Density profiles of fluids in some special symmetries

A free-energy-functional approximation based on a semi-empirical method is proposed. The main advantage of the free-energy-functional approximation is its accuracy compared with other models and its relative simplicity compared with other well-known weighted-density approximations. The free-energy-functional approximation is applied to predict the density profiles of the hard-sphere fluids and the Lennard–Jones fluids in some special symmetries. For the density profiles near a hard flat wall, the results reproduced the hard-sphere oscillatory structures qualitatively and quantitatively. For the density profiles of hard-sphere fluids confined in a spherical cage, the results are also in a fair agreement with the computer simulations. For Lennard–Jones fluids, two kinds of density-functional perturbation theories, the density-functional mean-field theory (DFMFT) and the density-functional perturbation theory (DFPT), examined. The results show that at higher temperature the DFPT compares well with computer simulations. However, the agreement deteriorates slightly as the temperature of the Lennard–Jones fluids is reduced. These results demonstrate that both the free-energy-functional approximation and the DFPT succesfully describe the inhomogeneous properties of classical fluids.