In gas phase synthesis systems, clusters form and grow via condensation, in which a monomer binds to an existing cluster. While a hard-sphere equation is frequently used to predict the condensation rate coefficient, this equation neglects the influences of potential interactions and cluster internal energy on the condensation process. Here, we present a collision rate theory-molecular dynamics simulation approach to calculate condensation probabilities and condensation rate coefficients. We use this approach to examine atomic condensation onto 6-56-atom Au and Mg clusters. The probability of condensation depends upon the initial relative velocity (v) between atom and cluster and the initial impact parameter (b). In all cases, there is a well-defined region of b-v space where condensation is highly probable, and outside of which the condensation probability drops to zero. For Au clusters with more than 10 atoms, we find that at gas temperatures in the 300-1200 K range, the condensation rate coefficient exceeds the hard-sphere rate coefficient by a factor of 1.5-2.0. Conversely, for Au clusters with 10 or fewer atoms and for 14- and 28-atom Mg clusters, as cluster equilibration temperature increases, the condensation rate coefficient drops to values below the hard-sphere rate coefficient. Calculations also yield the self-dissociation rate coefficient, which is found to vary considerably with gas temperature. Finally, calculations results reveal that grazing (high b) atom-cluster collisions at elevated velocity (>1000 m s-1) can result in the colliding atom rebounding (bounce) from the cluster surface or binding while another atom dissociates (replacement). The presented method can be applied in developing rate equations to predict material formation and growth rates in vapor phase systems.
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