Chemical insights, explicit chemistry, and yields of secondary organic aerosol from OH radical oxidation of methylglyoxal and glyoxal in the aqueous phase

Atmospherically abundant, volatile water-soluble organic compounds formed through gas-phase chemistry (e.g., glyoxal (C2), methylglyoxal (C3), and acetic acid) have great potential to form secondary organic aerosol (SOA) via aqueous chemistry in clouds, fogs, and wet aerosols. This paper (1) provides chemical insights into aqueousphase OH-radical-initiated reactions leading to SOA formation from methylglyoxal and (2) uses this and a previously published glyoxal mechanism (Lim et al., 2010) to provide SOA yields for use in chemical transport models. Detailed reaction mechanisms including peroxy radical chemistry and a full kinetic model for aqueous photochemistry of acetic acid and methylglyoxal are developed and validated by comparing simulations with the experimental results from previous studies (Tan et al., 2010, 2012). This new methylglyoxal model is then combined with the previous glyoxal model (Lim et al., 2010), and is used to simulate the profiles of products and to estimate SOA yields. At cloud-relevant concentrations ( ∼ 10−6− ∼ 10−3 M; Munger et al., 1995) of glyoxal and methylglyoxal, the major photooxidation products are oxalic acid and pyruvic acid, and simulated SOA yields (by mass) are ∼ 120 % for glyoxal and ∼ 80 % for methylglyoxal. During droplet evaporation oligomerization of unreacted methylglyoxal/glyoxal that did not undergo aqueous photooxidation could enhance yields. In wet aerosols, where total dissolved organics are present at much higher concentrations ( ∼ 10 M), the major oxidation products are oligomers formed via organic radical–radical reactions, and simulated SOA yields (by mass) are ∼ 90 % for both glyoxal and methylglyoxal. Non-radical reactions (e.g., with ammonium) could enhance yields.


Introduction
Water is predicted to be the largest component of fine particles (PM 2.5 ) globally (Liao and Seinfeld, 2005) and in regions with high relative humidity and hygroscopic aerosol species. Water in clouds, fogs, and aerosols provides an abundant and important medium for chemistry, including chemistry that forms secondary organic aerosol (SOA).
In a previous publication (Lim et al., 2010), we developed a full kinetic model including detailed radical chemistry to describe aqSOA formation via OH radical oxidation of glyoxal, an abundant and highly water-soluble compound Y. B. Lim et al.: Chemical insights, explicit chemistry, and yields of SOA formed through photooxidation of alkenes and aromatics. The current work is focused on methylglyoxal. Methylglyoxal is a common α-carbonyl in the atmosphere (Munger et al., 1995), with a globally estimated source of 140 Tg annually (Fu et al., 2008). It is formed from the photooxidation of both anthropogenic VOCs like aromatic hydrocarbons (Nishino et al., 2010) and biogenic VOCs including isoprene (Atkinson et al., 2006). The major sinks are gas-phase UV photolysis and photooxidation (Tadic et al., 2006;Fu et al., 2008). Like glyoxal, methylglyoxal also has great potential to form SOA through aqueous-phase reactions in clouds and wet aerosols, due to its high water solubility (H eff = 3.71 × 10 3 M atm −1 ; Betterton and Hoffmann, 1988), ability to form oligomers via acid catalysis, and reactivity with OH radicals (Blando and Turpin, 2000;De Haan et al., 2009;Sareen et al., 2010;Tan et al., 2010Tan et al., , 2012. Acetic acid (H eff = 5.50 × 10 3 M atm −1 ; Herrmann et al., 2005) is highly water soluble, atmospherically abundant both in the gas phase (∼ 300 ppt; Nolte et al., 1999) and in the aqueous phase (Khare et al., 1999), and also a major intermediate product of methylglyoxal + OH (Tan et al., 2012). It should be noted that methylglyoxal and acetic acid are much more reactive with OH radicals in the aqueous phase than in the gas phase (lifetimes in the aqueous phase are ∼ 26 min for methylglyoxal and ∼ 17 h for acetic acid; however, in the gas phase, lifetimes are ∼ 0.9 day for methylglyoxal and 17 days for acetic acid).
In this paper, a full kinetic model for the aqueous OH radical oxidation of methylglyoxal is proposed. Detailed radical chemistry includes peroxy radical (RO 2 ) chemistry initiated by bimolecular reactions (RO 2 -RO 2 reactions). We validate, in part, the methylglyoxal model by comparing results from aqueous photooxidation experiments developed by Tan et al. (2010Tan et al. ( , 2012 with model simulations of these experiments. Note that in aqueous photooxidation experiments, OH radicals are formed through UV photolysis of H 2 O 2 , whereas in the atmosphere, uptake from the gas phase is the dominant known source (Ervens et al., 2003a), with additional contributions from aqueous (e.g., Fenton, nitrate) reactions (Arakaki and Faust, 1998;Zepp et al., 1987). In this work, experimental results are better captured after taking into account the absorption of UV by H 2 O 2 and organic compounds. Finally, the combined glyoxal and methylglyoxal model is used to simulate aqSOA formation via OH radical oxidation under a range of atmospheric conditions, including cloud-relevant conditions (10 µM) and higher concentrations. Runs at 10 M are intended to provide insights into OH radical chemistry in wet aerosols using glyoxal or methylglyoxal as a surrogate for the mix of dissolved water-soluble organics (i.e., based on water-soluble organic carbon compounds of ∼ 2-3 µg C m −3 and estimated aerosol water concentrations of ∼ 10 µg m −3 at RH > 70 %; Hennigan et al., 2009;Volkamer et al., 2009). Note that non-radical chemistry is not included in these aerosol SOA yields. Methylglyoxal and glyoxal aqSOA yields are reported for conditions encountered by clouds and by wet aerosols based on two types of simulations: a "batch reactor" approach, in which the precursor (methylglyoxal or glyoxal) is depleted as OH radical reactions proceed, and a steady-state "continuously stirred tank reactor" (CSTR) approach, in which the precursor is replenished (held constant) in the aqueous phase.

Experiments used to evaluate chemical modeling
Aqueous methylglyoxal chemistry and yields are developed herein, making use of chemical theory and previously published aqueous photooxidation experiments conducted with OH radicals and methylglyoxal or acetic acid (an intermediate product). Experiments were conducted at cloud-relevant and higher concentrations, but concentrations were still several orders of magnitude lower than the concentrations of water-soluble organic compounds in wet aerosol. Experimental details are provided elsewhere (Tan et al., , 2012. Briefly, methylglyoxal (30, 300, and 3000 µM) or acetic acid (20, 100, and 1000 µM) was dissolved in 18 M Milli-Q water. OH radicals (10 −14 -10 −12 M) were generated by photolysis (254 nm with Hg UV lamp) of hydrogen peroxide. Reaction temperature was maintained at ∼ 25 • C. Dissolved O 2 measured at the beginning and the end of each experiment was saturated. pH decreased from 6.6 to 3.3 over the course of the 360 min experiments. Samples were analyzed by ion chromatography (IC), unit mass resolution electrospray ionization mass spectrometry (ESI-MS), and ESI-MS after preseparation in the IC (IC-ESI-MS). Control experiments were conducted for both organics (methylglyoxal and acetic acid) as follows: organic + UV, organic + H 2 O 2 , H 2 O 2 + UV, mixed standard + H 2 O 2 , and mixed standard + UV. Mixed standards contained pyruvic, acetic, formic, oxalic, glyoxylic, glycolic, succinic, and malonic acids (250 µM each). Note that H 2 O 2 was measured by the triiodide method (Banerjee et al., 1964) using a UV-visible spectrometer in H 2 O 2 + UV experiments.

Peroxy radical chemistry
Peroxy radical chemistry plays an important role in the aqueous chemistry of methylglyoxal, which is described in detail in Sect. 3. As in the gas phase, OH radical reactions in the aqueous phase produce peroxy radicals due to the presence of dissolved O 2 in atmospheric waters (Herrmann, 2003). Peroxy radicals subsequently undergo two possible reaction pathways: (1) self decomposition giving off HO 2 and forming acids, and (2) bimolecular RO 2 -RO 2 reaction. In the glyoxal-OH reaction, glyoxylic acid and oxalic acid are formed by the decomposition pathway, which is also the dominant pathway (Lim et al., 2010). In the methylglyoxal-OH reaction, pyruvic acid is formed by decomposition. However, further OH reactions of pyruvic acid and acetic acid, The pathway A is suggested by Benson (1965), forming alkoxy radicals, followed by decomposition (I) or 1,2-hydride shift (J). The pathway B forming no organic radical product (i.e., B is a concerted reaction) is suggested by Russell et al. (1957). Parent precursors can be acetic acid or pyruvic acid (b). Fragmented organic radicals (R*) are expected to be stabilized by a carboxylic group for acetic acid ((c) left) and a diol, which results from hydration of a carbonyl group for pyruvic acid ((c) right). two major products of the methylglyoxal + OH, involve RO 2 -RO 2 reactions. Figure 1a illustrates peroxy radical chemistry initiated by RO 2 -RO 2 reactions. For acetic acid/pyruvic acid + OH reactions, peroxy radicals form by the addition of O 2 to the primary carbon, followed by RO 2 -RO 2 reactions forming tetroxides. This pathway is preferred over decomposition because of the absence of a hydroxyl group nearby. Two wellknown decomposition pathways from tetroxide are alkoxy radical/O 2 formation (A in Fig. 1a) suggested by Benson (1965), and alcohol/aldehyde/O 2 formation (B in Fig. 1a) suggested by Russell et al. (1957). The Benson pathway (A) and the Russell pathway (B) are not related and are independent because the Russell pathway (B) is a concerted reaction, so none of the products are formed via alkoxy radical chemistry.
Alkoxy radicals formed in the Benson pathway (A) undergo either decomposition (I) or a 1,2-hydride shift (J) (Figs. 1, 2, and 3). In Fig. 1a, resulting products through decomposition of alkoxy radicals (I) are organic radicals (R q ) and aldehydes (=O). Gas-phase chamber studies suggest that decomposition of alkoxy radicals is likely to occur if a radical position in an organic radical product (R q ) is at secondary or tertiary carbons, and is enhanced when functional groups (e.g, hydroxyl or carboxylic groups) are adjacent to these carbons (Atkinson et al., 2007) due to radical stabilization (Lim and Ziemann, 2009). Alkoxy radicals formed in the aqueous phase contain hydroxyl/carboxylic functional groups since the parent organic precursors are water soluble. Decompo-sition in the aqueous phase (I) is, therefore, more favorable than in the gas phase. For acetic/pyruvic acid in the aqueous phase ( Fig. 1b), alkoxy radicals decompose to organic radicals and formaldehydes. Organic radicals are stabilized by a carboxylic group for acetic acid or a diol (since a carbonyl group will undergo hydration) for pyruvic acid (Fig. 1c), While significant 1,2-hydride shift (followed by O 2 reactions to form carbonyls) is not observed in the gas phase (Atkinson, 2007), alkoxy radicals in the aqueous phase do undergo 1,2-hydride shift. Although the detailed reaction mechanisms are not well understood, the 1,2-hydride shift is very likely to be assisted by water molecules (Von Sonntag et al., 1997).

Kinetic model
As done previously for glyoxal (Lim et al., 2010), we developed a full kinetic model for aqueous chemistry of methylglyoxal with OH radicals at cloud-and aerosol-relevant concentrations including the following: (1) the formation of organic acids such as acetic, glyoxylic, glycolic, pyruvic, oxalic, and mesoxalic acid (Lim et al., 2005;Tan et al., 2009Tan et al., , 2010Tan et al., , 2012; (2) organic radical-radical reactions to form higher carbon number acids and oligomers; and (3) peroxy radical chemistry, including self decomposition and bimolecular RO 2 -RO 2 reactions. The model was first validated by comparison against acetic acid + OH radical experiments (Tan et al., 2012), since acetic acid is an important intermediate product. Then, using the same rate constants, model predictions were compared with concentration dynamics from methylglyoxal + OH radical experiments (Tan et al., , 2012. Most of the kinetic rate constants were obtained from the literature documented in Tan et al. (2009Tan et al. ( , 2010Tan et al. ( , 2012, or determined using an estimation method based on structureactivity relationships (Monod et al., , 2008. Values from Ervens et al. (2003b) were also used for OH-radicalinitiated reactions. For the radical-O 2 (peroxy radical formation) and organic radical-radical reactions, the rate constants of 1 × 10 6 M −1 s −1 and 1.3 × 10 9 M −1 s −1 , respectively, were used as suggested by Guzman et al. (2006). The following were used for peroxy radical chemistry: a rate constant of 3 × 10 8 M −1 s −1 for bimolecular RO 2 -RO 2 reactions (Lim et al. 2010), a rate constant of 1 × 10 7 s −1 for the 1,2hydride shift (Gilbert et al., 1976), and a rate constant on the order of 10 6 to 10 7 s −1 for decomposition from the alkoxy radical (Gilbert et al., 1981).
This model, which we describe in detail in Sect. 3, was validated in part by comparison with laboratory experiments and then used to simulate the atmosphere.

Determining the rate constants for H 2 O 2 photolysis
The performance of a glyoxal model (Lim et al., 2010), which includes detailed radical reactions (e.g., H-atom abstraction by OH radicals, peroxy/alkoxy radical reactions, decompositions, and organic radical-radical reactions) was substantially improved at high concentrations (∼ mM) by including organic radical-radical reactions in the model. Below we describe a further improvement to the glyoxal model that we then apply also to methylglyoxal. Specifically, since OH radicals in experiments are produced in situ from H 2 O 2 photolysis and H 2 O 2 is light absorbing, we correct for light absorption by H 2 O 2 .
Previously , the rate constant (1.1 × 10 4 s −1 ) for 254 nm UV photolysis of H 2 O 2 at 0.15, 1.5, and 20 mM in experiments was determined by fitting modeled H 2 O 2 concentrations (R1-R7) to measurements in H 2 O 2 + UV control experiments ( Fig. 4a-c) as documented by Tan et al. (2009Tan et al. ( , 2012. However, in the previous work, light absorption by H 2 O 2 was not taken into account. The H 2 O 2 photolysis rate constant (k photo ) can be corrected using Beer's law, where b ext is extinction coefficient (M −1 cm −1 ) and L is path length (cm).
An extinction coefficient for H 2 O 2 of 18.4 M −1 cm −1 was used (Stefan et al., 1996). A path length of 0.80 cm provides the best fit for all three H 2 O 2 concentrations ( Fig. 4d-f). This value is reasonable since it is close to the actual path length of the reaction vessel (1.04 cm). Accounting for UV absorption by H 2 O 2 provides substantial improvement in the R 2 values at the highest concentration from R 2 = 0.80 ( Fig. 4a) to 0.96 with correction (Fig. 4d). Thus, in the revised model, Methylglyoxal and pyruvic acid are also light-absorbing compounds, and their photolysis reactions are included in the model -methylglyoxal photolysis is even corrected by using extinction coefficient of 12.7 M −1 cm −1 . However, these photolysis reactions turn out to be negligible during OH radical reactions because photolysis rates are much slower than OH radical reaction rates (Stefan et al., 1996;Tan et al., 2010).
Both simulated OH concentrations (∼ 10 −12 M) and simulated and measured pH (3 to 5) reasonably reflect cloud conditions (Faust, 1994;Hermann, 2003). Simulated dissolved O 2 remains saturated during the entire reaction ( Fig. S1 in Supplement), in agreement with measured O 2 at the beginning and end of experiments. Note that dissolved O 2 in atmospheric waters is expected to be saturated due to high the surface-to-volume ratio of cloud droplets and wet aerosols.

Atmospheric simulations
Unlike laboratory experiments, the major source of OH radicals in the atmospheric aqueous phase is believed to be uptake from the gas phase, although aqueous sources also contribute (e.g., through Fenton and nitrate reactions; Arakaki and Faust, 1998;Lim et al., 2005Lim et al., , 2010Zepp et al., 1987). In atmospheric simulations, the OH radical concentration in the aqueous phase was set to be constant at 2.44 × 10 −12 M, a value maintained by Henry's law equilibrium with the gasphase OH radical concentration of 2 × 10 6 molecule cm −3 (Finlayson-Pitts and Pitts, 2000). This is likely an upper bound, as discussed in Sect. 5. The initial concentration of H 2 O 2 in the aqueous phase was set to be zero. The maximum simulated H 2 O 2 concentration (largely formed via bimolecular HO 2 -HO 2 reactions in the aqueous phase) from photooxidation of 30 µM of initial glyoxal is ∼ 20 µM, which is reasonable in atmospheric waters according to Henry's law equilibrium with an atmospheric concentration of H 2 O 2 (∼ 0.2 ppb) in the gas phase (Warneck, 1999).
The following atmospheric processes are needed to model aqSOA: (1) glyoxal and methylglyoxal production via gasphase photooxidation, (2) glyoxal and methylglyoxal uptake by atmospheric waters (i.e., Henry's law equilibrium between gas-and aqueous-phase glyoxal and methylglyoxal), (3) uptake or condensed-phase production of oxidants (e.g., OH radicals), (4) aqueous-phase reactions in the atmospheric waters forming low or semivolatile products, and (5) gasparticle partitioning of products. Ideally, all these processes including detailed aqueous chemistry would be included in the model. When this is not practical, SOA yields can be useful, enabling prediction of SOA by multiplying the amount of "aqueous glyoxal reacted" in a time step by the estimated SOA yield. The production of particle-phase products via aqueous OH radical oxidation (step 4-5) can be approximated in a batch or CSTR framework. In the batch reactor approximation, aqueous-phase OH radical reactions are limited by photochemical production of glyoxal and methylglyoxal in the gas phase. Slow glyoxal/methylglyoxal production results in its depletion in the atmospheric waters by aqueousphase OH radical reactions. In the CSTR approximation, however, aqueous-phase OH radical reactions are not limited by gas-phase photochemical production of glyoxal and methylglyoxal. In contrast to the batch reactor, glyoxal and methylglyoxal are continuously taken up into atmospheric waters and never depleted in that medium. This is a better assumption when gas-phase production is faster than aqueous reaction. Which of these approximations is more appropriate depends on what the major precursors are in the particular study area. For example, a batch approximation would be appropriate if the dominant methylglyoxal precursors were toluene. The gas-phase lifetime of toluene due to OH (when [OH] in the gas phase is 2 × 10 6 molecule cm −3 (12 h daytime average); Finlayson-Pitts and Pitts, 2000) is ∼ 1 day (k = 5.63 × 10 −12 cm 3 molecule −1 s −1 ; Atkinson and Arey, 2003) and it produces ∼ 20 % methylglyoxal (Nishino et al., 2010). This methylglyoxal can dissolve in cloud/fog waters and react with OH radicals with the lifetime of 4.3 h (when [OH] in the aqueous phase is assumed to be 1 × 10 −13 M). A batch approximation is appropriate since in this case the gas-phase production of methylglyoxal is slower than the aqueous-phase OH oxidation of methylglyoxal. In contrast, a CSTR approximation would be more appropriate if the production of methylglyoxal was dominated by compounds like 1,3,5-trimethylbenzene (which produces ∼ 50 % methylglyoxal; Nishino et al., 2010). This is because the gas-phase lifetime of 1,3,5-trimethylbenzene due to OH radicals is only 2.5 h. Thus, in this case the gas-phase production of the methylglyoxal precursor is now faster than its aqueous oxidation.
While we expect OH oxidation to be the dominant daytime aqSOA formation pathway in clouds and an important contributor to wet aerosol chemistry (Lim et al., 2010), it should be recognized that the chemistry in wet aerosols is highly complex and poorly understood. Both radical and non-radical reactions are likely to occur in wet aerosols and the relative importance of these pathways may depend on the degree to which OH radicals are produced or recycled in the condensed phase, which is not well understood currently. Undoubtedly, organic-inorganic interactions play an important role in wet aerosol chemistry (e.g., formation of organosulfates and organic nitrogen compounds); the yields reported here are not intended to represent all processes, only aqSOA formed through OH radical reaction.

SOA yields from atmospheric photochemical simulations
Given where A is glyoxal or methylglyoxal and P i is product i, the product yield for P i (Y P i ) is given by ( Then the overall SOA yield (Y SOA ) is defined as where F i is the particle fraction of P i and [A] reacted is the concentration of unhydrated A reacted with OH radical in the aqueous phase. For glyoxal-OH reactions, the SOA-forming products are oxalate (OXLAC) and oligomers (OLIG). For methylglyoxal-OH reactions, the SOA-forming products are pyruvate (PYRAC), oxalate (OXLAC), and oligomers (OLIG).
To use these yields in a chemical transport model, the model must simulate the gas-phase concentration of A, the uptake of A into the aqueous phase, and the change in the aqueous concentration of A as a result of reactions with OH ([A] reacted ) over the course of a time step.
[A] reacted is then multiplied by Y SOA to produce SOA.

Product yield
In the previous glyoxal-OH model, the maximum yields of oxalic acid and oligomers were simulated (Lim et al., 2010), but in this work average yields are estimated. For example, the simulated molar yield of oxalic acid that is formed from the OH-radical-initiated reaction of 10 µM initial [glyoxal] is plotted with the reaction time (x axis) in Fig. 5a. In the previous work (Lim et al., 2010), the maximum yield of 0.91 was estimated. But in this work, Fig. 5a is replotted to 5b, where the x axis is [glyoxal] reacted and the y axis is [oxalic acid]; therefore, the slope represents the yield of oxalic acid. In Fig. 5b, oxalic acid increases as glyoxal reacts, then the curve drops sharply when glyoxal is depleted. The slope of ∼ 0.80, obtained by the linear regression on the product formation curve from the starting point of aqueous-phase photochemistry (t = 0) to the peak (t max = 38 min) giving a reasonably low error (R 2 ∼ 0.9), represents the average (molar) yield of oxalic acid. In CSTR simulation plots, oxalic acid continuously increases and never drops as glyoxal reacts (Fig. 5c). A similar oxalic acid yield (slope = 0.84 with R 2 ∼ 1) was obtained by linear regression over 60 min of aqueous-phase photochemistry.
Plots of batch simulations conducted from 10 µM to 10 M of initial glyoxal are similar to Fig. 5b (R 2 ≥ 0.9, 0 ≤ t ≤ t max , 20-40 min), with oxalic acid being the main product below ∼ 10 mM and oligomers above ∼ 10 mM. Oligomers were calculated as the sum of products with higher carbon number than the precursor (Lim et al., 2010). Plots of CSTR simulations conducted from 0.1 to 100 µM of initial glyoxal are similar to Fig. 5c (R 2 ∼ 1, 0 ≤ t ≤ 60 min), with oxalic acid being the main product.

Particle fraction
SOA yields also depend on what fraction of each aqueous product remains in the particle phase (Seinfeld and Pankow, 2003). We expect that oligomers stay entirely in the particle phase. In this work, we assume that dicarboxylic acid products of C 3 or higher, such as malonate (C 3 ) or tartrate (C 4 ), remain entirely in the particle phase. The gas-particle partitioning of the smaller organic acids (e.g., oxalate, pyruvate) depends on whether they are present in the atmosphere as acids or salts, since their salts have much lower vapor pressures (Limbeck et al., 2001;Martinelango et al., 2007;Smith et al., 2009;Ortiz-Montalvo et al., 2012). For example, the vapor pressure of oxalic acid (at 25 • C) is 8.26 × 10 −5 Torr (Saxena and Hildemann, 1996), whereas the vapor pressure of ammonium oxalate is 5.18 × 10 −8 Torr (EPA, 2011). In this work, we assume that 90 % of oxalate and 70 % of pyruvate remain in the particle phase (Lim et al., 2005;Ervens et al., 2007). However, these particle fractions could vary based on availability of organic/inorganic constituents (e.g., NH 3 , amines, sodium). Note that the yields calculated in this work neglect the formation of glyoxal and methylglyoxal oligomers through droplet evaporation (Loeffler et al., 2006;De Haan et al., 2009).

Aqueous-phase reactions of acetic acid with OH radical
Reaction mechanisms for the aqueous-phase OH radical oxidation of acetic acid are proposed in Fig. 2 The dominant H-atom abstraction from acetic acid occurs from the methyl group with a kinetic rate ∼ 5 times faster than abstraction from the carboxylic group (Tan et al., 2012).
Through O 2 addition to [HO(O)CC*H 2 ], the peroxy radical [HO(O)CH 2 OO*] forms, followed by RO 2 -RO 2 reactions. In the Benson pathway (A), the alkoxy radical decomposes Table 1. Product yields, particle-phase product yields and SOA yields.
Y OXLAC-P = particle-phase OXLAC yield; Y PYRAC-P = particle-phase PYRAC yield; Y OLIG-P = particle-phase OLIG yield to formaldehyde and carbon dioxide, or, via the 1,2-hydride shift, forms [HO(O)CC*H(OH)], which then becomes glyoxylic acid via O 2 reactions and is oxidized further to oxalic acid. In the Russell pathway (B), the organic products are glycolic acid and glyoxylic acid. OH/O 2 oxidation of glycolic acid forms [HO(O)CH 2 OO*], which again becomes glyoxylic acid, and is later oxidized to oxalic acid.
Note that Tan et al. (2012) did not observe oligomer formation from the OH radical (∼ 10 −12 M) oxidation of 1 mM acetic acid, whereas oligomers do form from the OH radical oxidation of glyoxal and methylglyoxal at identical concentrations (Tan et al., 2009. Oligomers form from glyoxal and methylglyoxal oxidation because of radical stabilization (Guzman et al., 2006;Lim et al., 2010). In the first H-atom-abstracted product of acetic acid (HO(O)C*H 2 ), the radical is rather unstable because it is at the primary carbon. In contrast, for glyoxal/methylglyoxal reactions, the radical is at the triply substituted carbon (i.e., carbon bound to three non-H atoms), and these stabilized radicals allow for oligomers' formation via radical-radical reaction (Lim et al., 2010;Tan et al., 2012). Based on these results, in this kinetic model radical-radical reactions are excluded when the radi-cal is on the primary carbon (e.g., acetic acid/pyruvic acid-OH radical reactions). Note that organic radical-radical reactions for all organic species except acetic and pyruvic acid are always "turned on" in our model. At low concentrations, organic radical-O 2 reactions are dominant, whereas at high concentrations organic radical-radical reactions are important. Figure 3 illustrates the reaction mechanisms for the aqueousphase OH radical reaction of methylglyoxal. Major products are pyruvic, acetic, and oxalic acid. Bold arrows indicate the major pathways. Pyruvic acid is the major firstgeneration product from OH radical reaction of methylglyoxal, and acetic acid is formed substantially from OH radical reactions of pyruvic acid and partially from bimolecular peroxy radical reactions and H 2 O 2 -pyruvic acid reactions. Oxalic acid is formed directly from glyoxylic and mesoxalic acids, which are products of every pathway shown in Fig. 3. The first step of the OH radical reactions is H-atom abstraction from the primary carbon (minor) or the carbon in between the diol (major), then peroxy radical formation by O 2 addition. In the minor pathway, peroxy radicals undergo RO 2 -RO 2 reaction, and form alkoxy radicals (the Benson pathway A) or C 3 organic compounds (the Russell pathway B). The alkoxy radical decomposes to formaldehyde and an organic radical compound, and this organic radical later becomes glyoxylic acid. The C 3 organic compounds from the Russell pathway B react with OH radical and eventually form mesoxalic acid. In the major pathway, peroxy radicals either decompose to pyruvic acid while losing HO 2 (major) or undergo RO 2 -RO 2 reaction (minor), which eventually leads to the formation of carbon dioxide and acetic acid. It should be noted that pyruvic acid reacts with H 2 O 2 and forms acetic acid, carbon dioxide, and water; however this is minor, and OH radical oxidation is the major pathway. The OH radical oxidation of pyruvic acid occurs by H-atom abstraction from the primary carbon or the carboxylic group. The peroxy radical from the radical on the primary carbon forms via O 2 addition, and undergoes RO 2 -RO 2 reaction. In this RO 2 -RO 2 reaction, oxalic acid and mesoxalic acid are eventually formed via Benson/Russell pathways and alkoxy radical chemistry. The organic radical product from H-atom abstraction from the carboxylic group decomposes to carbon dioxide and a C 2 aldehyde radical, which eventually becomes acetic acid.

Kinetic model
Reactions and rate/equilibrium constants used in the full kinetic model of glyoxal/methylglyoxal + OH are provided in Table S1. Detailed reaction mechanisms for the decomposition of tetroxides are still not understood, and therefore, calculation of the branching ratio for the two pathways A and B from theory is not possible (Dibble, 2007). In this work, the same branching ratio of 95 % (A) to 5 % (B) was used for acetic and pyruvic acids and methylglyoxal, and this branching ratio was determined based on the ESI-MS intensities of the acetic acid oxidation products and glyoxylic and glycolic acid with an assumption that glycolic acid is only produced in the Russell pathway (B), whereas glyoxylic acid is produced in both the A and B pathways (Figs. 2 and 3). Note that this branching ratio is expected to be independent of initial precursor concentration because decomposition of tetroxides is unimolecular decay.
Although there is a literature rate constant (6 × 10 7 M −1 s −1 ; Stefan and Bolton, 1999) for the OH radical reaction of pyruvic acid, to our knowledge, there are no detailed literature rate constants for H-atom abstraction from the primary carbon and from the carboxylic group. In this work a branching ratio of 85 % to 15 % (H-atom abstraction from the primary carbon vs. from the carboxylic group) was used based on the estimation method of Monod et al. (2005).

Model validation: simulating laboratory experiments
Previously, a full kinetic model for the aqueous chemistry of glyoxal with OH radical was developed by including detailed radical chemistry (Lim et al., 2010). In this work, the model was expanded by including comprehensive methylglyoxal-OH radical chemistry: OH radical reactions of acetic acid, pyruvic acid, and methylglyoxal, and light absorption by H 2 O 2 and light-absorbing organic compounds (e.g., methylglyoxal, pyruvic acid). The model, then, was validated by simulating the laboratory experiments of Tan et al. (2009Tan et al. ( , 2010Tan et al. ( , 2012.

Glyoxal-OH radical model
The light-absorption correction (Sect. 2.4) was validated by simulating glyoxal + OH experiments (Fig. 6). For lowconcentration experiments (initial [glyoxal] = 30 µM), oxalic acid predicted by the previous glyoxal model (Lim et al., 2010) and this new model are identical and agree well with the experimental results (Fig. 6a). Simulations are identical because the H 2 O 2 concentration (decreasing from 150 µM H 2 O 2 ) was too low to affect photochemistry. H 2 O 2 absorbed less than 1 % of the transmitted light, and therefore including light absorption in the model had a negligible effect on OH production from H 2 O 2 photolysis. However, the lightabsorption correction by H 2 O 2 substantially improves the glyoxal-OH radical model simulation (Fig. 6b) at the higher concentration (initial [glyoxal] = 3000 µM), where the initial H 2 O 2 concentration was 15 mM (note that higher H 2 O 2 concentrations were used in experiments with higher glyoxal/methylglyoxal concentrations in order to maintain similar OH concentrations in all experiments). Note that both the Lim et al. (2010) and the current model include organic radical-radical reactions, resulting in improved prediction of oxalic acid in the 3000 µM experiments compared to the Lim et al. (2005) dilute chemistry model. By correcting for light absorption by H 2 O 2 in the current work, the model now captures the timing of the peak (Fig. 6b).

Acetic acid-OH radical model
Next, the performance of the expanded model was evaluated by simulating acetic acid + OH experiments. Model performance was improved by including detailed peroxy radical chemistry: RO 2 -RO 2 reactions, the Benson/Russell pathways, and the alkoxy radical chemistry (Fig. 7). In the model, the rate constant for the 1,2-hydride shift from the alkoxy radical is set to be 1 × 10 7 s −1 (Gilbert et al., 1976), while decomposition rates vary: 5 × 10 6 , 8 × 10 6 , and 2 × 10 7 s −1 for initial [acetic acid] = 20, 100, and 1000 µM, respectively. Those values were determined by fitting to the experimental results, while their range is within literature values (∼ 10 6 - 10 7 s −1 ) from Gilbert et al. (1981). Ideally, the decomposition rate from the alkoxy radical is constant regardless of the initial acetic acid concentration due to being first order, but pH or cage effects by water molecules could affect the rate.

Methylglyoxal-OH radical model
Simulations of the methylglyoxal + OH experiments are shown in Fig. 8. The methylglyoxal-OH model contains the same parameters used in the acetic acid-OH radical model except the decomposition rate at the initial [methylglyoxal] = 3000 µM is 3.2 × 10 7 s −1 instead of 2 × 10 7 s −1 . Using these values, the performance of the model simulations was substantially improved (Fig. 8a, b). The best fit to the experimental results was obtained by neglecting pyruvic acid photolysis (see comparison, Fig. 8a) rather than including the literature rate constant and product (molar) yields for pyruvic acid photolysis (i.e., pyruvic acid → 0.45 acetic acid + 0.55 CO 2 , rate constant = 5 × 10 −4 s −1 ; Carlton et al., 2006). This has been observed previously for similar experiments conducted with acetone (Stefan et al., 1996;Stefan and Bolton, 1999). This is expected because the molar absorptivity of H 2 O 2 (Bolton and Carter, 1994) is much larger than the molar absorptivity of pyruvic acid. Thus, photolysis in this experimental system is negligible in the presence of OH radicals. Note that the purpose of the 254 nm UV lamp in these experiments is to provide an atmospherically relevant OH radical concentration in the aqueous phase and not to study photolysis. Figure 8c (initial [methylglyoxal] = 3000 µM) is interesting. Although the new model successfully fit oxalate measurements from the OH reactions of 30 and 300 µM of methylglyoxal, at 3000 µM it still does not capture the timing and the magnitude of oxalic acid formation until ∼ 200 min. Accounting for light absorption by H 2 O 2 is not sufficient to explain the oxalic acid profile in the 3000 µM methylglyoxal experiments. We hypothesize that this is because of  (Tan et al., 2012) and previous/current model simulations (using the model of Lim et al., 2005;this work). In (C), simulations were performed with and without the absorption (abs) correction by hypothetical light-absorbing organic products, with the same time profile as pyruvic acid, but a much higher extinction coefficient (1500 cm −1 M −1 ). the formation of light-absorbing organic products that have the same time profile as pyruvic acid but a higher extinction coefficient (1500 cm −1 M −1 ) at 254 nm. Incorporating these "pyruvic acid surrogates" into the model significantly improves the model performance, resulting in an excellent agreement to the experimental values. While we did not identify these light-absorbing products in our reaction vessel, light-absorbing (brown carbon) products of other methylglyoxal reactions have been observed by others. For exam-ple, Sareen et al. (2010) observed the presence of UV-lightabsorbing products with an estimated extinction coefficient of ∼ 5000 cm −1 M −1 from non-radical reactions of methylglyoxal in highly concentrated aqueous ammonium sulfate solutions. Our methylglyoxal-OH experiments did not contain ammonium sulfate or any other source of nitrogen. In these experiments light absorption could be due to a πconjugate system formed possibly via aldol condensation (Sareen et al., 2010;Lim et al., 2010;Noziere et al., 2010). Further work is needed to investigate this hypothesis.

aqSOA yields under atmospheric conditions
According to the field study by Munger et al. (1995), glyoxal and methylglyoxal concentrations in the cloud water are similar, ranging from ∼ 0.1 to 300 µM. For the CSTR runs, 10 −7 -10 −4 M glyoxal/methylglyoxal in the aqueous phase were considered. The equivalent gas-phase concentrations due to Henry's law are ∼ 0.3 ppt-0.3 ppb for glyoxal and ∼ 30 ppt-30 ppb for methylglyoxal, and those ranges reasonably agree with literature (Fu et al., 2008). For the batch reactor runs, 10 −7 -10 M of glyoxal/methylglyoxal concentrations were considered with the highest concentrations comparable to concentrations of water-soluble organics in wet aerosols.

Batch reactor approximation
Mass-based SOA yields for glyoxal and methylglyoxal are obtained using the batch reactor approximation are illustrated in Fig. 9 and summarized in Table 1. At cloud-relevant concentrations, Y SOA Batch(glyoxal) is 1.20 and is solely contributed by oxalate. Y SOA Batch(methylglyoxal) is 0.77, which is the sum of 0.66 from pyruvate and 0.11 from oxalate. Using glyoxal as a surrogate for dissolved watersoluble organics, the aerosol-relevant Y SOA Batch(glyoxal) is 0.94. If instead methylglyoxal is used as a surrogate for total dissolved water-soluble organics, the aerosol-relevant Y SOA Batch(methylglyoxal) is 0.94. Again, this material is predicted to be entirely oligomeric (note that detailed oligomer distributions for 1 M glyoxal and 1 M methylglyoxal are provided in Fig. S3). It should be recognized that the chemistry in wet aerosols is complex and poorly understood. It is unlikely that all dissolved, water-soluble organics in an aerosol particle will have the same ability to form oligomers. However, glyoxal or methylglyoxal are reasonable surrogates for dissolved water-soluble organics because (1) aldehydes and alcohols are the major known water-soluble organic precursors (Blando and Turpin, 2001), (2) they are remarkably reactive to OH radicals in the aqueous phase, (3) and they are expected to have similar oxidation mechanisms.
The total particle-phase yield as a function of concentration is given by Similarly, for methylglyoxal, the total particle-phase yield as a function of concentration is given by where [G] 0 is initial [glyoxal] and [MG] 0 is initial [methylglyoxal]. These particle-phase product yields were estimated by fitting to the simulations ( Fig. 9a and b) and making use of Eqs.
(3) and (4). Note that at 1 × 10 −2 M of initial glyoxal in Fig. 9a, the SOA yield is a minimum (56 %) for the following reason. For this initial glyoxal concentration substantial (up to 4.6 mM) H 2 O 2 forms by HO 2 + HO 2 and HO 2 + O − 2 reactions. The reaction of glyoxylic acid + H 2 O 2 forming formic acid competes with the reaction of glyoxylic acid + OH radicals to form oxalate, and also competes with organic radicalradical reactions to form oligomers (Lim et al., 2010). This finding from atmospheric simulation is consistent with previ-ous experimental results at similar concentrations suggesting a role for H 2 O 2 (Lee et al., 2012).

CSTR model
In order to estimate the yield, the reacted glyoxal or methylglyoxal concentrations should be known. Since it is not possible to directly obtain the reacted precursor concentrations in the steady-state CSTR model, they were calculated by summing the major products (e.g., oxalic acid, pyruvic acid, glyoxylic acid, formic acid, acetic acid, formaldehyde, and CO 2 ), and all of the stoichiometric coefficients are assumed to be 1 except for CO 2 , which is 2 because two CO 2 molecules are produced from one oxalic acid molecule. A linear regression method was used to get the product yield during ∼ 1 h of glyoxal-OH reaction and ∼ 20 min of methylglyoxal-OH reaction (Fig. 5c), resulting in R 2 values close to 1. At cloud-relevant concentrations, Y SOA CSTR(glyoxal) is 1.19 and solely contributed by oxalate (Fig. S2A). Y SOA CSTR(methylglyoxal) is 0.80, which is the sum of 0.76 from pyruvate and 0.044 from oxalate (Fig. S2B). These CSTR yields are quite similar to the batch yields at the same conditions ( Fig. 10a and b) and also summarized in Table 1.

O / C ratio
O / C ratios of aqSOA for glyoxal and methylglyoxal under atmospheric conditions are estimated based on yield fractions of oxalate (O / C = 2), pyruvate (O / C = 1), and oligomers ( Fig. 9a and b). According to FTICR-MS analysis, the O / C ratio of glyoxal oligomers (m/z − 200-500) is 1.2 (Lim et al., 2010) and the O / C ratio of methylglyoxal oligomers (m/z − 245-800) is 0.69 (Altieri et al., 2008). O / C ratios decrease from 2 to 1 for glyoxal (Fig. 9a) and from 1 to 0.7 for methylglyoxal (Fig. 9b), as initial concentrations of glyoxal or methylglyoxal increase from cloud conditions to wet aerosol conditions.

Conclusions
Volatile but highly water-soluble glyoxal (≤ 276 µM -the concentration measured in atmospheric waters), methylglyoxal (0.02-128 µM), and acetic acid/acetate (0.4-245 µM) are common organic compounds found in the atmosphere (Tan et al., 2012). They are mostly gas-phase photochemical fragments of anthropogenic/biogenic VOCs. Due to their small carbon number (C 2 -C 3 ), these compounds form no semivolatile products, and therefore no SOA by gas-phase oxidation alone. However, since they are water soluble, they form SOA via aqueous-phase photochemistry in atmospheric waters. In clouds, the major products of their reaction with OH radicals are oxalate and pyruvate, which remain in the particle phase by forming organic salts with inorganic or ammonium ions. In wet aerosols, the major products are oligomers, which stay entirely in the particle phase. The aqueous radical chemistry of these compounds is initiated predominantly by OH radicals, and the current understanding is that the main source of aqueous OH radicals is uptake from the gas phase. Peroxy radical chemistry is a key to understanding aqueous-phase OH radical reactions. At cloud-relevant conditions, H-atom-abstracted organic products react with dissolved O 2 forming peroxy radicals, which decompose to carboxylic acids (e.g., glyoxylic acid, oxalic acid, or pyruvic acid) and HO 2 . At aerosol-relevant conditions, oligomers are formed via radical-radical reactions. The bimolecular-diffused RO 2 -RO 2 reactions constitute important peroxy radical chemistry for OH radical reactions of acetic and pyruvic acid and methylglyoxal. Alcohols and carbonyls are produced in the Russell pathway, whereas alkoxy radicals are produced in the Benson pathway. Alkoxy radicals undergo subsequent decomposition or a 1,2-hydride shift.
In this work, a full kinetic model was developed based on detailed reaction mechanisms and validated against labora-tory experiments. The batch and CSTR simulations predict similar and substantial aqSOA yields. These simulation results are consistent with the expectation that aqueous chemistry is a substantial source of SOA globally. Although uncertainties are large, recent model studies (Carlton et al., 2008;Fu et al., 2008; suggest that the magnitude of aqSOA is comparable to SOA formed via gas-particle partitioning of semivolatile products from gas-phase oxidation of VOCs. Certainly, other water-soluble organic precursor will also undergo aqueous chemistry leading to SOA formation. While glyoxal and methylglyoxal are likely to be present at concentrations up to ∼ 10 mM (in sulfate-containing wet aerosols H eff for glyoxal has been enhanced by a factor of ∼ 500 according to Kampf et al., 2013), our work includes model runs at concentrations as high as molar. In these model runs, glyoxal and methylglyoxal are being treated as surrogates for the complex mixture of water-soluble organics in wet aerosols, recognizing that there are many water-soluble compounds that will exist in atmospheric waters and will form radicals via reaction with OH. In wet aerosols we expect that these radicals will react with each other. Thus, we expect that a complex array of oligomeric products will form in wet aerosols, not just tartaric and malonic acids.
The processes examined in this work depend on the availability of OH radicals in clouds, fogs, and wet aerosols . Uptake from the gas phase is generally thought to be the major source of OH radicals to atmospheric waters, and steady-state aqueous concentrations of OH radicals from the gas phase may be influenced by droplet surface-to-volume ratios and aqueous concentrations of reactants. The photo-Fenton reaction (i.e., the photooxidation of Fe ions in the presence of H 2 O 2 ) is considered the major source of OH radicals inside wet aerosols (Arakaki and Faust 1998;Lim et al., 2005Lim et al., , 2010. Photolysis of nitrite/nitrate (Hullar and Anastasio, 2011) and organic matter (Dong and Rosario-Ortiz, 2012) can also produce OH radicals in aqueous particles. However, the degree of OH radical formation or "recycling" in atmospheric waters is not well understood and could represent an important yet unrecognized oxidant source. The sources and fate of oxidants in wet aerosols constitute an important area of current and future research, and may determine to what degree condensed-phase oxidation reactions occur near the surface versus in the bulk of wet aerosols, and the relative importance of radical versus nonradical reactions in aerosols.
Another issue that could impact SOA yields pertains to the gas-particle partitioning of products. The gas-particle partitioning of the carboxylic acid products depends on the extent to which these products are present as carboxylate salts, which have lower vapor pressures than the corresponding acids (e.g., oxalic acid vs. ammonium oxalate; Ortiz-Montalvo et al., 2012). Available measurements put oxalate predominantly in the particle phase, presumably as a salt. However, gas-phase particle partitioning measurements of carboxylic acids are limited, and this might not be uniformly true.