Homogeneous nucleation in metal vapors. 5. A self-consistent kinetic model

Abstract

The kinetic model developed for the condensation of metallic vapors is based on the solution of the master equation for nmer growth (2 ≤ n ≤ 80): An + Ai + M ⇄ An+i + M. In these calculations the forward and reverse rate constants were related via kn→n+i/kn+i→n = K(c)n→n+i = ℛT exp[-(ΔG° n+i - ΔG° n - ΔG°i)/RT]; ΔG°1 ≡ 0 where ΔG°n is the standard Gibbs free energy increment for the association of n monomers. The corresponding enthalpy and entropy increments were either measured or calculated. "Constrained equilibrium" nmer densities were defined; these proved to be identical with Nnss (steady state densities) for n < n†, at which Nnss has a minimum. A kinetic criterion for the onset of condensation emerged from this analysis. We demonstrated that the transition from the constrained equilibrium for n < n† to avalanche cluster growth for n n < n† is not dependent on the presence of a maximum in the free-energy function, but is sensitive to the supersaturation ratio. The time to attain steady state was estimated, and we formulated an expression for the condensation flux at that condition.