Predictions of diffusion rates of organic molecules in secondary organic aerosols using the Stokes-Einstein and fractional Stokes-Einstein relations

Abstract. Information on the rate of diffusion of organic molecules within secondary organic aerosol (SOA) is needed to accurately predict the effects of SOA on climate and air quality. Often, researchers have predicted diffusion rates of organic molecules within SOA using measurements of viscosity and the Stokes-Einstein relation ( D  ∝ 1/η where D is the diffusion coefficient and η is viscosity). However, the accuracy of this relation for predicting diffusion in SOA remains uncertain. We measured diffusion coefficients over eight orders in magnitude in proxies of SOA including citric acid, sorbitol, and a sucrose-citric acid mixture. These results were combined with literature data to evaluate the Stokes-Einstein relation for predicting diffusion of organic molecules in SOA. Although almost all the data agrees with the Stokes-Einstein relation within a factor of ten, a fractional Stokes-Einstein relation ( D  ∝ C/η t ) with t  = 0.93 and C  = 1.66 is a better model for predicting diffusion of organic molecules in the SOA proxies studied. In addition, based on the output from a chemical transport model, the Stokes-Einstein relation can over predict mixing times of organic molecules within SOA by as much as one order of magnitude at an altitude ~ 3 km, compared to the fractional Stokes-Einstein relation with t  = 0.93 and C  = 1.66. These differences can be important for predicting growth, evaporation, and reaction rates of SOA in the middle and upper part of the troposphere. These results also have implications for other areas where diffusion of organic molecules within organic-water matrices is important.