Reversible and irreversible gas-particle partitioning of dicarbonyl compounds observed in the real atmosphere

. Glyoxal and methylglyoxal are vital carbonyl compounds in the atmosphere and play substantial roles in radical cycling and ozone formation. The partitioning process of glyoxal and methylglyoxal between the gas and particle phase via reversible and irreversible pathways could efficiently contribute to secondary organic aerosol (SOA) formation. However, the relative importance of two partitioning pathways still remain elusive, especially in the real atmosphere. In this study, we 10 launched five field observations in different seasons and simultaneously measured glyoxal and methylglyoxal in the gas and particle phase. The field-measured gas-particle partitioning coefficients were 5–7 magnitudes higher than the theoretical ones, indicating the significant roles of reversible and irreversible pathways in the partitioning process. The particulate concentration of dicarbonyls and product distribution via the two pathways were further investigated using a box model coupled with the corresponding kinetic mechanisms. We recommended the irreversible reactive uptake coefficient γ for glyoxal and 15 methylglyoxal in different seasons in the real atmosphere, and the average value of 8.0×10 -3 for glyoxal and 2.0×10 -3 for methylglyoxal best represented the the loss of gaseous dicarbonyls by irreversible gas-particle partitioning processes. Compared to the reversible pathways, the irreversible pathways played a dominant role, with a proportion of more than 90% in the gas-particle partitioning process in the real atmosphere and the proportion was significantly influenced by relative humidity and inorganic components in aerosols. However, the reversible pathways were also substantial, especially in winter, 20 with a proportion of more than 10%. These two pathways of dicarbonyls jointly contributed to more than 25% of SOAs in the real atmosphere. To our knowledge, this study was the first to systemically examine both reversible and irreversible pathways in the ambient atmosphere, strove to narrow the gap between model simulations and field-measured gas-particle partitioning coefficients, and revealed the importance of gas-particle processes for dicarbonyls in SOA formation. this study are five orders of magnitude higher than the theoretical ones but still 1–2 orders of magnitude lower than the field- 225 measured coefficients, especially in winter. The difference between the estimated partitioning coefficients and the field-measured ones suggests that the current understanding of the equilibrium in reversible formations cannot reasonably explain the gas-particle partitioning processes of dicarbonyls. There still exist extra pathways of reversible formation. Cross-oligomerization of glyoxal and methylglyoxal is nonnegligible and could form similar molecular structure products and contribute to SOA yield (Schwier et al., 2010). Esterification and amination of diols also occur in aerosol liquid water but are 230 negligible compared to hydration and polymerization (Zhao et al., 2006). However, these reactions are not further discussed here. The hydrates and oligomers mentioned above are the dominant forms of glyoxal/methylglyoxal in the particle phase, while the higher molecular oligomers up to nonamer could also exist with a relatively smaller but still significant fraction at equilibrium. Although the reactions are thermodynamically reversible, upon evaporation of the aerosol liquid water, the oligomer formation is faster than the evaporation of dehydrated dicarbonyls, and the dicarbonyl evaporation is limited (Liggio 235 et al., 2005b; Loeffler et al., 2006). This results in relatively stable oligomers and yielding SOA. Moreover, other nucleophilic could irreversibly produce formic acid, glycolic acid, and oligomers on particles without illumination or extra oxidants. Besides gas-particle partitioning, particulate dicarbonyls formed via the heterogeneous reaction of VOCs could contribute to the uncertainty in partitioning research. Dong 375 et al. (2021) recently revealed that aqueous photooxidation of toluene could yield glyoxal and methylglyoxal via a ring-cleavage process. Overall, the real gas-particle partitioning process of glyoxal and methylglyoxal is more complicated and their contribution to SOA formation is still indistinct; thus, more laboratory experiments and field measurements are urgently needed to improve our understanding of the gas-particle partitioning process for glyoxal and methylglyoxal. of gas- and

The meteorological station was co-located at our sampling site and provided meteorological parameters. Commom trace gases 90 like NO/NO2, SO2, CO, and O3 were detected online by Thermo 42i, 43i, 48i, and 49i analyzers, respectively. A TEOM 1400A analyzer was applied to measure the mass concentrations of PM2.5 and PM10, the results of which were consistent with the PM2.5 weighing results (Fig. S1). The time solution for all of the above data was 1 min. Detailed information about these five observations is shown in Table S1. 95 The gaseous carbonyl samples were eluted with acetonitrile (HPLC/GC-MS grade), and the particulate carbonyl samples on quartz filter were eluted with acidic DNPH solutions in the flask and then were shaken for 3 h at 4 °C with a rotation rate of 180 rpm in an oscillator (Shanghai Zhicheng ZWY 103D). The derived solutions were placed in darkness for 12-24 h to ensure complete derivatization, and then they were analyzed by high-performance liquid chromatography-ultraviolet (HPLC-UV) for separation and detection. The limit of detection (LOD) of this method was 50 pptv for gaseous carbonyls and 1 ng·m -3 for 100 particulate carbonyls. They were calibrated using a mixing standard solution with a concentration range of 0.1-10 μM, and the linearity was indicated by a correlation of determination (r 2 ) of at least 0.999. The detailed analysis method was presented in our previous study (Wang et al., 2009).

Sample extraction and analysis
The Teflon samples were also extracted by deionized water using an ultrasonic bath for 30 min at room temperature. The extracted solutions were analyzed by ion chromatography (Integrion and Dionex ICS 2000, USA) to measure the water-soluble 105 inorganic compounds (Na + , NH4 + , K + , Mg 2+ , Ca 2+ , Cl − , NO3 − , and SO4 2− ) and low-molecular-weight organic acids (formate, acetate, and oxalate) in aerosols.
suspended particles (mass concentrations of PM2.5 were used in this study). In Eq. (2), K p t (m 3 ·μg -1 ) are the theoretical gasparticle partitioning coefficients determined by Pankow's absorptive model, fom is the absorbing fraction of total particulate mass, MWOM (g·mol -1 ) is the mean molecular weight of the organic phase, and z is the activity coefficient of target compounds.
In the estimation of K p t in this study, fom and z are unity and MWOM = 200 g·mol -1 , as used in previous studies (Healy et al.,120 2008; Williams et al., 2010;Xie et al., 2014;Shen et al., 2018), and p L 0 (Pa) is the supercooled vapor pressure of compounds as a pure liquid at temperature T, which is calculated by the extended aerosol inorganic model (E-AIM, http://www.aim.env.uea.ac.uk/aim/ddbst/pcalc_main.php) (Clegg et al., 1998). In Eq. (3), K H f (M·atm -1 ) is the field-derived effective Henry's law coefficient; cp (μg·m -3 ) and cg (atm) are particle-and gas-phase concentrations of carbonyls, respectively; ALWC (μg·m -3 ) is the aerosol liquid water content calculated by the thermodynamic model ISORROPIA-Ⅱ(forward model, 125 metastable state), the results of which are comparable to the actual measured contents confirmed by previous studies (Guo et al., 2015)..

Observation results and partitioning coefficients calculation
3.1.1 Dicarbonyls in the gas and particle phase 130 We launched five field observations in different seasons. Table S1 details the information about the field observations, including observation periods, sample volume, and meteorological parameters. We totally collected 387 gas-phase samples and 130 particle-phase samples in four seasons. In these samples, carbonyls were simultaneously measured in both gas phase and particle phase. Ten carbonyls were measured in the gas phase and six carbonyls were measured in the particle phase. In this study, we mainly discuss the gas-particle partitioning processes of glyoxal and methylglyoxal because of their significant 135 roles in atmospheric chemistry. Figure 1 and Table 1 show the temporal characteristics and seasonal variation of glyoxal and methylglyoxal, respectively.
Gaseous dicarbonyls showed obvious seasonal variation. Concentrations in summer (0.99 ± 0.59 ppbv) were generally much higher than in other seasons, followed by autumn and spring, and the concentrations in winter were the lowest. This seasonal variation could be partly attributed to the higher temperature and more intensive radiation in summer, which could greatly 140 enhance the secondary formation of gaseous carbonyls via photochemical reactions. The diurnal variation in the dicarbonyls during summer support this interpretation of the data; gas-phase dicarbonyls exhibited obviously diurnal variations in summer, whereas this variation was irregular in other seasons (Fig. S2). The concentration levels of gaseous dicarbonyl in summer rapidly increased after sunrise, remained relatively high during the daytime (12:00-14:00), and then decreased at dusk.
Although methylglyoxal has a shorter lifetime compare to glyoxal (GL 2.9 h vs. MG 1.6 h) (Fu et al., 2008), its gas-phase concentration levels were generally higher than those of glyoxal, consistent with previous studies (Rao et al., 2016;Mitsuishi et al., 2018;Qian et al., 2019), mainly due to the relatively larger production from isoprene and acetone for methylglyoxal.
The concentrations of particulate dicarbonyls were an order of magnitude smaller than the gaseous concentrations using the unit of nanogram per cubic meter of air (ng/m 3 air). The average particulate glyoxal and methylglyoxal were 19.37 and 11.24 ng/m 3 , respectively, which were slightly higher than previously reported values (Zhu et al., 2018;Shen et al., 2018;Cui et al., 150 2021; Qian et al., 2019). Dicarbonyls measured in the particle phase also showed obvious seasonal variation. The particulate concentrations of the two dicarbonyls in winter (43.38 ± 32.42 ng/m 3 air) were 2-2.3 times higher than those in other seasons, suggesting that the dicarbonyls were more favored into the particle phase in winter. Moreover, particulate dicarbonyls in different seasons exhibited the same diurnal variation (Fig. S2). The particulate concentrations of dicarbonyls in daytime were generally higher than those in nighttime, especially in winter.

Gas-particle partitioning coefficient
Dicarbonyls could partition between gas and aerosol phases or the liquid phase, following Pankow's absorptive partitioning theory or Henry's law, respectively, as listed in Table 2. Both gas-particle partitioning coefficient (K p f ) and effective Henry's law coefficient (K H f ) were calculated on the basis of field-measured data and were in the range of 10 -4 -10 -2 m 3 ·μg -1 and 10 6 -10 8 M·atm -1 , respectively. The partitioning coefficient values of the two dicarbonyls exhibited the same seasonal variation, as 160 winter and spring > autumn > summer. A higher aerosol concentration accompanied by higher aerosol surface area concentration and lower relative humidity resulted in a higher partitioning coefficient in winter and spring, when heavy pollution and sandstorms always occurred. In the case of temperature variation varied from 265.53 K to 310.75 K in different seasons, lower temperature promoted the partitioning processes as K p f values for the dicarbonyls and temperature showed negative correlation with significant difference (p < 0.001) (Fig. S3). Moreover, The K p f and K H f values of glyoxal were 165 always higher than those of methylglyoxal, implying the former was more likely to partition to the particle phase; this could be attributed to their different structures. Glyoxal were more soluable and reactive because of the adjacent electron-poor aldehydic carbons, whereas methylglyoxal was more stable due to the reduced electron-deficient ketone moiety (Kroll et al., 2005).
Both K p f and K H f were relatively closed to those found in previous field-measured studies ( water. Figure S4 presents the Setschenow plot of dicarbonyls versus aqueous sulfate, nitrate, and ammonia (SNA) concentration in aerosol. The negative salting constant indicated the "salting in" effects, which could result in exponential solubility, for both glyoxal and methylglyoxal in the real atmospheric. Moreover, both K p f and K H f of dicarbonyls were more 180 than one magnitude higher than the reported laboratory partitioning coefficient values from chamber experiments (Healy et al., 2008;Healy et al., 2009), indicating that the real atmosphere is more favorable for the partitioning of gaseous dicarbonyls to the particle phase. Actual atmospheric environment conditions and complex particle compositions, such as higher ionic strength, could greatly affect the partitioning process and the chemical reactions in the aerosols.
To narrow the large discrepancy between field-measured partitioning coefficients and theoretical (or laboratory) ones, we 185 needed to further investigate the mechanism and product distribution of chemical reactions occurring in the aerosols during the partitioning processes. The products of the reversible pathway mostly have lower saturated vapor pressure, and thus leading to higher partitioning coefficients compared to monomer dicarbonyls. For example, the calculated vapor pressures of the products of glyoxal hydration and dimerization are, respectively, 5 and 10 orders of magnitudes less than that of glyoxal monomer (Hastings et al., 2005). Moreover, the products of the irreversible pathway, such as organic acids produced in radical 190 chemistry, also have lower vapor pressure and efficiently contribute to the underestimation of partitioning coefficients. The following sections further discuss the mechanism and product distribution of reversible and irreversible pathways to explain the partitioning process of dicarbonyls.

Reversible pathways
Gas-particle partitioning of dicarbonyls via a reversible pathway mainly consists of hydration and self-oligomerization. Since 195 glyoxal and methylglyoxal had high water solubility and reactivity, they could easily dissolve into aerosol liquid water and form hydrates, which are more reactive than their counterparts and could participate in continuous reactions to form highermolecular-weight oligomers. Hemiacetal/acetal formation (Loeffler et al., 2006) and aldol condensation (Haan et al., 2009) are the most thermodynamically favored oligomer reactions for glyoxal and methylglyoxal, respectively. The proposed mechanism for the reversible formation of glyoxal and methylglyoxal in aerosols is shown in Fig. S5. Overall, since the 200 products of the reversible pathway, including hydrates and oligomers, are thermodynamically unstable and could easily revert to their original monomer form during extraction and analysis, their total concentration could be presented as the measured particle-phase dicarbonyls from sampled quartz filters. Since glyoxal and methylglyoxal have similar trend under different conditions, we focused on the total concentration of the two dicarbonyls in the following discussion. As shown in Fig. 2a RH increased from <10% to 60%; however, from 60% to 80% RH, it exhibited the opposite trend and decreased with increasing RH. Moreover, under high RH conditions, the particulate concentration of dicarbonyls via a reversible pathway had a strong and positive dependence on particle acidity (pH). The product distribution of the reversible formation could well explain this phenomenon.
To roughly estimate the product distribution of the reversible pathway in the real atmosphere, we simplified reaction 210 mechanisms and calculated the product distribution on the basis of the equilibrium constant reported in previous literature ( is shown in Table S3. The seasonal variation could be attributed to the RH in different seasons -relatively high in summer and low in winter. As shown in Fig. 2b, the product distribution of the reversible formation has a strong dependence on RH. The proportion of dicarbonyls in hydrate forms increased with increasing RH and could reach more than 75% in high RH, while the proportion of dicarbonyls in oligomer forms exhibited the opposite trend. Hydrates play a dominant role in dilute solutions under high RH conditions with a relatively high aerosol liquid water concentration, which might hinder oligomer formation. Combined with the vapor pressure of dominant products, their gas-particle partitioning coefficient can be roughly estimated and can effectively fit the field-measured values, as shown in Fig. 2c. The estimated gas-particle partitioning coefficients in this study are five orders of magnitude higher than the theoretical ones but still 1-2 orders of magnitude lower than the field-225 measured coefficients, especially in winter. The difference between the estimated partitioning coefficients and the fieldmeasured ones suggests that the current understanding of the equilibrium in reversible formations cannot reasonably explain the gas-particle partitioning processes of dicarbonyls. There still exist extra pathways of reversible formation. Crossoligomerization of glyoxal and methylglyoxal is nonnegligible and could form similar molecular structure products and contribute to SOA yield (Schwier et al., 2010). Esterification and amination of diols also occur in aerosol liquid water but are 230 negligible compared to hydration and polymerization (Zhao et al., 2006). However, these reactions are not further discussed here. The hydrates and oligomers mentioned above are the dominant forms of glyoxal/methylglyoxal in the particle phase, while the higher molecular oligomers up to nonamer could also exist with a relatively smaller but still significant fraction at equilibrium. Although the reactions are thermodynamically reversible, upon evaporation of the aerosol liquid water, the oligomer formation is faster than the evaporation of dehydrated dicarbonyls, and the dicarbonyl evaporation is limited (Liggio species may also form oligomers with glyoxal and methylglyoxal and effectively prevent their evaporation. Besides reversible pathways, higher carbon number products with lower volatility were mainly formed through irreversible pathways, like radical reactions (e.g., OH radicals), which are fully discussed in the next section.

Irreversible pathways driven by hydroxyl radicals
Reactive uptake driven by hydroxyl radicals (OH) is the dominant process for glyoxal and methylglyoxal in their irreversible gas-particle partitioning pathways. Compared to other irreversible pathways, like imidazole formation, glyoxal/methylglyoxal + OH chemistry occurs on much shorter timescales (Teich et al., 2016). The reaction is the initial step for most radical-based chemistry of glyoxal/methylglyoxal and has been proven to be an important source of SOA in both cloud/fog droplets and wet 245 aerosols (Tan et al., 2012;Lim et al., 2013), producing low-volatility products such as organic acids, large multifunctional humic-like substances, and oligomers. The proposed mechanism for the irreversible pathway of glyoxal and methylglyoxal driven by hydroxyl radicals in aerosols is shown in Fig. S6. The OH radicals in aerosol liquid water are mainly from the direct uptake of gas-phase OH radicals with a Henry's law constant of 30 M/atm (Faust and Allen, 1993) and Fenton reactions, and Fenton reactions are closely related to hydrogen peroxide, iron ions, and manganese ions in the particle phase. The sources of 250 OH radicals are one of the major uncertainties in SOA formation (Ervens et al., 2014).
The irreversible reactive uptake coefficient γ could efficiently describe the irreversible pathway of the gas-particle partitioning process of dicarbonyls driven by OH radicals. We could estimate the reactive uptake coefficients γ based on the effective Henry's constant via theory calculation (Hanson et al., 1994;Curry et al., 2018) and then calculate the effective uptake rate keff, uptake, following Eqs. (4)- (7): where γ is the dimensionless uptake coefficient, v (m·s −1 ) is the gas-phase thermal velocity of glyoxal/methylglyoxal, Daq 260 (m 2 ·s -1 ) is the diffusion coefficient in the liquid phase, α is the dimensionless mass accommodation coefficient, H * (M·atm -1 ) is the effective Henry's law constant calculated by field-measured data in Table 2, R is the universal gas constant, k l (s -1 ) is the first-order aqueous loss rate, (kg·mol −1 ) is the average molar mass of gas-phase dicarbonyls, q is the parameter for measuring in-particle diffusion limitations, Rp (m) is the particle radius, l (m) is the diffusion reactive length, keff, uptake (s -1 ) is  40%). Moreover, the formulation describes the reactive uptake due to irreversible multiple-phase loss processes in the presence of OH. The uncertainty in the γ calculation is mainly attributed to the uncertainty in OH concentration, which was 3×10 -12 M on average and varied from 5.5×10 -14 to 8×10 -12 M (Herrmann et al., 2010).
The calculated γ and keff, uptake values for different seasons are listed in Table 3. The reactive uptake coefficients of glyoxal were in the range 10 -4 -10 -2 , and the average value of 8.0×10 -3 in this study was closed to the ones representing the loss of glyoxal 270 by surface uptake during the KORUS-AQ campaign in a very recent studies (Kim et al., 2022). And the value slightly exceeded the one commonly used in model simulations (γ = 2.9×10 -3 ), which was based on an experimental study for (NH4)2SO4 aerosols at 55% RH (Liggio et al., 2005a), and also far outweighs the uptake coefficients of glyoxal on clean and acidic gas-aged mineral particles (γ = 10 -6 -10 -4 ) (Shen et al., 2016), implying that a real atmospheric aerosol provides a far more reactive interface for physiochemical processes than that of mineral particles. Moreover, the reactive uptake coefficients of 275 methylglyoxal were slightly lower than those for glyoxal, with an average value of 2.0×10 -3 . Conflicting with previous experimental results, methylglyoxal exhibited unexpected salting-in effects in real atmospheric particles and had much higher uptake coefficients, which could be attributed to the increased reactivity of methylglyoxal with a high uptake coefficient under an atmospheric relevant concentration (Li et al., 2021). The γ values for both glyoxal and methylglyoxal exhibited similar seasonal variations, which were lowest in summer and reached their highest in winter. This seasonal variation could be 280 attributed to RH variation and particle composition. Moreover, the effective uptake rate (keff, uptake), which is regarded as a pseudo-first-order reaction rate, is a net result of competition between reversible and irreversible processes, and it varied from 10 -4 s -1 to 10 -5 s -1 in the real atmosphere in this study. As shown in Fig. 3a, the negative dependence of keff, uptake on RH also confirmed that the irreversible uptake of dicarbonyls could be inhibited in high RH conditions. And the relatively low SNA concentration under high RH conditions also attenuated the irreversible uptake as the weakening of ion effects (Figure 3b).

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Whereas, for a given RH, uptake coefficients γ for both glyoxal and methylglyoxal showed a weak dependence on the ratio of SNA (S:A and S:N) with significant scatter (Fig. S7).
Moreover, it was worth noting that under extremely low RH (<40%), the aerosol was not completely deliquescent, and the uptake coefficients based on Henry's law could not explain the irreversible pathways. Previous research indicated that the irreversible uptake of dicarbonyls could still occur under a low RH condition (Liggio et al., 2005a;De Haan et al., 2018), and 290 that these uptake values were generally lower due to the inefficient reactive uptake process onto the crystallized aerosols.

Reactive uptake of dicarbonyl compounds
We could not directly measure the particulate concentration of dicarbonyls via an irreversible pathway, as the dicarbonyls The total particulate concentration of glyoxal and methylglyoxal via irreversible pathway varied from several to more than 100 nanograms per microgram PM2.5 (ng/μg PM2.5), and it was strongly dependent on RH, as shown in Fig. 3c. Since the irreversible uptake coefficients γ of dicarbonyls tended to decrease with increasing RH due to the "salting-in" effects, both 300 glyoxal and methylglyoxal in this study exhibited high solubility in low RH conditions, where the aerosol water was coupled with concentrated inorganic solutions and relatively high ionic strength. Moreover, the total particulate concentrations of dicarbonyls were positively dependent on particle acidity under high RH conditions, while there were no obvious correlations under low RH conditions.
To further discuss the product distribution of the reaction of glyoxal/methylglyoxal with hydroxyl radicals, we used the kinetic steady-state approach. The average OH radical concentration setting in the modeling was 3.2×10 -12 M, which is based on the hypothesis of the Henry equilibrium of OH radicals between the gas and particle phase (Sander, 2015;Shen et al., 2018).
Oxalate can be considered as a tracer for this aqueous chemistry, since it does not have any other significant chemical sources.
Oxalate was detected in the particle-phase samples by ion chromatography. The modeling results of oxalate concentration 310 agreed well with the measured values, and their deviations were in the considered range (Fig. S7). Meanwhile, we can estimate the distribution of major products in irreversible glyoxal/methylglyoxal-OH radical chemistry under different RH conditions, as illustrated in Figure 3d. Generally, oxalate is the major product in wet aerosols, contributing ~60%, and its proportion increases with increasing RH. Besides oxalate, oligomers also play significant roles in glyoxal/methylglyoxal-OH radical chemistry with a contribution of ~30%, and their proportion is maximum under relatively low RH conditions. The RH 315 dependence of the product distribution could mainly be attributed to the particulate concentration of glyoxal/methylglyoxal, which significantly affects the OH radical chemistry. With relatively high carbonyl concentrations (0.1-10 M) in aerosol liquid water, self-reactions of organic molecules become more favorable, resulting in new carbon-carbon bonds and high molecular weight oligomers via radical-radical chemistry (Lim et al., 2013). Moreover, besides OH radical chemistry, reaction with sulfate and ammonium also contribute to the oligomer formation and irreversible uptake of gaseous dicarbonyls (Ortiz-320 Montalvo et al., 2014;Lim et al., 2016;Lin et al., 2015). The oligomer proportion could be more than 30% in concentrated carbonyl solutions (~0.1 M) and only account for 1% in diluted solutions (~0.01 M). in winter (92.9% for glyoxal and 92.8% for methylglyoxal). Overall, the irreversible pathway played a dominant role in the gas-particle partitioning process for both glyoxal and methylglyoxal in the real atmosphere, while the reversible pathway was also substantial and nonnegligible, especially in winter, with an proportion of ~10%. Furthermore, as discussed above, the particulate concentrations of dicarbonyls and their relative importance were influenced by environmental factors such as relative humidity and particle composition, which could jointly influence both the reversible and irreversible pathways of 335 dicarbonyls. As shown in Figure 4, the proportion of irreversible pathways in the gas-particle partitioning process for dicarbonyls increased with aqueous SNA concentrations, and reached maxium when SNA concentrations were more than 100 M under low RH conditions.

Relative importance of two partitioning pathways
Comprehensively considering the contribution of two pathways in partitioning processes could be conductive to ambient dicarbonyls simulations. Ling et al. (2020) found that the observation and simulation of the gas-phase concentration level of 340 dicarbonyls could reach reasonable agreement when the irreversible uptake and reversible partitioning were incorporated into the model, as these jointly contribute ~62% to the sink of dicarbonyls. Moreover, the contribution of gas-particle partitioning processes of dicarbonyls to SOA formation were higher as the two partitioning pathways were jointly considered. In this study, gas-particle partitioning processes of dicarbonyls accounted for a relatively large proportion of total particle mass (PM2.5), on the average of ~5% considering both reversible and irreversible gas-particle partitioning pathways. Since a large fraction of 345 PM2.5 mass in Beijing consists of SOAs (~30%) (Huang et al., 2014), we could roughly estimate the contribution of gas-particle partitioning processes of dicarbonyls to SOA yields (by mass). There were approximately 25% SOAs formed from glyoxal and methylglyoxal in this study. However, the particulate dicarbonyls calculated here only contained simple reversible pathways and irreversible pathways driven by OH radicals. More complicated chemical processes like NO3 radical chemistry were not considered, which still resulted in the underestimation of their contribution to SOA formation.

Conclusions
We simultaneously measured glyoxal and methylglyoxal concentration in the gas and particle phase in different seasons over urban Beijing. Based on field-measured data, the field-derived gas-particle partitioning coefficients were calculated and found https://doi.org/10.5194/acp-2022-86 Preprint. Discussion started: 9 February 2022 c Author(s) 2022. CC BY 4.0 License.
to be 5-7 magnitudes higher than the theoretical values. Such a large discrepancy provides field evidence that the gas-particle partitioning process does not occur by physical absorption alone but also results from the combined and simultaneous effects 355 of reversible and irreversible pathways. Hydration and oligomerization occurred in the reversible pathway, producing compounds with lower volatility in the condensed phase, and the irreversible pathway could accelerate the uptake of gaseous dicarbonyls. The two pathways jointly contributed to the underestimation of gas-particle partitioning of dicarbonyls.
This study systemically considers both reversible and irreversible pathways in the ambient atmosphere for the first time.
Compared to the reversible pathways, the irreversible pathways play a dominant role in the gas-particle partitioning process 360 for dicarbonyls, accounting for ~90% of this process. We recommend the irreversible reactive uptake coefficient for glyoxal and methylglyoxal in different seasons in the real atmosphere. The values we calculated here are higher than those used in model simulations to date, especially for methylglyoxal which exhibits an unexpected salting-in effect under an atmosphericrelevant concentration. We expect the application of these parameterizations will increase the calculated contribution of irreversible uptake of dicarbonyls to SOA formation and narrow the gap between model predictions and field measurements 365 of ambient dicarbonyl concentrations. Moreover, relative humidity and inorganic particle compositions are defined as the most important factor influencing particulate concentration and product distribution of dicarbonyls via both reversible and irreversible pathways, implying the significance of considering different RH conditions in dicarbonyl SOA simulations.
Furthermore, we note that there may be other potential explanations for the increase in particulate concentrations and the uncertainty in the gas-particle partitioning process. Physical adsorption of dicarbonyls could be enhanced by water-soluble 370 organics and mineral dust. Other reversible pathways, like adducts formed from glyoxal with inorganic species, like sulfate and ammonia, could also promote the gas-particle partitioning process. Irreversible pathways driven by other oxidants, like NO3 radicals, can also perform a substantial role. Shen et al. (2016) found that glyoxal could irreversibly produce formic acid, glycolic acid, and oligomers on particles without illumination or extra oxidants. Besides gas-particle partitioning, particulate dicarbonyls formed via the heterogeneous reaction of VOCs could contribute to the uncertainty in partitioning research. Dong Overall, the real gas-particle partitioning process of glyoxal and methylglyoxal is more complicated and their contribution to SOA formation is still indistinct; thus, more laboratory experiments and field measurements are urgently needed to improve our understanding of the gas-particle partitioning process for glyoxal and methylglyoxal.

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Data availability. The data are accessible by contacting the corresponding author (zmchen@pku.edu.cn).
Author contributions. In the framework of the five field measurements in different seasons, ZC and JH designed the study, and JH performed all carbonyl measurements used in this study, analyzed the data, and wrote the paper. ZC helped interpret the https://doi.org/10.5194/acp-2022-86 Preprint. Discussion started: 9 February 2022 c Author(s) 2022. CC BY 4.0 License.
results, guided the writing, and modified the manuscript. XQ and PD contributed to the methods of sampling and analyzing 385 gas-and particle-phase carbonyls. All authors discussed the results and contributed to the final paper.
Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. This work was funded by the National Natural Science Foundation of China (Grant number 41975163).

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We also thanked Shiyi Chen at Peking University for the providing the data for the meteorological parameters, trace gases and PM2.5 mass concentrations.          a [X]P, rever is the concentration of particle-phase carbonyl via reversible pathway (ng·μg -1 ) and its proportion (%).