Computer Simulation Of Liquid Crystal Films Based On 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 pah* potential model, such as Lebwohl-Lasher model (L-L model) . However this model only describe spatially isotropic interaction, excluding pairwise additive interaction.Recently, Gruhn and Hess proposed two spatially anisotropic pair potential, model I and model II, which approximately reproduced the elastic free energy density. In this paper, we investigate the orientational distribution and the N-I phase transition of the nematic liquid crystal (PAA) films, which confined by free surface, and study the orientational distribution of the 5CB film, which confined by rubbed-surface, with two spatially anisotropic pair potential.In the molecular field approximation, we solve the self-consistent equation for the molecular orientational distribution function by an iterative method, make a numerical calculation for two kinds of films, then give some conclusions as followed:(i) For free-surface liquid crystal films, Firstly, when t = 0, the orientational distribution is isotropic regardless the director of the film is along X, Y or Z axis in Lebwohl-Lasher model. However both the symmetry of the model I and the model II breaks, i.e., the free energy of the states is unequal, which corresponding to the director along X, Y or Z axis, moreover the state which the director is vertical to the film has the lowest free energy for model I, while for model II, the state which has the lowest free energy is the director lies in the surface plane of the film. Secondly, for the Lebwohl-Lasher model, the N-I phase transition temperature of liquid crystal film is less than that of the bulk system (tN-ItC), decreases with increaseing in finite sizes, there is exist LC. Whereas in model II, the N-I phase transition temperature of liquid crystal film is less than that of the bulk system (tN-I