Growth of atmospheric clusters involving cluster-cluster collisions: comparison of different growth rate methods

We simulated the time evolution of atmospheric cluster concentrations in a one-component system where not only do clusters grow by condensation of monomers, but cluster-cluster collisions also significantly contribute to the growth of the clusters. Our aim was to investigate the consistency of the growth rates of sub-3aEuro-nm clusters determined with different methods and the validity of the common approach to use them to estimate particle formation rates. We compared the growth rate corresponding to particle fluxes (FGR), the growth rate derived from the appearance times of clusters (AGR), and the growth rate calculated based on irreversible vapor condensation (CGR). We found that the relation between the different growth rates depends strongly on the external conditions and the properties of the model substance. The difference between the different growth rates was typically highest at the smallest, sub-2aEuro-nm sizes. FGR was generally lower than AGR and CGR; at the smallest sizes the difference was often very large, while at sizes larger than 2aEuro-nm the growth rates were closer to each other. AGR and CGR were in most cases close to each other at all sizes. The difference between the growth rates was generally lower in conditions where cluster concentrations were high, and evaporation and other losses were thus less significant. Furthermore, our results show that the conventional method used to determine particle formation rates from growth rates may give estimates far from the true values. Thus, care must be taken not only in how the growth rate is determined but also in how it is applied.