Elasticity of Polydomain Liquid Crystal Elastomers

TL;DR

This paper models the elasticity of polydomain liquid crystal elastomers, revealing how their cross-linking history affects their softness, hardness, and director patterns, with implications for low-field actuation.

Contribution

It extends neo-classical free energy models to polydomains, analyzing how cross-linking conditions influence their mechanical properties and director configurations.

Findings

Polydomains cross-linked in isotropic state are perfectly soft in the ideal limit.

Polydomains cross-linked in nematic state are mechanically harder with characteristic patterns.

Models agree with experiments showing supersoft responses in some polydomains.

Abstract

We model polydomain liquid-crystal elastomers by extending the neo-classical soft and semi-soft free energies used successfully to describe monodomain samples. We show that there is a significant difference between polydomains cross-linked in homogeneous high symmetry states then cooled to low symmetry polydomain states and those cross-linked directly in the low symmetry polydomain state. For example, elastomers cross-linked in the isotropic state then cooled to a nematic polydomain will, in the ideal limit, be perfectly soft, and with the introduction of non-ideality, will deform at very low stress until they are macroscopically aligned. The director patterns observed in them will be disordered, characteristic of combinations of random deformations, and not disclination patterns. We expect these samples to exhibit elasticity significantly softer than monodomain samples. Polydomains cross-linked in the nematic polydomain state will be mechanically harder and contain characteristic schlieren director patterns. The models we use for polydomain elastomers are spatially heterogeneous, so rather than solving them exactly we elucidate this behavior by bounding the energies using Taylor-like (compatible test strain fields) and Sachs (constant stress) limits extended to non-linear elasticity. Good agreement is found with experiments that reveal the supersoft response of some polydomains. We also analyze smectic polydomain elastomers and propose that polydomain SmC* elastomers cross-linked in the SmA monodomain state are promising candidates for low field electrical actuation.