# Ordering Kinetics of Canted and Uniform States in Nematic Liquid Crystals

Source: [Ordering Kinetics of Canted and Uniform States in Nematic Liquid Crystals](<https://www.sota2.com/research/paper/68fa3d841e209131ce8e0db6>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T01:33:04.015Z

Authors: Nishant Birdi, Varsha Banerjee, Sanjay Puri

Published: 2020-11-23T14:00:15.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2011.11405>)

[PDF](<https://arxiv.org/pdf/2011.11405.pdf>)