Theory and computation of directional nematic phase ordering

TL;DR

This paper presents a computational analysis of morphological instabilities in a nematic liquid crystal front during directional growth, incorporating anisotropic energy considerations and comparing sharp-interface and full simulation models.

Contribution

It introduces a Landau-de Gennes tensor model for first-order nematic transitions and develops a sharp-interface model to analyze morphological instabilities in liquid crystals.

Findings

Thermal instabilities observed in simulations align with experimental data.

Sharp-interface model limitations identified through comparison with full simulations.

Nonlinear regime shows defect formation and interfacial heterogeneities.

Abstract

A computational study of morphological instabilities of a two-dimensional nematic front under directional growth was performed using a Landau-de Gennes type quadrupolar tensor order parameter model for the first-order isotropic/nematic transition of 5CB (pentyl-cyanobiphenyl). A previously derived energy balance, taking anisotropy into account, was utilized to account for latent heat and an imposed morphological gradient in the time-dependent model. Simulations were performed using an initially homeotropic isotropic/nematic interface. Thermal instabilities in both the linear and non-linear regimes were observed and compared to past experimental and theoretical observations. A sharp-interface model for the study of linear morphological instabilities, taking into account additional complexity resulting from liquid crystalline order, was derived. Results from the sharp-interface model were compared to those from full two-dimensional simulation identifying the specific limitations of simplified sharp-interface models for this liquid crystal system. In the nonlinear regime, secondary instabilities were observed to result in the formation of defects, interfacial heterogeneities, and bulk texture dynamics.