Nematic textures in spherical shells

TL;DR

This paper investigates how the nematic textures in spherical shells change with thickness, revealing a transition from disclination lines to escaped configurations and providing an exact solution for the ground state.

Contribution

It introduces an exact solution for nematic ground states in spherical shells and analyzes their stability across different thicknesses.

Findings

Ultrathin shells favor four disclination lines.

Thicker shells prefer a three-dimensional escaped configuration.

The stability of textures against thermal fluctuations is analyzed.

Abstract

The equilibrium texture of nematic shells is studied as a function of their thickness. For ultrathin shells the ground state has four short 1/2 disclination lines but, as the thickness of the film increases, a three dimensional escaped configuration composed of two pairs of half-hedgehogs becomes energetically favorable. We derive an exact solution for the nematic ground state in the one Frank constant approximation and study the stability of the corresponding texture against thermal fluctuations.