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

Abstract

New hybrid weighted-density approximations (HWDA) based an both local and global average densities are proposed. In one of the approximtions the weighting function is constructed to satisfy the same homogeneous properties as the local weighted-density approximation (LWDA) proposed by Tanrona, in the other, the weighting function is consuueted to agree with that of Leidl and Wagner for the homogeneous fluid, Free energy functianals arr derived from these proposed weighted-density approximations by using expansions in term 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 Rat walls, the results are in good agreement with the computer simulations and comparable with those of the free energ). functiooal approximation of 'Tarawna even at the high density po3 = 0.9135. For the density profiles of h&-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 approvtmalions have the advantage of being simpler to apply.

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“…Unlike for the density profiles of hard-sphere fluids restricted by permeable walls [1,6], for the density profiles of hard-sphere fluid confined in spherical cages the GHWDA results show better agreement than the HWDA results, and compare with the computer simulations. Here, the interesting thing is that at higher density the HWDA does not describe correctly the physical behaviour of hard-sphere fluid near the centre of a spherical cage.…”

“…For the system of hard-sphere fluid confined in a spherical hard-wall cage of radius R, the resulting density profile equation [1] is given by…”

“…The density profiles are obtained by the numerical interaction between the old density profiles on the right-hand side and the new one on the left-hand side in equation (1). In applying equation (1), the excess free energy per particle of hard-sphere fluid, f (ρ), is taken from the quasi-exact Carnahan-Starling equation of state [11]:…”

“…From equations (2) and (9), we can easily obtain the one-particle direct correlation functions for the attractive contribution; c (1) (15) and for the c (1) …”

“…In a recent paper [1], we have proposed the hybrid-weighted-density approximation (HWDA) and global hybrid-weighted-density approximation (GHWDA). In one of the approximations the weighted function is constructed to satisfy the same homogeneous properties as the local weighted-density approximation (LWDA) proposed by Tarazona (see [2,3,4]); in the other, the weighting function is constructed to agree with that of Leidl and Wagner [5] for the homogeneous fluid.…”