The elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

TL;DR

This paper introduces an analytically solvable mean-field lattice model for nematic elastomers, revealing stress-strain coexistence, disorder effects, and phase transition modifications, providing insights into their complex mechanical and phase behavior.

Contribution

It combines liquid crystal and elasticity theories into a mean-field lattice model with quenched disorder, offering new analytical insights into nematic elastomer properties.

Findings

Existence of a stress-strain coexistence curve below a freezing temperature.

Disorder strength influences the stress-strain behavior, resembling a fluid's P-V diagram.

Random fields can soften the nematic-isotropic transition in monodomain samples.

Abstract

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau, and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random-fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.