Homogeneous nucleation cluster

Altman, I. S., I. E. Agranovskii, M. Choi and V A. Zagainov (2008) To the theory of homogeneous nucleation Cluster energy. Russian Journal of Physical Chemistry A, Focus on Chemistry 82, 2097-2102... 

An important approach to the study of nucleation of solids is the investigation of small droplets of large molecular clusters. Years ago, Turnbull showed that by studying small droplets one could eliminate impurities in all except a few droplets and study homogeneous nucleation at significant undercoolings [13]. 

In general, homogeneous nucleation of nanoparticles occurs when a solute (C) diffuses to surface of a cluster from a bulk solution, and then incorporates into the cluster through surface reaction until a nucleus (C ) is obtained ... 

Quite recently Raes (1985) applied the classical theory of homogenous nucleation originally developed by Bricard et al (1972) to atmospheres containing SO2, H2O and 218Po ions. Depending on the H2O and SO2 concentrations, ions could grow to a quasi-stable cluster which would evaporate upon electrical neutralization, or to a larger size which would survive neutralization. 

Katz described the homogeneous nucleation of a supersaturated vapour using J(i), the net rate at which clusters of size i grow to size i + 1 [63]. In this kinetic equation, J(i) is the difference between the rate at which clusters of size i add an additional monomer, and the rate at which clusters of size i + 1... 

The term binary homogeneous nucleation is used to describe the formation of particles from two different gas-phase compounds such as sulfuric acid and water such nucleation can occur when their individual concentrations are significantly smaller than the saturation concentrations needed for nucleation of the pure compounds. It is believed that in the atmosphere, formation of particles from low-volatility gases occurs not by condensation of a single species but rather by the formation and growth of molecular clusters involving at least two, and as described shortly, probably three or more different species. 

The reversible work, W, to homogeneously nucleate a cluster of a new phase in (unstable) equilibrium with the parent phase is the change in the Gibbs free... 

Early investigators determined that the formation of an aerosol initially required a surface for condensation. This surface could be made up of a small cluster of vapor molecules, an ion or ionic cluster, or it could be a small particle of some other material, termed a condensation nucleus. When condensation of a vapor takes place solely on clusters of similar vapor molecules, it is called spontaneous or homogeneous nucleation. When condensation occurs on a nucleus or dissimilar material, it is called heterogeneous nucleation. 

Homogeneous nucleation is thought to take place in three steps. First, the vapor must be supersaturated to an extent that condensation will take place second, small clusters of molecules or embryos must form third, the vapor must condense on these embryos so that the embryo grows into a full-fledged nucleus which subsequently becomes a droplet. For heterogeneous nucleation only two steps take place, the first and third. 

Unlike the CNT for homogeneous nucleation, whose theoretical foundation has not been advanced since late 30s, the theoretical formalism of the ion-induced nucleation theory has been recently improved and extended. The critical importance of the dipole moment of condensing monomers and pre-nucleation clusters have been pointed out in the series of recent publications of Nadykto with coauthors [34-39] and, more recently, Leopold with co-authors [69]. The classical ion-induced nucleation theory has been advanced through the incorporation of the effect of the polar host vapour molecule-charged cluster interactions and some of the serious shortcomings of the original model have been successfully corrected [36]. 

Considering these geometric factors, the rate for homogeneous nucleation of spherical clusters is... 

---