Studies of a version of scaled particle theory for nonadditive hard disks

Abstract

The scaled particle theory for nonadditive hard disks developed by Tenne and Bergmann [J. Chem. Phys. 70, 1952 (1979)] has been studied for binary mixtures of equal size particles with various values of the nonadditivity parameter and mole fraction. Above a certain special density, we find that there are two branches of solutions of the equations determining the thermodynamic properties of the system. An argument is given that one of these branches is unphysical and should be discarded. Nevertheless, it explains a kink in the free energy vs density plot, and other anomalous features of the results of Tenne and Bergmann. We conclude that the existence of a phase transition has not yet been established for this approximation. It is pointed out that the theory does not give scaled particle theory for pure liquids in the limit of zero concentration of one component.