Cluster and nanoparticle condensation and evaporation reactions. Thermal rate constants and equilibrium constants of Al_m, + Al_n-m ↔ Al_n with n = 2-60 and m = 1-8

The association reactions of Al atoms with Al_n clusters and nanoparticles and the unimolecular dissociation reactions of Al_n clusters and nanoparticles have been studied using classical molecular dynamics trajectory simulations. Thermal reaction rate constants of the association rate constant with m = 1 and the dissociation rate constant with m = 1-8 have been simulated, and subsequently, the association rate constants for m > 1 can be determined indirectly. It was found that the monomer association rate constants depend weakly on temperature. For the unimolecular dissociation reactions, the rate constants depend strongly on temperature, and the temperature dependences can be fitted using the Arrhenius equation. The results indicate that the unimolecular dissociation reaction has a high activation barrier that tends to increase with particle size and furthermore that the preferred dissociation process is always monomer emission. With both the monomer association and monomer emission rate constants, the standard Gibbs free energy changes of the Al_m + Al_n-m ↔ Al_n reactions on the ground-state potential energy surface with n = 2-20, 30, 40, 50, and 60 have been determined. These standard Gibbs free energy changes determined by the molecular dynamics trajectory simulations agree fairly well with the corresponding values determined by previous Monte Carlo equilibrium simulations. The rate constants determined in this study can be used to model the formation and growth of metal nanoparticles under a wide range of conditions from 1100 to 3300 K.