Equilibrium thermodynamic properties of binary hard-sphere mixtures from integral equation theory

The binary additive hard-sphere mixtures have been studied by the Ornstein-Zernike integral equation coupled with the Martynov-Sarkisov (MS) closure approximation. Virial equation of state is computed in the MS approximation. The excess chemical potential for the mixture is evaluated with a closed-form expression based on correlation functions. The excess Helmholtz free energy is obtained using the Euler relation of thermodynamics. Moreover, these thermodynamic quantities are obtained by the Boubl\'{i}k-Mansoori-Carnahan-Starling-Leland (BMCSL) formulas. Our findings for pressure and excess chemical potential for a number of binary sets of the mixtures from the MS approximation show good agreements with those obtained by the BMCSL formulas and available data in literature, having a maximum deviation of $5\%$ for a packing fraction up to 0.5. The maximum deviation of the excess free energy obtained for the mixtures is shown to be $\sim 16\%$ for a packing fraction of 0.5. To our knowledge, this work presents an initial calculation of an excess chemical potential of the system in the MS approximation.