Self-consistent equations of state for hard body mixtures

Abstract

The self-consistency (S-C) constraints on the solute chemical potential and equation of state are stated and employed to find corrections to thermodynamic functions in the colloidal limit for the most often used equations of state. It is shown that the S-C approach and Henderson's expression for the contact radial distribution functions yield the same correction term in the case of the Boublik—Mansoori—Carnahan—Starling—Leland (BMCSL) equation of state for hard spheres. For hard sphere (and hard convex body) mixtures a new variant of the equation of state and Helmholtz energy is proposed that fulfils better the self-consistency constraints than the frequently used equations. It is shown that the correction term for Δ_{μ 2} in hard convex body mixtures described by improved scaled particle theory differs from that for BMCSL only by the non-sphericity parameter. For the Kolafa—Boublik and modified scaled particle theory versions the correction terms are more complex.