Applications of the Peach-Koehler force in liquid crystals

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 [1]. Calculating the angular stress at a disclination in a liquid crystal is often challenging due to the effects of boundary conditions. In this work, we argue that the relevant angular stress can be identified by expanding the total angular stress around a disclination as a Laurent series, and eliminating the divergent stress from the disclination itself. We demonstrate this method by applying the Peach-Koehler force theory to two different problems: (a) Array of disclinations in a liquid crystal cell with patterned substrates, as the experiment of Babakhanova [2]. (b) Pair of disclinations in a long capillary tube with homeotropic anchoring. Our Peach-Koehler force theory predicts the positions of the disclinations for both problems, and the predictions are consistent with the results of minimizing the total free energy.

[1] C. Long, X. Tang, R. L. B. Selinger and J. V. Selinger, Soft Matter 17, 2265 (2021)

[2] G. Babakhanova et al., J. Appl. Phys. 128, 184702 (2020)