Disclination Asymmetry in Two-Dimensional Nematic Liquid Crystals with Unequal Frank Constants

TL;DR

This paper investigates how unequal Frank constants in two-dimensional nematic liquid crystals lead to asymmetry in disclination core energies, yet maintain equal bulk densities due to topological constraints, affecting the system's elastic properties.

Contribution

It reveals that unequal Frank constants cause disclination core energy asymmetry but do not alter the bulk density balance, impacting the understanding of nematic liquid crystal behavior.

Findings

Disclination core energies differ for +1/2 and -1/2 defects due to unequal Frank constants.

Topological constraints enforce equal bulk densities of disclinations.

Unequal core energies effectively renormalize elastic parameters like Gaussian rigidity.

Abstract

The behavior of a thin film of nematic liquid crystal with unequal Frank constants is discussed. Distinct Frank constants are found to imply unequal core energies for $+1/2$ and $-1/2$ disclinations. Even so, a topological constraint is shown to ensure that the bulk densities of the two types of disclinations are the same. For a system with free boundary conditions, such as a liquid membrane, unequal core energies simply renormalize the Gaussian rigidity and line tension.