2- Zw2/c2
I:;[.
2
47cik2+(a&) K
=0
4 112
]
}
If we rewrite the wave vectors as K (=w/c=2 nia) and K,, (= .P2 o / c =2 n: zia) for free space and the chiral nematic of average dielectric constant E, respectively, then the only nontrivial solutions occur when the determinant of the matrix is zero, i.e., the quadratic in k’2, given by
[(k’ + k)2 - ~ i ] [ ( k ’k)2 - - K;] -(a&)2K4 = 0
(25)
with roots k,, k, given by
4 ~ k2 ;
-(a&)2 K 4112 ] } (26)
From these two solutions we may obtain the ratios of Af/A- from Eq. (24) such that
Substitution of Eqs. (26) and (27) into Eq. (23) (i.e., the solution for u ) gives two
The difference between the wave vectors K~ and K~ (the dominant components of u1 and u2, respectively) gives rise to the optical activity of the chiral medium, i.e.,
d
=
1 ( K , - K2) radiandunit length. Further, 2
K, and K~ differ from K;, by terms of the order of (6 E ) ~and , hence a and b are small and of the order of ( 6 ~ )Equations . (28) and ( 2 9 ) mathematically describe the key optical properties of a chiral nematic planar texture for normally incident light [ 6 2 ] . We are now in a position to examine the behavior of the optical rotation as a function of K for different limiting conditions
2.2 Static Properties of Chiral Nematics
around, close to, and far away from k. A series expansion for K , and K~ within the limit of K~ - ~ ~ < < kand ignoring higher order terms [0(I?)] yields
d
=
2
which is the spectral width of the total reflection as given in Eq. (4) and [26]. In addition, Eqs. (31) and ( 3 2 ) give the following very simple but very important relationship for optical devices, namely,
(K1- K 2 )
q-(q2-(W
- ______
)
~~
4k
(30)
where q= K,-k2. 2 The optical rotation is complex if
(6 E ) +? ~ > q2, in which case the real part corresponds to the rotatory power and the imaginary part to circular dichroism. As stressed previously, there is no spectral feature contributing to this imaginary or loss term; therefore, the imaginary part of ydd has to be associated with the reflection of one of the components in a range bound by ( 6 ~2) 2 q to 2(6&) and centered at q=O,
wavelength in vacuo (air). Therefore
p = E&
(31)
which is identical to Eq. (3). If we consider the reflection band and assume Km =k , then the bounds for reflections are given by
2 and, since 6 q = 6 ( K m ) = 2 K,6K,-2k6Km, where
then
whence AA=pAn
AAAn -
; b n
2 K4 ‘I2
(32)
359
(33)
For chiral nematics, this relationship has been satisfactorily verified [46] over a range of A n from 0.04 to 0.15 and bandwidths of 10-50 nm have been readily achieved. This is important for spectral filters and optical mirrors. We can now consider the optical rotation in a wave vector range away from the selective reflection, i.e., q>>(8&) K4, by making a series expansion of Eq. (30) and ignoring terms of 0 ( K’) or higher. This gives
-
(34) and from (6&)’=Ann, K=27G/jl, q= K k - k 2 , and k=23.c/p, we obtain
(35) which is the de Vries equation [26] derived using the formalism of Kats and Nityananda [62, 631 and is equivalent to Eq. (8). There are numerous studies in the literature that have confirmed the form of the function Wand that it changes sign at A=& [59], as shown schematically in Fig. 4. In summary for a planar texture and normal incidence we have outlined the derivation of the solution of Maxwell’s wave equation and this has led to explicit expressions forp(=iA,), AA(=pAn), and optical rotatory dispersion. We are now in a position to study special cases of normal and oblique incidence. The previous derivation assumes a semiinfinite layer thickness. Real chiral nemat-
360
2
Chiral Nematics: Physical Properties and Applications
ic films have a finite thickness and this modifies the reflection properties of the film, as shown in Fig. 18. The semi-infinite case gives a reflection spectrum with a flat top and sharp edges, whilst the finite slab gives a principal maximum at & with subsidiary side bands for A > & + p A n . For a perfect, but finite, chiral nematic layer with normally incident light the normalized intensity reflection coefficient '32 is given by
%=
R2 u2 + b2 coth2(mb)
(36)
where R = n: AnlE, u = -2 n: (1 -A/&, ~ = + ( R ' - u ' ) ~ ' ~and , m is a constant equivalent to the number of layers in the rotating slab model. If m j m , then %= 1 within the range AA=R &ln:=p An as before. The term R is determined by the local birefringence (rill -n,), u is essentially the wavelength-de-
1
"
450
500 Wavelength (nm)
550
Figure 18. Reflection coefficient Yl as a function of wavelength for light normally incident on a chiral nematic planar film for (a) a semi-infinite and (b) a finite slab. The dots are experimental and the curves computed (see Eq. 36) (redrawn with data from [82]).
pendent term, and [b2coth (mb)]limits the amplitude, oscillations, and decay rate of the side bands. The constants can then be determined by computer curve fitting. In the experimental world, it is rare to detect the side bands due to inhomogeneities in the substrates and alignment layers (on the length scale of A)and the possibility of polydomain planar samples. If side bands are observed at normal incidence, then this indicates an extremely well aligned sample! Berreman and Scheffer [83, 841 and Dreher et al. [85] have experimentally verified the validity of Eq. (36) in such samples. Surface undulations, surface pretilt, and polydomains of chiral nematic material lead to the more normally experienced, bell-shaped curves of Fig. 19. The theory of light propagation in a chiral nematic for directions other than that of the helix axis is complex. Whilst for normally incident light the transmitted and reflected waves are, to a good approximation, circularly polarized, for oblique incidence these waves become elliptically polarized
400
500 600 Wavelength (nm)
Figure 19. Selectively reflected light as a function of wavelength for the chiral nematic cholesteryl oleyl carbonate at different temperatures (a) 20.68 "C, (b) 20.55"C, (c) 20.44"C, and (d) 20.5"C (redrawn from [ 9 ] ) .
2.2
and refracted. The first attempts at numerically solving this problem were by Taupiri [25] and Berreman and Scheffer [83] who used a 4x4 matrix multiplication method and then compared, with excellent agreement, their computational method with the experimental results. The analysis again used the spiraling ellipsoid model for ~ ( r ) . i.e., E,
=E + ( ~ E ) c o s ( ~ ~ z )
E ~ = , E-(~E)cos(~~z)
= E , =(6~)sin(2kz) E,, = & - ( 6 E )
where all other components are zero and the ellipsoid is prolate. (This gave the best agreement between theory and experiment [83].) If the helix axis is in the z direction, it can be assumed that the incident and reflected wave vectors are only in the xz plane and the dependence on they coordinate may be ignored [83]. Writing the wave as E,=E: exp [i(ot-k’x)], etc., then Maxwell’s equations may be written in matrix form as
Static Properties of Chiral Nematics
plication is repeated many times, in small steps of 6 z , to give the matrix for a final slab of chiral nematic material, which incorporates the substrate boundary conditions to give the complex transmitted and reflected waves. Berreman and Scheffer [83, 841 included a number of simplifying cyclic and symmetry properties of 9( z ) to reduce the number matrix multiplications necessary. The model agreed very well with the spectral features of the experimental data and confirmed that the assumption of the dielectric ellipsoid as prolate was very reasonable. Indeed, this work established that locally the chiral nematic is uniaxial and not biaxial. In a later study, Takezoe et al. [48] showed that, for oblique incidence, the sideband behavior was not symmetric for left- and righthanded circularly polarized light and they also established the conditions under which there was a band of total reflection for any polarization of incident light. It is clear that such studies are of considerable importance for understanding the propagation of light in a locally rotating reference frame, i.e., the
E,Z
-i H ,
36 1
0
1
or
To a first order approximation
where E is the unit 4x4 matrix and 9 is a 4x4 propagation matrix. The matrix multi-
chiral nematic helix, with significant implications for wideband optical devices reliant on diffuse or oblique illumination. The extreme case of oblique incidence occurs for light propagating orthogonal to the helix axis. Light polarized along this axis alway experiences a refractive index of ni independent of the helix pitch p . Interesting optics occur for light polarized at
362
2 Chiral Nematics: Physical Properties and Applications
right angles to the helix axis (z) since, following n the local refractive index varies sinusoidally between the limits of rill and nL. For long pitch systems, i.e., p> 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
-
observed for
k = ki - k ,
(39)
ki and kd are for the incident and diffracted waves, respectively, and k is the grating wave vector; the angles of the diffraction allow us to determine the helix pitch. This technique was used in depth to study how the helical pitch varied as a function of the composition for a number of chiral nematic materials [86] and this has become a standard technique for pitch measurement if p > 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-
Static Properties of Chiral Nematics
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 <<= W(nll+ nL). Assuming that the birefringence is small (i.e., An<<<), Eq. 42) for the peak wavelength reflection, &, at the domain is given by p Z cosp=m;t,
(43)
and from the geometrical optics and refraction at the interfaces we have
2P = Cpi + Cps sinei = ii sin& sine, = Z sin&
(44)
which in terms of the external angles and parameters gives
[
. cos 1 sin . -1 sinei
+ sin-1 (T)] sine, (45)
This relation is identical to Eq. ( 5 ) and, as discussed in Sec. 2.2.1 allows us to determinep in polydomain samples. For large An we have to take into account form birefringence, which leads to multiple scattering and complex phase properties. For low An and thin samples, where such scattering may be ignored, the technique gives reliable pitch data [22]. If &=pl(Zm), for normal incidence (m = 1) then this equation clearly demonstrates the blue shift, since c0s-l of the argument of Eq. (45) is always less than unity for 6, or Os#O (see Fig. 21).
'
Wavelength (nm)
Figure 21. Reflection spectra as a function of viewing angle (6- 6,)for a chiral nematic reflecting green light at normal incidence. The data were taken [89] for ei= 6,using an isoenergetic white light source with a black, nonreflecting back substrate.
2.2 Static Properties of Chiral Nernatics
The angular or selective diffraction of light by chiral nematics allows for an interesting comparison between chiral nematic and smectic A focal conic textures. Both are normally observed in white light using crossed polarizers. Macroscopically, the texture from the director profile in a thin film of each looks similar. Microscopically, the layer-like structure forming Dupin cyclides, as discussed in Sec. 2.2.1.1, is very different, and this provides a method of dis-. tinguishing between the two phases if the pitch of the chiral nematic is of the same order as the wavelength of light. If the sample exhibiting the focal-conic texture is mounted on a partially reflecting substrate, then polydomains inclined at a high angle a (see Fig. 20 b) will selectively reflect light onto this substrate and the light will be back-reflected back towards the observer, who without polarizers would observe specular colors. A number of geometries that display this effect in chiral nematics have been discussed [89] and lead to the conclusion (see p. 447 of [ 3 3 ] )that in such textures the helix axis is predominantly, or on average, in the plane of the sample, as would be the case if the helix axis is parallel to the local normal of the Dupin cyclides. This provides a further useful example of the ‘Bragg’ reflection model in chiral nematic liquid crystals and allows us to differentiate between the two types of focal-conic texture. The achiral smectic A ‘molecular’ layers may give rise to incoherent scattering in the focalconic texture, but they should not give selective colored reflection or transmission unless contained between crossed polarizers.
2.2.1.4 Pitch Behavior as a Function of Temperature, Pressure, and Composition The optical properties of a chiral nematic depend initially on the helix pitch p . For
365
some applications, such as optical fillers, the selective reflection or transmission properties should either be independent of temperature or frozen in a glass phase, as found in chiral nematic polymers [88]. For a chiral nematic material far from a phase transition (i.e., within l0OC) either to the isotropic or a lower temperature smectic phase, the pitch generally decreases only slowly with increasing temperature. This will depend on the chemical or molecular characteristics, as has been discussed in [ 101. For materials that show a rapid change of pitch with temperature, this occurs as a phase transition is approached. In approaching the isotropic phase, the order parameter decreases rapidly and discontinuously towards zero and the pitch decreases equally, depending on the strength of this weak first order phase transition. The temperature dependence of S was given in Eq. (1 3 ) , and in this transitional region the behavior is complicated by the existence of the so-called blue phases [90,91]. These are of little practical importance in the present context, but they are of theoretical interest as far as the subtleties of twisting power and structure in low order parameter systems are concerned ~921. As the temperature is decreased the chiral nematic structure transforms to a higher order phase. The phase may go through a first order phase transition and crystallize in which case the optical properties are of little interest herein. It may transform to a glass, in which case the optical properties, such as birefringence, pitch, etc., are frozen and may be used in static, or time and environment-independent devices or applications (as discussed in Sec. 2.5 of this Chapter), or it may go through a second order or second order plus a weak first order phase transition to a higher order liquid crystalline phase. Here, for simplicity, we are not considering the so-called re-entrant phases [ 14)
-
366
2 Chiral Nematics: Physical Properties and Applications
in nematics, and a typical pitch dependency spanning the isotropic to smectic A phase transitions is shown in Fig. 22. Two main theories have been developed that predict the behavior of the pitch as it diverges from finite in the N* phase to infinite in a nonchiral smectic phase. If T* is a critical temperature just below the actual N* to SmA transition, the theory of Alben [95] predicts the pitch as p=PO+
U
(T - T*)'
where p o is the helix pitch well away from the phase transition, u is a constant, and y is a critical exponent of the order of 2. Keating's theory [96] predicts that (47) where A and p are constants and the theory is based on a rotational analog of thermal expansion. It should be noted that both the-
tSmA-N*
6oo-
400
[ i
550-
1
130
:
135
140
145
Temperature (Celsius)
I
150
155
r
Figure 22. Reflectance maxima as a function of temperature for a chiral nematic at normal incidence. The material is a mixture of chiral nematic esters from Merck and demonstrates the pitch divergence on approaching either the isotropic or smectic A phase from the N" phase (see [46]).
ories are phenomenological, based on the assumption implicit in Landau-de Gennes theory that some order-dependent property depends on (T-T*)-Y for a second order phase transition. The exponent ydepends on which theory is being used to model the molecular behavior [30] and experimentally there appears to be little difference between these two theories (p. 130 of [9], [46]). The striking prediction of either theory in accord with experiment [9, 10,461 is the divergent behavior of the pitch as the N* to SmA phase transition is approached with decreasing temperature. This behavior forms the basis of the thermographic devices described in Volume 1 of the Handbook [91] and in Sec. 2.5 of this Chapter. Further, it has been shown that the range of color play or region of pitch divergence is approximately inversely proportional to the square of the heat of transition (at TNA)for a homologous series of chiral nematic materials [46]. This range, corresponding to the width of the visible spectrum, may be spread over a temperature interval of 20-30°C down to as little as 10-20C [22], depending on the chemical composition of the chiral nematic material being studied. In achiral nematics exhibiting a nematic to smectic A phase transition (at TNA), it is well known that TNA increases with increasing hydrostatic pressure and typically ATIAP- 10-1 K bar-'. Thus, at constant temperature, a change in pressure of -100 bars ( lo7 N mP2)would shift the TNA phase transition by 10"C. For the typical chiral nematics discussed above, this would shift the selective color reflection or pitch right through the visible spectral range. Such increases in helical pitch length with pressure (see Fig. 23) have been recognized for some time [99-1011 and, provided suitably robust devices can be made that are not subject to mechanical deformation, this presents new opportunities for pressure sensor devices.
2.2
0
500
1000
1
D
367
Static Properties of Chiral Nematics
-0.3 30
I
34
Pressure (bar)
I
38 42 46 Temperature (Celsius)
L
50
Figure 23. Pressure dependence of the selective reflection maxima for different cholesteryl oleyl carbonate (COC) and chloride (CC) mixtures. Compositions (by weight) are (a) COC :CC 74.8 : 25.2 and (b) COC: CC 80.1 : 19.9 (data adapted from [99]. (One bar equals lo5 N m-2.)
Figure 24. Variation of inverse pitch ( p - ' ) with temperature for a chiral nematic composed of 1.75 : 1 (by weight) of cholesteryl chloride (RH) and mysistate (LH). Here the pitch lengths were determined by laser diffraction (see Sec. 2.2.1) (data redrawn from
The helical rotary senses of a number of nonsterol chiral nematics have been studied by Gray and McDonnell [ 1021, and from the results a simple rule relating molecular structure, absolute configuration, and twist sense was proposed. This was used successfully as a predictive tool for a number of new mixtures. This is important in the current context for it is clear that mixtures of rightand left-handed materials may be made to exhibit a linear dependence of p-' on T ; p-' changes sign (see Fig. 24) and varies regularly across the whole chiral nematic range [86]. As well as the pitch changing sign, so too does the rotatory power. If, however, the second component making up the mixture has a lower temperature smectic phase, then this dependence becomes strongly curved. This has to some extent been quantified [46]. When a small concentration of neat chiral nematic is added to an achiral nematic matrix, then a large pitch (p) mixture is
formed in which P K c-I. This result is quantified in the form
W1).
27c = +4@c k =P
where c is the number of solute molecules/cm3 and p, commonly known as the microscopic twisting power of the solute, is a constant with dimensions of area, which depends on the solvent-solute interactions. This parameter allows us to predict mixture composition and behavior and is useful in relation to materials produced for TN devices. For mixtures composed of many chiral components, each with its own dependency of k (T), then the resultant twist is approximately equal to the weight average sum [ 1031 of all the component twists, i.e.,
l k ( T )=
c ci ki ( T )
(49)
1
where ciis the weight concentration of the ith component. The different ki may have
368
2
Chiral Nematics: Physical Properties and Applications
positive or negative values, which allow for subtle k(T) mixtures over broad temperature ranges. There will be exceptions to this simple additivity rule if, for example, some of the components have lower temperature smectic phases. Re-entrant phases also become a strong influencing factor. The sign change in p leads to a double color play across the critical temperature at whichp =O and a change in handedness of the reflecting film (see Fig. 25 and [105]). It is also worth noting at this point that, although we have constantly referred to the visible spectrum, this range actually extends from ultraviolet absorption bands at -350 nm up to infrared absorption at 10 pm; Figure 26 shows a range of specular reflection bands recorded in the range 2-10 pm [ 1061.
-
o
l
+
-3.0
0
SMECTIC CRYSTAL 40 60 80 Cholestelyl Chloride (mol.%)
20
100
Figure 25. Inverse of selective reflection maxima ( - p ) as a function of composition for a number of hinary chiral nematic mixtures. Here the components are: o cholesteryl formate/cholesteryl chloride (at 50 "C), A cholesteryl propionatekholesteryl chloride (at 60 "C), cholesteryl heptanoate/cholesteryl chloride (at 60"C), A cholesteryl lauratekholesteryl chloride (at 60°C) [105].
.sc "0
1.5
d .-
1.0
h
-Bz gz.$ B';
5
0.5 0
2
3
4
5 6 7 Wavelength (pm)
8
9
10
Figure 26. Infrared helical absorption spectrum for a 1.71 : 1.OO chiral nematic mixture of cholesteryl chloride:cholesteryl myristate (redrawn from [ 1061). The dashed line corresponds to spectral regions of strong infrared absorption.
Finally, it should be mentioned that the chiral additive used to create a chiral nematic phase does not have to be a mesogen itself - it has to be soluble at reasonable concentration levels to produce the desired pitch, but since it is now acting equally as an impurity, the normal phase transition properties of the host material may also be altered. Chiral nematic liquid crystals are highly sensitive in their optical properties, and may therefore be used as contaminant detectors. Equally photoresponsive additives, such as azo-based dyes, may be incorporated into a chiral nematic structure and on photoexcitation they change shape; since they then behave as an impurity they can easily alter the pitch or selective reflection properties. Such effects are normally reversible because of the trans-cis and cis-trans back reactions available. This gives a simple imaging device.
2.2.2 Elastic Properties In the important physical properties we have discussed so far, the molecular structure contributes to the bulk optical, electrical, and thermal properties of the chiral nemat-
2.2
ic. Implicit in the use of the director n notation is that in order to consider the behavior of these properties we consider the material as behaving as a continuous medium. The liquid crystal differs from a normal liquid in that it is anisotropic in its properties along n despite the random motion of individual molecules, and in that the director is continuous throughout the medium except at defects (Sec. 2.2.1.1). The director is apolar (i.e., n = - n ) in the absence of spontaneous polar order or in the presence of strong fields. In order to discuss the elastic constants and viscosity coefficients of chiral nematics we make no reference to molecular structure and only consider phenomena on the length scale of the director field, i.e., the material is treated as a continuum. There are significant differences between elastic deformations in liquid crystals and solids, the most basic being that in a shear process there is no effective translational displacement of molecules in a liquid crystal, since they can interchange and ‘slip’ past one another. Consequently, a purely shear deformation in a liquid crystal conserves elastic energy. We are considering a liquid; there are therefore no permanent forces opposing a change in distance between two points, so that in a ‘bent’ liquid crystal, i.e., curved director profile, we must look for restoring forces that oppose such curvature. This is particularly true if we apply external fields or forces to produce orientational or translational motion of the director or fluid. In the next section we will derive the form of the Helmholtz free energy density, F d , for chiral and achiral nematics in terms of director deformations, the splay ( k , twist (k2*), and bend ( k 3 3 )elastic constants, and k the chiral nematic twist vector (k=2n/p). We will then show that application of external E or H fields leads to Frkedericksz (Frederiks) and other transitions depending on the sign of the dielectric anisotropy (A E ) , the diamag-
Static Properties of Chiral Nematics
369
netic susceptibility (Ax), the orientation of the helix axis ( z ) (with respect to the field off and on conditions), and the undisturbed pitch of the helix p ( E , H=O). The external field produces a torque on the director and a change in the free energy density, which in turn leads to new equilibrium structures. These new structures will depend critically on the magnitude (and sign) of the electromagnetic and optical properties as well as the elastic constants, and in chiral nematics specifically there exist a number of intermediate structures related to the twisted macroscopic nature of the phase. These will be discussed in some depth.
2.2.2.1 Continuum Theory and Free Energy The foundations of continuum theory were first established by Oseen [61] and Zocher [ 1071 and significantly developed by Frank (651, who introduced the concept of curvature elasticity. Erickson [ 17, 181 and Leslie [15, 161 then formulated the general laws and constitutive equations describing the mechanical behavior of the nematic and chiral nematic phases. In the continuum theory of liquid crystals, the free energy density (per unit volume) is derived for infinitesimal elastic deformations of the continuum and characterized by changes in the director. To do this we introduce a local right-handed coordinate (x,y , z ) system with ( z ) at the origin parallel to the unit vector n ( r ) and .x and y at right angles to each other in a plane perpendicular to z. We may then expand n ( r ) in a Taylor series in powers of x,y , z , such that the infinitesimal change in IZ ( r ) varies only slowly with position. In which case
n, = n , x + a2y + a3z + O(r2) n, = uqx + u5y + u g z + 0 ( r 2 ) n7 = 1 + 0 ( r 2 )(r2 = x2 + y2 2)
(50)
370
2 Chiral Nematics: Physical Properties and Applications
and
where
kIJ. . = kJ’. . with
an a4 = 2, a5 = -, an, a, = -an, dz
ax
1 5 i, j 1 6
(51)
av
We can further invoke the following requirements:
Since we are considering infinitesimal changes, we may ignore 0 ( r 2 )terms and partial derivatives of n, are zero. The components of strain are then (see Fig. 27)
1. An arbitrary choice of coordinate system. We could therefore redefine a permissible system x’, y’ and z’ with new curvature components ki. As the free energy density, f, must be as before, this restricts the moduli kj and k,. 2. The only requirement on the x-axis was that it was perpendicular to z , and therefore to n . Hence any rotation of the coordinate system around z is allowed (i.e., in a uniaxial system, rotation about z does not change the phyiscal description, and F would be invariant).
Twist: a4 (= t l )= --dY a2 (= t 2 )= dn, JY
ax
~
( 51a) Free energy considerations allow us to postulate [59] for an incompressible fluid that the free energy F of the liquid crystal in any particular configuration, relative to that in a state of uniform orientation, is the volume integral off, a free energy density, which is a quadratic function of the six differential coefficients which measure the curvature ai
l$
= jf d z V
1 aiaj f = ki ai + -kd 2 Splay : 4= an 1
JY
-_.. --A Y Twist : -0,
an
=1
dx
x
__---
1-
Bend :
&-k
&-I-
4” JY
-_-_.-.
xA/---
__---
&L
m
..-_-.
-_
---* Y
Figure 27. Graphical representation of the splay, twist, and bend elastic deformations in the chiral nematic phase; u l = s l ,u5=s2, u 4 = t l , u,=t,, u,=b, and a6=b2 (see Eq. 51a).
2.2 Static Properties of Chiral Nematics
A rotation of 45” gives the further equation ki2 -klS
-
(54)
k23 - k24 =
and rotation through an arbitrary angle gives one more equation kl2+ kl4=O 3
k1, = - k l 4 = k25 = -k45
(55)
Of the six hypothetical moduli, ki,two are zero and only two are independent
k; = ( k ,k2 0 - k2 k10)
(56)
Of the thirty-six moduli k,, eighteen are zero and only five are independent kll
‘62
k12
k22
I
k15
ki2
0
0
0 0
0 0
-k12
k15
k24
k12
-k12
kll
0
0
-
+ k2 = 0, k12 = 0
k33
where k , =k , - k 1 2- k Z 4 . So far we have only assumed that the system is a liquid with rotational symmetry. If the molecules are nonpolar with respect to the preferentially ordered axis (n),as is empirically the case in nematic and chiral nematic phases, or if polar molecules are distributed with equal probability in each direction, then the choice of the sign of n is arbitrary. Hence we can employ the condition n =-n, i.e., transform, such that x’=x, y’=-y, z’=-z, which gives
6:. = -alx’ + a2y’ + a32’+ 0(r2)
n;. = - q x ’ + asy’ + a,z’ + 0 ( r 2 )
(58)
and invariance offgives for first order terms
kl=O,
The effect of this condition of nonpolarity is that many of the terms in the matrices of moduli vanish. A further element of formalism in this argument is the arbitrary insistence on righthanded coordinates. Unless the molecules are enantiomorphic (i.e., chiral) or enantiomorphically arranged, this condition may also be relinquished. This is the case provided the phase is composed of nonchiral molecules. Thus we can cancel further terms contributing to the elastic moduli in both nematic and nonchiral smectic liquid crystals. From the condition of enantiomorphy (i.e., nonchirality) we have x’=x, y’=-y, z’=z giving
5
1
nx’=alx’-a3y’+ua3Z’+O(r ) n-,.. =uqx‘-u~y‘+agZ‘+O(r )
oj
k 5 = 0 , k,=O
as well as. for second order terms
37 1
(60)
Hence the most general dependence of free energy density on curvature in molecularly uniaxial liquid crystals is the matrix as given previously, but in the special cases of nonpolarity and in the absence of enantiomorphy, k2 and k I 2vanish. Hence to summarize, Eqs. ( 5 1a), (56) and (57) express the more general dependence of the free energy density on curvature in a uniaxial liquid crystal. Further restrictions then apply dependent on the physical properties, i.e., nonenantiomorphic and nonpolar kl = 0, k2 = 0, kI2 = 0 nonenantiomorphic and polar kl # 0, k 2 = 0, k l 2 = 0 enantiomorphic (chiral) and nonpolar k1 = 0, k2 # 0, k12 = 0 enantiomorphic (chiral) and polar k , # 0, k2 # 0, k12 # 0
(61)
The general expression for the free energy density is
372
f
2 Chiral Nematics: Physical Properties and Applications
= kl(s1+ s 2 ) + k2 (ti + t2 )
1 1 +kll(s1+ s2I2 + 5 k 2 2 ( t i + t 2 I 2 2 1 +k33 (b: + b? ) -k k12 (sl + s2 ( t l + t2 ) 2 (62) - (k22 + k24 )(s1 s2 + tl t2
and we note at the origin that
V .n = s1 + s2 -n . v x n = t2 + tl (n.V x n ) 2=b12+b?
I V . [(n.Q n - n ( V . n ) ] = s l s 2 + t 2 t 2 2
(63)
Equation (53) can be then further simplified using so = - kl l k l l , ko = - k2 lk22 1 kll so2 + 1 k22 t i and f,'= f + 2 2
(64)
which corresponds to a new, generally lower free energy density, including optimum splay and twist. This replaces the uniform orientation expression which we had earlier. Putting f into a coordinate-free notation, we have the more compact form
f , = 1 k11( V . ~t- SO ) 2 2 SPLAY -
+ 21 k22 (n . V XII + t o ) 2 -
TWIST
+1 k33 [(n . QnI2 2 BEND
-kI2(V.n)(lt. V X ~ ) POLAR -
1
( k 2 2 + k24 )
.((V.n)2+(V~&)V 2 -L . V&) (65) SURFACE
The orientational elastic constants kl k2,, and k3, have magnitudes of typically lo-" N. Note that here we have described the bulk properties of the material and that in actual devices the free energy is modified by surface forces and electric or magnetic fields. We will return to this below. For both chiral and achiral nematic phases the materials are nonpolar, macroscopically, hence so=O and k12=0 from Eq. (61). Further, the last term of Eq. (65) has the form of a diver,gence, which may be converted into a surface integral [ 1081when integrating over the volume of the liquid crystal. This surface term is negligible when considering the bulk properties of the achiral or chiral nematic film. The reduced form of the free energy density then becomes Fd
1 k11( V . n ) 2 =2
+ 21 [(k22n . V x n )+ kI2 -
+-1
2
( k 3 3 n xV X ~ ) ~
(66)
which is in the form of the free energy in chiral nematic phases, given in Eq. (2), when the lowest energy structure has a finite twist of k radianslmeter [=27dp] and corresponds to the director field
[ t1 t 11
n = cos -z+$
,sin
-z+$
,O
(67)
given in Eq. (1) and Fig. 1 . If q = O we have an achiral nematic where
1 k12(divn)2+-1 k2, (n . ~ u r l n ) ~ Fd = 2 2 1 + 2 k33 ( n x ~ u r l n ) ~ (68) -
The usual depiction of the splay, twist, and bend deformations is shown in Fig. 28. The twisted nature of the chiral nematic phase often ensures that a number of differ-
2.2
00 00
000
ooanQ
00 00 00 TWIST
SPLAY
BEND
Figure 28. Schematic diagrams of (a) splay, . . (b) twist, and (c) bend deformations in a chiral nematic. (N. B. Although we use ellipses to represent the deformations they are director. not molecular, properties.)
ent equilibrium structures can be established in the presence of external fields of different magnitude, and often, frequency. The structures induced will also depend critically on the magnitude (and sign) of the dielectric, magnetic, and flexoelectric anisotropies and coefficients, respectively. The external fields couple with the macroscopic properties to alter the director field and to give extra terms in the free energy density expansion such that generally Fd
= Feldstlc
Fdielectric
+ Ftlexoelectric
+ Frnagnet~c
(69)
where: (1) Felastlc is the free energy density in the steady state due to the splay, twist, and bend deformations, and the helix twist, as given in Eq. (67),
(2) Fdlelectrlc is the contribution to the free energy density due to the coupling of the dielectric anisotropy A E (arising in nonpolar systems from the polarizability anisotropy) with the external electric field E , such that
and is the dielectric constant perpendicular to n. Note here that &Idoes not couple with n and therefore has no effect on the director field. The factor 4 7 ~ :has been includ-
Static Properties of Chiral Nematics
373
ed for consistency with the S . I. system of units. The sign of A & therefore defines the direction of preferential motion of n in the applied field, and the coupling gives rise to a quadratic effect in the external field due to the (n . E)2 term.
(3) Flnagnetlc is the contribution to the free energy density due to the coupling of A x , the magnetic anisotropy, defined as A x = ~ , ~ -with x ~ , the externally applied magnetic field B. A x is usually positive for aromatic ring structures (and some cholesteryl esters are negative), and arises from the diamagnetic anisotropy. The free energy density in the local magnetic field H is then given by ~ ~ a ~ n t . lI i c = - - [ x I ~ ~ + ~ x ( n(71) .H)~]
2 where again x L H 2 does not contribute to motion of the director field, and the coupling gives rise to a quadratic effect in the field due to the (n . H ) 2term. (4) FflexOelectrlcis the contribution to the free energy density due to the coupling of the flexoelectric polarization Pflexwith the applied electric field E , such that Fflexoelectric
=-E
. f'flex
(72)
where
Pflex= e,n( V .n ) + e , ( n x V x n )
(73)
and e, and eb are the splay and bend flexoelectric coefficients, respectively. e , and eb may differ both in sign and quite significantly in magnitude, thereby giving rise to quite different orientation effects of the director field n . In these cases, where the flexoelectric effect dominates over any dielectric term, the coupling is linear with E . In the above description we have limited ourselves to the main interactions that lead to large-scale deformations or reorienta-
374
2 Chiral Nematics: Physical Properties and Applications
tions of the director field and therefore marked changes in the optical properties of chiral nematic materials. These deformations lead to Frkedericksz transitions, helix unwinding, linear and nonlinear optical responses, etc., in the presence of an external coupling field and will be discussed in detail in Sec. 2.4. Other weak effects that might involve electroclinic phenomena in long (-) pitch chiral nematic systems are outside the scope of the present chapter. In the following section we will consider the time-dependent or dynamic implications of director deformations, which will lead us in turn to discuss field-induced transient phenomena in chiral nematic liquid crystals in Sec. 2.4.
2.3 Dynamic Properties of Chiral Nematics The static theory discussed in the previous section describes the equilibrium situation in chiral nematics very well - in general, theory and experiment are in good accord. The dynamic situation is less clear. On the molecular scale, the chiral nematic and nematic phases are identical; the question then becomes, ‘how does the macroscopic twist or helicity modify the vector stress tensor of the achiral nematic phase defined by the socalled [ 1091 Leslie friction coefficients a,- a,?’ Experimentally, viscosity coefficients that are then related to the Leslie coefficients are measured in a way that depends specifically on the experiment being used to determine them. The starting point for discussion of dynamic properties is to use classical mechanics to describe the time dependencies of the director field n (r, t), the velocity field v(r, t ) , and their interdependency. Excellent reviews of this, for achiral nematics, are to be found in [59,109,
1lo], and a concise overview of the derivation of static and dynamic properties based on continuum theory is given in [ 1111. The problem is encapsulated by the simple fact that in a dynamics experiment, such as viscometry, the coupling of hydrodynamic equations relating v ( r , t ) and it (r, t ) implies that n then, generally, becomes ill-defined. For example, the measured viscosity depends on shear rate, surface and flow-induced alignment, the presence of defects and instabilities, and a myriad of other experimental conditions, such as sample geometry, cell thickness, applied electric or magnetic field, etc. These experimental conditions are so important that apparent bulk viscosities may differ by several orders of magnitude from those predicted by continuum theory and applicable at the director level. With these observations in mind, we will present an outline of the main theoretical considerations and experiments where these predictions have been tested.
2.3.1 Viscosity Coefficients As discussed in Sec. 2.2.2.1, the foundations of the continuum model were laid by Oseen [61] and Zocher [ 1071 some seventy years ago, and this model was reexamined by Frank [65], who introduced the concept of curvature elasticity to describe the equilibrium free energy. This theory is used, to this day, to determine splay, twist, and bend distortions in nematic materials. The dynamic models or how the director field behaves in changing from one equilibrium state to another have taken much longer to evolve. This is primarily due to the interdependency of the director n (r, t ) and v (r, t ) fields, which in the case of chiral nematics is made much more complex due to the longrange, spiraling structural correlations. The most widely used dynamic theory for chiral
2.3
and achiral nematics is due to Ericksen [ 17, 181andLeslie [15,16,109],andthisisbased on the formulation of general conservation laws and constitutive equations to describe their mechanical behavior. It is assumed that the director field is a continuous function, whose direction can change systematically from point to point in the medium (ignoring singularities of the type discussed in Sec. 2.2.1. l), and that external fields can result both in director reorientation and a bulk translational motion of the chiral nematic medium. In the following outline we will use Leslie’s original nomenclature [ 109, 11 11 where possible and the Cartesian notation, in which repeated indices are subject to the usual summation convention, i.e., a comma followed by an index denotes partial differentiation with respect to the corresponding spatial coordinate, and a superimposed dot indicates a material time derivative, e.g., T,i=aTlaxi, v,=avilaxj, and V = d Vld t. The chiral nematic is considered incompressible, i.e., of constant density p with a nonpolar unit director n (i.e., n n = 1). This implies that the external forces and fields responsible for the elastic deformation, viscous flow, etc., are much weaker than the intermolecular forces giving rise to the local order, i.e., between the chiral molecules. We will consider a volume of material V bounded by a surface S ; v and w represent linear velocity and local angular velocity, respectively, i.e.,
w=n.ri v.v=0
per unit time, and h as the flux of heat out of the volume per unit area per unit time. These are customary energy balance terms for a conventional isotropic liquid. For liquid crystals we introduce the following new terms to enable us to balance the conservation of energy equation: G is the generalized or director body force per unit volume (arising, for example, from a body couple created by an external magnetic or electric field), s is a generalized or director stress vector per unit area, which is related to the couple stress acting on liquid crystal surfaces, and o is a scalar which represents rotational kinetic energy of the material element (i.e., an intertial constant). With these assumptions we can now write the conservation laws for a chiral nematic:
1. Conservation of mass
2. Conservation of linear momentum Jp+dV=jFdV+jtdS V
V
S
(77)
3. Conservation of angular momentum [ ( p r x v) + (ori x %)]dV V
=
1[ ( r x f ) + ( n x G ) ] d V + 5 [ ( rx t )+ ( n x s)]dS V
s
(74)
4. Conservation of energy
(75)
=j(f.Y+G.ri+Q)dV
and
375
Dynamic Properties of’ Chiral Nematics
j ( p v .v +ori . n + U ) dV V
due to the assumption of incompressibility. Further, we define f as the body force per unit volume, t as the stress vector per unit area, I/ as the internal energy per unit volume, Q as the heat supply per unit volume
V
+ j ( t . Y + s . ri - h ) dS S
(79)
Equation (78) can be written [I091 as Oseen’s equation [59],i.e.
376
2
j OK dV =
V
V
Chiral Nematics: Physical Properties and Applications
(G + g)dV + s dS S
(80)
where g is the intrinsic director body force, with the dimensions of torque per unit volume, which is independent of G . Further ti=t,Vj, the surface force per unit area acting across the plane whose unit normal is vj and si=s, vj,the director surface force, as previously defined. Conversion of surface integrals into volume integrals and rearranging leads to the conservation laws in the following differential form, (i)
p = 0,
independent and arbitrary functions we obtain
and
with @i=aeyknj(Nk+dk,,np)and a i s a constant. Equation (85) then gives
(81)
(ii) ~ l i ~ = J ; : + t ~ , ~ ,
(82)
(iii) o E j = Gi+ gi + sij,j,
(83)
(iv) U = Q - hi,,+ t, dij + sij Nij - g, Nz,(84) where tij - ski n j , k
+ gi nj = tjj - skj ni,k g j ni NI. = k.I - w .I knk N.. v = n?I . - w .lk nk , J. 2d.. = v.1,J . + v J.. 1 . (I 2w.. = v.I , J . + v J.. 1 . (I
Here Ni may be interpreted as the angular velocity of the director relative to that of the bulk fluid, and it should be noted that to is asymmetric. From the Helmholtz free energy per unit volume (i.e., F= U - T S ) ,the form of the energy conservation given by Eq. (84), and the entropy inequality, i.e.,
dt v
SdV where S is
Following the Leslie thermodynamic formulation for the constitutive relations, i.e., that t i j , gi, and p ian be resolved into separate static (elastic) and hydrodynamic (viscous) parts, namely t.. = t!!+.; . lJ
U
gi = gio + i z
pi = p;
+ ji
we obtain
the entropy per unit volume, we obtain the following entropy inequality for a system in isothermal equilibrium (85) t..d.. +s.. - g .1N .1 - p .1 T,1. - F - S T - @ . 1,z. >-O !J 1J 1J where &-hi- T p i is introduced as a dummy vector and pi is the entropy flux per unit area per unit time. Since T i , d, and nu are
lJ
with pq = 0
2.3
Dynamic Properties of Chiral Nematics
377
and the inequality (Eq. 86) simplifies to
+ ginj= Fji + gj ni and the entropy Further, tCj generation per unit volume is then T i = Q - h;,i + ff eijk [nj ( N k + dkp F Z p )] . ,1
+iji
dij
- i. Ni
(91)
The hydrodynamic components of and hi are then
tij
gi,
np dk, n; nj + a2 Ni nj +a3N j ni + a4dji + a5diknk n j +a6 djk nk ni + a7 eipqT qn j np
= a1 nk
+a8 e j p q T q ni np i i
ti,,
= -(YI Ni + ~2 dij nj
(92)
+
eipq
np Tq 1 (93)
h; = K I Ti + K 2 nk Tk nj +K3 eipq
np N q + K4 e;,, np dqr nr
(94)
(95) where a,-a, are the six Leslie coefficients, as defined for achiral nematics, a, and ag are two additional temperature-dependent viscosity coefficients that couple thermal and mechanical effects with K1-K4 (the coefficients of thermal conductivity in chiral nematics). The early experimental evidence for this coupling of thermomechanical effects in chiral nematics is due to Lehmann [ 1121. We will return to these experimental results along with a discussion of flow propertiey below and convective instabilities in Sec. 2.4.3. From Eq. (90), the entropy inequality gives
tl, dlJ - ii Nl - ki Ti - aa etjk nj
(Nk + dhp np) Ti
(96)
Clearly these inequalities underline the greater complexity involved in the analysis of the dynamic properties of chiral nematics in comparison with achiral nematics. Simplifications have been suggested [ 1 131 based on the work of Parodi [114], which, besides the relations in Eq. (95), suggests that K~ = K and K4 = a,+ ag. It remains true, however, that to date it has been difficult experimentally to define conditions that isolate these different viscosity coefficients and thermal properties, since this implies decoupling IE (r, t ) and v (r, t ) when n spirals relatively tightly on the optical length scale. Interesting experiments have, nonetheless, been carried out, which demonstrate the unusual viscometric (i.e., non-Newtonian) properties of chiral nematics with apparent viscosities that increase by five or six orders of magnitude on crossing from the isotropic to the chiral nematic phase 11 1-51.
2.3.2 Lehmann Rotation The first recorded example of thermomechanical coupling, as explained in the Les-
378
2 Chiral Nematics: Physical Properties and Applications
lie-Ericksen theory, in chiral nematics appears to be due to Lehmann [ 1121. In his experiments he observed droplets of chiral nematic, which on heating from below appeared to evolve a complex rotating and spiraling director pattern within the droplet walls. Following Leslie’s equations, this effect may be explained as follows: the temperature gradient acts as a directional or polar field, which in turn, through the lack of mirror symmetry in chiral nematics, leads to the thermomechanical cross terms. These produce a torque or axial vector, which then leads in turn to the director rotation and transport. In a parallel experiment using a polar electric (i.e., dc) field, similar ‘Lehmann’ rotations were observed [ 1161, which serves to underline the validity of the Leslie analysis. It is therefore interesting to follow this analysis further [ 1091. A chiral nematic film is assumed to be a semi-inifinite planar sample with its helix axis in the z direction bound by planes at z=O and z=d. The director n is described as in Eq. (1) with $=O, i.e., [cosO(z, t), sin e(z, t), 01. The boundary conditions are that there are (1) no external body forces, (2) no heat sources within the liquid crystal, and ( 3 ) that the velocity vector is zero, i.e., fi=Gi=dU=wU=O and that T = T ( z ) . Conservation of angular momentum [Eq. (83)] then gives
a2e ae a T 2 = Yl at - Y3 =&
0
at
where
and Fo is the free energy density in the ground state, or absence of elastic deformations. For such time-independent situations
a2e= ae = 0 ,
~-
at at simplify to
and the above equations
and
whence T
j q d< = A Z + B
0
and
where A , B, C, and D are all constants of integration set by the boundary conditions. If we assume the polar field comes from the temperature gradient between z =d and z=O, i.e., T, - To,and that the director is unbound at the surfaces (i.e., weak anchoring), then the surface torques or couple stresses r i l = f ? G k n i S l k are zero, which leads to
The energy balance per unit volume (Eq. 91) then gives
-
(
Y1,,-Y3-
aZ
-
at
(99)
If the material constants are assumed to be, in a first approximation, independent of
2.3
temperature (i.e., far from a phase transition), 8= w t + f ( z ) and T=g ( z ) ,then the conservation of angular momentum and the energy balance (Eqs. 98 and 99) give
and
a2.f
ag
k22 2- Y3 -+
az
az
Yl w = 0
with solutions g=
and
-
(
3
wz+Aexp y3-
+B
If 8=$ for z=O and T ( z )are as defined above. we have
379
Dynamic Properties of Chiral Nematics
2.3.3 Macroscopic Flow The macroscopic flow properties of chiral nematics are very different from those of an achiral nematic, due primarily to the long range helicoidal structure. As shown in Fig. 29 [115], the apparent viscosity qapp can vary by a factor of lo6 at the same temperature in the same chiral nematic material, depending on the shear rate. The lower shear rates in capillary flow experiments lead to higher values of qappin comparison to the rotational shear field experiments. The reader can try a simple experiment by placing two drops of the same nematic base material, but one doped with a chiral twisting agent to give visible reflections, on a glass slide. On tilting the slide, the achiral nematic drop can be seen to flow at a significantly greater rate than the chiral compound. The flow of the chiral compound is
and CHOLESTERIC
Thus in Leslie's prediction [ 1 171, the director rotates about the helix axis with an angular velocity a.If the surface anchoring is strong, the solutions become static and result in a modified twisted helix configuration. Equally, if A T= ( T ,-To) =0, the solution for 8 leads to a static regular helix of pitch p = 2 7c k,,l(k- a).As we will see when studying capillary flow, the anchoring conditions are critical for observing the consequences of thermomechanical coupling in chiral nematic systems.
I10
i
ISOTROPIC
I20
130
140
Temperature (Celsius)
Figure 29. Apparent viscosity, qapp,of the chiral nematic cholesteryl acetate as a function of temperature for different shear rates. Capillary flow (s-I) 10 ( V ) , SO (x), 100 ( ), 1000 (v), SO00 ( );rotational shear (s-I) lo4 ( A ) , and normal liquid behavior at very high shear rate ( 0 ) (redrawn from [ 1 151).
380
2 Chiral Nematics: Physical Properties and Applications
much more akin to that of a smectic material, and the complete uncertainty of viscosity measurements in chiral nematic materials is encapsulated in this very simple experiment. Is the chiral nematic phase really so highly non-Newtonian or are these orders of magnitude differences in qappdue to more to the experimental environment? Do the Leslie coefficients, as extended to chiral nematics, have validity, and how might we examine them? There appears to be no concrete experimental evidence to answer these questions, but there are strong indications that support the base concepts, and so we will review some of the key experimental results to date. It is important, however, to remember at the outset that the boundary conditions, implicit in the Leslie theory, and the length scale of the experiment, as related to monodomain behavior, are fundamental in relating theory to experiment in these chiral nematic structures. One of the simplest experiments in ordinary liquids to measure viscosity is to measure the classical Poiseuille flow in a capillary tube. For a tube of radius R, with a mass flow of Q per second and a pressure drop of p per unit length, the apparent viscosity is given by
where p is the fluid density. Such pioneering measurements have been carried out on chiral nematics and lead to the high values of apparent or bulk viscosities referred to in references [ 115, 1181. In related torsional viscometry, consisting of parallel glass plates, similar high values of qapphave been obtained [ 1191. The latter authors have discussed [120, 1211 how the direction of the helix axis, relative to the substrates and in the bulk, depending on the shear rate, affect the data. Later results [122] have, via the Poiseuille flow techniques, established that
0.221
0
,
,
,
,
,
0.25
0.50
0.75
1.00
1.25
Shear Rate (lo3 s-l) Figure 30. Apparent viscosity, qaPp,in Poiseuille flow as a function of the shear rate for different chiral nematic pitch lengths (in micrometers); 1.9 ( O), 2.6 (x), 3 (+), 3.9 ( O ) , 6 (A), 9.1 ( 0 ) , and m ( V ) (redrawn from [122]). The helical axis was normal to the flow.
the flow normal to the helix axis is little different in chiral nematics from achiral nematics. These authors (Fig. 30) varied the helical pitch in a series of controlled experiments and showed that in their geometry the helix axis was orthogonal to the capillary walls and therefore to the flow direction at all points in the capillary. In this geometry, at long pitch lengths, the experiment would give an average of the Miesowicz [ 1231 viscosity coefficients q2 [= %(a,+ 2 a,+ a, + as)] and q3 (=%a,)for nematics. Hence for ‘in-plane’ shear, the viscosities for the achiral and chiral systems would not be expected to be so different, as indeed was observed [ 1221. In ‘thick’ capillaries, where R - 300500 ym, Helfrich [124] observed quite spectacularly different increased apparent viscosities, which he explained in terms of ‘permeation’. The Helfrich suggestion is that flow takes place along the helix axis ( 2 ) without the helical structure itself moving. In this model the director, n , is at all times orthogonal to the capillary cell walls (Fig. 31) and strongly anchored to them.
2.3
W
Figure 31. Schematic diagram of the Helfrich model of permeation in a chiral nematic. The flow is along the helix axis (z)at low shear rates and maintains the z direction distribution (see text).
The translational motion in the z direction is then achieved by the rotational motion of the director. (This can easily be visualized in terms of a corkscrew boring into a cork. The transverse view of the path in the cork is always the chiral screw, whilst the bulk of the corkscrew itself translates along the helix or screw axis.) In more mathematical terms, the energy dissipated by the motion due to the pressure gradient must equal that dissipated by the precessional or rotational motion. In this case, the viscous torque rexerted by the director is given by r = n x g where g in scalar form is given by -y, k v and v is the linear velocity in the z direction (see Eq. 93) and y, is negative in Leslie’s theory. For a pressure gradient of dpld z we have Yl
2
dp
(kv) =-vdz
The fluid flow, Q, ignoring edge effects or boundary layers, is Q=-
.nR2( d p l dz) Y1k2
which from Poiseuille’s law (see Eq. 105) gives
yl k2 R2
Vapp = - ___
8
-
Typical experimental dimensions R 300500 pm and k - 1-2 pm suggest that qaPp--lo6 yl, which is in good accord with
Dynamic Properties of Chiral Nematics
38 1
the experimental data [ 1151 for qapp.The Helfrich permeation model has been derived [ 1251 in an elegant use of the Leslie theory both for flow between parallel plates and in capillary tubes. In the latter case it has also been shown that the velocity profile is constant across the radius apart from in the interface region very close to the capillary walls. This interface and the production of quasi-infinite monodomain samples appears to be of considerable importance in experimental arrangements designed to test the theoretical predictions of the Leslie theory. It is an experimental observation that in capillary tubes the director configuration must always give either a disclination line at the center (along z ) for homeotropic surface alignment, or, in the Helfrich model, at the edges for either homeotropic or planar (x,y ) surface conditions. In the latter case, the dislocations would be bipolar in the x,y plane and spiral in the z direction. Measurements using capillaries are therefore always delicate. Either the radius is small and surface effects become important or the radius is large, in which case it is difficult to produce monodomain samples throughout the flow volume. Experimentally, we appear to be always in the situation in which it is extremely difficult to control, adequately, both n ( r , t ) and v (r, t ) independently. Techniques such as dynamic or quasielastic light scattering, in which director motion is probed at the local level, might be of great value in these helicoidal systems (see p. 295 of reference [30]). It is possible to simplify the problems posed by three dimensions by examining the flow between parallel plates, i.e., in two dimensions. This allows the director to be well controlled in ‘planar’ cells with a flow across the helix axis, and this has been considered analytically and numerically [126, 1271 as well as experimentally [ 1281, with qualitative agreement between the results. However,
382
2 Chirdl Nematics: Physical Properties and Applications
this still only leads to information on and ~ 2 rather , than the needed to test the theoretical predictions [lo91 of the LeslieEricksen theory. There is still clearly a great need for further experimental studies on chiral nematic systems if thermomechanical coupling is to be understood in these materials. This is of considerable importance if the dynamics of electro- and magneto-optical phenomena are to be exploited fully, either theoretically or practically, in chiral nematic systems. In the next section we will consider these field-induced distortions in more detail.
2.4 Field-Induced Distortions in Chiral Nematics The distortions induced by external fields applied to chiral nematic liquid crystals give rise to a remarkably wide range of electro-, magneto-, thermo-, and even opto-optic effects. These range from their use in twisted nematic devices, and a resulting technology that dominates the flat panel display market, through fundamental studies of magnetically and electrically induced Freedericksz transitions, thermometry, thermography, and imaging techniques, to their use as optical elements in laser technology. In the present sections we will review how the various static and dynamic properties, which we have already discussed, lead to such a wide range of uses and applications. The starting point is to reconsider Eqs. (1) and (2). In the presence of an external field, the free energy density is modified by a term involving the coupling between the electro-magnetic (or other) bulk anisotropic property and the field (see Eq. 69). This leads to reorientation of the director n in order to minimize this addition-
al term. In chiral nematics the director has a twist term, due to k in the free energy expression, which, in the general case of an applied field, will lead to distortion of the helix and therefore a change in the bulk and, particularly, optical properties. The helix pitch may be long @>>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
2 Chiral Nematics: Physical Properties and Applications
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, qZ<<4,<
-
sin kz cos kz -
+ k33 cos4 kz(
a2@ ax --k22 sin22kz a2e - (k22 - kll) 2 4 ax2 sin2kz- a2@ + kll ksin2kz-ae ax az aZ
-k33
8 = 80sin q,x cos qz @ = (q& + 43 cos2kx)cosqXxsin qz z
.(kf3+gr+kllcos - kll sin 2kz-
and
ax
these limits. Thus for
%I] (107)
as a@
-= O
we have,
under the assumption of slowly varying a
If we assume that the total energy 3= F d V, V then
where
a = - (k, sin2 kz + k33 cos2 k z ) .
(2+ k g )
13)
(2 k22 + k33 - kll) cosq, zsinq, x (114)
2.4
Field-Induced Distortions in Chiral Nernatics
3 a5
Using the limitations of ql<
or again
which lead to $0
=
k8o 4x
Under these approximations, the free energy density, taking into acount undulations, is
If we now apply a magnetic field normal to the layers, the total free energy
Ft = F u m + Fmagnetic where -
A x ( n .H ) 2 2
Fmag - - -
( 1 19)
36 and if __ -0, we have
ae
The limiting conditions are if q?+O or 00 then H +03, remembering that qzis fixed by the cell dimensions. If qx+00, the bend (k33) mode is excited, whilst if qx 4 0 , the amplitude of the twist mode diverges rapidly with decreasing qn. The optimum wave vector [591 occurs for a mixture of twist and bend modes such that
Thus the periodic distortion depends critically on the relationship between the chiral nematic pitch and the cell dimensions. Therefore these phenomena are only observed for cells in which the thickness is considerably greater than the helix pitch [ 1351. For low threshold fields, the diamagnetic anisotropy should be high with low bend and twist elastic constants. For the conical distortion, Leslie [ 1 3 3 ] has derived a critical field, HcD, given by
H& = 1 (kl1 q: AX
+ k33 k 2 )
and as we shall see in the next section the critical field for the helix unwinding (chiral nematic to homeotropic nematic) transition HCNis given by
Since k > > q Z , the threshold field for the Helfrich periodic distortion is much lower than that for either the conical or the helix unwinding distortions. The inter-relation of, primarily, the bend and twist elastic constants defines which of the latter two modes
386
2 Chiral Nemdtics: Physical Properties and Applications
is observed in thinner cells or at higher field strengths. A further complication arises here in that the derivations of the different critical fields are calculated from the free energy expression (Eq. 2) with increasing field and for deformations induced in a texture that is initially planar. The critical fields vary [ 13 11 with decreasing field, depending on time and the ratio of dlp. On relaxing back for the helix unwound texture (H>H,,), the chiral nematic may form a metastable focal-conic texture with a long lifetime, even as H+ 0. Since these distortions are related to pitch changes, the reflection and transmission properties, both polarization state and wavelength, will alter with increasing and decreasing H. These optical changes are also observed in electric fields and will be discussed in the following sections. The more subtle deformations, as between the Helfrich and the conical distortion modes, are often more readily observed by capacitance measurements than by optical techniques for long pitch systems in thick cells [136]. The most spectacular optical changes occur for the chiral nematic to nematic field-induced transition and occur readily for a field applied across the helix axis for A x positive materials.
anchoring. The interesting case occurs for A x > 0 and planar alignment, since this leads to a clear chiral nematic to nematic helix unwinding distortion which involves only p , Ax, and k22 (see Eq. 126). This structural transition is depicted in Fig. 33. The director n in these experiments is orthogonal to z and spirals in the x, y plane (see Eq. 1). Since A x is positive (i.e., xII>xL),then j/2(xL+xI,)>xL and the director rotates in plane to minimize the free energy relative to H . The helix axis remains in the z direction, but gradually unwinds as H approaches a critical distortion field, HcN,to become planar nematic with an infinite pitch above HCN(Fig. 34). This results in the selected reflection color moving to longer wavelengths until the pitch becomes infinite [136,138]. This dependence of the pitch on the applied field has been examined theoretically [ 132,1391 and we will consider this further. Initially, the sample is assumed to be fairly thick (i.e., d > p ) and in a planar texture. For zero or low fields, the helix will be arranged as in Fig. 33 a. At intermediate fields
2.4.2 Magnetic Fields Normal to the Helix Axis In this section we will consider the magnetic field induced distortions for a field applied orthogonally (i.e., in the x, y plane) to the helix axis or z direction. For A x < 0, similar distortions to those discussed earlier will occur due to the director rotating in the field H to minimize the free energy, i.e., with the helix in the x, y plane and n in the z direction. The distortions will be the same, but with slightly different boundary conditions depending on the pitch, cell thickness, and
H=O
O
H'HCN
Figure 33. Schematic representation of the untwisting of a chiral nematic helix for a magnetic field H normal to the helix axis ( z ) with A x > O . A denotes regions where the helix becomes distorted and B denotes regions of 180" twist walls. For H>H,,, the helix has infinite pitch.
2.4
387
Field-Induced Distortions in Chiral Nematics
= L j [ [ s - k )2k 2 2 - A ~ H 2
+ const. where, as before, k=27clp, the undistorted helix wave vector. The equilibrium condition is then 10 I 0
0
H/Hm
Figure 34. Magnetic field dependence of the relative pitch p (H)/p(0) in a chiral nematic. These data come from [ 1371 and correspond to PAA doped with cholesteryl acetate.
H < H C N , with H in the x direction [i.e., H = ( H , 0, O)], the directors will deform to distort the helix, as shown in Fig. 33b. These directors originally pointing (on average) with a greater anisotropy component in the x direction will deform to be parallel to H , i.e., in the x direction (at B), having a tightly twisted region at the ‘points’ or positions (A) with the director along y , i.e., orthogonal to H . These correspond to a succession of 180” twist walls. With further increasing field, the regions or ‘walls’ such as B become unwound so that the directors realign along the field and the areas A on average expand, thereby increasing the effective pitch. The helix becomes fully unwound for H>H,. Mathematically this is described as follows. The field H is along z (i.e., H = h , 0, 0) and the director (see Eq. 1) is n = (cos v, sin v,0), where y = k z + $. For thick cells in which d>>p, $ is a constant defined by the surface alignment and can be ignored. We will consider pitch deformations ‘far away’ from the substrate. The free energy density of the system is then given by
k22(
d2W - A X H 2 s i n t y c o s v = 0 g)
(127)
which gives
z = 2a5,F, (a) for
and R12
dv
Fi(a)= j (I-a 2 sin . 2 y)Il2 In this notation, a is a constant determined from the condition that 3 is a minimum, z = p (H)/2, i.e., the half pitch of the field distorted structure or the distance between twist walls, F , ( a ) is a complete integral of the first kind, and 5, relates to the wall ‘thickness’, which is of the order of 2 t 2 ( H ) [30, 1391. The free energy is then given by
kz
kz
1
(q+p)
where
a2 = (I + p)-’ and h = (t2k)-’
(128)
388
2 Chiral Nematics: Physical Properties and Applications
and
fi (a)=
A12
5 (1- a2sin2yl)1’2dyl 0
Here F2 (a)is an elliptic integral of the second kind. Minimizing the free energy as in p= 0 leads to the previous sections for A
For z(H=O)=n/p(O), i.e., the undisturbed helix, and z (H)=7t/p (H) we get
If z(H) +m, then a+ 1, F 2 ( a ) and for H=HCN,i.e., the helix unwinding field, we have h =7t/2 or -03,
where p=p(O), as defined in Eq. (126). Experimentally it has been verified that HCNis inversely proportional to p [ 1401 for relatively long pitch systems and that Eq. (131) is experimentally valid [137, 1401. It should also be noted that the pitch divergence only occurs close to HCNas the number of pitch walls rapidly decreases to zero. A further interesting observation is that for low field H<
2.4.3 Electric Fields Parallel to the Helix Axis Many of the magneto-optic effects described earlier are readily observed in electric fields when the magnetic free energy term Fmagnetic [=-Ax/2 (n . is replaced by the [=-Ad4 7t (n . HI2]. electric term Fdielectric Materials developments [ 144,1501in recent years have produced a wide range of nematic materials with high A& (positive or negative) with low voltage displays in mind. Access to their chiral analogs, through neat materials or mixtures, led to a similarly wide range of chiral nematic materials. These are now of such a high purity that many of the original conduction problems encountered with Schiffs-base materials, such as MBBA, have now disappeared. As a result of these highly significant improvements, it is generally easier to study distortions in chiral nematics in electric rather than magnetic fields. It is, however, instructive initially to study the general case where the free energy density includes a term Fconductive related to the conductivity anisotropy o(=oll-oL)as well to A& [134, 1511. Here o,, and o, are defined as relative to the local director n , as is usual. If we assume an initial planar texture, then the macroscopic conductivities will be q,and o,, with z defining the helix aixs as before and
a2]
provided the cell thickness d>p. Thus in the following analysis we are still in the coarse grain model [30]. Further, we ignore charge injection at the electrodes-simple SiO barrier layers prevent this experimentally. We first consider the case for E parallel to z, i.e., along the helix, and we assume a DC field. (Note that at high frequen-
2.4
Field-Induced Distortions in Chiral Nematics
cies 2 1 O3 Hz the dielectric phenomenon dominates in the distortions to be discussed later.) To analyze this we have to consider the Carr-Helfrich mechanism [ 124, 15215.51 due to mobile charges, as well as that due to the Helfrich distortion previously discussed for magnetic fields, i.e., layer fluctuations parallel to z , as defined in Eq. (1 1 1 ). (Note that in the de Gennes layer model [30] 8 = k, u.) Therefore we write the current J in terms of the total field Et due to the field applied externally E and that caused by the Carr-Helfrich charges, i.e.,
Jz0-E
where J z is a constant. The condition of charge conservation ( V .J = O ) leads to
ax
and E, due to the Carr-Helfrich mechanism is the lateral field component. The density of the mobile charge carriers, p,, is then 1 v.( E . E ) pc = 47t
and the vertical electric forcef, due to these carriers is then = PcE
and since fd=dTdldx
The total electric force felectricacting on the chiral nematic layers is
The elastic restoring force,fe,,,,i, is given by
and at the threshold (i.e., Eth) felectric+ felastic=O. The optimum wave vector k, is given by Eq. (120), q?=n/d, and k=2nlp, therefore
or ( 1 35)
.fc
structure distorts. This is determined from the dielectric torque acting on the structure, i.e.,
( 1 33)
For the distorted structure E the helix axis will have small components in the x direction as before, and therefore in the small deformation approximation we have
26:=o or J,=O
389
(137)
There is a further forcefd, due to changes in the dielectric tensor as the chiral nematic
and from Eq. (132) we have
Thus, as was shown for the magnetic case (see Eq. 124), the threshold field, Ep?, is proportional to ( ~ d ) - ' / For ~ . long pitch systems and thick cells, these effects are readily observed [ 156-1591 in moderate electric fields (-a few volts/micrometers) and this analysis has been extended to the general case of ac fields [ 1341 to give
390
2 Chiral Nematics: Physical Properties and Applications
then EPD 1631. As o increases towards oc, diverges markedly [ 1641, and this differentiates between the two regimes (i.e., A&>O 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 d
2.4.4 Electric Fields Normal to the Helix Axis The electro-hydrodynamic instabilities discussed previously are essentially independent of the sign of A E, since they are induced by the anisotropy of the conductivity. Thus applying fields perpendicular to the helix axis induces deformations dependent primarily on the sign of AD. In thick cells (d>p) the same instabilities are produced, depending on the sign of AD, in cells with E parallel or perpendicular to the helix axis. Obviously the effects for A o>O are inverted to those for A o
39 I
nar textures in which d>>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
2 Chiral Nematics: Physical Properties and Applications
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
Chiral Nematics: Physical Properties and Applications
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
Chiral Nematics: Physical Properties and Applications
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-
Applications of Chiral Nematics
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
2 Chiral Nematics: Physical Properties and Applications
‘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
Chiral Nematics: Physical Properties and Applications
lously high, and this can also be switched in an electric field to produce devices. For very short pitch systems, p << A,we can use flexoelectric phenomena to switch 'homeotropic' chiral textures and produce optical modulators. The fabrication processes for chiral and achiral nematics are essentially the same, and this leads to interesting developments using polymer-dispersed liquid crystal (PDLC), droplet or network stabilized devices. Herein we will briefly review these different electrooptic device modes from the point of view of the chiral nature of the phase, and this will lead on to some recent innovations which appear to be quite promising for novel applications.
2.5.3.1 Long 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,
Applications of Chiral Nematics
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
2 Chiral Nematics: Physical Properties and Applications
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,,)
Applications of Chiral Nematics
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) Short pitch chiral nematics in a planar alignment would, following Eq. (167), have very high threshold voltages compared with TN, STN, or WT displays and further, the switching would be from an isotropic optical texture with a tightly spiraling director to a homeotropic texture. Thus, unless a dye is included, there would be no optical contrast. If an aligned focal-conic texture is produced, however, in which the optical axis of the helix defines a macroscopic birefringent texture, then such a system could be switched to the homeotropic state through dielectric coupling, or tilted via flexoelectric coupling. The threshold voltage for the former effect would still be relatively high,
404
2 Chiral Nematics: Physical Properties and Applications
and it is the flexoelectric effect that interests us here. Flexoelectric effects were observed in chiral nematic systems some 10 years age [28], and these have recently been reexamined theoretically [29, 1771 and experimentally [29, 1761to show that the flexoelectric tilt angle is linear in the applied field, independent of temperature, and gives -100 ps response times. This, therefore, has great potential for moderately fast electrooptic linear modulators. Tilt angles of y=22.5", i.e., optimum switching between crossed polarizers on field reversal, were readily obtained at 33°C for fields of 80 V p-' in 2 pm thick cells. For modulators, the optical signal needs to be restricted to angles 5 15" to ensure a linear response between crossed polarizers, i.e., for E150 V pm-'. The materials used in these studies were not optimized for flexoelectric responses, and in recent further studies [274] better materials in a polymer-dispersed geometry have been used to give tilt angles of 15" at 40 V pm-' with response times of -120 ps at 25 "C. On removal of the field, the polymer network ensured that the texture returned to the uniform uniaxial helix alignment of the off state, rather than a focal-conic texture. It is interesting that for the polymer-stabilized geometry, chiral nematics that exhibit dielectric rather than flexoelectric coupling for such short pitch systems ( p - 0 . 3 pms) give effective refractive index contol useful for phase, as well as intensity, modulators. Thus flexoelectric and related phenomena in controlled short pitch chiral nematic structures are clearly areas of great potential for holographic and modulation devices [178).
2.6 Conclusions and the Future The chiral nematic (or cholesteric) was the first of the recognized thermotropic liquid crystalline phases, and it has led to over a century of intensive study and research. As we have tried to outline in this chapter, the understanding of optical properties, textures, defects, and elastic and dynamic properties have all stemmed from the pioneering work carried out on chiral (and achiral) nematic phases. This has led to significant advances in the understanding of electro-magnetic properties, which in turn has led to a number of modern electro-, magneto-, and opto-optic devices. The twisted nematic is just one example amongst the more normally recognized thermal applications of chiral nematics. With the success of TN and STN devices in complex displays, it might be thought that everything there was to be done had been done with chiral nematics. Manifestly this is not true. The recent papers on 'active' flexoelectric and 'passive' optical components and devices adequately demonstrate that there is still much to be done. It is only now that we are really beginning to understand the complexity of chirality in liquid crystals. Mother Nature, as with the reflections from the beetle Plusoitis resplendens, got there before we did. To quote [27], we have a look 'back to the future' for our new inventions and exploitations. Acknowledgements The author thanks his wife Janet for sacrificing her summer holiday to this contribution, his son Marcus for producing many of the figures and always having the appropriate reflective comment, his research group for supporting his absence (probably with glee), and Leona Hope for interpreting the many squiggles meant to be super or subscripts, for preparing such a perfect manuscript (the errors are all down to the author), and devotion well beyond the call of duty. Finally, the author would like to thank George Gray and Jorn Ritterbusch for all their helpful guidance, support, and perseverence.
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[212] M. Parsley, The Hallcrest Handbook of Thermochromic Liquid Crystal Technology, Hallcrest Product and Information, Illinois, U.S.A. 1991. [213] N. Oguchi, I. Ikami, A. Hhe, Jpn. Patent 7 435 114,1970. [214] J. E. Vandegaer, Microencapsulation - Processes and Applications, Plenum, New York 1974. [215] T. L. Hodson, J. V. Cartmell, D. Churchill, J. W. Jones, U. S. Patent 3 585 381,1971. [216] EuropeanPatent, 1 161039,1968and3872050, 1973. [217] J. L. Fergason,SIDDig. Tech. Pap. 1985,16,68. [218] J. W. Doane, N. A. Vaz, B.-G. Wu, S. Zumer, Appl. Phys. Lett. 1986, 48, 269. [219] P. S. Drzaic, J. Appl. Phys. 1986, 60, 2142. [220] N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 1987, 146, 1 and 17. [221] J. L. West, Mol. Cryst. Liq. Cryst. 1988, 157, 427. [222] I. Nyirjesy, M. R. Abernathy, F. S. Billingsley, P. Bruns, J. Reproductive Med. 1977, 18, 165. [223] J. T. Crissey, E. Gordy, J. L. Fergason, R. B. Lyman, J. Invest. Dermatol. 1964,43, 89. [224] M. Gautherie, C. M. Gros, Cancer 1980, 45, 51. [225] R. C. Margolis, L. S . Shaffer, J. Am. Obstetrics Assn. 1974, 73, 910. [226] C. Ambrosie, C. Bourcle, Gaz. Med. France 1975, 82, 628. [227] B. Y. Lee, S. S. Trainov, J. L. Madden, Arch. Phys. Med. Rehab. 1973,54, 123. [228] G. D. Dixon, Muter: Eval. 1977,35, 51. [229] W. E. Woodmansee, H. L. Southworth, Muter: Eval. 1968,26, 149. [230] H. E. Steinicke, D. D. Patent Appls. 224670A, 1984, and 236 175A, 1985. [231] M. Karner, U. Schaper, Jpn. J. Appl. Phys. 1994,33,6501. [232] P. L. Garbarino, R. D. Sandison, J. Electrochem. SOC.1973,120,834. [233] L. C. Mizell, AlAA Rep. 1971, A7-40738. [234] P. L. Garbarino, R. D. Sandison, IBM Tech. Discl. Bull. 1972, 15, 1738. [235] H. E. Shaw, U. S. Patent 3590371,1971. [236] P. Ireland, T. V. Jones, AGARD Con$ Proc. 1984, CP390. [237] A. A. Watwe, D. K. Hollingsworth, Experimental Thermal Fluid Sci. 1994, 9, 22. [238] P. G. Grodzka, T. C. Bannister, Science 1975, 187, 165. [239] K. W. Vantreuren, Z. Wang, P. R. Ireland, T. V. Jones, J. Turbomachinery Trans. ASME 1994, 116, 369. [240] M. A. Wall, UKAtom Energy Research Establishment, Bibliography, AERE-Bib, 1972,18 1. [241] R. D. Ennulat, J. L. Fergason, Mol. Cryst. Liq. Cryst. 1971, 13, 149.
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Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
Chapter V Non-Chiral Smectic Liquid Crystals
Synthesis of Non-Chiral Smectic Liquid Crystals John W Goodby
1.1 Introduction The synthesis of nonchiral smectic liquid crystals is a broad topic for discussion, however, it can be divided into subsections in two different ways. For example, smectic systems can be split into metallomesogens and nonmetallomesogens, alternatively, they can be divided into materials for (1) mesophase structure elucidation and classification [I], (2) property-structure correlations [2]; and ( 3 ) host systems for ferroelectric and antiferroelectric mixtures. In the following sections template structures used for the synthesis of smectic materials will be described, followed by discussions of the syntheses of materials that have extensive histories in the elucidation of smectic phase structures, and finally of the syntheses of smectogens that are useful in applications.
1.2 Template Structures for the Synthesis of Smectogens Smectic liquid crystal phases can be divided into phases that have structures where the long axes of the molecules are either inclined or orthogonal to the layer planes. In
addition, the molecules can have long range positional order as in crystal smectic phases (i.e., B, E, J, G, H, and K) or short range order as in smectic liquid crystal phases (i.e., SmA, SmB, SmC, SmI, and SmF) (see Chap. I of this Volume). Whether a material exhibits tilted phases or not, or long range positional order or not, has been found to be dependent to a large degree on the nature of the functional groups, the lengths of the peripheral aliphatic chains, and the length and breadth of the central rigid core region of the molecular structure of a smectogen. At a crude level the type of smectic mesophase formed by a smectogen depends on molecular shape, with the following subunits being important: (1) the rigid core, (2) polar functional groups, (3) laterally appended groups, and (4) peripheral substituents and chains. From property-structure correlations developed over many years of studying the relationships between molecular structure and mesophase formation, some idealized molecular shapes that support smectic phase generation have been identified [ 3 ] . A pictorial representation of a variety of molecular templates that have been found in smectic systems is shown in Fig. I . In this figure, the mesogenic core unit is depicted as an ellipsoid, but, it may con-
412
1
Synthesis of Non-Chiral Smectic Liquid Crystals
Cslamilic
Mesogenlc Pair
swallow-ta,led
Trtmer
Poly-calenar
LaterallyconnectedDtmer
Banana-shaped
Siamese Twin
Pyramidal or Bowl-shaped Core
~”
Telramer wilh Spherical Core
Figure 1. Some template structures for smectic liquid crystals.
Dendrimer
tain a number of carbocyclic, aromatic or heterocyclic rings and accompanying linking groups and lateral functional groups. The peripheral groups, which are essentially aliphatic chains are shown as ‘wiggly’ lines. The immediate impression from Fig. 1 is that smectogens do not necessarily have molecular shapes that are confined to being rod- or lath-like or calamitic! The molecules can have bent shapes, be bowlic or pyramidal [4], X- or cross-shaped [ 5 ] , or even spherical [6]. Essentially, examination of the varieties of molecular templates that support smectic phase formation indicates that molecules will find a number of ways,
through molecular deformation or by sharing space, to form lamellar structures. For example, consider the extreme case of the spherical dendrimers [ 7 ] , see Fig. 1. The mesogenic units in the periphery of the dendrimer will group together to give a quasirodlike molecular shape which will be more likely to stabilize smectic phase formation. Thus, the molecular architecture deforms in order to accommodate smectic phase formation, see Fig. 2. For compounds with less flexible structures, smectic mesophases can be formed if the molecules are able to share space, thereby reducing the void volume in the structure of the mesophase [8]. Typical
1.2 Template Structures for the Synthesis of Smectogens
413
Figure 3. Cross-shaped smectogens
Figure 2. An example of a dendritic smectogen.
examples of compounds with cross-shaped molecular structures that support smectic mesophase formation are metallomesogens, such as the asymmetrically substituted copper(I1) Pdiketonate complexes [ 5 ] (see Fig. 3). In the structure of the mesophase formed by these types of molecules, the shorter arms of the cross-shaped systems are thought to overlap, thereby allowing the molecules to pack tightly together. These systems have been shown to be optically uniaxial, which suggests that even if the local ordering is biaxial, any biaxiality does not persist over large distances. Given that there is a very wide variety of template structures that will support smectic phase formation, the object of this review
cannot be to discuss the syntheses of examples of compounds with molecular structures corresponding to each template. Instead, it is probably more important, and intuitive, to focus on the more significant types of smectic material. These materials tend to be drawn from the more traditional/conventional lath-like structural templates for smectogens, where the template incorporates a simple linear core that has one or two peripheral groups associated with it as shown at the top left of Fig. 1 . More detail concerning the molecular architecture of this simple template can be incorporated as shown in Fig. 4. In this template, the core structure is further divided to show the linking groups, terminal substituents, polar/apolar groups positioned at the termini of the core, and lateral groups attached to the core. Architecture (i) in Fig. 4 tends to be the template that will give the largest diversity of mesophase type in comparison to architecture (ii). For example system (i)
414
Synthesis of Non-Chiral Smectic Liquid Crystals
1
%(A)-
W
M Z is a linking group 'Rand 'R are aliphatic chains X and Y are lateral substiuenls A and B are usually polar linking groups W is alerminal group
(ii)
Examples:
2 = CHzCH,, (CH& CH=CH, C S , COO, COS, CH=CHCOO. N=N, CH=N, CH,O, COCH,, CONH, or nothing elc X and Y = H, CHs,C2H,. C.HPn+,. F, CI. Br, I,CF3,CCI,, CN. COOH. NO,, NH,, N(CH&. OH, or several of these
A and B = CH,, 0.S, Se, NH, NCH, elc W = H. C H , OCH,. CF3, C,Fs. CN. F, CI. Br, I. NO,, N(CHd,, COOH, OH etc Strunures of Some Common Core Ring Components
Figure 4. Architectural components of smectogens.
with two peripheral aliphatic chains will be more likely to support the formation of tilted mesophases in comparison to structure (ii). Thus, it is common when the two peripheral aliphatic chains are extended in length that there will be a cross-over from orthogonal phase to tilted mesophase formation. Only under specific architectural conditions will a system with a single aliphatic chain exhibit tilted mesophases [9]. For instance, Fig. 5 shows two cyano-terminated phenyl benzoates, when the polarity of the cyano group is reduced by the conjugation of the carbonyl function of the ester linking group, then tilted smectic C phases are seen, but where the polarity is reinforced by conjugation to the ether oxygen of the ester, only orthogonal phases are found. This result is relatively general and spans a wide
-
Cr79.SmA 79 N 86.5.
I
- -
Cr 67 (.SmC 33) SmA 98 I
Figure 5. Two cyano terminated phenyl benzoates.
variety of materials where the melting points and recrystallization temperatures are much lower than those shown in the example.
1.2.1 Terminal Aliphatic Chains For systems that have two terminal aliphatic chains that can be independently varied in length, tilted phases tend to occur when the two lengths are similar to one another. At short chain lengths, usually orthogonal phases such as smectic B, crystal B, and crystal E occur. In some cases the upper temperature transitions to the smectic A and smectic B phases can occur so close together that a transition from the nematic phase or the liquid phase to the smectic B phase appears to occur only through a transient smectic A phase. This transition is sometimes called a liquid or nematic to SmAB transition [lo] (Fig. 6 ) . As the chain lengths of both peripheral aliphatic groups are increased, tilted smec-
1.2 Template Structures for the Synthesis of Smectogens
-
SmA 106) .N 127 I
Cr 110
-
Cr 115 SmA 126 * I
C,oHaO
Cr 121 (. N 114) * I
Figure 6. Effect of terminal chain length on smectic phase formation.
tic C phases are usually observed first, followed by smectics I and F, underlying these phases there is the possibility of forming more ordered modifications such as J, G, H, or K. At very long chain lengths, the tilted phases sometimes, but not always, disappear to give systems that just exhibit smectic A phases [ I 11. Thus, if we were to plot the incidence of phase type, rather than transition temperatures, as a function of peripheral chain length for system (i) (i.e., varying R' and R2 in length) as shown in Fig. 4, then a graph would obtained that is similar to the one shown in Fig. 6. It should be emphasized that this figure is an idealized one and reflects data taken for a wide number of investigations, however, by no means do all material groups fit this picture; there are in fact many subtle variations. For systems where there is only one terminal alipahtic chain, typically no tilted smectic phases are observed, and orthogonal phases predominate. The smectic A phase is the commonest modification ob-
415
-
\ /
Figure 7. Three structures for comparison that have only one terminal chain.
served, followed by the smectic B, crystal B and E phases. Figure 7 shows a comparison of three materials that have only one terminal aliphatic chain, but where the terminal ring of the core has the possibility of the incorporation of a heteroatom (nitrogen) [ 121. It can be seen from this figure that the nematic phase still tends to dominate over smectic phases, and that the smectic phases observed are all smectic A in type.
1.2.2 Polar Groups Situated at the End of the Core The discussion above applies to most systems irrespective of core types, linking groups, and lateral groups, but not polar groups positioned at the termini of the core structures. The terminal core groups A and B (shown in Fig. 4 (i)) can be very important in determining whether or not tilted mesophases are formed. It was found over a large number of studies that when functional groups A and B are polar (but not hydrogen bonding) a higher incidence of tilted smectic phases is observed [ 131. Figure 8 demonstrates this effect for a set of substituted phenyl biphenyl carboxylates [ 141. In this family the oxygen atoms at the termini of the core are systematically removed. With both oxygen atoms present the mate-
416
1 Synthesis of Non-Chiral Smectic Liquid Crystals
Cr 110 * SmB 116. SmC 165 * SmA 200 - 1
Cr 110 * SmB 110.5 * SmC 132.5 SmA 184 * I
Cr98 * SmB 112 * SmC 125 *SmA 171 * N 173 * I
Figure 8. Effect of dipolar groups at the ends of the core.
rial exhibits a tilted smectic C phase, as the oxygen atoms are removed the temperature range and the upper transition temperature of the smectic C phase fall, and when there are no ether links present the tilted smectic C phase disappears. This result is typical of many material systems resulting in the experimental observations being made the basis for McMillan's theoretical model of the smectic C phase [ 151. In this model McMillan termed the dipoles associated
with the groups at the termini of the core as 'out-board terminal dipoles'. The coupling of the terminal outboard dipoles at the smectic A to smectic C phase transition was assumed to generate a torque which resulted in the molecules being tilted over in their layers, as shown in Fig. 9. However, as with most studies concerning the relationship between molecular structure and the types of smectic liquid crystal phase observed, this is not the whole story. If methyl branching points are incorporated into the terminal aliphatic chains without the inclusion of out-board dipolar groups, then tilted smectic phases can be returned, as shown
