Perturbative expansion for the half-integer rectilinear disclination line in the Landau-de Gennes theory

TL;DR

This paper develops a perturbative approach to analyze the structure and free energy of half-integer disclination lines in nematic liquid crystals within the Landau-de Gennes theory, highlighting differences from traditional director models.

Contribution

It introduces a consistent perturbative expansion for the Landau-de Gennes theory around specific degenerate solutions, providing first-order corrections for the order parameter and free energy.

Findings

First-order corrections to the order parameter field

First-order free energy calculations

Comparison with Frank-Oseen-Zocher model

Abstract

The structure of the half-integer rectilinear disclination line within the framework of the Landau-de Gennes effective theory of nematic liquid crystals is investigated. The consistent perturbative expansion is constructed for the case of $L_2\neq 0$. It turns out that such expansion can be performed around only a discrete subset of an infinite set of the degenerate zeroth order solutions. These solutions correspond to the positive and negative wedge disclination lines and to four configurations of the twist disclination line. The first order corrections to both the order parameter field as well as the free energy of the disclination lines have been found. The results for the free energy are compared with the ones obtained in the Frank-Oseen-Zocher director description.