Computer Simulation Studies of Anisotropic Systems, III. Two-Dimensional Nematic Liquid Crystals

Abstract

We have studied a two-dimensional ensemble of cylindrically symmetric particles interacting via a weak anisotropic potential using the Monte Carlo technique of computer simulation. The calculation is simplified by confining the particles to the sites of a triangular lattice. The internal energy, specific heat, second rank orientational order parameter and second rank orientational pair correlation function were calculated at various temperatures. The variation of the order parameter and pair correlation function shows that the system exhibits a transition from an orientationally disordered to a partially ordered phase. The temperature dependence of the specific heat suggests that the transition is second order or higher.

The possibility of the existence of order-disorder transitions in two dimensions is discussed. The results of the simulation are then compared with the predictions of a molecular field theory of orientational phase transitions. As expected the theory is found to be in poor agreement with the calculations.