Equations of state for hard-sphere fluids

Abstract

Equations of state and contact values of hard-sphere radial distribution functions (rdf's) which are given by a linear combination of the Percus— Yevick and scaled-particle virial expressions are considered. In the one-component case the mixing coefficientθ(η) is, in general, a function of the volume fractionη. In mixtures the coefficientθ(η i ,d i ), in general, depends upon the volume fractionη i , and diameterd i , of each species,i andj. For the contact valuesY ij of the rdf's, the mixing coefficientsΘ ij (η k ) also depend on speciesi andj. Density expansions for the exactθ for the one-component hard-sphere fluid are obtained and compared with several approximations made in earlier works and in our own work, as well as with simulations. For a mixture, it turns out that one cannot obtain the exact fourth virial coefficient by using a linear combination of the Percus-Yevick and scaled-particle virial expressions forY ij unless one allowsΘ ij to depend on mole fractionsx i even at the zeroth order of its density expansion. We also find thatΘ ij must depend on particle speciesi andj in order to satisfy the exact limits obtained earlier by Sung and Stell. A new equation of state for the binary hard-sphere mixture which satisfies all the exact limits we have considered is suggested.