Cluster translation and growth in density functional theories of homogeneous nucleation

Abstract

Density functional theories of nucleation relate the thermodynamic properties of a supersaturated vapor to a density profile which is usually interpreted as that of a critical cluster. It is argued here that mean field density functional theory gives a profile which includes a small amount of translational motion, as well as growth, of the cluster. These fluctuations, equivalent to those of a hard sphere gas in a suitably-shaped potential well, must be factored out before the nucleation rate is obtained. Correction for the growth fluctuation has little effect and the usual Zeldovich factor is reasonably accurate. However, correction for translational motion leads to a large enhancement to the usual nucleation rate expression, by a factor approximately proportional to the ratio of liquid to vapour densities and between about 106 and 108 for nonane under usual experimental conditions. © 1997 American Institute of Physics.