Monte Carlo study of the ordering in a strongly frustrated liquid crystal.

We have performed Monte Carlo simulations to investigate the temperature dependence of the ordering of the side chains of the X-shaped liquid crystal molecules which are arranged in a hexagonal array. Each hexagon contains six side chains, one from each side of the hexagon. Each liquid crystal molecule has two, dissimilar, side chains, one that contains silicon and one that contains fluorine. Like chains attract each other more strongly than unlike chains and this drives an order-disorder transition. The system is frustrated because it is not possible to find a configuration in which all the hexagons are occupied by either all silicon or all fluorine chains. There are two phase transitions. If only pairwise interactions are included it is found that there is an interesting fluctuating phase between the disordered phase and the fully ordered ground state. This did not agree with the experiments where an intermediate phase was seen that had long range order on one of the three sublattices. Agreement was found when the calculations were modified to include attractive three-body interactions between the silicon chains.