Scaled particle theory for nonadditive hard spheres: Solutions for general positive nonadditivity

A complete scheme for a scaled particle theory for hard spheres with nonadditive diameters is developed. As macroscopic representation of the nonadditive hard spheres a cavity surrounded by a family of concentric selectively permeable membranes is used. The resulting equations are solved explicitly for a binary mixture with positive nonadditivity. Independent of the scheme used, scaled particle theory predicts a demixing phase transition at high density and sufficient nonadditivity. The critical value for the nonadditivity parameter is found to be ${\Delta }^c=0.215\mathrm{}$. Agreement with the few Monte Carlo results available is good.