Toward a molecular theory of vapor-phase nucleation. I. Identification of the average embryo

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Abstract
A statistical-mechanical theory of vapor-phase nucleation is developed which improves on that introduced by Reiss, Katz, and Cohen (RKC), and revised by Reiss, Tabazadeh, and Talbot (RTT) by identifying a physical embryo appropriate to the nucleation process. Put in the simplest manner, the goals of this paper are (1) to define embryos in such a manner that their thermodynamic properties can be easily calculated by means of computer simulation; (2) to define embryos in such a manner that (ideally) they can be used as entities in terms of which the systematic exact evaluation of the classical phase integral can be performed, and the equilibrium distribution of embryos therefore determined. This model of a pre-nucleating embryo prevents redundant counting of configurations in the partition function needed to derive the metastable equilibrium distribution of embryos. The embryo definition does not artificially constrain the molecules within the embryo, but remains only a procedural device for organizing the counting. The present treatment also resolves a problem not noticed by RTT involving an inconsistency concerning dimensions in their theory. Using the embryo definition the metastable equilibrium distribution of embryos is derived. Finally, a brief discussion of how the distribution can be used in a theory of nucleation rate is provided. Work is presently under way on the rate theory.