Diffusion coefficients of organic molecules in sucrose–water solutions and comparison with Stokes–Einstein predictions

Abstract

Abstract. The diffusion coefficients of organic species in secondary organic aerosol (SOA) particles are needed to predict the growth and reactivity of these particles in the atmosphere. Previously, viscosity measurements, along with the Stokes–Einstein relation, have been used to estimate the diffusion rates of organics within SOA particles or proxies of SOA particles. To test the Stokes–Einstein relation, we have measured the diffusion coefficients of three fluorescent organic dyes (fluorescein, rhodamine 6G and calcein) within sucrose–water solutions with varying water activity. Sucrose–water solutions were used as a proxy for SOA material found in the atmosphere. Diffusion coefficients were measured using fluorescence recovery after photobleaching. For the three dyes studied, the diffusion coefficients vary by 4–5 orders of magnitude as the water activity varied from 0.38 to 0.80, illustrating the sensitivity of the diffusion coefficients to the water content in the matrix. At the lowest water activity studied (0.38), the average diffusion coefficients were 1.9  ×  10−13, 1.5  ×  10−14 and 7.7  ×  10−14 cm2 s−1 for fluorescein, rhodamine 6G and calcein, respectively. The measured diffusion coefficients were compared with predictions made using literature viscosities and the Stokes–Einstein relation. We found that at water activity  ≥  0.6 (which corresponds to a viscosity of  ≤  360 Pa s and Tg∕T  ≤  0.81), predicted diffusion rates agreed with measured diffusion rates within the experimental uncertainty (Tg represents the glass transition temperature and T is the temperature of the measurements). When the water activity was 0.38 (which corresponds to a viscosity of 3.3  ×  106 Pa s and a Tg∕T of 0.94), the Stokes–Einstein relation underpredicted the diffusion coefficients of fluorescein, rhodamine 6G and calcein by a factor of 118 (minimum of 10 and maximum of 977), a factor of 17 (minimum of 3 and maximum of 104) and a factor of 70 (minimum of 8 and maximum of 494), respectively. This disagreement is significantly smaller than the disagreement observed when comparing measured and predicted diffusion coefficients of water in sucrose–water mixtures.