Kinetic extensions of the nucleation theorem

Abstract

Kinetic extensions of the nucleation theorem (KNT) are derived using the law of mass action and detailed balance. Results are obtained for the first- and higher-order derivatives of the nucleation rate, J, with change in supersaturation, S, in terms of the cumulants, κn, of a molecular distribution of reciprocal equilibrium cluster growth rates. At constant temperature we find d ln J/d ln S=κ1+1, an exact formulation of the nucleation theorem in terms of nucleation rate, and the extension dn ln J/d(ln S)n=(−1)n+1κn for the higher-order derivatives (n⩾2). The case n=2 is related to the Kelvin relation. Analysis of recent water vapor nucleation rates [Wölk and Strey, J. Phys. Chem. B 105, 11683 (2001)] provides molecular-based estimates for κ1 and κ2 suitable for comparison with the predictions of classical nucleation theory. The KNT is applied to ion-induced nucleation from the gas phase, by a sequence of reversible chemical reactions, and extensions to multistep kinetics and multicomponent nucleation are presented. Nucleation theorems enable one to deduce molecular-level properties directly from macroscopic rate measurements. Here we show these properties are not those of a single cluster, the critical nucleus, as approximate forms of the theorems would suggest, but instead are averages over a weighted distribution of clusters near critical size.