Applications of the Peach-Koehler Force in Liquid Crystals
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.
Keywords
Cite
@article{arxiv.2309.15315,
title = {Applications of the Peach-Koehler Force in Liquid Crystals},
author = {Cheng Long and Jonathan V. Selinger},
journal= {arXiv preprint arXiv:2309.15315},
year = {2025}
}