Universal Elasticity and Fluctuations of Nematic Gels

TL;DR

This paper investigates the universal elastic properties of nematic gels, revealing scale-dependent moduli and stability of nematic order against fluctuations, with implications for understanding amorphous solids with orientational order.

Contribution

It introduces a theoretical framework showing that nematic gels exhibit universal, scale-dependent elastic behavior governed by a nontrivial fixed point, extending understanding of amorphous solids with orientational order.

Findings

Shear modulus vanishes at long scales.

Poisson ratio becomes universally negative.

Elasticity remains non-Hookean at low strains.

Abstract

We study elasticity of spontaneously orientationally-ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized for example by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infared fixed point. Namely, at long scales, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local hetergeneities down to d_lc < 3.