The Monte Carlo Simulation Of The Hybrid Nematic Liquid Crystal Based Upon Spatially Anisotropic Pair Potential

For studying macroscopic characteristic of liquid crystal based on molecular interaction,we usually describe the interaction with pair potential model, such as Lebwohl-Lasher model (L-L model). However this model only describe spatially isotropic interaction. Gruhn and Hess proposed a spatially anisotropic pair potential, which approximately reproduced the elastic free energy density.Monte Carlo simulation is an important method to study liquid crystal statistical physics. Its basic idea is: In order to solve mathematics, physics and chemistry and other issues, we will set up a probabilistic model or random process, the measurement sample of the main contribution will give us the solution of the issues.We will use the Monte Carlo simulation method to study the hybrid nematic liquid crystal films in this paper. First, Lebwohl-Lasher model was introduced, the molecular centers of mass are located at the sites of the 30*30*10 lattice. At the four lateral faces of the simulation sample we have employed periodic boundary conditions. The confinement is introduced as an additional layer of fixed spins whose orientation corresponds to the direction parallel to the layer. The relation between extrapolate layer and liquid crystal layer can be considered as the relation in the liquid crystal layers. We have got the transition between the bent-director structure and the biaxial structure with director exchange, which fits well to what is described in other papers.Subsequently, we choose the spatially anisotropic pair potential, the confinement is also introduced as an additional layer of fixed spins whose orientation corresponds to the direction induced by the walls. The handling of the six boundaries are the same as the Lebwohl-Lasher model. We have got the transition between the bent-director structure and the biaxial structure with director exchange and the non-linear distribution of director. The film's symmetry was broken. This facts verify the nonlinear conclusions in elastic theory and liquid crystal materials ( K1≠K3).