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

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.

arXiv comment8 pages, 3 figures

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• Colloidal smectics in button-like confinements: experiment and theory
• Ionically charged topological defects in nematic fluids
• Screw Symmetry, Chiral Hydrodynamics and Odd Instability in Active Cholesterics