Non-Gaussian chain statistics and finite extensibility in liquid crystal elastomers

TL;DR

This paper develops an anisotropic finitely extensible chain model for liquid crystal elastomers, linking elastic behavior to monomer orientation distributions using a maximum entropy approach, with implications for understanding their nonlinear elasticity.

Contribution

It introduces a novel anisotropic chain energy model for liquid crystal elastomers based on maximum entropy principles, extending classical rubber elasticity models.

Findings

Derived a new chain energy expression coupling elasticity and orientation distribution.

Provided a fourth order Taylor expansion relating to nematic moments.

Established a theoretical framework for finite extensibility in liquid crystal elastomers.

Abstract

In this work we will derive an anisotropic generalisation of the finitely extensible chain model, due to Kuhn and Gr\"un, which is well known in rubber elasticity. This provides a chain energy that couples elastic behaviour to a probability distribution describing the orientations of liquid crystal monomers within a main chain elastomer. The key point is to invoke a maximum relative entropy assumption on the distribution of bond angles in an observed chain. The chain energy's fourth order Taylor expansion is also given, which couples to the second and fourth moments of the nematic distribution function only.