Applications of the Peach-Koehler Force in Liquid Crystals

TL;DR

This paper develops a method to calculate the Peach-Koehler force in liquid crystals, enabling prediction of disclination behavior under various conditions, with results matching energy minimization predictions.

Contribution

It introduces a novel approach to compute the Peach-Koehler force in liquid crystals, extending the force theory from solids to liquid crystal disclinations.

Findings

Force calculation method for liquid crystal disclinations.

Predicted equilibrium defect structures match energy minimization.

Applicable to various geometries and boundary conditions.

Abstract

In solids, external stress induces the Peach-Koehler force, which drives dislocations to move. Similarly, in liquid crystals, an external angular stress creates an analogous force, which drives disclinations to move. In this work, we develop a method to calculate the relevant angular stress either analytically or numerically, and hence to determine the force on a disclination. We demonstrate this method by applying the Peach-Koehler force theory to four problems: (a) Single disclination in a liquid crystal cell between two uniform in-plane alignments perpendicular to each other. (b) Array of disclinations in a liquid crystal cell with patterned substrates. (c) Pair of disclinations in a long capillary tube with homeotropic anchoring. (d) Radial hedgehog or disclination loop inside a sphere with homeotropic anchoring, and its response to an applied magnetic field. In all of these problems, the Peach-Koehler force theory predicts the equilibrium defect structure, and the predictions are consistent with the results of minimizing the total free energy.