Modeling Dipolar and Quadrupolar Defect Structures generated by Chiral Islands in Freely-Suspended Liquid Crystal Films

TL;DR

This paper provides a detailed theoretical analysis of quadrupolar interactions between chiral islands in smectic C liquid crystal films, revealing how defect structures depend on chirality and elastic anisotropy.

Contribution

It introduces a Landau model to numerically analyze defect energetics and equilibrium configurations in chiral liquid crystal films with novel quadrupolar interactions.

Findings

Quadrupolar structures form between islands of different handedness.

Defect trajectories depend on elastic anisotropy and material chirality.

The model predicts equilibrium configurations for various parameters.

Abstract

We report a detailed theoretical analysis of novel quadrupolar interactions observed between islands, which are disk-like inclusions of extra layers, floating in thin, freely suspended smectic C liquid crystal films. Strong tangential anchoring at the island boundaries result in a strength +1 chiral defect in each island and a companion -1 defect in the film, these forming a topological dipole. While islands of the same handedness form linear chains with the topological dipoles pointing in the same direction, as reported in the literature, islands with different handedness form compact quadrupolar structures with the associated dipoles pointing in opposite directions. The interaction between such heterochiral island--defect pairs is complex, with the defects moving to minimize the director field distortion as the distance between the islands changes. The details of the inter-island potential and the trajectories of the -1 defects depend strongly on the elastic anisotropy of the liquid crystal, which can be modified in the experiments by varying the material chirality of the liquid crystal. A Landau model that describes the energetics of freely mobile defects is solved numerically to find equilibrium configurations for a wide range of parameters.