Kinetic theory of nucleation based on a first passage time analysis: Improvement by the density-functional theory

A recent kinetic theory of nucleation [see, e.g., E. Ruckenstein and B. Nowakowski, J. Colloid Interface Sci. 137, 583 (1990)] is based on molecular interactions and avoids the traditional thermodynamics. The rate of emission of molecules from a cluster is found via a first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution function of a surface molecule located in the potential field created by the cluster. The liquid cluster was assumed to have sharp boundaries and uniform density. In the present paper, this assumption is removed by using the density-functional theory to find the density profiles. Thus, more accurate calculations of the potential field created by the cluster, its emission rate, and nucleation rate are obtained. The modified theory is illustrated by numerical calculations for a molecular pair interaction potential combining the dispersive attraction with the hard-sphere repulsion.