Kinetic extensions of the nucleation theorem
نویسندگان
چکیده
Kinetic extensions of the nucleation theorem ~KNT! are derived using the law of mass action and detailed balance. Results are obtained for the firstand higher-order derivatives of the nucleation rate, J, with change in supersaturation, S, in terms of the cumulants, kn , of a molecular distribution of reciprocal equilibrium cluster growth rates. At constant temperature we find d ln J/d ln S5k1 11, an exact formulation of the nucleation theorem in terms of nucleation rate, and the extension d ln J/d(ln S)5(21)kn for the higher-order derivatives (n>2). The case n52 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 k1 and k2 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. © 2003 American Institute of Physics. @DOI: 10.1063/1.1565098#
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