Self-consistent binary cluster size distributions: nucleation of sulfuric acid–water vapors

The incorporation of additional information on free energies of small clusters in a cluster distribution based on the capillarity approximation is considered in relation with self-consistency (SC). The concept of fictitious average monomers is applied to expand the self-consistent form of a unary size distribution to cover also the distribution of a binary system. The experimental data on the free energies of monohydrates and dihydrates of sulfuric acid are used to obtain the partially self-consistent size distribution of clusters. Using these distributions, the concentrations of sulfuric acid and water, required for obtaining a unit nucleation rate, are calculated and compared among themselves and with experimental concentrations. Free energies of cluster formation are estimated by the thermodynamically consistent classical theory taking into account the difference between interior and surface compositions of a cluster. The partially self-consistent size distribution gives the best agreement with experimental data. The self-consistent distribution of the proposed form overestimates hydration and, therefore, largely underestimates nucleation rates compared to experimental rates.