Monte Carlo Simulation Of The Finite Molecular Films Of The Nematic Liquid Crystal

In order to calculate the characteristics of the physical system, the common method is to account the interested values along the route which is created by basic equation in phase space. However the Monte Carlo(MC) method is a different one in the computational physics simulation. Firstly, the system is described by a Hamilton value. Then we should choose an appropriate ensemble and finally we can calculate all the observable values through the distribution and partition function contacted with the ensemble. So the essential idea of MC method is to receive the thermodynamic observables value by sampling the primary contributions.It is shown that the liquid crystal molecules parallel to the substrate surface as a result of substrate potential which arises from being coated with polymer film and rubbed. The order distribution and order parameter are always concerned with theory and experiment. In this paper we just study them through MC method.We firstly do over the well-known Lebwohl-Lasher(L-L) model and then study the bulk phase transition of liquid crystal. The result is received accordantly to the literature. Finally the thin liquid crystal films between the two rubbed substrates are studied by Monte Carlo simulation. In the paper, we adopt L-L model pair potential and constrain the center of molecules mass on simple cubic lattice (203) sites, if we only consider neighboring interaction and the periodic boundary condition for thin film paralleling to rubbed substrate, we can get numerical results of orientation order and order distribution for each thin film. We found that the orientation order of the thin film between rubbed substrates is distinct to the bulk system and is contacted with surface potential intension. At the same time the transition temperature shifts comparingwith bulk system. In addition from our simulation the order on surface is no longer axial symmetry but biaxial symmetry, namely induced biaxial character. We compare our results with molecule field theory's timely and found them according with each other very well. In conclusion we say this paper's results can be used to instruct the directional distribution of liquid crystal on substrate surface.