Statistical thermodynamics of the nematic liquid crystal free surface

Abstract

The possible development of stable density oscillations in the form of a structured liquid-vapour density transition at the surface of simple liquids has been proposed and the thermodynamic consequences for the surface tension discussed. The principal effect on the surface tension-temperature characteristic is that just beyond the triple point certain systems should show a surface tension which increases with temperature: moreover, such behaviour has been observed experimentally. We now extend the treatment to include the orienta- fional contributions to the surface excess quantities for a nematic liquid crystal. It is found that the possibility exists both for the development of positive slopes and discontinuities in the surface tension-temperature characteristic. We find that the slope a δr / δT is determined as a competition between orientational order and spatial disorder which develops at the liquid surface. Should the situation corresponding to highly ordered orientational states occur, the γ (T) characteristic will show a positive slope, although with increasing temperature and spatial delocalisation of the liquid surface the usual monotonic decreasing function will be regained. Again, discontinuities in the slope and absolute value of the γ (T) charac- teristic would be expected with the discontinuous variation of the order parameter at the nematic-isotropic transition temperature.