A predictive model for salt nanoparticle formation using heterodimer stability calculations

Acid–base clusters and stable salt formation are critical drivers of new particle formation events in the atmosphere. In this study, we explore salt heterodimer (a cluster of one acid and one base) stability as a function of gas-phase acidity, aqueous-phase acidity, heterodimer proton transference, vapor pressure, dipole moment and polarizability for salts comprised of sulfuric acid, methanesulfonic acid and nitric acid with nine bases. The best predictor of heterodimer stability was found to be gas-phase acidity. We then analyzed the relationship between heterodimer stability and J4×4, the theoretically predicted formation rate of a four-acid, four-base cluster, for sulfuric acid salts over a range of monomer concentrations from 105 to 109 molec cm−3 and temperatures from 248 to 348 K and found that heterodimer stability forms a lognormal relationship with J4×4. However, temperature and concentration effects made it difficult to form a predictive expression of J4×4. In order to reduce those effects, heterodimer concentration was calculated from heterodimer stability and yielded an expression for predicting J4×4 for any salt, given approximately equal acid and base monomer concentrations and knowledge of monomer concentration and temperature. This parameterization was tested for the sulfuric acid–ammonia system by comparing the predicted values to experimental data and was found to be accurate within 2 orders of magnitude. We show that one can create a simple parameterization that incorporates the dependence on temperature and monomer concentration on J4×4 by defining a new term that we call the normalized heterodimer concentration, Φ. A plot of J4×4 vs. Φ collapses to a single monotonic curve for weak sulfate salts (difference in gas-phase acidity >95 kcal mol−1) and can be used to accurately estimate J4×4 within 2 orders of magnitude in atmospheric models.