Waves at the nematic-isotropic interface: nematic-non-nematic and polymer-nematic mixtures

Abstract

We extend the theory for surface modes at the nematic-isotropic interface1,2,3,4 to study comparatively two systems: nematic-non-nematic and polymer nematic mixtures. We employ the dynamical generalization of the Landau de Gennes model for the orientational (non-conserved) order parameter, coupled with the Cahn Hilliard equation for concentration (conserved parameter), and include hydrodynamic degrees of freedom. The densities to include the coupling between the concentration of the nonnematogen and polymer fluids 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, the 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.