Binary non-additive hard sphere mixtures: Fluid demixing, asymptotic decay of correlations and free fluid interfaces

Using a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large (positive) non-additivity the mixture phase separates into two fluid phases with different compositions. We calculate bulk fluid-fluid coexistence curves for a range of size ratios and non-additivity parameters and find that they compare well to simulation results from the literature. Using the Ornstein-Zernike equation, we investigate the asymptotic, r->infinity, decay of the partial pair correlation functions, g_ij(r). At low densities there occurs a structural crossover in the asymptotic decay between two different damped oscillatory modes with different wavelengths corresponding to the two intra-species hard core diameters. On approaching the fluid-fluid critical point there is Fisher-Widom crossover from exponentially damped oscillatory to monotonic asymptotic decay. Using the density functional we calculate the density profiles for the planar free fluid-fluid interface between coexisting fluid phases. We show that the type of asymptotic decay of g_ij(r) not only determines the asymptotic decay of the interface profiles, but is also relevant for intermediate and even short-ranged behaviour. We also determine the surface tension of the free fluid interface, finding that it increases with non-additivity, and that on approaching the critical point mean-field scaling holds.