The interfacial properties of a model of a nematic liquid crystal

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Abstract
We have developed a statistical-mechanical theory for the interfacial properties of molecular fluids characterized by strongly anisotropic pairwise potentials. The theory, which is a generalization to molecular fluids of the mean-field (or van der Waals) theory for the Helmholtz free energy of non-uniform fluids of spherical molecules, was applied to the nematic-isotropic and nematic-vapour interfaces of a simple model of a nematic liquid crystal. Our model exhibits three fluid phases—a nematic, an isotropic liquid and a vapour—which can co-exist in pairs, and which also simultaneously co-exist at a low temperature triple point, T tr. We present explicit results for the global phase diagram of the model which are in good qualitative agreement with data on real liquid crystals. We have studied in detail the various fluid interfaces occurring in different regions of the phase diagram. We present results of numerical calculations for the density and orientational order parameter profiles of a nematic-isotropic interface at T tr for various values of the anisotropy ratio characterizing the liquid crystal. We find that although the change in orientational order parameter is much larger than the change in density at the interface, the surface tension is still dominated by density fluctuations. We have also investigated the properties of the nematic-vapour interface at various temperatures below the triple point. We find that there is no excess orientational order at the free interface of our model. Furthermore we find a continuous wetting or surface-induced disordering transition at the triple point temperature. The liquid-vapour surface tension of the model was found to be discontinuous at T tr, with the surface tension less in the isotropic phase, which is in agreement with the results for some liquid crystals. The results of these calculations, and in particular the possibility of a surface phase transition at T tr suggest a new and useful way of interpreting experimental data on the liquid-vapour surface tension of a liquid crystal close to the nematic-isotropic transition.