Point Defects, Chirality and Singularity Theory in Cholesteric Liquid Crystal Droplets

TL;DR

This paper develops a theoretical framework for understanding point defects in cholesteric liquid crystal droplets, linking singularity theory with defect structures and chirality constraints.

Contribution

It introduces a novel application of singularity theory to classify and analyze defects in cholesteric droplets, revealing topological constraints on defect transformations.

Findings

Identifies defect types with specific singularities, such as $D_4^{-}$ and $T_{4,4,4}$.

Shows radial defects cannot be converted into chiral structures with a single handedness.

Demonstrates surface frustration of chirality due to topological constraints.

Abstract

We develop a theory of point defects in cholesterics and textures in spherical droplets with normal anchoring. The local structure of chiral defects is described by singularity theory and a smectic-like gradient field establishing a nexus between cholesterics and smectics mediated by their defects. We identify the defects of degree $-2$ and $-3$ observed experimentally with the singularities $D_4^{-}$ and $T_{4,4,4}$, respectively. Radial point defects typical of nematics cannot be perturbed into chiral structures with a single handedness by general topological considerations. For the same reasons, the spherical surface frustrates the chirality in a surface boundary layer containing regions of both handedness.