Liquid Crystals

This book on liquid crystals reports on the new perspectives that have been brought about by the recent expansion of frontiers and overhaul of common beliefs.

First, it explores the interaction of light with mesophases, when the light or matter is endowed with topological defects. It goes on to show how electrophoresis, electro-osmosis and the swimming of flagellated bacteria are affected by the anisotropic properties of liquid crystals.

It also reports on the recent progress in the understanding of thermomechanical and thermohydrodynamical effects in cholesterics and deformed nematics and refutes the common belief that these effects could explain Lehmann's observations of the rotation of cholesteric droplets subjected to a temperature gradient. It then studies the physics of the dowser texture, which has remarkable properties. This is of particular interest in regards to nematic monopoles, which can easily be generated, set into motion and collided within it.

Finally, this book deals with the spontaneous emergence of chirality in nematics made of achiral molecules, and provides a brief historical context of chirality

Auteur
Pawel Pieranski works at Laboratoire de Physique des Solides in Orsay, France. He has published a two-volume textbook on liquid crystals, written in collaboration with Patrick Oswald, and has conducted extensive research in many different areas of the field of liquid crystals.

Maria Helena Godinho is Associate Professor at NOVA University Lisbon, Portugal. Between 2016 and 2020 she was Vice President of the International Liquid Crystal Society. In 2019 she was awarded the Fréedericksz Medal by the Russian Liquid Crystal Society.

Contenu

Preface xi

Chapter 1. Singular Optics of Liquid Crystal Defects **1
**Etienne BRASSELET

1.1. Prelude from carrots 1

1.2. Liquid crystals, optics and defects: a long-standing trilogy 1

1.3. Polarization optics of liquid crystals: basic ingredients 3

1.3.1. The few liquid crystal phases at play in this chapter 3

1.3.2. Liquid crystals anisotropy and its main optical consequence 3

1.3.3. Polarization state representation in the paraxial regime 5

1.3.4. Polarization state evolution through uniform director fields 6

1.3.5. Effective birefringence 8

1.3.6. Polarization state evolution through twisted director fields 9

1.4. Liquid crystal reorientation under external fields 15

1.5. Customary optics from liquid crystal defects 16

1.5.1. Localized defects structures in frustrated cholesteric films 17

1.5.2. Elongated defects structures in frustrated cholesteric films 20

1.5.3. Regular optics from other topological structures 24

1.5.4. Assembling photonic building blocks with liquid crystal defects 31

1.6. From regular to singular optics 34

1.6.1. What is singular optics? 34

1.6.2. A nod to liquid crystal defects 37

1.6.3. Singular paraxial light beams 38

1.6.4. Generic singular beam shaping strategies 41

1.7. Advent of self-engineered singular optical elements enabled by liquid crystals defects 44

1.7.1. Optical vortices from a cholesteric slab: dynamic phase option 44

1.7.2. Optical vortices from a nematic droplet: geometric phase option 45

1.8. Singular optical functions based on defects: a decade of advances 47

1.8.1. Custom-made singular dynamic phase diffractive optics 47

1.8.2. Spontaneous singular geometric phase optics 47

1.8.3. Directed self-engineered geometric phase optics 52

1.8.4. From single to arrays of optical vortices 58

1.9. Emerging optical functionalities enabled by liquid crystal defects 58

1.9.1. Spectrally and spatially adaptive optical vortex coronagraphy 59

1.9.2. Multispectral management of optical orbital angular momentum 67

1.10. Conclusion 69

1.11. References 70

**Chapter 2. Control of Micro-Particles with Liquid Crystals 81
**Chenhui PENG and Oleg D. LAVRENTOVICH

2.1. Introduction 81

2.2. Control of micro-particles by liquid crystal-enabled electrokinetics 82

2.2.1. Liquid-crystal enabled electrophoresis 85

2.2.2. Liquid crystal-enabled electro-osmosis 91

2.3. Controlled dynamics of microswimmers in nematic liquid crystals 96

2.4. Conclusion 104

2.5. Acknowledgments 107

2.6. References 107

Chapter 3. Thermomechanical Effects in Liquid Crystals **117
**Patrick OSWALD, Alain DEQUIDT and Guilhem POY

3.1. Introduction 117

3.2. The EricksenLeslie equations 121

3.2.1. Conservation equations 121

3.2.2. Molecular field 123

3.2.3. Constitutive equations 125

3.3. Molecular dynamics simulations of the thermomechanical effect 130

3.3.1. Molecular models 130

3.3.2. Constrained ensembles 131

3.3.3. Computation of the transport coefficients 133

3.3.4. Analysis of the results 134

3.4. Experimental evidence of the thermomechanical effect 135

3.4.1. The static Éber and Jánossy experiment 136

3.4.2. Another static experiment proposed in the literature 140

3.4.3. Continuous rotation of translationally invariant configurations 142

3.4.4. Drift of cholesteric fingers under homeotropic anchoring 165

3.5. The thermohydrodynamical effect 174

3.5.1. A proposal for measuring the TH Leslie coefficient : theoretical prediction 175

3.5.2. About the measurement of the TH Akopyan and Zel'dovich coefficients 178

3.6. Conclusions and perspectives 184

3.7. References 185 **Chapter 4. Physics of the Do...