Fluctuations in Nematic Liquid Crystals under the Thermal Gradient

Abstract

The critical dynamical behavior of homeotropic nematic liquid crystals heated from above is investigated in connection with the convection instability. This is done by employing the Boussinesq approximation and an incompressibility assumption, and basing on the linearized hydrodynamic equations. It is found that one of the viscous modes and the combinational mode of “twist” and “bending” remain unchanged, whereas, one of the coupling modes among the thermal diffusion mode, the viscous mode and the combinational mode of “splay” and “bending” shows the critical slowing down, when the instability threshold is approached. An explicit expression for the correlation function which describes the light scattering is obtained. Its power spectrum, which reduces to a single Lorenzian at the equilibrium state, breaks up into three Lorenzians as the temperature gradient increases.