Study Of Distortions In Nematic Liquid Crystals Based Upon Spatially Anisotropic Pair Potential

The essential task of liquid crystal statistical physics is studying macroscopic properties of liquid crystal based on molecular interaction. The molecule of liquid crystal is organic macromolecule, so we usually describe the interaction with pair potential model, such as Lebwohl-Lasher model (L-L model) . However, this model only describes spatially isotropic interaction, excluding pairwise additive interaction.Recently, Gruhn and Hess proposed a spatially anisotropic pair potential, which approximately reproduced the elastic free energy density. Then Romano and Luckhurst obtained two pair potential models, i.e. model I and model II. In this paper, 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, ie. model I and model II. Then we give some conclusions as followed:First, we can obtain the correct threshold magnetic field of the basic Freedericksz transition by model I, but we can't by model II.Second, we can describe the director profiles in a hybrid nematic cell by model I, but we can't by model II.Third, model I has not inner easy direction, but model II has.