Direct correlation functions for negatively non-additive hard spheres in the PY approximation

Abstract

We investigate, within the Percus-Yevick (PY) approximation, the functional form of the direct correlation functions c_ij (r) for symmetric binary mixtures of hard spheres with negatively non-additive diameters R_ij (i.e. two-component systems with R ₁₁=R ₂₂=≡R and R ₁₂<R, at equimolar concentration). A partial exact solution is obtained when−R/2ˇ-α≡R ₁₂-R<0 and, by introducing appropriate, simple, polynomial approximations to two functions X ₁₂(r) and Y ₁₁(r) contributing, respectively, to c ₁₂(r) and c ₁₁(r), the problem of solving the Ornstein-Zernike (OZ) integral equation is reduced to an algebraic one, i.e. to solving a system of a few (usually non-linear) algebraic equations in some unknown parameters. A very good agreement is found between our approximate solutions and the exact PY ones. Finally, a numerical Carnahan-Starling-type equation of state is presented and a successful comparison with Monte Carlo simulation data of Adams and McDonald is made.