Study of distortions in nematic liquid crystals based upon spatially anisotropic pair potential

Distortions of nematic liquid crystals are studied based upon the molecular pair potential model which is spatially anisotropic and dependent on elastic constants of liquid crystals. The perfect nematic order is assumed in the theoretical treatment, which means the orientation of the molecular long axis coincides with the director of liquid crystal and the total free energy equals to the total interaction energy. Three kinds of the basic Freedericksz transition are investigated analytically and numerical calculations are made for the director profiles in a hybrid nematic cell. Two mapping schemes from the elastic energy to the pair potential, proposed recently in the literature, are checked. Only one scheme can give the result consistent with the continuum theory.