Ordering Kinetics of Canted and Uniform States in Nematic Liquid Crystals

TL;DR

This study uses Monte Carlo simulations to analyze the ordering kinetics in 3D nematic liquid crystals, revealing distinct canted and uniform states with different coarsening behaviors and defect structures.

Contribution

It introduces a detailed Monte Carlo analysis of nematic liquid crystal ordering, highlighting the existence of canted morphologies and their unique scaling and defect characteristics.

Findings

Canted morphologies occur for λ < -0.3 with a λ-dependent tilt angle.

Structure factor follows Porod law in canted regime, indicating defect annihilation.

Domain growth follows Lifshitz-Allen-Cahn law, L(t) ~ t^{1/2}.

Abstract

We undertake a comprehensive Monte Carlo (MC) study of the ordering kinetics in nematic liquid crystals (NLCs) in 3-dimensions $(d=3)$ by performing deep quenches from the isotropic $(T>T_c)$ to the nematic $(T<T_c)$ phase. The inter-molecular potential between the nematogens, represented by continuous $O(3)$ spins with inversion symmetry, is accurately mimicked by the {\it generalised Lebwohl Lasher} (GLL) model. It incorporates second and fourth order Legendre interactions, and their relative interaction strength is $\lambda$. For $\lambda <-0.3$, we observe {\it canted} morphologies with a $\lambda$-dependent angle-of-tilt between the neighbouring rod-like molecules. For $\lambda \geq-0.3$, the molecules align to yield {\it uniform} states. The coarsening morphologies obey {\it generalized dynamical scaling} in the two regimes, but the scaling function is not robust with respect to $\lambda$. The structure factor tail in the canted regime follows the {\it Porod law}: $S(k,t)\sim k^{-4}$, implying that the coarsening dynamics is due to the annihilation of interfacial defects. This is unexpected, as the GLL model is characterised by a continuous order parameter. The uniform regime on the other hand, exhibits the expected {\it generalized Porod decay}: $S(k,t)\sim k^{-5}$, characteristic of scattering from {\it string defects}. Finally, the domain growth obeys the {\it Lifshitz-Allen-Cahn law}: $L(t)\sim t^{1/2}$ for all values of $\lambda$. Our results for the novel {\it canted} regime are relevant for a large class of systems with orientational ordering, e.g. active matter, membranes, LC elastomers, etc. We hope that our work triggers-off stimulating investigations in them.