Dynamics of nematic elastomers

We study the low-frequency, long-wavelength dynamics of soft and semisoft nematic elastomers using two different but related dynamic theories. Our first formulation describes the pure hydrodynamic behavior of nematic elastomers in which the nematic director has relaxed to its equilibrium value in the presence of strain. We find that the sound-mode structure for soft elastomers is identical to that of columnar liquid crystals. Our second formulation generalizes the derivation of the equations of nematohydrodynamics by Forster et al. to nematic elastomers. It treats the director explicitly and describes slow modes beyond the hydrodynamic limit.

Figure 1

Symmetry directions. The $t$ direction is perpendicular to the plane containing the equilibrium director ${\mathbf{n}}_0$ and the wave vector $\mathbf{q}$ of a generic excitation. The $T$ direction is perpendicular to $\mathbf{q}$ and the $t$ direction.

Figure 2

Schematic polar plot (arbitrary units) of the sound velocities $c_t$ (solid line), $c_1$ (short-dashed line), and $c_2$ (long-dashed line).