Spherical seed mediated vapor condensation of Lennard-Jones fluid: a density functional theory approach

Vapor to liquid condensation in presence of spherical seed particle of any arbitrary radius ranging from zero to infinity has been investigated using density functional theory, by modeling the local Helmholtz free energy density functional as well as the density profile at the vapor-liquid interface. A general theory is, thus, obtained which provides the different modes of nucleation based on the size of the seed ranging from zero (corresponding to the homogeneous mode of nucleation) to infinity (corresponding to the heterogeneous nucleation on flat surface). The theory is applied to the Lennard-Jones fluid and the optimized shape (i.e., contact angle) and formation free energy of droplets of any arbitrary size have been obtained in this work. The change of the shape (optimized) with the variation of the size of the liquid droplet as well as with the size of the solid substrate has been studied, thus predicting the shape-size relationship in the course of vapor to liquid heterogeneous nucleation on a spherical solid substrate of any particular size. The spinodal decomposition of vapor has also been observed at higher strength of the solid-fluid interaction. The results have been compared with the results of the conventional classical nucleation theory.