A statistical theory of orientational ordering at the free surface of a liquid of ellipsoidal molecules

Abstract

The surface tension γ of a system of ellipsoidal molecules is evaluated approximately using a generalized Fowler-Kirkwood-Buff model. The pair potential is modelled as u(r/σ) where r is the centre of mass distance and σ is an angle dependent range parameter determined by the shape anisotropy of the molecule. It is shown that if the pair correlation function g scales as g(r/σ) γ can be mapped onto the value for a system of spheres, multiplied by an angular integral which takes into account approximately both the anisotropic molecular shape as well as possible orientational order. It is shown that γ is lowered when the orientational order parameter Q ≠ 0, implying that isotropic molecular liquids may be partially ordered near the free surface. The surface favours parallel ordering of rod-like particles in a direction in the plane of the surface. For plate-like particles, ordering with the plates in the plane of the surface is favoured. In both cases the anchoring energies increase sharply with the shape anisotropy of the molecule. These results are qualitatively consistent with the surface properties of non-polar nematic liquid crystals.