Viscosities, diffusion coefficients, and mixing times of intrinsic fluorescent organic molecules in brown limonene secondary organic aerosol and tests of the Stokes–Einstein equation

Viscosities and diffusion rates of organics within secondary organic aerosol (SOA) remain uncertain. Using the bead-mobility technique, we measured viscosities as a function of water activity (a_w) of SOA generated by the ozonolysis of limonene followed by browning by exposure to NH₃ (referred to as brown limonene SOA or brown LSOA). These measurements together with viscosity measurements reported in the literature show that the viscosity of brown LSOA increases by 3–5 orders of magnitude as the aw decreases from 0.9 to approximately 0.05. In addition, we measured diffusion coefficients of intrinsic fluorescent organic molecules within brown LSOA matrices using rectangular area fluorescence recovery after photobleaching. Based on the diffusion measurements, as the a_w decreases from 0.9 to 0.33, the average diffusion coefficient of the intrinsic fluorescent organic molecules decreases from 5.5×10⁻⁹ to 7.1×10⁻¹³cm²s⁻¹ and the mixing times of intrinsic fluorescent organic molecules within 200nm brown LSOA particles increases from 0.002 to 14s. These results suggest that the mixing times of large organics in the brown LSOA studied here are short (<1h) for a_w and temperatures often found in the planetary boundary layer (PBL). Since the diffusion coefficients and mixing times reported here correspond to SOA generated using a high mass loading ( ∼ 1000µgm⁻³), biogenic SOA particles found in the atmosphere with mass loadings  ≤ 10µgm⁻³ are likely to have higher viscosities and longer mixing times (possibly 3 orders of magnitude longer). These new measurements of viscosity and diffusion were used to test the accuracy of the Stokes–Einstein relation for predicting diffusion rates of organics within brown LSOA matrices. The results show that the Stokes–Einstein equation gives accurate predictions of diffusion coefficients of large organics within brown LSOA matrices when the viscosity of the matrix is as high as 10² to 10⁴Pas. These results have important implications for predicting diffusion and mixing within SOA particles in the atmosphere.