Toward a molecular theory of vapor-phase nucleation. II. Fundamental treatment of the cluster distribution

A statistical mechanical theory of the cluster distribution involved in homogeneous vapor-phase nucleation is presented based on the stochastic nature of physical clusters. This new approach supports the work of Ellerby, Weakliem, and Reiss (Paper I of this series) by deriving their results by a different, though equally rigorous method. Furthermore, the present treatment is more direct and transparent, avoiding completely the need to construct the partition function for the entire vapor, requiring instead the consideration only of the probability of an individual cluster. This circumvents the problem of complicated configuration counting involved in the partition function approach, and therefore eliminates the potentially tedious explanations corresponding to it. The increased simplicity and clarity of the method presented here result in new insights and discoveries concerning the cluster distribution. For example, the distribution is now understood in relation to fluctuation theory, and is cast in terms of an equilibrium constant for cluster formation. Beyond this, the meaning of the free energy of cluster formation in the theory is now thoroughly understood. This approach complements that of Ellerby, Weakliem, and Reiss, and advances the understanding and exposition of a viable theory of vapor-phase nucleation.