Towards a Chemical Mechanism of the Oxidation of Aqueous Sulfur Dioxide via Isoprene Hydroxyl Hydroperoxides (ISOPOOH)

. In-cloud chemistry has important ramifications for atmospheric particulate matter formation and gas-phase chemistry. Recent work has shown that, like hydrogen peroxide (H 2 O 2 ), the two main isomers of isoprene hydroxyl 15 hydroperoxide (ISOPOOH) oxidize sulfur dioxide dissolved in cloud droplets (SO 2,aq ) to sulfate. The work revealed that the pathway of SO 2,aq oxidation with ISOPOOH differs from that of H 2 O 2 . We investigate the chemical mechanisms of oxidation of SO 2,aq with ISOPOOH in the cloud-relevant pH range of 3-6 and compare them with the previously reported mechanisms of oxidation of SO 2,aq with H 2 O 2 , methyl hydroperoxide and peroxyacetic acid. The organic products of the reaction are identified and two pathways are proposed. For 1,2-ISOPOOH, a higher yield pathway via proposed radical intermediates yields 20 methyl vinyl ketone (MVK) and formaldehyde, which can react to hydroxymethanesulfonate (HMS) when SO 2,aq is present. A lower yield non-fragmentation oxygen addition pathway is proposed that results in formation of isoprene-derived diols (ISOPOH). Based on global simulations, this mechanism is not a significant pathway for formation of MVK and formaldehyde relative to their gas-phase formation but, as previously reported, it can be regionally important for sulfate production. The study adds to previous work that highlights similarities and differences between gas-phase and cloud-droplet processing of 25 reactive organic carbon. 0.28-0.36, 0.95-1.31 and 1.40-1.52 Tg ∙ yr −1 of MVK, acetic acid, HCHO, HMS and 1,2-ISOPOH, respectively (ranges 235 are for the differences in yields across the experimental pH range). The production of MVK from these ISOPOOH+SO 2,aq oxidation pathways is equivalent to 0.5% of the total global production under present conditions. Under preindustrial conditions, the total atmospheric burden of SO 2 decreases; thus, the amount of ISOPOOH reacting with SO 2,aq decreases somewhat: 2.4 Tg ∙ yr −1 of gas-phase 1,2-ISOPOOH react with SO 2,aq , representing 1.6% of the global respective losses of the isomer and 1.0% of the global production of sulfate. The reaction of 1,2-ISOPOOH+ SO 2,aq results in 0.23-0.30, 0.01-0.04, 240 0.16-0.21, 0.55-0.76 and 0.80-0.88 Tg ∙ yr −1 of MVK, acetic acid, HCHO, HMS and 1,2-ISOPOH, respectively. The production of MVK from these ISOPOOH+ SO 2,aq oxidation pathways is equivalent to 3.7% of the total global production under pre-industrial conditions. These results show that the importance of these pathways lies in the production of sulfate on regional scales, especially for isoprene-dominated regions, rather than the formation of the organic reaction products. The conversion of bisulfite to sulfate via the 1,2-ISOPOOH pathway can contribute up to ~ 50% of total sulfate production in 245 pristine regions such as the Amazon, and ~ 3% in more polluted regions such as the Southeast United States under current atmospheric conditions (Dovrou et al., 2019b). The Southeast United States is an area of interest as NO x levels are decreasing,

In the gas-phase, ISOPOOH is oxidized by OH to primarily produce isoprene epoxydiols (IEPOX), which contribute to secondary organic aerosol (SOA) mass Surratt et al., 2010;Lin et al., 2012;Nguyen et al., 2014;McNeill, 2015;Zhang et al., 2018). St Clair et al. (2016) investigated the gas-phase oxidation mechanism of ISOPOOH and elucidated 40 some non-IEPOX oxidation pathways, and Krechmer et al. (2015) observed the formation of non-IEPOX low volatile organic compounds that contribute to SOA. These pathways are summarized and compiled into a complete gas phase mechanism in the work of Wennberg et al. (2018).
Having Henry's law constants on the order of 10 5 M • atm −1 , ISOPOOH isomers can partition into cloud and fog water and 45 participate in condensed-phase reactions (Rivera-Rios, 2018). Dovrou et al. (2019b) showed that ISOPOOH oxidizes sulfur dioxide (SO2,aq) in cloud and fog water, producing sulfate (SO 4 2− ). Aqueous hydrogen peroxide (H 2 O 2 ) oxidizes SO2,aq to sulfate with a 100% yield with a rate constant that increases with decreasing pH (Lind et al., 1987). Dovrou et al. (2019b) reported that at pH=5.5 the rate constant for oxidation of SO2,aq by 1,2-ISOPOOH is equal, within uncertainty, to that of oxidation of SO2,aq by H 2 O 2 at pH=5.5, while the rate constant of the oxidation for SO2,aq by 4,3-ISOPOOH is an order of magnitude lower. 50 The rate constants for the reactions of both ISOPOOH isomers with SO2,aq have a much smaller pH dependence than that of H2O2 + SO2,aq. Similar to H2O2, the sulfate yield at pH=4.5 and 3 is 100% for both ISOPOOH isomers. However, Dovrou et al. (2019b) showed that for pH=5.5 the sulfate yield is only 67% and 83% of the reacted SO2,aq for 1,2-ISOPOOH and 4,3-ISOPOOH, respectively (Table 1). Due to its higher abundance, solubility and rate of reaction with SO2,aq, 1,2-ISOPOOH contributes much more to atmospheric sulfate production than the 4,3 isomer (Dovrou et al., 2019b). 55 The differences between both the sulfate yield and the pH-dependence of rate constants suggest that the chemical mechanisms of SO2,aq oxidation via H2O2, and ISOPOOH are different. Hoffman and Edwards (1975)
Hydrogen peroxide (H 2 O 2 ) was purchased from Sigma Aldrich (30 wt. % in H 2 O) and filtered Milli-Q water and deuterium oxide (D2O) were used as solvents.
2-Methyl-3-butene-1,2-diol (1,2-ISOPOH) was synthesized, following the procedure in Zhang et al. (2012) and Bates et al. 75 (2014), by hydrolysing 2-methyl-2-vinyloxirane. Approximately 5400 mg of 2-methyl-2-vinyloxirane was dissolved in 54 mL of 0.1 M HCl at 50°C for 30 min. The procedure was modified by saturating the reaction mixture with sodium chloride (NaCl), instead of lyophilizing it. Subsequently, the diol was isolated via extraction with diethyl ether. The diethyl ether solution was then evaporated under reduced pressure to isolate the diol. The purity of the diol was determined to be 70% using NMR analysis, and the identified impurities were diethyl ether, water, and the 1,2-ISOPOH dimer. 80 Samples for kinetics experiments were prepared with a ratio of , as discussed in Dovrou et al. (2019b). The concentrations of the IC and NMR experiments were 10s of μΜ and a few mM, respectively, based on the sensitivity of the methods. For the NMR analysis of standards, 1 mM concentrations were used. After completion of reactions, 0.1-2 mM standards were added to identify proposed products by observing increases in the intensity of the corresponding 85 peaks in the spectra.

Ion chromatography and NMR analysis
A Dionex ICS-5000+ Ion Chromatography (IC) system and an Agilent I500B NMR were used to analyze the samples and quantify sulfate produced. The AG12A guard column and the AS12A analytical column (Dionex Ionpac) were selected in order to separate sulfur-containing species (Dovrou et al., 2019a). The mobile phase was 4.5 mM:1.4 mM sodium carbonate: 90 sodium bicarbonate with flow rate 1.5 mL • min −1 (Dovrou et al., 2019b). 1 H-NMR was used to identify the organic reaction products. 16 and 32 scan averages were chosen, with a relaxation delay 45 sec and at proton operating frequency 400 MHz. All experiments were repeated at least four times, and each sample was prepared separately prior to analysis and temperature and pH were monitored. DMSO, methanol and 3-(trimethylsilyl)-1-propanesulfonic acid sodium salt ((CH 3 ) 3 Si(CH 2 ) 3 SO 3 Na) 95 were used as internal standards for quantitative yields.

GEOS-Chem simulations
GEOS-Chem simulations were performed identically to those described in Dovrou et al. (2019b). In brief, GEOS-Chem model version 11-02d, which includes bromine chemistry relevant to SO2 oxidation, was used as a base, and the chemical mechanism was updated with the isoprene chemistry described in Bates and Jacob (2019). Emissions of isoprene were derived from the 100 MEGAN v2.1 inventory and scaled uniformly to 535 Tg • yr −1 . The simulations performed are described in detail in the work of Dovrou et al. (2019b). All simulations were performed at 4˚ latitude by 5˚ longitude horizontal resolution with 72 vertical levels and spun up for one year, after which annual and summertime simulations were used for the results reported herein under both modern (2016) and pre-industrial conditions, in which anthropogenic emissions are removed and the global methane distribution is scaled down by 60%. 105 Fig.1 shows the NMR spectra of 1,2-and 4,3-ISOPOOH standards in D2O (broad peak at 4.7ppm) together with the NMR spectra after reaction of ISOPOOH with a two-fold excess of SO2,aq at three different pH values. After completion of the SO2,aq +ISOPOOH reaction at pH=5.5 the ISOPOOH precursors are not observable and a number of high intensity 1 H-NMR signals 110 are observed. Signals with the same shifts are observed under more acidic conditions but with slightly lower intensity, while some of the smaller peaks from the pH=5.5 spectra of both isomers are not observed in the pH=4.5 and 3 spectra. This is consistent with the hypothesis that the reaction and product distribution have a pH dependence and suggests competition between different reaction paths. These different paths may also explain the pH dependence of the observed sulfate yields.

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Products were identified via comparison of 1 H-NMR spectra of standards as well as spiking SO2,aq+ISOPOOH mixtures after completion of reaction with standards of the proposed products. Methyl vinyl ketone (MVK), methacrolein (MACR) and (hydrated) formaldehyde (HCHO), all major products of gas-phase oxidation, were identified by their 1 H-NMR chemical shifts (St. Clair et al., 2016). Due to its higher importance, the 1,2-ISOPOOH reaction and products were examined in more detail.
Reaction 3 has two pathways oxidizing S(IV) to S(VI): a higher yield pathway, R3a, forming sulfate and methanol and a lower 135 yield pathway, R3b, forming methyl bisulfite. Lind et al.'s (1987) results for CH3OOH and CH3(O)OOH are consistent with a fast initial equilibrium, like R1, followed by rearrangement to the products. In addition, Lind et al. (1987) stated that at pH values above 4.8 the CH3(O)OOH reaction had 140 another mechanism, but the authors did not elaborate, only stated that the mechanism was first-order in both reactants. R3a and R4 are effectively oxygen atom transfer reactions, analogous to the net R1-R2 reactions of H2O2. R3b forms an organosulfate as the stable reaction product (Lind et al., 1987). In our discussion of ISOPOOH reaction pathways we focus on the atmospherically more important 1,2-ISOPOOH. Based on the product distribution we propose a non-fragmentation pathway for 1,2-ISOPOOH forming 1,2-ISOPOH (22% molar yield at pH=5.5) and two fragmentation pathways producing 145 MVK (30% molar yield at pH=5.5) together with formaldehyde/HMS (>30% molar yield at pH=5.5) and acetic acid (5% molar yield at pH=5.5) with other small species such as CO. These pathways accounting for 57% of 1,2-ISOPOOH reaction at pH=5.5 will be discussed below.

Non-fragmentation pathway
Analogous to R1, we also consider an initial fast equilibrium of ISOPOOH with SO2,aq. However, because of the lower 150 symmetry than H2O2, there are two possibilities, depending on which peroxy O is involved in the nucleophilic attack on sulfur. Peroxysulfite from R5a will rearrange to sulfate following R2. The organo peroxysulfite from R5b could potentially rearrange to form an organosulfate (R6a) which is known to rapidly hydrolyze forming sulfate and ISOPOH (Darer et al., 2011;Hu et al., 2011). This rapid hydrolysis of tertiary sulfate likely also applies to the organo peroxysulfite. The hydrolysis product (R6b) is again ISOPOH and peroxysulfite, which will rearrange to sulfate following R2.
(R6a) 160 (R6b) The net outcome of all pathways is effectively an oxygen atom transfer from 1,2-ISOPOOH to sulfite to form sulfate and 1,2-ISOPOH. This net mechanism is consistent with the NMR spectra and IC analysis which show clear evidence for ISOPOH and sulfate production. This effective reaction path is shown in the left-hand side of Fig. 3[1]. This pathway accounts for 22% of 1,2-ISOPOOH reaction at pH=5.5. 165

Fragmentation pathways
1,2-ISOPOH only has about 2/3 of the yield of MVK at all pH values which is strong evidence that an additional pathway, likely not present for CH3OOH, exists. MVK and formaldehyde, either as its hydrate or as the adduct with the excess SO2,aq, are in fact the highest yield products. These products have to involve breaking of the carbon backbone, which strongly suggests a radical mechanism. The products are identical to those resulting from oxidation of isoprene by OH under high-NO conditions, 170 which involves an alkoxy radical (1,2-ISOPO, Fig. 3). In addition, the products are identical to those observed for gas-phase ISOPOOH reacting on metal surfaces (Rivera-Rios et al., 2014). For the latter process, Rivera-Rios et al. (2014) proposed cleavage of the 1,2-ISOPOOH peroxy bond producing 1,2-ISOPO which rapidly forms MVK and formaldehyde. The high sulfate yield at all pHs implies that both the ISOPOH and the fragmentation channel have to produce sulfate. In combination with the previous results mentioned above, we propose that the second pathway involves cleavage of the peroxy bond of the 175 organo peroxysulfite resulting in 1,2-ISOPO, which rapidly forms MVK/formaldehyde, and a sulfite radical. The sulfite radical rapidly reacts with O2 producing a peroxysulfate radical, which can undergo further reaction, e.g., with SO2,aq or organic molecules to form sulfate and oxidized organics (Neta and Huie, 1985;Yang et al., 2015). The subsequent (secondary) reaction of HCHO with SO2,aq explains formation of HMS and thus the pathway forms MVK, HCHO and the sulfite radical as first generation products with the sulfite radical likely forming sulfate subsequently (Fig. 3) (Dovrou et al., 2019a;Munger et al., 180 1984;Munger et al., 1986). This pathway accounts for 30% of 1,2-ISOPOOH reaction at pH=5.5. The observation of acetic acid also requires a fragmentation of the backbone. This pathway likely involves formation of additional formaldehyde and CO, which are both not quantifiable in our experiments. For this reason, this is the most uncertain pathway although it is clear that it accounts for 5% of 1,2-ISOPOOH reaction at pH=5.5, which makes the sum of the non-185 fragmentation and the two fragmentation pathways 57% at pH=5.5 (Rivera-Rios et al., 2014;).
There likely are three contributors to the carbon yield of less than 100%. Hydrated formaldehyde could not be quantified due to interference with D2O although this likely is already accounted for in the MVK and acetic acid pathways. However, MVK could also repartition to the gas-phase, as discussed in section 4; thus, its aqueous contribution might be underestimated. It is 190 likely that formation of CO or other small molecules that potentially partition to the gas-phase are not detected by NMR.
Lastly, it is also possible that numerous small-yield products are formed that are below the NMR detection limit.

pH dependence
The sulfate yield increases while the observed carbon decreases with decreasing pH, and the ratio of ISOPOH to MVK is pH independent. Moreover, at lower pH, ISOPOH and MVK molar yields are reduced by no more than 10%, and the acetic acid 195 path is greatly reduced. We propose two explanations for the fact that the observed carbon balance decreases with decreasing pH. Kok et al. (1986) showed that the formation of HMS is a factor of 10 slower at pH=4 than pH=5, which could explain that at pH≤4.5 the sulfate yield observed in the oxidation of SO2,aq with ISOPOOH is 100%, indicating that SO2,aq is oxidized faster to sulfate than reacting with formaldehyde to form HMS, while pH=5.5 the sulfate yield is lower. Thus, the decreased HMS yield is attributed to slow HMS formation so that more formaldehyde stays in the hydrated form which could not be quantified. 200 Second, at lower pH acetic acid may partition to the gas-phase and thus it cannot be observed. The results do not provide a clear explanation for the lower sulfate yield at pH=5.5. The non-fragmentation (ISOPOH) pathway, which is more important at pH=5.5, cannot explain this as it should have a 100% sulfate yield. Thus, the cause has to result from one of the fragmentation pathways. It is possible that at higher pH the sulfite radical has a lower yield of forming sulfate, however, studying this goes beyond the scope of this work. 205 In summary, we observe clear evidence for a non-fragmentation pathway that likely is similar to the mechanism of H2O2 and CH3OOH. A difference to CH3OOH is that in contrast to methyl bisulfate the organo sulfates from ISOPOOH hydrolyze easily, especially the tertiary one from 1,2-ISOPOOH. The non-fragmentation pathway effectively corresponds to an oxygen atom transfer and in contrast to H2O2 and CH3OOH this is not the major pathway. We observe fragmentation pathways that we 210 hypothesize involve cleavage of the peroxy bond based on previous work on ISOPOOH. Such a pathway was not observed for CH3OOH as the product of this channel would be neither methanol nor methyl bisulfate. There are at least two fragmentation pathways, with the major observed one producing MVK and HCHO, which subsequently forms HMS, and a minor one forming acetic acid and probably small molecules including CO. It is likely that additional smaller molecules that partition to the gas- phase are formed as well as other molecules at low concentration that cannot be detected via NMR, which could include 215 organo-sulfur compounds from the reaction of the sulfite radical with organics.

Conclusions and atmospheric implications
This work is primarily useful as a foundation for the mechanistic understanding of the reactivity of multifunctional organic hydroperoxides with SO2,aq. It shows that they have a significantly more complex behaviour with channels analogous to H2O2 and CH3OOH but also fragmentation channels. Understanding the mechanisms of these oxidation reactions can help clarify 220 the composition of cloud droplet residual aerosols and adds new pathways to the isoprene oxidation mechanism.
In the atmosphere, MVK and MACR will partition to the gas-phase as they have high vapor pressures of 11 and 16 kPa and low Henry's law constants of 41 and 6.5 M • atm −1 , respectively (Iraci et al., 1999). The diffusion time of MVK in a cloud droplet is less than 25 seconds. The rate of the reaction of MVK with SO2,aq was estimated using NMR analysis, from which 225 we estimate a lower limit for the rate constant of k≥ 10 4 M −1 • s −1 . However, considering the diffusion time, SO2,aq and expected MVK concentrations, the formation of the organosulfur compound by reaction of MVK with SO2,aq is unlikely in the atmosphere.
The annual production of the products formed via the reaction of ISOPOOH with SO2,aq in the atmosphere was calculated 230 using the estimated ISOPOOH amount participating in this reaction from GEOS-Chem (Jacob et al., 2001;Park et al., 2004;Alexander et al., 2012;Dovrou et al., 2019b). Globally, it is estimated that, under current conditions, 4.2 Tg • yr −1 of gasphase 1,2-ISOPOOH reacts with SO2,aq, representing 3.2 % of the global loss of the ISOPOOH isomer and 1.7% of the global production of sulfate (Dovrou et al., 2019b). The 1,2-ISOPOOH pathway contributes to the production of 0.40-0.53, 0.02-0.06, 0.28-0.36, 0.95-1.31 and 1.40-1.52 Tg • yr −1 of MVK, acetic acid, HCHO, HMS and 1,2-ISOPOH, respectively (ranges 235 are for the differences in yields across the experimental pH range). The production of MVK from these ISOPOOH+SO2,aq oxidation pathways is equivalent to 0.5% of the total global production under present conditions. Under preindustrial conditions, the total atmospheric burden of SO2 decreases; thus, the amount of ISOPOOH reacting with SO2,aq decreases somewhat: 2.4 Tg • yr −1 of gas-phase 1,2-ISOPOOH react with SO2,aq, representing 1.6% of the global respective losses of the isomer and 1.0% of the global production of sulfate. The reaction of 1,2-ISOPOOH+ SO2,aq results in 0.23-0.30, 0.01-0.04, 240 0.16-0.21, 0.55-0.76 and 0.80-0.88 Tg • yr −1 of MVK, acetic acid, HCHO, HMS and 1,2-ISOPOH, respectively. The production of MVK from these ISOPOOH+ SO2,aq oxidation pathways is equivalent to 3.7% of the total global production under pre-industrial conditions. These results show that the importance of these pathways lies in the production of sulfate on regional scales, especially for isoprene-dominated regions, rather than the formation of the organic reaction products. The conversion of bisulfite to sulfate via the 1,2-ISOPOOH pathway can contribute up to ~50% of total sulfate production in 245 pristine regions such as the Amazon, and ~3% in more polluted regions such as the Southeast United States under current atmospheric conditions (Dovrou et al., 2019b). The Southeast United States is an area of interest as NOx levels are decreasing, creating an atmosphere where hydroperoxide formation can be favored, which may increase their contribution to sulfate formation; in a simulation without anthropogenic emissions, the contribution of ISOPOOH to sulfate formation increases from ~3% to ~20% (Dovrou et al., 2019b). 250 Data availability. The data used in this work are available upon request. Please email Eleni Dovrou (dovrouel@gmail.com) Supplement. Supplemental information is available at xx.