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.

Abstract. 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 (aw) 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 aw decreases from 0.9 to 0.33, the average diffusion coefficient of the intrinsic fluorescent organic molecules decreases from 5.5×10-9 to 7.1×10-13 cm2 s−1 and the mixing times of intrinsic fluorescent organic molecules within 200 nm brown LSOA particles increases from 0.002 to 14 s. These results suggest that the mixing times of large organics in the brown LSOA studied here are short (<1 h) for aw 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 (∼1000 µg m−3), biogenic SOA particles found in the atmosphere with mass loadings ≤10 µg m−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 104 Pa s. These results have important implications for predicting diffusion and mixing within SOA particles in the atmosphere.

&lt;p&gt;&lt;strong&gt;Abstract.&lt;/strong&gt; 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&amp;#8211;Einstein relation have been used to estimate diffusion rates of organics within SOA particles or proxies of SOA particles. To test the Stokes&amp;#8211;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 are 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 varies by 5&amp;#8211;7 orders of magnitude as the water activity varied from 0.38 to 0.88, 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 1.8&amp;#8201;&amp;#215;&amp;#8201;10&lt;sup&gt;&amp;#8722;5&lt;/sup&gt;, 1.6&amp;#8201;&amp;#215;&amp;#8201;10&lt;sup&gt;&amp;#8722;6&lt;/sup&gt; and 7.6&amp;#8201;&amp;#215;&amp;#8201;10&lt;sup&gt;&amp;#8722;6&lt;/sup&gt;&amp;#8201;&amp;#181;m&lt;sup&gt;2&lt;/sup&gt;&amp;#8201;s&lt;sup&gt;&amp;#8722;1&lt;/sup&gt; for fluorescein, Rhodamine 6G and calcein, respectively. The measured diffusion coefficients were compared with predictions made using literature viscosities and the Stokes&amp;#8211;Einstein relation. We found that at a water activity &amp;#8805;&amp;#8201;0.6 (which corresponds to a viscosity &amp;#8804;&amp;#8201;360&amp;#8201;Pa&amp;#8201;s and T&lt;sub&gt;g&lt;/sub&gt;/T&amp;#8201;&amp;#8804;&amp;#8201;0.81) predicted diffusion rates agreed with measured diffusion rates within the experimental uncertainty. (T&lt;sub&gt;g&lt;/sub&gt; 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&amp;#8201;&amp;#215;&amp;#8201;10&lt;sup&gt;6&lt;/sup&gt;&amp;#8201;Pa&amp;#8201;s and a T&lt;sub&gt;g&lt;/sub&gt;/T of 0.94) the Stokes&amp;#8211;Einstein relation under-predicted the diffusion coefficients of fluorescein, Rhodamine 6G and calcein by a factor of 95 (minimum 7 and maximum of 980), a factor of 17 (minimum 1 and maximum 165) and a factor of 56 (minimum 7 and maximum 465), respectively. The observed disagreement is significantly smaller than the disagreement observed when comparing measured and predicted diffusion coefficients of water in sucrose-water mixtures.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Abstract.&lt;/strong&gt; Viscosities and diffusion rates of organics within secondary organic aerosol (SOA) remain uncertain. Using the bead-mobility technique, we measured the viscosities as a function of water activity (a&lt;sub&gt;w&lt;/sub&gt;) of SOA generated by the ozonolysis of limonene followed by browning by exposure to NH&lt;sub&gt;3&lt;/sub&gt; (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&amp;#8211;5 orders of magnitude as the a&lt;sub&gt;w&lt;/sub&gt; 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&lt;sub&gt;w&lt;/sub&gt; decreases from 0.9 to 0.33, the average diffusion coefficient of the intrinsic fluorescent organic molecules decreases from 5.5&amp;#8729;10&lt;sup&gt;-9&lt;/sup&gt;&amp;#8201;cm&lt;sup&gt;2&lt;/sup&gt;&amp;#8201;s&lt;sup&gt;-1&lt;/sup&gt; to 7.1&amp;#8729;10&lt;sup&gt;-13&lt;/sup&gt;&amp;#8201;cm&lt;sup&gt;2&lt;/sup&gt;&amp;#8201;s&lt;sup&gt;-1&lt;/sup&gt; and the mixing times of intrinsic fluorescent organic molecules within 200&amp;#8201;nm brown LSOA particles increases from 0.002&amp;#8201;s to 14&amp;#8201;s. These results suggest that the mixing times of large organics in the brown LSOA studied here are short (&lt;&amp;#8201;1&amp;#8201;hr) for a&lt;sub&gt;w&lt;/sub&gt; and temperatures often found in the PBL. Since the diffusion coefficients and mixing times reported here correspond to SOA generated using a high mass loading (~&amp;#8201;1,000&amp;#8201;&amp;#181;g&amp;#8201;m&lt;sup&gt;-3&lt;/sup&gt;), biogenic SOA particles found in the atmosphere with mass loadings &amp;#8804;&amp;#8201;10&amp;#8201;&amp;#181;g&amp;#8201;m&lt;sup&gt;-3&lt;/sup&gt; are likely to have higher viscosities and longer mixing times. 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 10&lt;sup&gt;2&lt;/sup&gt; to 10&lt;sup&gt;4&lt;/sup&gt;&amp;#8201;Pa&amp;#8201;s. These results have important implications for predicting diffusion and mixing with SOA particles in the atmosphere.&lt;/p&gt;

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