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 DC required to drive fluid–fluid phase separation is determined as a function of the ratio !! 1 of the diameters of the two species. DC(!) is found to decrease with ! and to go through a minimum for !’ 0.015 before increasing sharply as !! 0, irrespective of the total packing-fraction " 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 0.019 !9 0.1.