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

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.

Early stage domain coarsening of the isotropic-nematic phase transition.

We study numerically the early stage domain coarsening dynamics of the temperature driven isotropic-nematic (I-N) liquid crystal phase transition. System of rod like objects which interact via the modified Lebwohl-Lasher pairwise interaction is considered in 3D. The coarsening dynamics is followed using Brownian molecular dynamics. The box-restricted lattice point fluctuations are allowed in order to get rid of lattice geometry enforced phenomena. We analyze order parameter growth and domain coarsening in the early regime of the I-N phase transition as a function of the quench rate. We show that soon after the transition bimodal distribution of domains appears, where the shorter branch gradually vanishes. The behavior of the system is in accordance with predictions of the Kibble-Zurek mechanism which was originally introduced to model conditions in the early universe.

Annihilation of nematic point defects: pre-collision and post-collision evolution.

The annihilation of the nematic hedgehog and anti-hedgehog within an infinite cylinder of radius R is studied. The semi-microscopic lattice-type model and Brownian molecular dynamics are used. We distinguish among the i) early pre-collision, ii) late pre-collision, iii) early post-collision, and iv) late post-collision stages. In the pre-collision stage our results agree qualitatively with the existing experimental observations and also continuum-type simulations. The core of each defect exhibits a ring-like structure, where the ring axis is set perpendicular to the cylinder symmetry axis. For xi(0)d/(2R) > 1 the interaction between defects is negligible, where xi(0)d describes the initial separation of defects. Consequently, the defects annihilate within the simulation time window for xi(0)d/(2R) < 1. For close enough defects their separation scales as xi(d) [see text] (t(c)- t)(0.4+/-0.1), where t(c) stands for the collision time. In elastically anisotropic medium the hedgehog is faster than the anti-hedgehog. In the early pre-collision stage the defects can be treated as point-like particles, possessing inherent core structure, that interact via the nematic director field. In the late pre-collision stage the cores reflect the interaction between defects. After the collision a charge-less ring structure is first formed. In the early post-collision stage the ring adopts an essentially untwisted circular structure of the radius xi(r). In the late post-collision stage we observe two qualitatively different scenarios. For mu = xi(r)/R < mu(c) approximately 0.25 the ring collapses leading to the escaped radial equilibrium structure. For mu > mu(c) the chargeless ring triggers the nucleation growth into the planar polar structure with line defects.

Molecular dynamics study of the isotropic-nematic quench.

Effects of cylindrical and spherical confinement on the kinetics of the isotropic-nematic quench is studied numerically. The nematic liquid crystal structure was modeled by a modified induced-dipole--induced-dipole interaction. Molecules were allowed to wander around points of a hexagonal lattice. Brownian molecular dynamics was used in order to access macroscopic time scales. In the bulk we distinguish between the early, domain, and late stage regime. The early regime is characterized by the exponential growth of the nematic uniaxial order parameter. In the domain regime domains are clearly visible and the average nematic domain size xi(d) obeys the dynamical scaling law xi(d)-t(gamma). The late stage evolution is dominated by dynamics of individual defects. In a confined system the qualitative change of the scaling behavior appears when xi(d) becomes comparable to a typical linear dimension R of the confinement. In the confining regime (xi(d)>or=R) the scaling coefficient gamma depends on the details of the confinement and also the final equilibrium nematic structure. The domain growth is well described with the Kibble-Zurek mechanism.