Fluid–fluid and fluid–solid phase separation in nonadditive asymmetric binary hard-spheremixtures

Abstract

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