Dynamics of smectic elastomers.

We study the low-frequency, long-wavelength dynamics of liquid crystal elastomers, crosslinked in the smectic-A phase, in their smectic-A, biaxial smectic and smectic-C phases. Two different yet related formulations are employed. One formulation describes the pure hydrodynamics and does not explicitly involve the Frank director, which relaxes to its local equilibrium value in a nonhydrodynamic time. The other formulation explicitly treats the director and applies beyond the hydrodynamic limit. We compare the low-frequency, long-wavelength dynamics of smectic-A elastomers to that of nematics and show that the two are closely related. For the biaxial smectic and the smectic-C phases, we calculate sound velocities and the mode structure in certain symmetry directions. For the smectic-C elastomers, in addition, we discuss in some detail their possible behavior in rheology experiments.