Free-energy model for the inhomogeneous hard-sphere fluid mixture and density-functional theory of freezing

A free-energy density functional for the inhomogeneous hard-sphere fluid mixture is derived from general basic considerations and yields explicit analytic expressions for the high-order direct correlation functions of the uniform fluid. It provides the first unified derivation of the most comprehensive available analytic description of the hard-sphere thermodynamics and pair structure as given by the scaled-particle and Percus-Yevick theories. The infinite-order expansion around a uniform reference state does not lead, however, to a stable solid, thus questioning the convergence of the density-functional theory of freezing.