Highly Viscous States Affect the Browning of Atmospheric Organic Particulate Matter.

Initially transparent organic particulate matter (PM) can become shades of light-absorbing brown via atmospheric particle-phase chemical reactions. The production of nitrogen-containing compounds is one important pathway for browning. Semisolid or solid physical states of organic PM might, however, have sufficiently slow diffusion of reactant molecules to inhibit browning reactions. Herein, organic PM of secondary organic material (SOM) derived from toluene, a common SOM precursor in anthropogenically affected environments, was exposed to ammonia at different values of relative humidity (RH). The production of light-absorbing organonitrogen imines from ammonia exposure, detected by mass spectrometry and ultraviolet-visible spectrophotometry, was kinetically inhibited for RH < 20% for exposure times of 6 min to 24 h. By comparison, from 20% to 60% RH organonitrogen production took place, implying ammonia uptake and reaction. Correspondingly, the absorption index k across 280 to 320 nm increased from 0.012 to 0.02, indicative of PM browning. The k value across 380 to 420 nm increased from 0.001 to 0.004. The observed RH-dependent behavior of ammonia uptake and browning was well captured by a model that considered the diffusivities of both the large organic molecules that made up the PM and the small reactant molecules taken up from the gas phase into the PM. Within the model, large-molecule diffusivity was calculated based on observed SOM viscosity and evaporation. Small-molecule diffusivity was represented by the water diffusivity measured by a quartz-crystal microbalance. The model showed that the browning reaction rates at RH < 60% could be controlled by the low diffusivity of the large organic molecules from the interior region of the particle to the reactive surface region. The results of this study have implications for accurate modeling of atmospheric brown carbon production and associated influences on energy balance.

Introduction

Atmospheric particulate matter (PM) can directly and indirectly affect global climate[1] and adversely impact human health.[2,3] PM also participates in atmospheric chemical cycles through uptake, reaction, and release of trace gases.[4,5] Organic material comprises a large fraction of the submicron particulate mass suspended in the atmosphere.[6,7] Some organic PM absorbs light in the ultraviolet-to-visible region, and the absorption typically has a strong wavelength dependence.[8−10] This light-absorbing organic PM, commonly referred to as “brown carbon,” can redistribute the absorption of radiation, at times leading to warming in the lower troposphere with attendant effects on climate radiative forcing and photochemistry.[11−13]

Brown carbon can be directly emitted from primary sources,[8,14] such as biomass burning,[15] or produced in the atmosphere as secondary organic material (SOM).[16−18] Light absorption by SOM depends on precursor type as well as the oxidation pathways active in its production. For example, SOM derived from aromatic precursors tends to be more than an order of magnitude more absorptive than that derived from terpenoid precursors.[17] The presence of molecular heteroatoms, such as nitrogen and sulfur, can further enhance light absorption.[19−21] The physicochemical properties of organic particles, including optical properties, dynamically evolve during the PM lifetime in the atmosphere.[7,22] The reactive uptake of gaseous molecules and particle-phase chemistry can produce chromophores.[18,23] Uptake and particle-phase reactions of ammonia to produce imines can enhance light absorption for several types of SOM.[16] Chromophores can also be photobleached by photolysis and reactions with atmospheric oxidants.[22,24]

Although the detailed reactions governing the evolution of brown carbon are complex, an important governing factor might be the phase state of the SOM. Diffusivity in this reaction matrix might under some conditions be low enough to determine overall rates of chemical reaction,[25−27] both toward chromophore production and loss.[28,29] Until recently, organic PM was modeled as a low-viscosity liquid,[30] implying that the transformation and interactions between light-absorbing compounds and gas-phase species can occur throughout the particle volume for typically sized accumulation-mode atmospheric particles. The assumption of low viscosity, however, is challenged by recent observations.[31−33] Many organic compounds and their mixtures form amorphous solid or semisolid states upon dehydration.[34] Ambient and laboratory organic particles can rebound at moderate relative humidity (RH) upon impact with a hard surface, indicating that these particles are not liquid.[31,35,36] Depending on viscosity η, the physical state of the rebounding particles can be solid (i.e., glassy, η > 1012 Pa s) or semisolid (i.e., η of 102 to 1012 Pa s). Direct viscosity measurements have been made for several types of SOM,[37−41] and the Stokes–Einstein relation linked the measured viscosities to inferred diffusivities for large organic molecules.[27] This relation, however, can break down for the diffusion of small molecules within a matrix of larger molecules[42,43] or in the vicinity of the glass transition.[44−46] Glass transition temperatures have been measured for several atmospherically relevant organic compounds,[47−49] and SOM is believed to become glassy at temperatures representative of the upper troposphere, with possible implications for ice nucleation processes.[50−55] The possibility that SOM might become glassy in the lower atmosphere at warmer temperatures and lower RH remains a topic of continuing research.[55−58]

High viscosities suggest that diffusivities can become sufficiently low to impose kinetic limitations on the rates of particle-phase reactions for time scales relevant to atmospheric processes. Even so, there can be significant differences between transitions in physical properties (i.e., rebound and liquefaction) and transitions in chemical reactivity or regimes of gas-particle partitioning. Li et al.,[25] for example, observed sharp increases in chemical reactivity at 20% RH for toluene-derived SOM aerosol particles. Liu et al.[56] likewise observed a nonlabile-to-labile transition at 20% RH for evaporation of semivolatile organic compounds (SVOCs) from toluene-derived SOM films. These transition RH values were significantly lower than the transition RH of 65% for particle rebound.[36] Accurate predictions of transitions in chemical reactivity should take into account the interplay among diffusivity, chemical rate constants, and particle size (cf. Figure a). In this regard, several kinetic models have included explicit treatment of reactant diffusivities.[59−63] The key parameters in these models were the diffusivity values of small molecules, such as OH, O3, NO3, H2O, NH3, and amines, as well as the diffusivity values of large organic molecules constituting the particle matrix.[27,61,62] The lack of data for constraining the values of these parameters, however, hindered model confidence, including the modeling of secondary brown carbon production along in-particle chemical pathways.

Figure 1

(a) Schematic of ammonia reactive uptake for a highly viscous droplet in the left panel and a well-mixed liquid droplet in the right panel. The accessible reactive volume is highlighted in both panels. (b) A simplified mechanism of ammonia uptake and brown carbon production for SOM derived from aromatic precursors. For instance, SOM carbonyls can react with ammonia to produce imines, which in turn oligomerize to yield conjugated light-absorbing organonitrogen compounds.[67] This browning pathway competes with other reactions that may not produce chromophores, such as the NH3-neutralization of SOM carboxylic acids to form ammonium salts.[25,26,68]

As a focus of interpretation and analysis of the study described herein, the hypothesis is that slow diffusion associated with the high viscosity can limit rates of mass transfer and hence rates of condensed-phase reactions, including the reactions that produce brown carbon (cf. Figure a–b). The experiments described herein combined three types of measurements to investigate how highly viscous states can affect the browning of atmospheric organic particulate matter. (1) Particle-phase mass spectra were recorded following exposure of SOM particles to ammonia. The analysis focused on the production of organonitrogen imines (-C=N). Although these species only accounted for on the order of 10% of nitrogen uptake,[25] they can contribute to most of the light absorption (Figure b). The production of ammonium salts, which are typically not light absorbing, was presented in ref (25) for the same experiments. (2) Absorption spectra after ammonia exposure were recorded using an ultraviolet–visible spectrophotometer (UV–vis). The production of brown carbon was assessed from these data sets. (3) The water desorption rates from SOM thin films were measured using a quartz-crystal microbalance (QCM). Diffusivity values of small molecules were obtained through analysis of these data sets and used to estimate diffusion rates of ammonia within SOM.

The experiments focused on the reactions of ammonia with toluene-derived SOM. Toluene-derived SOM was chosen to represent a class of anthropogenic contributions to the atmosphere.[64] Toluene-derived SOM produced under low-NO conditions is weakly light absorbing.[17] The absorption can be greatly enhanced, however, in the presence of nitrogen-containing compounds.[17,65,66] An important source of light-absorbing nitrogen-containing species can be the multiphase reactions between ammonia and SOM, as illustrated in Figure b.[16,21,23] Toluene-derived SOM has high viscosity at low RH. It becomes brittle for <20% RH.[40] The high viscosity can impose mass transfer limitations on rates of evaporation, uptake, and in-particle mixing of semivolatile compounds.[56,58] The limitations disappear at elevated RH because water can act as a plasticizer and soften the material.[48]

Results and Discussion

Highly Viscous States and Brown Carbon Production

In a first set of experiments, a particle population of toluene-derived SOM was exposed to 5 ppm ammonia for a reactor residence time of 370 s in a continuous-flow mixing volume (cf. Supporting Information, Section S1 and Figure S1). After the reaction, the abundance of the nitrogen-containing ions produced for RH > 65% was 5–20 times higher than that produced for RH < 20% (Figure a). The produced organonitrogen imines were quantified by the CHN+ ion family by the high-resolution mass spectrometry (Figure b) and used to determine the mass concentration MON of organonitrogen. The organonitrogen mass fraction, given by the ratio MON/Morg where Morg represents the mass concentration of total organic species, is plotted in Figure c for different values of relative humidity. The fraction increases from low to high RH. The interpretation is that diffusion limitations on mass transfer in highly viscous SOM completely inhibited the production of organonitrogen species for RH < 20% (Figure a).[40] A transition from diffusion-limited to saturated uptake occurred across 20% to 60% RH, which is consistent with previous viscosity measurements showing that this type of SOM is semisolid across this RH range.[36,40] Above 60% RH, the fraction MON/Morg did not change for further increases in RH, which is consistent with the behavior of liquid SOM in this RH range.[36,40] Diffusion was rapid in the liquid, meaning that it became quickly saturated with NH3 and diffusion did not limit rates of reaction.

Figure 2

Organonitrogen production and changed optical properties of toluene-derived SOM exposed to ammonia at different RH values. (a) Nitrogen-containing ion fraction calculated as the signal intensity of each nitrogen-containing ion normalized by the signal intensity of the most abundant ion at the same nominal mass. Results are shown for toluene-derived SOM reacted with ammonia for high and low RH. (b1–b6) High-resolution mass spectral features corresponding to panel (a), showing isolation of the nitrogen-containing ion. (c) The ratio of organonitrogen mass concentration MON to total organic mass concentration Morg at different RH values. Error bars represent the estimated measurement uncertainty. Red shading represents the model error associated with the uncertainties of input parameters. (d1) Absorptive indices k on left axis and mass absorption coefficients Eabs on right axis from 280−320 nm for toluene-derived SOM. (d2) Same as panel (d1) but for 380–420 nm. The red curves in panels (c), (d1), and (d2) represent model results based on obtained diffusivities (i.e., Figure b,c). (e) Mass absorption coefficient as a function of wavelength for SOM-laden Teflon filters for initial conditions, ammonia-exposed conditions at low RH (<20% RH), and ammonia-exposed conditions at high RH (>65%). Shading regions I and II denote the spectral window represented in panels d1 and d2, respectively.

Figure 3

Diffusivity (left axis) and mixing time scale (right axis) for a 100 nm particle at 293 K. (a) Water diffusivity DH and mixing time scale τH for the reference compound of sucrose. (b) Water diffusivity and mixing time scale for several types of secondary organic material (SOM). (c) Diffusivity Dorg of large organic molecules and mixing time scale τorg for toluene-derived SOM. Shading in panel (a) represents estimated domains of solid, semisolid, and liquid states. Shading in panel (b) represents uncertainty in the determination of DH(aw) (this work). The dashed pink lines in panel (c) represent the uncertainty of the Vignes parametrization, as estimated from a Monte Carlo simulation. Parameters are presented in Table S3.

In a second set of experiments, optical properties were studied. Teflon filters laden with toluene-derived SOM were exposed to 500 ppb ammonia at fixed RH for 24 h (Supporting Information, Section S2). The RH among different experiments was varied from <5% to 90%. After ammonia exposure, browning of the filters was observed for RH > 65% but not for RH < 20%. Initial and reacted samples were extracted in methanol, and absorption spectra were recorded using an ultraviolet–visible spectrophotometer.

The absorptive indices k and the mass absorption coefficients Eabs were calculated, and the results are shown in Figure d,e (cf. Supporting Information, Section S2).[17] As a point of reference, a k value of 0.004 is typical of brown carbon in the urban atmosphere in a window of 380–420 nm.[69] The experiments herein found that k = 0.001 ± 0.0005 for the initial toluene SOM, meaning that the material was initially weakly absorbing. The value of k did not change significantly when exposed to ammonia for RH < 20%. It increased, however, to 0.004 ± 0.001 for toluene SOM exposed to ammonia at RH > 65%. Further results as a function of relative humidity are shown in Figure d1 for a band from 280 to 320 nm and in Figure d2 for a band from 380 to 420 nm. Solar radiation in the these two bands regulates the photolysis of O3 and NO2, respectively.[17]

The results show that the enhancement of light absorption strongly depended on RH (Figure d1 and 2d2). As the RH increased from less than 20% to greater than 60%, k280–320 and k380–420 increased by 50% and 400%, respectively. The dependence of chromophore-production on RH agreed with the RH dependence of organonitrogen production, although the two experiments had different exposure times and characteristic length scales (i.e., the radius of the particle or the thickness of the film) (cf. Table S1). These experimental results can be explained by the diffusion limitations on reaction rates.

A model was developed to capture the RH-dependent behavior of the production of organonitrogen species (Figure c) and the altered optical properties (Figure d1 and 2d2) (cf. Section S3). The complex chemical mechanisms were subsumed in the model as an effective second-order reaction between ammonia and the reactive organic species in the SOM matrix. Processes included (1) the uptake of NH3 at the surface of the SOM under the assumption of rapid Henry’s law equilibration between the gas phase and surface region (Figure b), (2) the diffusion of the small ammonia molecule into the SOM matrix (Figure a), (3) the diffusion of large reactive organic molecules from the interior region of the SOM to its surface (Figure a), and (4) chemical reactions and depletion of both reactants (Figure b). Both diffusivities in processes (2) and (3) depended on the water content of the SOM and hence on RH. At low RH, either or both diffusion processes limited rates of mass transfer and observed reaction rates.

Regimes of possible mass-transfer limitations on overall rates of reaction were considered within the model framework of accessible reaction volume.[61] This volume depended on the reacto-diffusion lengths of both ammonia and reactive organic species. The reacto-diffusion length, representing the characteristic distance that a typical reactant diffuses before reaction, depended on the reactant diffusivity and the reaction rate (Supporting Information, Section S3). In the case that a particle consists of highly viscous material, the reactant diffusivity became slow enough that the reacto-diffusion length was shorter than the characteristic size L of the particle. Reaction occurred prior to full mixing and a concentration gradient developed inside the volume of the particle, meaning that only a partial volume of the particle was effectively accessible to reaction (Figure a, left). By comparison, for a particle composed a liquid of low viscosity, the reacto-diffusion length was much larger than L, meaning that the reactant was well mixed and the entire volume of the particle was accessible to reaction (Figure a, right).

The reacto-diffusion lengths and the accessible reaction volume were modeled as a function of RH for two sets of parameters representing ammonia exposure in different experimental configurations (Supporting Information, Figure S2 and Table S1). The first set represented the experiments conducted in the continuous-flow mixing volume for SOM particles in aerosol form (Experiment 1). The second set represented the experiments for SOM thin films (Experiment 2). These two sets of experiments differed in gas-phase ammonia concentrations, characteristic length scales (i.e., particle size or film thickness), and exposure times. Model results and a comparison to the measurements are plotted in Figure c, 2d1, and 2d2. Red shading represents the range of model outputs for a Monte Carlo approach to the uncertainty of each input parameter. The observations lie within the shaded region representing model results. Although the model herein makes several simplify assumptions, the success in capturing the observations supports the hypothesis that reactant diffusivities, including both the diffusivity of small NH3 molecules and the diffusivity of large organic molecules, can control overall rates of condensed-phase reaction rates and browning reactions. For RH < 20%, the reacto-diffusion lengths of both ammonia and the SOM molecules were shorter than the radius of typical atmospheric particles in the accumulation mode (Figure a, left, and Supporting Information, Figure S2). Ammonia completely reacted in the surface region of the particle. At the same time, the mass transfer of organonitrogen reaction products into the interior of the SOM and the mass-transfer replacement by fresh organic reactants from the interior were both slow. The accessible reactive volume was smaller than 10% of the total particle volume, and consequently the overall rate of reaction was limited by diffusion (Supporting Information, Section S3 and Figure S2b). By comparison, for RH > 65% the reacto-diffusion lengths of NH3 as well as SOM molecules were modeled to increase to 102 nm and 104 nm, respectively, indicating that these reactants would be well mixed in accumulation-mode atmospheric particles and that mass transfer would not limit the overall rate of reaction.

A simulation was carried out for extension to ambient conditions. For urban environments, a gas-phase NH3 concentration of 10 ppb is typical, and aromatic precursors are abundant.[70] Particle diameter in the simulation was varied from 30 to 1000 nm.[71] In the absence of diffusion limitations, the estimated time for reaction (i.e., browning) was modeled as 15 h (Supporting Information, Section S3 and Table S1). This case represented high RH (>80%) for which the whole particle volume was accessible to reaction (Figure S2b). For low RH (<20%), the volume accessible to rapid reaction (i.e., at the maximum rate) was <20% (Figure S2b), and the estimated time to complete browning reactions throughout the particle volume exceeded several days. Slow browning under these conditions could be entirely offset by the rapid photobleaching reactions in the atmosphere.[72] For both low and high RH, the reacto-diffusion length of the organic species was modeled as the chief regulator of the volume accessible to reaction. The reacto-diffusion length of the organic species was estimated as 1 order of magnitude greater than that of NH3 (Figure S2a), even as the diffusivity of NH3 was several orders of magnitude higher than that of the organic species (Figure ). The explanation is that the concentration of NH3 at the particle surface could not exceed that prescribed by Henry’s law, and this concentration was many orders of magnitude lower than that of the reactive organic species constituent to the particle (cf. Supporting Information, Section S3 and Table S1). As a result, the reaction time scale and likewise the reacto-diffusion length of the organic species was much longer than those of NH3.

Diffusivities of Small and Large Molecules in the SOM Matrix

For the model of accessible reaction volume, estimates of the diffusivities of small and large molecules were employed. The diffusivity values DH of water, measured in this study and representative of a small molecule, were taken as a surrogate for those of NH3, given the similarities between NH3 and H2O in molecular weight and hydrogen bonding (section ). The diffusivity values of organic species Dorg were estimated based on previous studies on viscosity,[40] evaporation of semivolatile compounds,[56] and rates of reactive uptake[25] (section ).

Small-Molecule Diffusivities

Small-molecule diffusivity, as represented by water, was probed based on the rates of water evaporation from SOM organic films. The retrieved water diffusivity values were then tested and validated against observed rates of water condensation to SOM films. Water diffusivity values were used to represent the values of ammonia diffusivity within SOM particles. The films were grown by deposition of SOM aerosol particles on quartz crystal substrates. The aerosol particles were produced by the oxidation of volatile organic compounds (VOCs) in a flow reactor (Supporting Information, Section S1 and Figure S1).[17,73,74] Toluene photo-oxidation, m-xylene photo-oxidation, and α-pinene ozonolysis were studied (Table S2). The diffusivity data set for toluene-derived SOM was used in the model. The results for other types of SOM are presented herein for comparison.

Grown films were exposed to a series of humidification and drying cycles at 293.15 ± 0.1 K, and mass changes because of water uptake or release were continuously monitored by a quartz-crystal microbalance (Figure S3). Water diffusivity DH was retrieved from these measurements using a diffuso-kinetic model applied to the evaporation data sets during drying (cf. Supporting Information, Section S4). The DH values depended on water content, and a Vignes form was assumed in the model (Supporting Information, Section S4.5).[75] The Vignes form was based on diffusivities in pure water and dry material along with a nonideal mixing rule. The parameters were optimized by fitting the modeled water desorption rates to the measurements (Supporting Information, Figure S4 and Table S3). The DH values were further associated with water activity aw, taken as RH/100, using the hygroscopic growth curves measured for equilibrium states (Figure S5).

As a test of the method, DH(aw) results obtained for sucrose in this study compared to previous studies are plotted in Figure a. There is good agreement. Sucrose undergoes a moisture-induced glass transition at aw = 0.3 at 293 K.[50]Figure a shows that the corresponding DH value at this transition is 3 × 10–15 m2 s–1.[76] This value of DH serves as an approximate reference herein for the glass transition. In addition, for the measurements of the SOM films, the retrieved DH values obtained when drying were subsequently checked by modeling water uptake when humidifying, and there was good agreement between predictions and observations (Supporting Information, Figure S3).

The DH(aw) results are plotted in Figure b for the three types of SOM of this study. The shading represents uncertainty. Comparison to available data sets in literature are also shown. Figure b shows that the approximate reference value of DH for the glass transition occurs at aw = 0.2 for toluene-derived and m-xylene derived SOM, implying that these aromatic-derived SOMs are highly viscous under low RH. In agreement, Song et al.[40] observed that toluene-derived SOM particles shattered when poked at 17% RH, demonstrating a brittle material.

The DH(aw) values of toluene-derived and m-xylene-derived SOMs are similar to one another (cf. Figure b). These results might then at least to some extent be generalizable to SOM derived from other aromatic precursors, which are largely of anthropogenic origin. By comparison, the DH(aw) values for α-pinene-derived SOM, as a representative of biogenic sources, are significantly greater for aw < 0.65 (Figure b). These differences between anthropogenic and biogenic precursors are further highlighted in recent literature.[56,58]

For aw > 0.65, the DH(aw) values become similar among the three SOMs, and based on shifts in particle rebound the SOMs are liquid in this regime (i.e., η < 102 Pa s).[36] The semisolid-to-liquid transition for sucrose also occurs at aw = 0.65. The in-common aw value of 0.65 for the semisolid-to-liquid transition among these systems appears, however, to be coincidental. For instance, the transition for isoprene-derived SOM, based on rebound, occurs at aw = 0.40.[36]

In Figure b the DH(aw) values reported herein are compared to the DH(aw) results reported by Price et al.[77] and Lienhard et al.[51] for α-pinene ozonolysis. There is agreement among all studies for aw > 0.8 but significant differences for lower activities. The values reported in the literature deviate from each other by up to 2 orders of magnitude for low aw (<0.2), and the results of the present study lie midway between the two literature results. The spread in values can arise from several factors. Price et al.[77] extracted filter samples using water, Lienhard et al.[51] extracted samples using methanol, and the SOM characterized herein was total SOM without extraction. The chemical composition and hence properties of the extracted SOM can differ from that of total SOM.[41] Another possibility is that the composition can differ among SOMs prepared differently. For instance, the O:C atomic ratio depends on conditions of production.[78] These different factors can affect the differing DH(aw) results among the studies. A common result among all three studies, however, is that DH(aw) values of biogenically α-pinene-derived SOM at the dry state (aw < 0.05) are significantly higher than the corresponding values of the studied anthropogenically aromatic-derived SOMs and sucrose.

Large-Molecule Diffusivities

Compared to the diffusivities of small molecules, the diffusivities Dorg of the large organic molecules can be orders of magnitude smaller. They likewise can depend on the water activity (i.e., the water content).[48] Estimated values of Dorg(aw) for the large molecules making up toluene-derived SOM are plotted in Figure c. These estimates are based on several different approaches, including (1) diffusivity estimated from viscosity based on the Stokes–Einstein equation,[36,40] (2) diffusivity estimated from evaporation rates,[56] and (3) diffusivity estimated based on rates of reactive uptake.[25] The different approaches agree within an order of magnitude. The parameters of a Vignes-form fit of Dorg(aw), optimized to the data plotted in Figure c, are listed in Table S3. The fit is shown in Figure c as the pink line, and uncertainty based on the underlying data is represented by the dashed lines. Panels (a) to (c) of Figure confirm that for fixed awDorg(aw) is 104 to 106 times smaller than small-molecule diffusivity represented by DH(aw). The largest differences in Dorg between small and large molecules are for the lowest aw.

Mixing Times

Diffusivity can be used to estimate the characteristic mixing time τ within a particle under the assumption of rapid Henry’s law equilibration between the gas phase and surface region of the particle and in the absence of a chemical reaction, as follows:[79]where L is the geometric radius of a spherical nonporous particle and D is the diffusivity. The mixing times for 100 nm particles are given on the right axes of Figure a–c for the diffusivity values listed on the left axes. Atmospheric processes, such as water uptake and cloud activation, establish reference time scales, which are typically considered longer than 1 min.

The analysis represented in Figure b suggests that the mixing times for a small molecule represented by water throughout the volume of 100 nm particles composed of toluene-derived SOM and α-pinene-derived SOM are 10 and 0.01 s, respectively, for aw = 0.05 at 293 K. Compared to the reference time scale of 1 min, small-molecule diffusion is effectively facile at 293 K even in the highly viscous material. The implication is that diffusion is kinetically impeded but not arrested on time scales relevant to atmospheric processes.[43,76] For higher aw, mixing times are effectively instantaneous for small molecules with respect to most commonly considered atmospheric processes. To the extent that the SOM particles studied herein represent surrogates of atmospheric organic PM, the conclusion is that in the absence of in-particle chemical reactions, small molecules reach homogeneous concentrations effectively instantaneously within such particles for the temperatures and water activities relevant to most conditions of the atmospheric boundary layer.[80] For lower temperatures representative of the upper free troposphere, diffusivities can significantly decrease and mixing times can be significantly longer.[76]

The right axis of Figure c represents the mixing time of eq for large organic molecules within 100 nm particles of toluene-derived SOM. The mixing time exceeds the characteristic time of atmospheric relevance (1 min) for aw ≤ 0.4. The implication is that in-particle diffusion can limit the mass transfer of organic molecules in the gas-particle partitioning processes.[56] One possible effect under atmospheric conditions is that the evolution of number-diameter distribution of the particle population can be affected.[81]

Conclusions

Predicting the production of brown carbon in the atmosphere and the evolution of its optical properties is challenging and remains highly uncertain. Many complex processes must be considered. The results of the present study imply that the lack of information about the species diffusivities within organic PM can be one factor, among many others, that contributes to these uncertainties. Species diffusivities can also influence other important atmospheric processes, including multiphase chemistry. Uptake and in-particle diffusion of small-molecule atmospheric photo-oxidants like OH, O3, and NO3 within a large-molecule environment of atmospheric PM are commonplace.[27,61,82,83] Slow species diffusivities in the organic matrix can impede these multiphase chemical reactions. In that context, the results presented herein further highlight that anthropogenic contributions to atmospheric PM appear to favor more viscous states and reduced diffusivities compared to biogenic SOM, suggesting an underestimated or overlooked pathway of human influences on atmospheric chemistry and climate.[56,58]