Density profiles of hard-sphere fluids restricted by hard and permeable walls

Abstract

New hybrid weighted-density approximations (HWDA) based on both local and global average densities are proposed. In one of the approximations the weighting function is constructed to satisfy the same homogeneous properties as the local weighted-density approximation (LWDA) proposed by Tarazona (1985); in the other, the weighting function is constructed to agree with that of Leidl and Wagner (1993) for the homogeneous fluid. Free energy functionals are derived from these proposed weighted-density approximations by using expansions in terms of the density. They are applied to predict the density profiles of hard-sphere fluids restricted by hard and permeable walls and in spherical cages. For the density profiles of fluids confined between hard flat walls, the results are in good agreement with the computer simulations and comparable with those of the free energy functional approximation of Tarazona even at the high density rho sigma 3=0.9135. For the density profiles of hard-sphere fluids restricted by permeable walls with a finite height and in spherical cages, the results are also in good agreement with the computer simulations. These results show that although the free energy functionals differ, the new approximations and LWDA produce equally accurate results for the inhomogeneous hard-sphere fluids investigated. The new approximations have the advantage of being simpler to apply.