Cooling a spherical nematic shell

TL;DR

This paper investigates the temperature-driven phase transition of nematic liquid crystals on spherical shells, revealing how curvature influences the critical temperature and stable nematic textures, with exact analytical results and stability analysis.

Contribution

It provides exact calculations of the critical temperature and nematic textures at the transition, considering the effects of curvature and stability of configurations.

Findings

Critical temperature depends on sphere curvature

Tetrahedral nematic configuration is the only stable texture

Exact nematic textures are determined at the transition

Abstract

Within the framework of Landau-de Gennes theory for nematic liquid crystals, we study the temperature-induced isotropic-nematic phase transition on a spherical shell. Below a critical temperature, a thin layer of nematic coating a microscopic spherical particle exhibits non-uniform textures due to the geometrical frustration. We find the exact value of critical threshold for the temperature and determine exactly the nematic textures at the transition by means of a weakly nonlinear analysis. The critical temperature is affected by the extrinsic curvature of the sphere, and the nematic alignment is consistent with the Poincar\'e-Hopf index theorem and experimental observations. The stability analysis of the bifurcate textures at the isotropic-nematic transition highlight that only the tetrahedral configuration is stable.