Smectic-$A$ elastomers with weak director anchoring

TL;DR

This paper investigates the behavior of smectic-A elastomers with weak director anchoring, predicting instabilities and director-layer normal tilt under various deformations using a generalized rubber elasticity model.

Contribution

It introduces a weak-anchoring model for smectic-A elastomers and analyzes their mechanical response, including instabilities and director tilt, under different deformation modes.

Findings

Predicts shear-induced smectic-C-like order

Calculates stress and tilt angle as functions of deformation

Identifies instability towards shear with smectic-C order

Abstract

Experimentally it is possible to manipulate the director in a (chiral) smectic-$A$ elastomer using an electric field. This suggests that the director is not necessarily locked to the layer normal, as described in earlier papers that extended rubber elasticity theory to smectics. Here, we consider the case that the director is weakly anchored to the layer normal assuming that there is a free energy penalty associated with relative tilt between the two. We use a recently developed weak-anchoring generalization of rubber elastic approaches to smectic elastomers and study shearing in the plane of the layers, stretching in the plane of the layers, and compression and elongation parallel to the layer normal. We calculate, inter alia, the engineering stress and the tilt angle between director and layer normal as functions of the applied deformation. For the latter three deformations, our results predict the existence of an instability towards the development of shear accompanied by smectic-$C$-like order.