Elliptic Phases: A Study of the Nonlinear Elasticity of Twist-Grain Boundaries

TL;DR

This paper develops a mathematical model for twist-grain boundaries in smectic A liquid crystals, analyzing their stability and deformation energies, and relating their structure to minimal surface geometries.

Contribution

It provides an explicit representation of twist-grain boundaries, enabling detailed energy calculations and stability analysis, which advances understanding of liquid crystal defect structures.

Findings

90-degree grain boundaries are particularly stable

Interaction energy depends on bending and compression contributions

Relation to Schwarz D surface elucidates geometric structure

Abstract

We develop an explicit and tractable representation of a twist-grain-boundary phase of a smectic A liquid crystal. This allows us to calculate the interaction energy between grain boundaries and the relative contributions from the bending and compression deformations. We discuss the special stability of the 90 degree grain boundaries and discuss the relation of this structure to the Schwarz D surface.