Computer simulation studies of anisotropic systems

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Abstract
We have studied the surface behaviour of the Lebwohl-Lasher model nematogen using the Monte Carlo technique of computer simulation. Two states of the nematogen have been investigated, one with normal periodic boundary conditions and the other with boundary conditions employed for just two dimensions thus forming two free surfaces orthogonal to the third dimension. We have determined the variation of the internal energy and the second rank orientational order parameter, associated with individual layers, with their distance from the surface, as a function of the temperature. The order in the surface is found to be less than in the bulk nematogen although this difference is far less for the isotropic phase than for the nematic. This suppression of the surface orientational order is in accord with the surface tension simulated for the nematogen. Thus the surface tension decreases rapidly with increasing temperature in the nematic mesophase but then is essentially independent of temperature in the isotropic phase. Direct evaluation of the surface tension suggests that, to within the statistical error of the simulation, this is continuous at the nematic-isotropic transition. However, we have been able to show that the surface tension of the nematic phase is slightly greater than for the isotropic phase from the small reduction in the transition temperature produced by the creation of the free surfaces. We have also developed a molecular field theory for the surface properties of the Lebwohl-Lasher nematogen and this has been tested using the results of our Monte Carlo simulation. In particular the theory greatly overestimates the reduction in the surface tension at the transition from the nematic to the isotropic phase. However other properties, such as the variation of the order parameter with the separation from the surface and the temperature dependence of the surface tension, are predicted in better agreement with the results of the simulation.

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