Density profiles of fluids confined in spherical cages

Abstract

Two different free-energy functional approximations, which are the hybrid-weighted-density approximation (HWDA) and global hybrid-weighted-density approximation (GHWDA) proposed by Kim, Calleja and Rickayzen, have been applied in the study of the density profiles of hard-sphere and Lennard-Jones fluids confined in spherical cages. For the density profiles of hard-sphere fluid, both the HWDA and the GHWDA at lower density are in a good agreement with the computer simulations. However, at higher density the GHWDA shows better agreement than the HWDA and compares well with the computer simulations. For the Lennard-Jones fluid, the density-functional perturbation theory (DFPT) based on the second-order perturbation theory of the uniform liquid has been examined. The calculated results show that the DFPT compares well with computer simulations although the agreement deteriorates slightly as the temperature of the Lennard-Jones fluid is reduced.