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. Diffusion can be important for predicting the growth, evaporation, and reaction rates of SOA under certain atmospheric conditions. 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. Using rectangular area fluorescence recovery after photobleaching (rFRAP), we determined diffusion coefficients of fluorescent organic molecules over 8 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 the diffusion of organic molecules in SOA. Although almost all the data agree with the Stokes–Einstein relation within a factor of 10, a fractional Stokes–Einstein relation (D∝1/ηξ) with ξ=0.93 is a better model for predicting the 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 overpredict mixing times of organic molecules within SOA by as much as 1 order of magnitude at an altitude of ∼3 km compared to the fractional Stokes–Einstein relation with ξ=0.93. These results also have implications for other areas such as in food sciences and the preservation of biomolecules.

To predict important secondary organic aerosol (SOA) properties, information on viscosity or diffusion rates within SOA is needed. Ozonolysis of β-caryophyllene is an important SOA source; however, very few viscosity or diffusion rate measurements have been performed for this SOA type and none as a function of relative humidity (RH). In this study, we measured viscosity as a function of RH for SOA generated from the ozonolysis of β-caryophyllene using the poke-flow technique. At an RH of 0 and 48%, the viscosity was between 6.9 × 105 and 2.4 × 107 Pa s, and between 1.3 × 103 and 5.6 × 104 Pa s, respectively. Based on these viscosities and the fractional Stokes–Einstein equation, characteristic mixing timescales of organics within 200 nm β-caryophyllene SOA particles range from ∼0.2 h at 0% RH to <3 s at 48% RH, suggesting that these particles should be well-mixed under most conditions in the lower atmosphere. The chemical composition of the SOA was also determined using nano-desorption electrospray ionization mass spectrometry. The measured chemical composition and the method of DeRieux et al. (ACP, 2018) were used to predict the viscosity of β-caryophyllene SOA. If the mass spectra peak abundances were adjusted to account for the sensitivity of the electrospray ionization to larger molecular weight components, the predicted viscosity overlapped with the measured viscosity at 0% RH, while the predicted viscosities at 15–48% RH were slightly higher than the measured viscosities. The measured viscosities also overlapped with viscosity predictions based on a simple mole-fraction based Arrhenius mixing rule.

Abstract. When simulating the formation and life cycle of secondary organic aerosol (SOA) with chemical transport models, it is often assumed that organic molecules are well mixed within SOA particles on the timescale of 1 h. While this assumption has been debated vigorously in the literature, the issue remains unresolved in part due to a lack of information on the mixing times within SOA particles as a function of both temperature and relative humidity. Using laboratory data, meteorological fields, and a chemical transport model, we estimated how often mixing times are < 1 h within SOA in the planetary boundary layer (PBL), the region of the atmosphere where SOA concentrations are on average the highest. First, a parameterization for viscosity as a function of temperature and RH was developed for α-pinene SOA using room-temperature and low-temperature viscosity data for α-pinene SOA generated in the laboratory using mass concentrations of ∼ 1000 µg m −3 . Based on this parameterization, the mixing times within α-pinene SOA are < 1 h for 98.5 % and 99.9 % of the occurrences in the PBL during January and July, respectively, when concentrations are significant (total organic aerosol concentrations are > 0.5 µg m −3 at the surface). Next, as a starting point to quantify how often mixing times of organic molecules are < 1 h within α-pinene SOA generated using low, atmospherically relevant mass concentrations, we developed a temperatureindependent parameterization for viscosity using the roomtemperature viscosity data for α-pinene SOA generated in the laboratory using a mass concentration of ∼ 70 µg m −3 . Based on this temperature-independent parameterization, mixing times within α-pinene SOA are < 1 h for 27 and 19.5 % of the occurrences in the PBL during January and July, respectively, when concentrations are significant. However, associated with these conclusions are several caveats, and due to these caveats we are unable to make strong conclusions about how often mixing times of organic molecules are < 1 h within α-pinene SOA generated using low, atmospherically relevant mass concentrations. Finally, a parameterization for viscosity of anthropogenic SOA as a function of temperature and RH was developed using sucrose-water data. Based on this parameterization, and assuming sucrose is a good proxy for anthropogenic SOA, 70 and 83 % of the mixing times within anthropogenic SOA in the PBL are < 1 h for January and July, respectively, when concentrations are significant. These percentages are likely lower limits due to the assumptions used to calculate mixing times.

Measurements of the water activity-dependent viscosity of aerosol particles from two techniques are compared, specifically from the coalescence of two droplets in a Holographic Optical Tweezers (HOT) and poke-and-flow experiments on particles deposited onto a glass substrate. These new data are also compared with the fitting of Dimer Coagulation, Isolation and Coalescence (DCIC) measurements. The aerosol system considered in this work are ternary mixtures of sucrose-citric acid-water and sucrose-NaNO3-water, at varying solute mass ratios. Results from HOT and poke-and-flow are in excellent agreement over their overlapping range of applicability (~10 3-10 7 Pa s); fitted curves from DCIC data show variable agreement with the other two techniques because of the sensitivity of the applied modelling framework to the representation of water content in the particles. Further, two modelling approaches for the predictions of the water activity-dependent viscosity of these ternary systems are evaluated. We show that it is possible to represent their viscosity with relatively simple mixing rules applied to the subcooled viscosity values of each component or to the viscosity of the corresponding binary mixtures. ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. The Supporting Information includes three additional figures and four additional tables as indicated in the main manuscript (PDF).

Abstract. The viscosities of three polyols and three saccharides, all in the non-crystalline state, have been studied. Two of the polyols (2-methyl-1,4-butanediol and 1,2,3-butanetriol) were studied under dry conditions, the third (1,2,3,4-butanetetrol) was studied as a function of relative humidity (RH), including under dry conditions, and the saccharides (glucose, raffinose, and maltohexaose) were studied as a function of RH. The mean viscosities of the polyols under dry conditions range from 1.5  ×  10−1 to 3.7  ×  101 Pa s, with the highest viscosity being that of the tetrol. Using a combination of data determined experimentally here and literature data for alkanes, alcohols, and polyols with a C3 to C6 carbon backbone, we show (1) there is a near-linear relationship between log10 (viscosity) and the number of hydroxyl groups in the molecule, (2) that on average the addition of one OH group increases the viscosity by a factor of approximately 22 to 45, (3) the sensitivity of viscosity to the addition of one OH group is not a strong function of the number of OH functional groups already present in the molecule up to three OH groups, and (4) higher sensitivities are observed when the molecule has more than three OH groups. Viscosities reported here for 1,2,3,4-butanetetrol particles are lower than previously reported measurements using aerosol optical tweezers, and additional studies are required to resolve these discrepancies. For saccharide particles at 30 % RH, viscosity increases by approximately 2–5 orders of magnitude as molar mass increases from 180 to 342 g mol−1, and at 80 % RH, viscosity increases by approximately 4–5 orders of magnitude as molar mass increases from 180 to 991 g mol−1. These results suggest oligomerization of highly oxidized compounds in atmospheric secondary organic aerosol (SOA) could lead to large increases in viscosity, and may be at least partially responsible for the high viscosities observed in some SOA. Finally, two quantitative structure–property relationship models (Sastri and Rao, 1992; Marrero-Morejón and Pardillo-Fontdevila, 2000) were used to predict the viscosity of alkanes, alcohols, and polyols with a C3–C6 carbon backbone. Both models show reasonably good agreement with measured viscosities for the alkanes, alcohols, and polyols studied here except for the case of a hexol, the viscosity of which is underpredicted by 1–3 orders of magnitude by each of the models.

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Abstract. Information on liquid–liquid phase separation (LLPS) and viscosity (or diffusion) within secondary organic aerosol (SOA) is needed to improve predictions of particle size, mass, reactivity, and cloud nucleating properties in the atmosphere. Here we report on LLPS and viscosities within SOA generated by the photooxidation of diesel fuel vapors. Diesel fuel contains a wide range of volatile organic compounds, and SOA generated by the photooxidation of diesel fuel vapors may be a good proxy for SOA from anthropogenic emissions. In our experiments, LLPS occurred over the relative humidity (RH) range of ∼70 % to ∼100 %, resulting in an organic-rich outer phase and a water-rich inner phase. These results may have implications for predicting the cloud nucleating properties of anthropogenic SOA since the presence of an organic-rich outer phase at high-RH values can lower the supersaturation with respect to water required for cloud droplet formation. At ≤10 % RH, the viscosity was ≥1×108 Pa s, which corresponds to roughly the viscosity of tar pitch. At 38 %–50 % RH, the viscosity was in the range of 1×108 to 3×105 Pa s. These measured viscosities are consistent with predictions based on oxygen to carbon elemental ratio (O:C) and molar mass as well as predictions based on the number of carbon, hydrogen, and oxygen atoms. Based on the measured viscosities and the Stokes–Einstein relation, at ≤10 % RH diffusion coefficients of organics within diesel fuel SOA is ≤5.4×10-17 cm2 s−1 and the mixing time of organics within 200 nm diesel fuel SOA particles (τmixing) is 50 h. These small diffusion coefficients and large mixing times may be important in laboratory experiments, where SOA is often generated and studied using low-RH conditions and on timescales of minutes to hours. At 38 %–50 % RH, the calculated organic diffusion coefficients are in the range of 5.4×10-17 to 1.8×10-13 cm2 s−1 and calculated τmixing values are in the range of ∼0.01 h to ∼50 h. These values provide important constraints for the physicochemical properties of anthropogenic SOA.

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.