On the thermodynamics of hard spheres near a soft repulsive wall

Abstract

We extend the variational method based on the Gibbs-Bogolioubov inequality to the case of fluids against a wall. We investigate the influence of the softness of the wall on the free energy of the system. For small packing fraction we consider a density expansion. The variational results are compared with the exact ones which are given by a direct expansion of the free energy. A comparison between variational and perturbation methods has been done for small packing fraction and also for a case corresponding to the liquid state. The accuracy of the present extension of the variational method to a surface phenomena is found as good as in the bulk fluid. A very simple expression is given for the change on surface tension when we go from the perfect hard wall to soft repulsive wall.