Hypernetted-chain closure with bridge diagrams. Asymmetric hard sphere mixtures

Abstract

Methods of calculating the first two terms in the density expansion of the bridge function are given. The closure to the Ornstein–Zernike equation is now exact to two orders in density beyond the hypernetted-chain or Percus–Yevick approximations. The bridge function is resummed as a Padé approximant, and the results for hard spheres are relatively accurate over the whole density regime. The closure is shown to yield physically reasonable results for highly asymmetric mixtures. Infinitely dilute hard sphere solutes with diameters up to 30 times that of the hard-sphere solvent are also considered. The Derjaguin approximation for rescaling the force between spheres to the interaction free energy between planes is examined and found to give the dominant curvature correction.