Dynamical Scaling In Two Dimensional Quenched Uniaxial Nematic Liquid Crystals

TL;DR

This study investigates the phase ordering kinetics of two-dimensional uniaxial nematic liquid crystals after a quench, revealing a scaling law similar to the 2D O(2) model and confirming theoretical predictions about topological defects and correlation functions.

Contribution

The paper demonstrates the asymptotic growth law and topological defect behavior in 2D uniaxial nematic liquid crystals using long-time simulations, aligning with 2D O(2) model predictions.

Findings

Growth law L(t) ~ t/ln(t) confirmed at long times

Presence of 1/2-disclination points affects structure factor

Correlation functions match 2D O(2) model predictions

Abstract

The phase ordering kinetics of the two-dimensional uniaxial nematic has been studied using a Cell Dynamic Scheme. The system after quench from T=infinity was found to scale dynamically with an asymptotic growth law similar to that of two-dimensional O(2) model (quenched from above the Kosterlitz - Thouless transition temperature), i.e. L(t) ~ t/ln(t/t0 ^{1/2} (with nonuniversal time scale t0). We obtained the true asymptotic limit of the growth law by performing our simulation for sufficiently long time. The presence of topologically stable 1/2-disclination points is reflected in the observed large-momentum dependence k ^{-4} of the structure factor. The correlation function was also found to tally with the theoretical prediction of the correlation function for the two-dimensional O(2) system.