A molecular theory of the homogeneous nucleation rate. I. Formulation and fundamental issues

A molecular theory of the rate of homogeneous vapor phase nucleation is for mulated. The ultimate goal is a theory that contains no ad hoc assumptions or arbitrary parameters having magnitudes that must be assigned in an ad ho c manner. The centerpiece of the theory is a defined cluster denoted as the n/v-Stillinger cluster, a hybrid that combines the original Stillinger clu ster and the more recent n/v cluster. The Stillinger component assures that redundancy is avoided in the characterization of the cluster and the n/v c omponent makes the Monte Carlo simulation of the free energy of the cluster relatively simple, and also allows dynamics to weight the importance of a cluster to the nucleation rate process. In the companion paper (paper II), dealing with the application of the theory to argon vapor, it is shown that the avoidance of redundancy is of primary importance to the non ad hoc nat ure of the theory. The theory provides a standard against which subtle inco nsistencies in earlier theories, both molecular and phenomenological, are r evealed, and should provide guidance for the development of necessary, usef ul, future phenomenological theories. Earlier theories are described in suf ficient detail to allow a clear discussion of such inconsistencies. This is not just a review, since the illustration of important connections and rel ationships, not carefully examined in the past, forms one of the major goal s of the exposition. A fairly general theory for the nucleation rate is giv en and some of the parameters entering the theory are discussed. This paper provides the basis for its application to argon vapor in paper II. (C) 199 9 American Institute of Physics. [S0021-9606(99)50213-4].