Structures and correlation functions of multicomponent and polydisperse hard-sphere mixtures from a density functional theory

The structures of nonuniform binary hard-sphere mixtures and the correlation functions of uniform ternary hard-sphere mixtures were studied using a modified fundamental-measure theory based on the weight functions of Rosenfeld Rosenfeld, Phys. Rev. Lett. 63, 980 (1989)] and Boublik-Mansoori-Carnahan-Starling-Leland equation of state Boublik, J. Chem. Phys. 53, 471 (1970); Mansoori et al., J. Chem. Phys. 54, 1523 (1971)]. The theoretical predictions agreed very well with the molecular simulations for the overall density profiles, the local compositions, and the radial distribution functions of uniform as well as inhomogeneous hard-sphere mixtures. The density functional theory was further extended to represent the structure of a polydisperse hard-sphere fluid near a hard wall. Excellent agreement was also achieved between theory and Monte Carlo simulations. The density functional theory predicted oscillatory size segregations near a hard wall for a polydisperse hard-sphere fluid of a uniform size distribution.