Pawel Pieranski - Liquid Crystals

1 Cover

2 Title Page SCIENCES Physics of Soft Matter , Field Director – Françoise Brochard-Wyart Lyotropic and Thermotropic Liquid Crystals , Subject Heads – Pawel Pieranski and Maria Helena Godinho

3 Copyright First published 2021 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK www.iste.co.uk John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.wiley.com © ISTE Ltd 2021 The rights of Pawel Pieranski and Maria Helena Godinho to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2021934282 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78945-040-8 ERC code: PE3 Condensed Matter Physics PE3_13 Structure and dynamics of disordered systems: soft matter (gels, colloids, liquid crystals, etc.), liquids, glasses, defects, etc.

4 Preface

5 1 Singular Optics of Liquid Crystal Defects 1.1. Prelude from carrots 1.2. Liquid crystals, optics and defects: a long-standing trilogy 1.3. Polarization optics of liquid crystals: basic ingredients 1.4. Liquid crystal reorientation under external fields 1.5. Customary optics from liquid crystal defects 1.6. From regular to singular optics 1.7. Advent of self-engineered singular optical elements enabled by liquid crystals defects 1.8. Singular optical functions based on defects: a decade of advances 1.9. Emerging optical functionalities enabled by liquid crystal defects 1.10. Conclusion 1.11. References

6 2 Control of Micro-Particles with Liquid Crystals 2.1. Introduction 2.2. Control of micro-particles by liquid crystal-enabled electrokinetics 2.3. Controlled dynamics of microswimmers in nematic liquid crystals 2.4. Conclusion 2.5. Acknowledgments 2.6. References

7 3 Thermomechanical Effects in Liquid Crystals 3.1. Introduction 3.2. The Ericksen–Leslie equations 3.3. Molecular dynamics simulations of the thermomechanical effect 3.4. Experimental evidence of the thermomechanical effect 3.5. The thermohydrodynamical effect 3.6. Conclusions and perspectives 3.7. References

8 4 Physics of the Dowser Texture 4.1. Introduction 4.2. Generation of the dowser texture 4.3. Flow-assisted homeotropic ⇒ dowser transition 4.4. Rheotropism 4.5. Cuneitropism, solitary 2π-walls 4.6. Electrotropism 4.7. Electro-osmosis 4.8. Dowser texture as a natural universe of nematic monopoles 4.9. Motions of dowsons in a wound up dowser field 4.10. Collisions of dowsons 4.11. Motions of dowsons in homogeneous fields 4.12. Stabilization of dowsons systems by inhomogeneous fields with defects 4.13. Dowser field submitted to boundary conditions with more complex geometries and topologies 4.14. Flow-induced bowson-dowson transformation 4.15. Instability of the dowson’s d- position in the stagnation point 4.16. Appendix 1: equation of motion of the dowser field 4.17. References

9 5 Spontaneous Emergence of Chirality 5.1. Introduction 5.2. Chirality: a historical tour 5.3. Concluding remarks 5.4. Acknowledgments 5.5. References

10 List of Authors

11 Index

12 End User License Agreement

1 Chapter 1Figure 1.1. Colorful arrangement of carrots recalling an orientational defect wi...Figure 1.2. (a) Lehmann posing close to his crystallization microscope. (b and c...Figure 1.3. Illustration of the three liquid crystal phases appearing in this ch...Figure 1.4. Polarization ellipses and their characteristic angles (ψ, χ). Linear...Figure 1.5. (a) Definition of the director in the spherical coordinate system. (...Figure 1.6. Illustration of the Mauguin regime for a “long-pitch” left-handed ch...Figure 1.7. Circular Bragg reflection for a right-handed cholesteric. Typically,...Figure 1.8. Reflectance spectrum of a normally incident co-handed circularly pol...Figure 1.9. Definition and behavior of o- and e-waves incident on a cholesteric ...Figure 1.10. Illustration of the director reorientation in the presence of an el...Figure 1.11. (a) Frustrated cholesteric film with unwound helix when p/L is larg...Figure 1.12. Diffractive optics from metastable localized defect structures in f...Figure 1.13. (a) Refractive optics from localized defect structures in frustrate...Figure 1.14. (a) Natural white light imaging of the four types of cholesteric fi...Figure 1.15. (a) Left: XPOL image of a spontaneous 1D phase grating made of CF1s...Figure 1.16. (a) Simulated director field of a CF2 structure. Inset: transverse ...Figure 1.17. (a) Simulated director field of a structure that corresponds to a C...Figure 1.18. Simulated lensing effect experienced by light propagating on-axis a...Figure 1.19. (a) Simulated waveguiding of an azimuthally polarized beam with a d...Figure 1.20. (a) Top: concentric lamellar structure of a smectic A filament ende...Figure 1.21. (a) TM lasing illustration in an optically pumped radial nematic dr...Figure 1.22. (a) Left: illustration of the 3D director field associated with the...Figure 1.23. (a) Elastic multipoles from spherical particles. From left to right...Figure 1.24. XPOL images of self-assembled packing of localized defect structure...Figure 1.25. (a) Calculated intensity and phase of the random superposition of 4...Figure 1.26. (a) Map of lines of equal degree of polarization in the atmosphere ...Figure 1.27. (a) Polarization ellipses around generic C points, whose naming was...Figure 1.28. Illustration of singularity removal of nematic disclination lines w...Figure 1.29. (a) Maps of intensity (top) and phase (bottom) of Laguerre–Gauss mo...Figure 1.30. Main kinds of vortex beam shaping strategies. (a) Optical profilome...Figure 1.31. Two distinct experimental situations leading to the spontaneous gen...Figure 1.32. (a) Optical vortex generation from a radial nematic droplet trapped...Figure 1.33. Experimental demonstrations of singular diffraction gratings produc...Figure 1.34. (a) Calculated meridional (left panel) and transverse (at z = L/2, ...Figure 1.35. (a) Experimental voltage-tunable vortex purity of an isolated umbil...Figure 1.36. (a) Typical XPOL observation of a random distribution of disclinati...Figure 1.37. Illustration of several approaches to generate localized umbilics i...Figure 1.38. Main self-induced optical vortex generation processes based on ligh...Figure 1.39. (a–d) Field-induced arrays of umbilics in nematic films with perpen...Figure 1.40. (a) Lyot’s Drawing of his coronagraph. Copyright: Observatoire de P...Figure 1.41. Laboratory demonstration of optical vortex coronagraphy using liqui...Figure 1.42. (a,b) Evolution of the core and transverse swirl of localized magne...Figure 1.43. (a) Binary star sunset image from the movie Star Wars: A New Hope. ...Figure 1.44. (a) Principle of multispectral modulation of the orbital angular mo...