Fluctuations in bounded cells of liquid crystals in an external field

Abstract

Spatial correlation functions of orientation fluctuations in bounded cells of smectic and nematic liquid crystals are calculated taking into account the effect of external fields and finiteness of the energy of anchoring to the surface. The cases of positive and negative anisotropies of magnetic susceptibility or permittivity are considered. The calculations are based on the division of degrees of freedom into bulk and surface ones and on the reduction of the computation of the continual integral determining the correlation function to the solution of the Euler equation with corresponding boundary conditions of the first or third kind. The obtained correlation functions are used for describing the intensity of light scattered in nematics for the planar and homeotropic orientations. It is shown, in particular, that the measurements of the angular dependence of the scattered light intensity may serve as a reliable method for determining the energy of anchoring of a liquid crystal to a substrate for different values of the external field.