Symmetry breaking in nematic liquid crystals: analogy with cosmology and magnetism

Abstract

Universal behavior related to continuous symmetry breaking in nematic liquid crystals is studied using Brownian molecular dynamics. A three-dimensional lattice system of rod-like objects interacting via the Lebwohl-Lasher interaction is considered. We test the applicability of predictions originally derived in cosmology and magnetism. In the first part we focus on coarsening dynamics following the temperature driven isotropic-nematic phase transition for different quench rates. The behavior in the early coarsening regime supports predictions made originally by Kibble in cosmology. For fast enough quenches, symmetry breaking and causality give rise to a dense tangle of defects. When the degree of orientational ordering is large enough, well defined protodomains characterized by a single average domain length are formed. With time subcritical domains gradually vanish and supercritical domains grow with time, exhibiting a universal scaling law. In the second part of the paper we study the impact of random-field-type disorder on a range of ordering in the (symmetry broken) nematic phase. We demonstrate that short-range order is observed even for a minute concentration of impurities, giving rise to disorder in line with the Imry-Ma theorem prediction only for the appropriate history of systems.

Inhomogeneous relaxation dynamics and phase behaviour of a liquid crystal confined in a nanoporous solid

“…Both the collective orientational (isotropic-to-nematic) and the translational (smectic-toliquid or smectic-to-nematic) transitions have turned out to be significantly affected by finite size and interfacial (solid-liquid or liquid-liquid) interactions introduced by confining walls [1][2][3][4][5][6] or the geometrical constraints in nanoporous media [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Defects in Planar Cell Polarity of Epithelium

“…Namely, rich variety of LC phases and structures reached via symmetry-breaking phase transitions enables realization of almost all qualitatively different TDs in nature. Adequate analogies in TDs in LCs and in several other physical systems were demonstrated, that is, analogy in symmetry breaking in LCs, cosmology, and magnetism [25]. In the present study, we extend these ideas to the epithelial tissue topology.…”

“…Broken continuous symmetry has strong impact: (i) it is the reason behind LC softness and (ii) it enables existence of TDs [25].…”

“…The key property of TDs is a topological charge, which is a conserved property. In many cases, TDs exhibit behavior which is reminiscent to electrostatics [25]. For example, for each defect, there exists an antidefect.…”

Liquid Crystals as Phase Change Materials for Thermal Stabilization

“…Then, we expressed the average contributions of the condensation nematic term and elastic term to the average free energy density as follows [23][24][25]:…”