Waves at the nematic-isotropic interface: thermotropic nematogen-non-nematogen mixtures

We develop a theory for surface modes at the nematic-isotropic interface in thermotropic nematogen-non-nematogen mixtures. We employ the dynamical generalization of the Landau-de Gennes model for the orientational (nonconserved) order parameter, coupled with the Cahn-Hilliard equation for concentration (conserved parameter), and include hydrodynamic degrees of freedom. The theory uses a generalized form of the Landau-de Gennes free-energy density to include the coupling between the concentration of the non-nematogen fluid and the orientational order parameter. Two representative phase diagrams are shown. The method of matched asymptotic expansions is used to obtain a generalized dispersion relation. Further analysis is made in particular cases. Orientational order parameter relaxation dominates in the short-wavelength limit, while in the long-wavelength limit viscous damping processes become important. There is an intermediate region (depending on the temperature) in which the interaction between conserved parameter dynamics and hydrodynamics is important.