Waves at the nematic-isotropic interface

We examine surface modes at the nematic-isotropic interface in polymer-liquid-crystal mixtures using the dynamical Landau-de Gennes model for the orientational (non-conserved) order parameter coupled with Cahn-Hilliard equation for concentration (conserved order parameter) and with hydrodynamic degrees of freedom. The generalized dispersion relation is obtained and analyzed in particular cases. Orientational order parameter relaxation dominates in the short wavelength limit, while in the long wavelength limit viscous damping becomes important. The effect of polymer is to increase the surface tension and as a consequence the relaxation rate in the hydrodynamic limit. Finally, we discuss how to measure experimentally the dispersion relation