A statistical mechanical method to evaluate the energy of formation of water clusters attached to a foreign particle surface is described, with the binding energy being evaluated on a molecular level, using semiempirical modified neglect of diatomic overlap (MNDO) theory. The model is applied to water nucleation on a silicon oxide surface. The binding energy contribution, which represents the energy of formation at T=0 K, is found to slightly (but not negligibly in the thermal sense) increase with the number of hydrogen bonds between the water cluster and the condensation nucleus whose surface is made of silicon oxide. An analytic expression is developed to fit the binding energy contribution as a function of cluster size. At lower temperatures, a linear relationship is found between the log of the nucleation rate and reciprocal temperature for fixed saturation ratio. However, at higher temperatures, this relationship deviates from linearity. The deviation is sufficient to suggest the existence of a critical temperature for which the nucleation rate reaches a maximum. Furthermore, another kind of critical temperature is found, which corresponds to a minimum cluster critical size (at fixed saturation ratio). These are found to almost coincide for the cases of heterogeneous and homogeneous nucleation.
C. K. Lutrus et al., "Temperature and Supersaturation Dependent Nucleation Rates of Heterogeneous Water by Molecular Cluster Model Calculation," Journal of Chemical Physics, vol. 99, no. 12, pp. 9962-9971, American Institute of Physics (AIP), Aug 1993.
The definitive version is available at https://doi.org/10.1063/1.465395
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