Explicit Demonstration of Geometric Frustration in Chiral Liquid Crystals

TL;DR

This paper investigates geometric frustration in chiral liquid crystals confined in cylindrical and planar geometries, demonstrating how size and boundary conditions influence the formation of different space-filling structures through theory and simulations.

Contribution

It explicitly demonstrates how geometric frustration affects the structure of chiral liquid crystals in confined geometries, combining theoretical analysis and simulations.

Findings

Double-twist configuration forms in small cylinders

Larger cylinders favor space-filling structures like cholesteric or blue phases

Free energy depends on system size, natural twist, and disclination energy

Abstract

Many solid materials and liquid crystals exhibit geometric frustration, meaning that they have an ideal local structure that cannot fill up space. For that reason, the global phase must be a compromise between the ideal local structure and geometric constraints. As an explicit example of geometric frustration, we consider a chiral liquid crystal confined in a long cylinder with free boundaries. When the radius of the tube is sufficiently small, the director field forms a double-twist configuration, which is the ideal local structure. However, when the radius becomes larger (compared with the natural twist of the liquid crystal), the double-twist structure cannot fill space, and hence the director field must transform into some other chiral structure that can fill space. This space-filling structure may be either (1) a cholesteric phase with single twist, or (2) a set of double-twist regions separated by a disclination, which can be regarded as the beginning of a blue phase. We investigate these structures using theory and simulations, and show how the relative free energies depend on the system size, the natural twist, and the disclination energy. As another example, we also study a cholesteric liquid crystal confined between two infinite parallel plates with free boundaries.