Binary hard-sphere solute-solvent radial distribution function in the colloidal limit: exact calculation from an equation of state

An exact formula is derived relating the contact value of the solute-solvent radial distribution function for an additive binary hard-sphere (HS) mixture at infinite dilution, g ^∞ ₁₂(d ₁₂), to the mixture equation of state (EOS) (1 denotes the solvent and 2 denotes the solute). This result can also be considered to be a consistency condition involving approximations for g ^∞ ₁₂(d ₁₂) and for the mixture EOS. Employing three approximate HS mixture equations of state from the literature, we use our formula to derive corresponding analytical approximations for g ^∞ ₁₂(d ₁₂) In addition, new computer simulations were performed to obtain accurate results for g ^∞ ₁₂(d ₁₂) and for g ^∞ ₁₂(r ₁₂) at the solute-solvent diameter ratios {1, 3, 5, 7, 10, 20} and the reduced solvent density ρ? = 0.8. We compare our results for g ^∞ ₁₂(d ₁₂) with the simulation results and with the results of approximate analytical expressions for g ^∞ ₁₂(d ₁₂) proposed by several workers. The results obtained from our formula in conjunction with two of the EOS expressions considered are more accurate than all previously proposed approximations, with the exception of the approximation of Matyushov and Ladanyi 1997, J. chem. Phys., 107, 5815], which is of comparable accuracy.