Abstract
We study the characteristics of nematic structures in a randomly perturbed nematic liquid crystal (LC) phase. We focus on the impact of the samples history on the universal behavior. The obtained results are of interest for every randomly perturbed system exhibiting a continuous symmetry-breaking phase transition. A semimicroscopic lattice simulation is used where the LC molecules are treated as cylindrically symmetric, rod-like objects interacting via a Lebwohl-Lasher (LL) interaction. Pure LC systems exhibit a first order phase transition into the orientationally ordered nematic phase atT=Tcon lowering the temperatureT. The orientational ordering of LC molecules is perturbed by the quenched, randomly distributed rod-likeimpuritiesof concentrationp. Their orientation is randomly distributed, and they are coupled with the LC molecules via an LL-type interaction. Only concentrations below the percolation threshold are considered. The key macroscopic characteristics of perturbed LC structures in the symmetry-broken nematic phase are analyzed for two qualitatively different histories atT≪Tc. We demonstrate that, for a weak enough interaction among the LC molecules andimpurities, qualitatively different history-dependent states could be obtained. These states could exhibit either short-range, quasi-long-range, or even long-range order.
Highlights
Domains often appear in phases of broken continuous symmetry [1, 2]
We study the characteristics of nematic structures in a randomly perturbed nematic liquid crystal (LC) phase
We focus on the impact of history on nematic structures in randomly perturbed LCs
Summary
Domains often appear in phases of broken continuous symmetry [1, 2]. The reason behind this is causality that is a finite speed of the information propagation [3]. Nematic liquid crystals (LCs) comprise a convenient, simple, and experimentally relatively accessible system to study the domain patterns In the past few decades, several studies have analyzed the phase transition and structural behavior of mixtures of LCs with aerosil spherical particles [10,11,12,13,14] These mixtures represent adequate experimental model systems to study the influence of qualitatively different origins of disorder on phases with broken continuous symmetries. We use random anisotropy nematic (RAN) lattice model in which rod-like impurities and LC molecules interact via a LebwohlLasher type interaction [15] Such systems roughly simulate the mixtures of LCs and aerosils.
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