Liquid Crystals. Pawel Pieranski

      Preface

      The story of liquid crystals is that of a transgression of frontiers and a breaking of common beliefs.

      Indeed, liquid crystals were discovered by a biochemist, Friedrich Reinitzer, who shared his perplexity with a physicist, Otto Lehmann. Subsequently, crystallographers, mineralogists, experts in optics, magnetism, thermodynamics, chemists, etc., contributed to the recognition of liquid crystals as new states of matter, called mesophases by George Friedel, endowed with structures intermediate to those of isotropic liquids and crystals.

      Mesophases are so fragile that they can be easily perturbed by moderate mechanical, electric, magnetic or thermal stresses that generate various defects, such as disclinations, dislocations, walls, monopoles or multipoles. Remarkably, these defects were also observed to appear spontaneously during phase transitions.

      Inspired by experimental discoveries, theorists and mathematicians became fascinated by the symmetries of mesophases and recognized these beautiful and mysterious defects as topological singularities of vectorial, tensorial or complex fields. This led to the introduction of the concept of order parameters, resulting from symmetry breaking. In this frame, the generation of topological defects during certain phase transitions appeared as a natural, expected consequence. It was thus appreciated that the physics of liquid crystals and their defects had a permeable border with the Kibble–Zurek mechanism in cosmology.

The discovery of liquid crystals was made in substances extracted from carrots. Prior to that, Mettenheimer and Virchov observed birefringent lamellar mesophases in aqueous solutions of myelin, a substance extracted from nerve tissues. Mesophases also appear in solutions of cellulosic compounds or in suspensions of elongated particles, such as cellulose nanocrystals, tobacco mosaic viruses or bacteria. Therefore, from their origin, liquid crystals share a border with living matter.

      In this book, the borders with cosmology and living matter, as well as other borders will be crossed several times. The title Liquid Crystals – New Perspectives announces that when borders are crossed, new perspectives are unlocked.

      The first chapter, Singular Optics of Liquid Crystal Defects, explores a terra incognita: the light–matter interaction that occurs when light and/or matter are endowed with topological defects. It tells how the physics of topological defects in liquid crystals has progressively enriched liquid crystal optics as singular optics have developed. This is rooted in a few generic features: the self-organization capabilities of soft matter systems and their sensitivity to external stimuli. Remarkably, all of the assets of liquid crystals that make them ubiquitous in our daily life as liquid crystal displays, now open up several options to explore fundamental optical phenomena, based on the coupling between the polarization and spatial degrees of freedom. Also, this allows us to envision the development of future applications, for instance in optical imaging, beam shaping and the manipulation of matter by light.

      The second chapter, Control of Micro-Particles with Liquid Crystals, transgresses two frontiers. First, that between liquid crystals and electro-kinetic phenomena. The authors show how electrophoresis and electro-osmosis, well known from studies with isotropic liquids, acquire new unexpected features when the anisotropy and nonlinear hydrodynamics of liquid crystals are switched on. The second transgression is that of the frontier with living matter. The quasi-random swimming motion of flagellated bacteria in isotropic liquids becomes ordered in lyotropic liquid crystals and even more fascinating in the presence of topological defects, disclinations.

      The third chapter, Thermomechanical Effects in Liquid Crystals, crosses the border between liquid crystals and out-of-equilibrium thermodynamics. Anisotropy and nonlinear hydrodynamics of liquid crystals radically alter the phenomena driven by thermal gradients. For example, the threshold of the Rayleigh–Bénard instability in nematics is known to be lowered by a factor of 1000 with respect to isotropic liquids. The thermomechanical and thermohydrodynamical effects discussed in this chapter are even more original because they do not exist in isotropic fluids. Once again, they become fascinating in the presence of topological defects. This chapter breaks the common belief about a unique explanation, in terms of the Leslie theory, of the Lehmann effect, i.e. the rotation of cholesteric droplets driven by a thermal gradient.

The fourth chapter, Physics of the Dowser Texture, transgresses the common belief about the ephemeral character of a distorted nematic texture, bearing varying names in the past: splay-bend state, H state, inversion wall, quasi-planar or flow-aligned. Dubbed as the dowser texture because of its resemblance with the wooden tool of dowsers, this texture is in fact not unstable but only metastable and in certain conditions can be preserved indefinitely. As its complex order parameter eiϕ is degenerated with respect to the phase ϕ, the dowser texture is sensitive to vector fields and as a consequence it is endowed with unprecedented properties called cuneitropism, rheotropism and electrotropism. The dowser texture also appears as a natural universe of nematic monopoles and antimonopoles that can be set in motion and brought to collisions, resulting in the annihilation of monopole–antimonopole pairs, analogous to the annihilation of electron-positron pairs in hadron colliders.

      The fifth chapter, Spontaneous Emergence of Chirality, deals with nematics, which are made up of achiral molecules. It begins with a very detailed historical tour leading to the birth of the concept of chirality. The tour starts with the discovery of double refraction in Iceland spar crystals by Erasmus Bartolinus in 1669, followed by the crucial contributions of Huygens, Malus, Arago, Brewster, Biot, Fresnel and Faraday, leading to the epoch marking the discovery of molecular chirality by Louis Pasteur. The work of Pasteur gave birth to a common belief that the optical activity of materials results from the existence of molecular chirality. The observations of chiral textures in lyotropic nematics discussed in this fifth chapter break this common belief and unlock new perspectives.

      We would like to thank Mme Françoise Brochard-Wyart for the invitation to write this book. Its contours were fixed thanks to Tigran Galstian, who invited six of the authors to the 18th Conference on Optics of Liquid Crystals, in Quebec.

      The printing in color of this book was sponsored by : 1) Marie Curie Grant N¡838199, 2) Department of Physics and Materials Science at The University of Memphis, Memphis, Tennessee (USA), 3) National Science Foundation (USA) grant DMR-1905053 entitled “Active colloids with tunable interactions in liquid crystals”, 4) Laboratoire de Physique at Ecole Normale Supérieure de Lyon, Lyon (France), 5) Laboratoire de Physique des Solides at Université Paris-Saclay, Orsay (France), 6) i3N/CENIMAT, NOVA School of Science and Technology, NOVA University of Lisbon (Portugal), 7) School of Materials Science and Engineering at Georgia Institute of Technology, Atlanta, Georgia (USA).

      The writing of this book lasted for about one year. Once the work was finished, we were tempted to say, following the Eulogy of Leonhard Euler by Marquis de Condorcet, that:

      ...the pleasure to work is a sweeter