Scaled particle theory for non-additive hard spheres

A general formalism for the scaled particle theory is developed for mixtures of hard spheres with non-additive diameters. A comparison of the various possibilities suggests that an approach which uses semi-permeable membranes characterized by osmotic pressure differences is the best macroscopic representation of large non-additivity in the interaction. For the Widom-Rowlinson model the equations of state based on this model show excellent agreement with the exact one-dimensional solution up to high densities. They represent a considerable improvement over the results obtained from the solution of the Percus-Yevick equation. In three dimensions, scaled particle theory leads to a critical density for the de-mixing phase transition, which is smaller than the value obtained from mean field theory. There is evidence why the Percus-Yevick approximation leads to too large critical densities.