On the Statistical Mechanics of Nucleation Theory

Abstract

Some statistical‐mechanical aspects of the theory of homogeneous nucleation in condensation of droplets from supersaturated vapor are considered, but no attempt is made to dispense with the standard capillarity approximation. It is shown that the major differences between current approaches of this type lie in the replacement factor, which describes the contributions arising from the fact that net motions of the cluster as a whole in the stable condensed phase are unavailable to it in the vapor. Calculation of this factor depends on the model assumed for the bulk liquid. Arguments are presented to show that the Dunning model of free translation and rotation of clusters in the bulk liquid is unrealistic and yields replacement factors which are much too low, i.e., ∼10⁻¹⁶. A method is proposed for determining the replacement factor for condensation from measurements of nucleation rate in freezing. It is concluded that the original Lothe—Pound replacement factor of 10⁻³ is not greatly in error. Thus the factor of disagreement between theory and observation, at least in the case of water vapor and the vapors of certain polar and asymmetric molecules, stands at approximately 10¹⁴−10¹⁷, the theory predicting homogeneous nucleation rates which are much too high.