Homogeneous and inhomogeneous hard-sphere mixtures: Manifestations of structural crossover

Various manifestations of structural crossover in the properties of a binary mixture of hard-spheres are studied. For homogeneous mixtures that are sufficiently asymmetric, there is a crossover line in the phase diagram such that for thermodynamic states that lie on one side, the decay of the three bulk pair correlation functions is oscillatory with a common wavelength approximately equal to the diameter of the smaller spheres, and for states on the other side, the common wavelength is approximately the diameter of the bigger spheres. Using density functional theory it is shown that structural crossover manifests itself in the intermediate range decay of (i) the one-body density profiles of a hard-sphere mixture adsorbed at planar walls, (ii) the effective (depletion) potential between two big hard-spheres immersed in the same binary mixture, and (iii) the solvation force, or excess pressure, of the same mixture confined between two planar hard walls. The structural crossover line is determined exactly for a one-dimensional binary mixture of hard-rods and evidence is presented, based on density functional theory calculations and Monte-Carlo simulations, for structural crossover in homogeneous binary mixtures of hard-disks in two dimensions. By considering a multicomponent mixture of hard-spheres, with an appropriate bimodal distribution of diameters, it is argued that structural crossover should still occur in the presence of polydispersity and that these results could be relevant to colloidal mixtures where correlation functions can be measured using real-space techniques.