Smectic-C tilt under shear in Smectic-A elastomers

TL;DR

This paper models how shear strain induces Smectic-C-like tilt in Smectic-A elastomers, comparing theoretical estimates with recent experimental results and discussing stability issues in different shear geometries.

Contribution

It generalizes a previous elastomer model to predict tilt angles under shear and compares these predictions with recent experimental data.

Findings

Shear induces Smectic-C-like tilt in Smectic-A elastomers.

Model predictions agree with experimental tilt angles in simple shear.

In-plane compression geometries may cause instabilities.

Abstract

Stenull and Lubensky [Phys. Rev. E {\bf 76}, 011706 (2007)] have argued that shear strain and tilt of the director relative to the layer normal are coupled in smectic elastomers and that the imposition of one necessarily leads to the development of the other. This means, in particular, that a Smectic-A elastomer subjected to a simple shear will develop Smectic-C-like tilt of the director. Recently, Kramer and Finkelmann [arXiv:0708.2024, Phys. Rev. E {\bf 78}, 021704 (2008)] performed shear experiments on Smectic-A elastomers using two different shear geometries. One of the experiments, which implements simple shear, produces clear evidence for the development of Smectic-C-like tilt. Here, we generalize a model for smectic elastomers introduced by Adams and Warner [Phys. Rev. E {\bf 71}, 021708 (2005)] and use it to study the magnitude of Smectic-C-like tilt under shear for the two geometries investigated by Kramer and Finkelmann. Using reasonable estimates of model parameters, we estimate the tilt angle for both geometries, and we compare our estimates to the experimental results. The other shear geometry is problematic since it introduces additional in-plane compressions in a sheet-like sample, thus inducing instabilities that we discuss.