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

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 Delta_C required to drive fluid–fluid phase separation is determined as a function of the ratio xi < 1 of the diameters of the two species. Delta_C(xi) is found to decrease with xi and to go through a minimum for xi = 0.015 before increasing sharply as xi -> 0, irrespective of the total packing-fraction eta 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 < xi < 0.1