Elastic Instability and Stripe Domains in Liquid Crystalline Elastomers

We consider the elastic and orientational response of a uniform nematic elastomer subjected to an extension perpendicular to its director. By allowing a possibility of local shear in the material, we show that the effect of "soft elasticity" leads to a new regime of director reorientation, through a highly non-uniform stripe domain state (in contrast to earlier predictions and observations of a discontinuous uniform director jump). The molecular theory developed here gives predictions on two levels: of the general texture of the stripe state plus the interval of strains in which it occurs, and of topological properties of the director rotation that are very general and depend only on chain anisotropy of elastomer but not on details of the specific material. On the other hand, parameters like the threshold strain for the domain formation depend on the chemical composition and on the model used to describe its effect. We discuss and explain experimental observations of stripe domains both in the perpendicular geometry and when the stretching direction is at an oblique angle to the director, leading to asymmetric stripes and different topology.