Distribution of density fluctuations in a molecular theory of vapor-phase nucleation

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Abstract
A statistical-mechanical theory of the distribution of density fluctuations involved in homogeneous vapor-phase nucleation is presented which improves on previous work. Specifically, a refined characterization of a physical cluster is developed. This cluster is known as an i/v cluster, since it is defined by both a molecular number i and a volume v (i/v is the average density of molecules in the cluster). The i/v cluster represents the density fluctuations that have the potential to serve as condensation centers for the formation of liquid drops. The refinement involves a so-called shell molecule which defines the volume v. The equilibrium distribution of the refined i/v clusters is derived, using an approach involving fluctuation theory. This method is as rigorous as prior approaches and, moreover, sheds light on the nature of the cluster distribution and the cluster itself. Through an analysis of a cluster defined without a shell molecule, it is shown that the shell molecule is necessary if the cluster characterization is to be consistent with the fundamental statistical-mechanical description of the supersaturated vapor. Finally, as a by-product of this work, it is shown that the awkwardness of the constant-pressure ensemble associated with its expression as a sum over volume is automatically removed once the necessary presence of a shell molecule is recognized.