Biaxial Nematic Liquid Crystals E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 890

Veröffentlichungsjahr: 2015

Beschreibung

In the nematic liquid crystal phase, rod-shaped molecules move randomly but remain essentially parallel to one another. Biaxial nematics, which were first predicted in 1970 by Marvin Freiser, have their molecules differentially oriented along two axes. They have the potential to create displays with fast switching times and may have applications in thin-film displays and other liquid crystal technologies.
 
This book is the first to be concerned solely with biaxial nematic liquid crystals, both lyotropic and thermotropic, formed by low molar mass as well as polymeric systems. It opens with a general introduction to the biaxial nematic phase and covers:
 
• Order parameters and distribution functions
 
• Molecular field theory
 
• Theories for hard biaxial particles
 
• Computer simulation of biaxial nematics
 
• Alignment of the phase
 
• Display applications
 
• Characterisation and identification
 
• Lyotropic, thermotropic and colloidal systems together with material design
 
With a consistent, coherent and pedagogical approach, this book brings together theory, simulations and experimental studies; it includes contributions from some of the leading figures in the field. It is relevant to students and researchers as well as to industry professionals working in soft matter, liquid crystals, liquid crystal devices and their applications throughout materials science, chemistry, physics, mathematics and display engineering.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

Dedication

About the Editors

List of Contributors

Preface

Chapter 1: Introduction

1.1 Historical Background

1.2 Freiser Theory

1.3 Nematic Order Parameters

1.4 Nematic Tensor Order Parameters

1.5 Theoretical Phase Diagrams

1.6 Landau–de Gennes Theory

1.7 Computer Simulation

1.8 Other Theoretical Issues

1.9 Applications

1.10 Characterisation

1.11 Lyotropic and Colloidal Systems

1.12 Molecular Design

References

Chapter 2: Biaxial Nematics: Order Parameters and Distribution Functions

2.1 Introduction

2.2 The Cartesian Language

2.3 The Spherical Tensor Language

2.4 Extension to Biaxial Nematics

2.5 Fourth-Rank Order Parameters

2.6 The Singlet Orientational Distribution Function

2.7 Appendices

Acknowledgements

References

Chapter 3: Molecular Field Theory

3.1 Introduction

3.2 General Mathematical Theory

3.3 Non-Polar Molecules

3.4 Polar Molecules

References

Chapter 4: Hard Particle Theories

4.1 Introduction

4.2 Theoretical Approaches

4.3 Board-Like Models

4.4 Bent-Core Models

4.5 Rod–Plate Mixtures

4.6 Conclusions and Speculations

Acknowledgements

References

Chapter 5: Landau Theory of Nematic Phases

5.1 Introduction

5.2 Symmetry of Biaxial Nematics and Primary Order Parameters

5.3 Landau Expansion

5.4 Conclusion

Acknowledgements

References

Chapter 6: Computer Simulations of Biaxial Nematics

6.1 Introduction

6.2 Order Parameters

6.3 Model Potentials and Applications

6.4 Conclusion

Acknowledgements

6.5 Appendices

References

Chapter 7: Continuum Theory of Biaxial Nematic Liquid Crystals

7.1 Introduction

7.2 Continuum Model and Energies

7.3 Dynamic Equations

7.4 Equilibrium Equations

7.5 Conclusion

References

Chapter 8: The Alignment of Biaxial Nematics

8.1 Introduction

8.2 Alignment by an External Electric or Magnetic Field

8.3 Surface Alignment

8.4 Flow Alignment

8.5 Lower Symmetry Biaxial Nematics and Hierarchical Domain Structures

Acknowledgements

References

Chapter 9: Applications

9.1 Introduction

9.2 Thin-Film Electro-Optic Devices

9.3 Non-Device Applications of Biaxial Nematic Liquid Crystals

9.4 Conclusion

References

Chapter 10: Characterisation

10.1 Textures of Nematic Liquid Crystals

References

10.2 Refractive Index Studies

References

10.3 Orientational Order Parameters of Nematic Liquid Crystals Determined by Infrared and Raman Spectroscopy

References

10.4 NMR Spectroscopy

References

10.5 Structural Studies of Biaxial Nematics: X-Ray and Neutron Scattering

Chapter 11: Lyotropic Systems

11.1 Introduction

11.2 Phase Diagrams

11.3 The Potassium Laurate–Decanol–Water Mixture: A Working Example

11.4 The Intrinsically Biaxial Micelles Model

11.5 Theoretical Reconstruction of the Lyotropic Nematic Phase Diagram: a Landau-Like Approach

11.6 Conclusions

Acknowledgements

References

Chapter 12: Colloidal Systems

12.1 Introduction

12.2 Onsager Theory and Extensions

12.3 Special Features of Colloids and Colloidal Liquid Crystals

12.4 Biaxiality in Mixtures of Rods and Plates

12.5 Particles with Inherent Biaxial Shape

12.6 Concluding remarks

References

Chapter 13: Thermotropic Systems: Biaxial Nematic Polymers

13.1 Introduction

13.2 Main-Chain Liquid Crystal Polymers

13.3 Side-Chain Liquid Crystal Polymers

13.4 Comparison of Attachment Geometries – Influence of Molecular Dynamics and Molecular Shape

13.5 Conclusion

References

Chapter 14: Low Molar Mass Thermotropic Systems

14.1 Preamble

14.2 Introduction and General Considerations

14.3 Single Component

14.4 Mixtures

14.5 Concluding Remarks

References

Chapter 15: Final Remarks

References

Index

End User License Agreement

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Guide

cover

Table of Contents

Preface

Begin Reading

List of Illustrations

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.11

Figure 3.8

Figure 3.9

Figure 3.10

Figure 3.12

Figure 3.13

Figure 3.14

Figure 3.15

Figure 3.16

Figure 3.17

Figure 3.18

Figure 3.19

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 5.9

Figure 5.10

Figure 5.11

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Figure 6.9

Figure 6.10

Figure 6.11

Figure 7.1

Figure 7.2

Figure 7.3

Figure 7.4

Figure 7.5

Figure 8.1

Figure 8.2

Figure 8.3

Figure 9.1

Figure 9.2

Figure 9.3

Figure 9.4

Figure 9.5

Figure 9.6

Figure 9.7

Figure 10.1.1

Figure 10.1.2

Figure 10.1.3

Figure 10.1.4

Figure 10.1.5

Figure 10.1.6

Figure 10.1.7

Figure 10.1.8

Figure 10.1.9

Figure 10.1.10

Figure 10.1.11

Figure 10.1.12

Figure 10.1.13

Figure 10.1.14

Figure 10.2.1

Figure 10.2.2

Figure 10.2.3

Figure 10.3.1

Figure 10.3.2

Figure 10.3.3

Figure 10.3.4

Figure 10.3.5

Figure 10.3.6

Figure 10.3.7

Figure 10.3.8

Figure 10.4.1

Figure 10.4.2

Figure 10.4.3

Figure 10.4.4

Figure 10.5.1

Figure 10.5.2

Figure 10.5.3

Figure 10.5.4

Figure 11.1

Figure 11.2

Figure 11.3

Figure 11.4

Figure 11.5

Figure 11.6

Figure 11.7

Figure 11.8

Figure 11.9

Figure 11.10

Figure 11.11

Figure 11.12

Figure 12.1

Figure 12.2

Figure 12.3

Figure 12.4

Figure 12.5

Figure 12.6

Figure 13.1

Figure 13.2

Figure 13.3

Figure 13.10

Figure 13.4

Figure 13.5

Figure 13.6

Figure 13.7

Figure 13.8

Figure 13.9

Figure 13.11

Figure 14.1

Figure 14.2

Figure 14.3

Figure 14.4

Figure 14.5

Figure 14.6

Figure 14.7

Figure 14.8

Figure 14.9

Figure 14.10

Figure 14.11

Figure 14.12

Figure 14.13

Figure 14.14

Figure 14.15

Figure 14.16

Figure 14.17

Figure 14.18

Figure 14.19

Figure 14.20

Figure 14.21

List of Tables

Table 2.1

Table 2.2

Table 3.1

Table 3.2

Table 11.1

Table 12.1

Table 14.1

Table 14.2

Biaxial Nematic Liquid Crystals

Theory, Simulation, and Experiment

Edited by

GEOFFREY R. LUCKHURST AND TIMOTHY J. SLUCKIN

University of Southampton, United Kingdom

This edition first published 2015

© 2015 John Wiley & Sons, Ltd

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Library of Congress Cataloging-in-Publication Data

Biaxial nematic liquid crystals : theory, simulation, and experiment / edited by Geoffrey R. Luckhurst and

Timothy J. Sluckin.

pages cm

Includes index.

ISBN 978-0-470-87195-9 (cloth)

1. Nematic liquid crystals. 2. Liquid crystals–Spectra. 3. Liquid crystals–Research. I. Luckhurst, G. R. II.

Sluckin, Timothy J.

QC174.26.W28B53 2014

530.4′29–dc23

2014017305

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

ISBN: 9780470871959

Professor Dr Klaus Praefcke 3rd January 1933 – 20th November 2013

This book is dedicated to our colleague Klaus Praefcke who made many innovative contributions to the molecular design and creation of liquid crystals including the elusive biaxial nematic phase.

About the Editors

Geoffrey Luckhurst was educated at the University of Hull where he graduated in 1962 with a first class honours degree in Chemistry. He then moved to the Department of Theoretical Chemistry at the University of Cambridge where he studied solution effects in ESR spectroscopy for his doctorate; this was awarded in 1965. His primary research supervisor was Alan Carrington, FRS, although he also worked with Leslie Orgel, FRS, and Christopher Longuet-Higgins, FRS. On leaving Cambridge he moved to Zürich where he was employed at the Varian Research Laboratories as their ESR spectroscopist. In 1967 he returned to England having been appointed as a Lecturer in Chemical Physics at the University of Southampton. Subsequently he has held posts there as Reader (1970), Personal Professor (1977) and Professor of Chemical Physics (1979). He currently holds the title of Emeritus Professor, which was awarded in 2004.

Geoffrey is an Honoured Member of the International Liquid Crystal Society of which he is a former President; he was elected an Honorary Member of the Royal Irish Academy in 2010. He has been awarded the Harrison Memorial Prize of the Chemical Society, the Meldola Medal of the Royal Institute of Chemistry, the Marlow Medal of the Faraday Society, the Corday-Morgan Medal and Prize of the Chemical Society, the Gray Medal of the British Liquid Crystal Society and the Fredericksz Medal and Diploma of the Russian Liquid Crystal Society. Together with Ed Samulski he founded the International Journal Liquid Crystals in 1986; Taylor & Francis, its publishers, have marked the success of the journal by the creation of the Luckhurst–Samulski Prize for the best paper published in each year. He remains research active and, following the discovery of the twist-bend nematic phase, has been much involved, with others, investigating this fascinating new liquid crystal phase.

Tim Sluckin was born in London in 1951. He studied natural sciences and mathematics at Jesus College, Cambridge, receiving the BA (1971) and MMath (1972) degrees. His PhD, on the theory of liquid helium, was from Nottingham University (1975). After postdoctoral posts in the USA and at the University of Bristol, he was appointed to a lectureship in mathematics at the University of Southampton in 1981. Since 1995 he has been Professor of Applied Mathematical Physics in Southampton. During this period he has lectured widely internationally, and has spent sabbatical periods in France, Italy, Israel and Slovenia. His main research interests in Southampton have been in the theory of liquid crystals and other soft matter. He is particularly well-known for his books (with David Dunmur and Horst Stegemeyer) on the history of liquid crystals – Crystals that Flow (Taylor & Francis, 2004), Fluidos Fora da Lei (IST Press, Lisbon, in Portuguese, 2006, translated by Paulo Teixeira), and Soap, Science and Flat Screen TVs (Oxford University Press, 2010). Outside liquid crystals, he also has other scientific research interests in the theoretical modelling of problems in the biological and social sciences.

List of Contributors

Roberto Berardi

, Dipartimento di Chimica Industriale “Toso Montanari”, Università di Bologna and INSTM, Bologna, Italy

Paul D. Brimicombe

, School of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom

Felicitas Brömmel,

Institute for Macromolecular Chemistry, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany

Patrick Davidson

, Laboratoire de Physique des Solides, Université Paris-Sud, Orsay, France

Ingo Dierking

, School of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom

Heino Finkelmann

, Institute for Macromolecular Chemistry, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany

Yves Galerne

, Institut de Physique et Chimie des Matériaux de Strasbourg UMR 7504 (CNRS-Université Strasbourg), Strasbourg, France

Anke Hoffmann

, Institut für Anorganische und Analytische Chemie, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany; Institute for Macromolecular Chemistry, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany

Antoni Kocot

, Institute of Physics, University of Silesia, Katowice, Poland

Matthias Lehmann

, Institut für Organische Chemie, Organische Materialien, Universität Würzburg, Würzburg, Germany

Lech Longa

, Marian Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland

Geoffrey R. Luckhurst

, Chemistry, Faculty of Natural and Environmental Sciences, University of Southampton, Southampton, United Kingdom

Louis A. Madsen

, Department of Chemistry, Virginia Tech, Blacksburg, VA, United States of America

Andrew J. Masters

, School of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, United Kingdom

Antonio M. Figueiredo Neto

, Instituto de Física, Universidade de São Paulo, São Paulo, Brazil

Antonio J. Palangana

, Departamento de Física, Universidade Estadual de Maringá, Maringá, Brazil.

Demetri J. Photinos

, Department of Materials Science, University of Patras, Patras, Greece

Timothy J. Sluckin

, Division of Mathematical Sciences, University of Southampton, Southampton, United Kingdom

Iain W. Stewart

, Department of Mathematics and Statistics, University of Strathclyde, Glasgow, United Kingdom

Jagdish K. Vij

, School of Engineering, Trinity College Dublin, The University of Dublin, Dublin, Ireland

Epifanio G. Virga

, Department of Mathematics, University of Pavia, Pavia, Italy

Gert J. Vroege

, Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Research Institute, Utrecht University, Utrecht, The Netherlands

Claudio Zannoni,

Dipartimento di Chimica Industriale “Toso Montanari”, Università di Bologna and INSTM, Bologna, Italy

Preface

To kill an error is as good a service as, and sometimes even better than, the establishing of a new truth or fact.

Charles Darwin

It is only relatively recently that the biaxial nematic liquid crystal phase has been the object of much intense study. But as with many good scientific tales, the story of this phase has its roots many years ago with a single imaginative pioneer. The pioneer was the theoretical physicist Marvin Freiser and the date was 1970. Freiser hailed from the IBM Thomas J. Watson Research Centre in Upstate New York, which at that time, despite (or perhaps because of this fact) being funded by an industrial organisation, was a centre for multiple, significant advances in pure science.

In noting that rather than possessing a rod-like shape – as usually assumed – most thermotropic, mesogenic molecules were in fact closer to being board-like, Freiser had opened a scientific Pandora's box. In consequence he realised that the mesogen should be expected to exhibit not one but two nematic phases, a uniaxial and a biaxial. The formation of a second nematic phase not only possessing novel properties, but also one which could have potential applications, stimulated considerable interest, as well as not a little controversy. To begin with it was theoreticians who took the lead, by exploring in some detail the broad molecular factors responsible for the new phase and its stability. Following in the tradition of Wilhelm Maier and Alfred Saupe, who first examined the statistical mechanical properties of uniaxial nematic liquid crystals as a function of temperature, these theoreticians focussed principally on thermotropic mesogens.

It was to be Alfred Saupe who yet again played an important role in the development of the field. But ironically the first liquid crystal to be found to form what proved to be a biaxial nematic was a lyotropic. In an elegant experimental investigation published as early as 1980, Yu and Saupe determined the concentrations as well as temperatures at which the biaxial nematic existed. They also showed how optical measurements and NMR spectroscopy could be used with confidence to identify the phase biaxiality. Subsequently Malthête and then Chandrasekhar tackled the problem of the thermotropic biaxial nematic by suggesting that molecules with both rod-like and disc-like features might form the biaxial phase but this did not meet with the same success.

The acceleration of work in the field, both theoretical and experimental, since the 1990s, as well as the increase in the number of workers in the field, suggested to the Editors that the time had come to summarise the field and take stock of progress. Not all areas in the field have yet reached their final form. Although some controversies in the field remain new ones are entering it. But sufficient progress has been made that a more mature view of the subject is now apparent. It is in this spirit that we offer this volume to its readers. The authors of chapters in this collection have all made significant contributions to our understanding of biaxial nematics, and all are sufficiently distinguished that their views on aspects of the field are certainly worthy of note. In assembling their chapters we have been guided by the book The Molecular Physics of Liquid Crystals, edited by Luckhurst and Gray. Here the contributions were arranged in a logical sequence reflecting the connections between them and described in an essentially common language enhancing the book's pedagogical quality. This was a recipe that seems to have worked well.

In the nature of subjects in the throes of rapid progress, notation in the area of biaxial nematic liquid crystals has not yet reached consistency or consensus. The Editors of this volume have nevertheless tried to maintain a degree of coherence in nomenclature between the contributions of different authors. We have not been entirely successful in this endeavour, but we ask forgiveness of our authors for intervening in their carefully prepared manuscripts, in the pursuit of a greater good. It is our hope that our attempts at consistency will stand the test of time.

We are grateful to colleagues in the field for long, stimulating and often provocative discussions, over the years, on the subject of biaxial liquid crystals; theory, simulation and experiment. As well as the colleagues who have made specific contributions to this book, we mention, in particular, David Dunmur, Duncan Bruce, Shohei Naemura and Martin Bates. For helping us to a successful conclusion and for the quality of our book, we are also grateful to the Editors at Wiley, Jenny Cossham, Sarah Keegan, Emma Strickland, Phil Weston, and, in particular, Gill Whitley. Finally, we wish to thank the contributors for their expertise which has made the intellectual quality so high. Such a book has, as might have been expected, taken longer than it should, and we hope that they will feel that the result is worth both their effort and, perhaps in particular, their patience.

Geoffrey R. Luckhurst and Timothy J. Sluckin University of Southampton, United Kingdom November 2014

Chapter 1Introduction

Geoffrey R. Luckhurst1 and Timothy J. Sluckin2

1Chemistry, Faculty of Natural and Environmental Sciences, University of Southampton, Southampton, United Kingdom

2Division of Mathematical Sciences, University of Southampton, Southampton, United Kingdom

1.1 Historical Background

Liquid crystals are so named because the original pioneers, particularly Friedrich Reinitzer and Otto Lehmann, observed fluids which exhibited what they interpreted as crystalline properties [1]. After some years it became clear that these materials were all optically anisotropic. Hitherto all optically anisotropic materials had indeed been crystalline, but nevertheless, in principle, the properties of anisotropy and of crystallinity could be regarded as distinct.

Until the discovery of liquid crystals, optical anisotropy had been regarded as a function of crystal structure, and was often regarded as part of the study of optical mineralogy. By anisotropy we mean that the velocities of light waves in a particular direction depend on the polarisation of the waves. An alternative way of considering this is to note that a light beam incident on an anisotropic material is usually split into two beams inside the material; the material is said to be doubly refracting or birefringent. From far away, the rather dramatic manifestation of this phenomenon is the appearance of two different images of the same object when viewed through a slab of such a material. When a beam is viewed through a smaller birefringent slab, the two beams may still overlap when they exit the sample. Then the two beams can interfere destructively after exiting the slab. In non-monochromatic beams (i.e. usually), the consequence will be bright interference fringes. Historically speaking, birefringent media were traditionally divided into two categories, known as uniaxial and biaxial, which we now briefly describe.

Of these the uniaxial media were rather simpler. The crystals exhibit trigonal, tetragonal or hexagonal symmetry [2]. All such materials possess a single optical axis, which is also an axis of symmetry for the crystal. The origin of the term uniaxial comes from this one axis. In general optical propagation in any given direction inside a uniaxial material divides itself into ordinary and extraordinary beams. The velocity of the ordinary waves is determined by components of the dielectric tensor in the plane perpendicular to the optical axis. Only the propagation of the extraordinary wave is affected by the dielectric component in the optical axis direction. The ordinary and extraordinary beams correspond to eigenmodes of Maxwell's equation for propagation in the direction in question. The key property of a uniaxial medium is that there is a single direction – the optical axis – along which the velocities of light with perpendicular polarisations are equal. In this case the two different optical eigenmodes become degenerate.