Uniform distortions and generalized elasticity of liquid crystals

TL;DR

This paper defines and characterizes uniform distortions in nematic liquid crystals, including new phases like twist-bend nematics, and explores their generalized elastic properties with a simple free-energy model.

Contribution

It introduces a precise definition of uniform distortions, classifies all such distortions into two families, and analyzes their elastic behavior including new phases.

Findings

Uniform distortions are classified into two families with two scalar parameters.

All uniform distortions correspond to R. Meyer's heliconical structures.

The generalized elasticity includes both uniform and non-uniform distortions, revealing elastic frustration.

Abstract

Ordinary nematic liquid crystals are characterized by having a uniform director field as ground state. In such a state, the director is the same everywhere and no distortion is to be seen at all. We give a definition of uniform distortion which makes precise the intuitive notion of seeing everywhere the same director landscape. We characterize all such distortions and prove that they fall into two families, each described by two scalar parameters. Uniform distortions exhaust R. Meyer's heliconical structures, which, as it has recently been recognized, include the ground state of twist-bend nematics. The generalized elasticity of these new phases is treated with a simple free-energy density, which can be minimized by both uniform and non-uniform distortions, the latter injecting a germ of elastic frustration.