Thermal fluctuations and anomalous elasticity of homogeneous nematic elastomers

TL;DR

This paper develops a unified nonlinear elasticity theory for nematic elastomers, revealing universal incompressibility, shear modulus ratios, and anomalous elasticity behavior driven by a low-temperature fixed point in three dimensions.

Contribution

It introduces a rotationally invariant nonlinear elasticity framework and analyzes thermal fluctuations, providing exact predictions for 3D nematic elastomers.

Findings

Homogeneous nematic elastomers are universally incompressible.

A universal ratio of shear moduli is established.

Anomalous elasticity is governed by a nontrivial fixed point in 3D.

Abstract

We present a unified formulation of a rotationally invariant nonlinear elasticity for a variety of spontaneously anisotropic phases, and use it to study thermal fluctuations in nematic elastomers and spontaneously anisotropic gels. We find that in a thermodynamic limit homogeneous nematic elastomers are universally incompressible, are characterized by a universal ratio of shear moduli, and exhibit an anomalous elasticity controlled by a nontrivial low temperature fixed point perturbative in D=3-epsilon dimensions. In three dimensions, we make predictions that are asymptotically exact.