Re-examination of Homogeneous Nucleation Theory: Statistical Thermodynamics Aspects

Abstract

An analysis of the equilibrium concentration of critical clusters in a supersaturated vapor is developed from the grand canonical ensemble representation of statistical mechanics, Callen's axiomatic formulation of thermodynamics and the standard capillarity approximation of nucleation theory. It is concluded that: (1) There is a small correction to the Kelvin equation for the equilibrium of a small droplet with the vapor; (2) The conclusion of Frenkel and Lothe and Pound in regard to the equilibrium concentration of critical nuclei is essentially correct for the case of no orientational degeneracy in the rigid‐body rotation of a cluster; (3) For an orientationally degenerate cluster, the Lothe‐Pound 10¹⁷ factor of correction to classical nucleation theory is no longer valid, but is replaced by a 10⁸ correction factor; (4) The revision of nucleation theory proposed by Reiss and Katz is erroneous.