Homogeneous nucleation in vapor-liquid phase transition of Lennard-Jones fluids: a density functional theory approach

Density functional theory (DFT) with square gradient approximation for the free energy functional and a model density profile are used to obtain an analytical expression for the size-dependent free energy of formation of a liquid drop from the vapor through the process of homogeneous nucleation, without invoking the approximations used in classical nucleation theory (CNT). The density of the liquid drop in this work is not the same as the bulk liquid density but it corresponds to minimum free energy of formation of the liquid drop. The theory is applied to study the nucleation phenomena from supersaturated vapor of Lennard-Jones fluid. The barrier height predicted by this theory is significantly lower than the same in CNT which is rather high. The density at the center of the small liquid drop as obtained through optimization is less than the bulk density which is in agreement with other earlier works. Also proposed is a sharp interface limit of the proposed DFT of nucleation, which is as simple as CNT but with a modified barrier height and this modified classical nucleation theory, as we call it, is shown to lead to improved results.