Two new exact criteria for hard-sphere mixtures

Abstract

Two exact criteria are derived for multicomponent hard-sphere mixtures with additive diameters, based on geometrical arguments similar to those employed by scaled particle theory. Both criteria involve derivatives with respect to particle size of excess chemical potentials at infinite dilution in the mixture. One relates these derivatives to the contact values of the pair distribution functions and the other to the compressibility factor of the mixture. We show an application of the second criterion to evaluating hard-sphere mixture equations of state.