Nematic Liquid Crystal Phase Transition Monte Carlo Simulation

Nowadays in the field of liquid crystals, the nematic liquid crystals are the important objects all the time. The liquid crystals forming the nematic phase are mostly like rod. Through the experiment and the theory, confirm that the nematic liquid crystal system can bring the phase transition that from isotropic to nematic phase, from unixial to biaxial nematic phase with the temperature decreasing.In the article we use a basic model the rigid rod to simulate the nematic liquid crystals. The interaction between the liquid crystals is related with the rod-rod angle and relative length of the rods. Then using the Monte Carlo simulating method we have discussed the effect of the structure of the liquid crystal molecules on the phase behavior of the liquid crystals system. With lots of steps of Monte Carlo simulating, the system reached the balance distribution. At last, did the statistical average on the physical parameters in the balance distribution. Under the different shapes of the molecules, that is, different structure, we got the relationship between the order parameters and the temperature. The result showed that for the fixed temperature the biaxial nematic was related with the axiai symmetry of the molecular shapes. When the symmetry is relatively high, the system can be in the positive or negative nematic phase. If the asymmetry of the molecules increases, the system could have a phase transition from unixial nematic to biaxial nematic. Generally, the shape of the biaxial nematic molecules is between rod-like and disk-like. Following that we have researched the relationships between the order parameters of the liquid crystal system and the temperature in the different crystal lattice structures that are simple cube, two-dimensional crystal lattice, body center cube and the face center cube. Considering the effects of the number of the neighbouring molecules on the phase transition, the results showed that the increase of the neighbouring molecules could increase the phase transition temperature of the system at a certain extent.