Fluid-fluid and fluid-solid phase separation in nonadditive asymmetric binary hard-sphere mixtures

Very asymmetric mixtures of hard spheres naturally arise in the modellization of colloidal dispersions. Effective potentials have emerged as a powerful tool for describing these systems and have often been employed to extract the phase diagram in both the additive and nonadditive cases. However, most theoretical investigations have been carried out by means of mean-field-like approaches, so their quantitative accuracy remains to be assessed. Here we employ previously determined effective potentials for nonadditive hard-sphere mixtures to study the fluid-fluid phase transition by the hierarchical reference theory (HRT), which is designed to take realistically into account the effects of long-range fluctuations on phase separation. Fluid-solid equilibrium is addressed by supplementing HRT with thermodynamic perturbation theory for the solid phase. We apply this approach both to a potential with adjustable nonadditivity parameter (Louis et al 2000 Phys. Rev. E 61 R1028) and to the Asakura-Oosawa (AO) potential, which represents an extreme case of nonadditivity. Our results for the phase diagram, including modified hypernetted chain (MHNC) calculations, are compared to those of other liquid-state theories and are found to agree nicely with available simulation data. Unlike commonly adopted liquid-state theories, HRT is capable both of getting arbitrarily close to the fluid-fluid critical point, and of giving nontrivial critical exponents. In particular, the fluid-fluid coexistence curve is much flatter than that obtained via perturbation theory, in agreement with a recent finite-size scaling Monte Carlo analysis of the AO model.