Chiral ground states in a nematic liquid crystal confined to a cylinder with homeotropic anchoring

TL;DR

This paper investigates the ground state configurations of nematic liquid crystals in cylindrical confinement, revealing chiral symmetry breaking and the conditions favoring twisted or escaped states based on elastic constants and geometry.

Contribution

It introduces a detailed analysis of chiral ground states in nematic liquid crystals confined to cylinders using the singular potential method, highlighting the influence of elastic anisotropy and geometry.

Findings

Twisted configurations with disclinations are favored at small radii.

Escaped configurations become ground states at larger radii.

Near degeneracy between twisted and escaped states is affected by splay-bend contrast.

Abstract

The singular potential method in the Q tensor order parameter representation is used to determine the ground state configuration of an elastically anisotropic nematic liquid crystal when confined to a cylindrical geometry with homeotropic anchoring. Ground states of broken chiral symmetry are found for sufficiently small values of the twist elastic constant relative to bend and splay constants. For small cylinder radius, twisted configurations, which feature two disclinations lines that wind around the long axis of the cylinder, are generally found to minimize the free energy of the nematic. For larger radii, ground state configurations are (non singular) escaped configuration. Twisted and untwisted escaped configurations are almost degenerate in energy in this region. This near degeneracy is broken when splay-bend contrast is allowed.