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.

Diffusivity measurements of volatile organics in levitated viscous aerosol particles

“…The high-viscosity breakdown of Stokes-Einstein reported in this study and by others (Power et al, 2013;Price et al, 2015;Chenyakin et al, 2017) begs the question of how the hydrodynamic radii relate to the magnitude of the discrepancy between prediction and measured diffusivities. We try to address this question in Fig.…”

“…For comparison, diffusivities of other molecules in aqueous sucrose are shown. The diffusivities of fluorescein, rhodamine 6G and calcein (Chenyakin et al, 2017) in aqueous sucrose at 21.4 • C are roughly an order of magnitude smaller than the PEG-4 diffusivities at 19.5 • C. While PEG-4 is smaller and lighter, the molecular masses and hydrodynamic radii of these fluorescent dyes are comparable or larger than sucrose, and the measured diffusivities seem to agree with the diffusivity of sucrose in aqueous sucrose measured by (Price et al, 2016) at 23.5 • C. As expected, the PEG-4 diffusivities fall below the diffusivity of water in aqueous sucrose (Zobrist et al, 2011).…”

“…The diffusivity of water is shown in light blue and was taken from the parametrizations of Zobrist et al (2011) and Price et al (2014). The data points for fluorescein, rhodamine 6G and calcein, shown in green, were taken from Chenyakin et al (2017). PEG-4 (this study, 19 • C) is shown red.…”

“…Several bulk and levitated aerosol particle techniques, based on isotopic tracers, fluorescence and mass transport measurements, have emerged to measure water diffusivity in highly viscous systems (Zobrist et al, 2011;Price et al, 2014;Lienhard et al, 2015;Davies and Wilson, 2016;Marshall et al, 2016). Few studies have addressed the diffusion of larger molecules (Champion et al, 1997;Price et al, 2016;Chenyakin et al, 2017) such as VOCs. Marshall et al (2016) studied the suppression of the evaporation of maleic acid in viscous sucrose aerosol and its dependence on RH, but stopped short of ascribing diffusivities, choosing instead to describe diffusion limitations qualitatively as apparent reduction in vapor pressure.…”

Mixing times of organic molecules within secondary organic aerosol particles: a global planetary boundary layer perspective

“…For the calculations, a hydrodynamic radius of 0.38 nm was used for the diffusing organic molecules within SOA based on an assumed molecular weight of 175 g mol −1 (Huff Hartz et al, 2005), a density of 1.3 g cm −3 (Chen and Hopke, 2009;Saathoff et al, 2009), and spherical symmetry. The StokesEinstein equation should give reasonable values when the radius of the diffusing molecules is roughly greater than or equal to the radius of the matrix molecules and when the viscosity of the matrix is relatively small (400 Pa s) (Chenyakin et al, 2017;Price et al, 2016). When the viscosity of the matrix is large (10 6 Pa s), the Stokes-Einstein equation can underpredict diffusion coefficients of organic molecules in Figure 2.…”