Smectic elastomer membranes.

We present a model for smectic elastomer membranes which includes elastic and liquid-crystalline degrees of freedom. Based on our model, we determined the qualitative phase diagram of a smectic elastomer membrane using mean-field theory. This phase diagram is found to comprise five phases, viz., smectic- A -flat, smectic- A -crumpled, smectic- C -flat, smectic- C -crumpled, and smectic- C -tubule phases, where in the latter phase, the membrane is flat in the direction of mesogenic tilt and crumpled in the perpendicular direction. The transitions between adjacent phases are second-order phase transitions. We study in some detail the elasticity of the smectic- C -flat and the smectic- C -tubule phases which are associated with a spontaneous breaking of in-plane rotational symmetry. As a consequence of the Goldstone theorem, these phases exhibit soft elasticity characterized by the vanishing of in-plane shear moduli.