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

Abstract

A molecular theory of the rate of homogeneous vapor phase nucleation is formulated. The ultimate goal is a theory that contains no ad hoc assumptions or arbitrary parameters having magnitudes that must be assigned in an ad hoc manner. The centerpiece of the theory is a defined cluster denoted as the n/v-Stillinger cluster, a hybrid that combines the original Stillinger cluster 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 component 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 nature of the theory. The theory provides a standard against which subtle inconsistencies in earlier theories, both molecular and phenomenological, are revealed, and should provide guidance for the development of necessary, useful, future phenomenological theories. Earlier theories are described in sufficient detail to allow a clear discussion of such inconsistencies. This is not just a review, since the illustration of important connections and relationships, not carefully examined in the past, forms one of the major goals of the exposition. A fairly general theory for the nucleation rate is given and some of the parameters entering the theory are discussed. This paper provides the basis for its application to argon vapor in paper II.

Nucleation of Water and Methanol Droplets on Cations and Anions: The Sign Preference

“…Since typically the density of ions involved in the cloud-chamber experiments is extremely low, it is reasonable to assume that a cluster contains one ion at most. Intercluster interactions can also be neglected [21,23]. Maximizing the partition function of the supersaturated vapor gives the most probable cluster size distribution n w …”

“…This MC method is based on the physical cluster theory [21]; namely, a supersaturated vapor is viewed as a mixture of physical clusters, and a configuration of supersaturated vapor is described by the cluster-size distribution ͕n w i , n s i ͖, where n w i and n s i are the number of clusters containing i molecules, and 0 and 1 ion, respectively. The total number of ion-containing clusters is N s P i 0 n s i .…”

“…However, incorporation of molecular structures of hydrogen-bond molecules in DFT requires many approximations [20] which render calculation of barrier to nucleation semiquantitative. To accurately predict the sign preference of hydrogen-bonding systems, a combined molecular-theory/computer-simulation approach [21] is called for. In this Letter, we report computer simulation results of barrier to the cation-and anion-induced water and methanol condensation in the absence of an external electric field.…”

A dynamical definition of quasibound molecular clusters

“…More sophisticated treatments, such as the n/v-Stillinger cluster introduced by Reiss and co-workers, are rather complex. An excellent review of recent progress in this area and the application of these ideas to nucleation theory is provided by Senger et al [15].…”

Molecular dynamics simulation of atomic clusters in equilibrium with a vapour

“…Only the largest cluster in the simulation box is regarded as the cluster, smaller entities that satisfy the Stillinger definition are considered to be part of the surrounding vapour. It has been shown that a small variation of Stillinger radius in the neighbourhood of 1:5s does not lead to a significant change in the cluster equilibrium size distribution [4,25].…”