On the critical non-additivity driving segregation of asymmetric binary hard sphere fluids

Abstract

A previously proposed version of thermodynamic perturbation theory, appropriate for singular pair interactions between particles, is applied to binary mixtures of hard spheres with non-additive diameters. The critical non-additivity ΔC required to drive fluid–fluid phase separation is determined as a function of the ratio ξ ≤ 1 of the diameters of the two species. ΔC(ξ) is found to decrease with ξ and to go through a minimum for ξ ≃ 0.015 before increasing sharply as ξ → 0, irrespective of the total packing-fraction η of the mixture. These results are the basis of an estimate of the range of size ratios for which a binary mixture of additive hard spheres exhibit a fluid–fluid miscibility gap. This range is conjectured to be 0.01 ≲ ξ ≲ 0.1.