Theory of Liquid Crystal Elastomers: From Polymer Physics to Differential Geometry

TL;DR

This paper unifies two theoretical frameworks for liquid crystal elastomers using differential geometry, elucidating how temperature variations influence their director orientation and geometric structure.

Contribution

It bridges neoclassical and geometric elasticity theories of liquid crystal elastomers through a differential geometry formalism, enhancing understanding of their temperature-dependent behavior.

Findings

Unified theoretical description of liquid crystal elastomers.

Clarified the response of director and geometry to temperature changes.

Connected microscopic and macroscopic models through differential geometry.

Abstract

In liquid crystal elastomers, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymer networks. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation tensor, and a geometric elasticity theory based on the difference between the actual metric tensor and a reference metric. Here, we connect those two approaches using a formalism based on differential geometry. Through this connection, we determine how both the director and the geometry respond to a change of temperature.