Figure 2a and b shows the measured product evolution from Experiments 1 and 2a under dry conditions. A range of sulfur-containing products were measured in both the gas and aerosol phases, shown as stacked colored traces. Changes in concentrations are given in parts per billion of sulfur (Δ ppb S) and are presented as a function of atmosphere-equivalent OH exposure time. Shown in grey is the amount of DMS oxidized over the course of the experiment. By the end of the experiment, only a fraction of the DMS had been consumed, since OH exposures were not high enough to fully deplete the DMS. In Exp. 1 (high-NO conditions, Fig. 2a), HONO was used as the OH precursor, and the NO was kept at ∼50 ppb by continuous addition, ensuring that the dominant fate of the RO2 radicals was reaction with NO (τbi<0.1 s). After ∼12 h of atmosphere-equivalent OH exposure, 104 % (100 %–124 %, 1σ) of the reacted sulfur was measured as products, indicating excellent sulfur closure. The uncertainty in sulfur closure includes uncertainty in both gas-phase and particle-phase measurements (see Supplement for more details). The initial dip in the first 2 h may be due to loss of products to surfaces such as the chamber wall or sampling lines. It is likely that there is an equilibrium between the sampling line and the gas phase. This drop, of 1–2 ppb S, represents a relatively small portion of the total sulfur reacted by the end of the experiment.

Major sulfur-containing products in Exp. 1 were SO2, particulate MSA, and particulate sulfate, with 48 % of the product sulfur found in the particle phase. The measured MSA : sulfate ratio (∼2.5:1) is in broad agreement with those reported in Chen et al. (2012). Minor species observed included dimethyl sulfoxide (DMSO), C2H6SO2 (likely dimethyl sulfone, DMSO2), and methane sulfinic acid (MSIA), known products from the addition channel, as well as CH2SO2 (likely a thioacid, which may be formed as an OH oxidation product of HPMTF, Jernigan et al., 2022a) and CH3SO6N (likely methanesulfonyl peroxynitrate, formed from CH3S(O)2OO + NO2). No HPMTF was observed in these experiments, which is expected given the short bimolecular RO2 lifetime.

In Exp. 2a (low-NO conditions, Fig. 2b), H2O2 was the OH precursor, and NO and HO2 levels were sufficiently low (∼10 and 100 ppt, respectively) enough for RO2 isomerization to dominate (τbi>10 s). HO2 generated from H2O2+ OH is expected to promote the formation of CH3SCH2OOH from Reaction (R2); however, we cannot distinguish CH3SCH2OOH from its isomer, DMSO2. Product distributions are dramatically different than those under high-NO conditions. The total sulfur products measured accounted for nearly all (90 % (64 %–118 %)) of the reacted DMS sulfur; this sulfur closure is good but slightly worse than in Exp. 1. The larger uncertainty range is due to the uncertainty of the HPMTF calibration in the I- CIMS. However, the near-sulfur closure, derived from multiple independently calibrated instruments, combined with the HPMTF yields (discussed in Sect. 3.3) suggest that our estimated sensitivity is reasonably accurate, and thus our overall uncertainty of total sulfur may be an overestimate.

Due to the long RO2 bimolecular lifetime (τbi>10 s), the dominant product is HPMTF from CH3SCH2OO isomerization; this accounts for about half of the reacted sulfur (60 % of the measured product sulfur). It is expected that a negligible amount (1 % or less) of HPMTF was lost to the chamber walls under the experimental condition here based on its estimated vapor pressure (see the Supplement). The time series of C2H4SO3-12C2 in the I- CIMS (C2H4SO3 ⚫ I-) and in the NH4+ CIMS (C2H4SO3 ⚫ NH4+), shown in Fig. S2, match very well. This indicates that there was negligible N2O5 formation from the residual NOx in the chamber, since N2O5 is not measurable by the NH4+ CIMS, and therefore our quantification of HPMTF-12C2 in Exp. 2a with I- CIMS is free of N2O5 interferences. Only 3.3 % (3.1 %–5.4 %) of the reacted sulfur was found in the aerosol by the end of the experiment.

The (near-)sulfur closure of the experiments, in which virtually all the reacted sulfur was measured as products, enables a comparison with the mechanistic model. MCM predictions for the two experiments described above (Exp. 1 and 2a) are shown in Fig. 2c and d; individual species are also compared in Figs. S3 and S4. Under high-NO conditions, measurements and model predictions (Figs. 2a and c, S3) agree well for gas-phase species and for total particulate sulfur. However, the two differ greatly in terms of particle-phase composition: AMS measurements indicate ∼70 % of the particle-phase sulfur is MSA, with the remainder as sulfate; by contrast, the model predicts that sulfate dominates, with a negligible (∼0.1 %) contribution from MSA. This suggests the mechanism may underestimate the rate of MSA formation (a result consistent with recent studies; Wolleson de Jonge et al., 2021; Shen et al., 2022) and/or overestimate the rate of sulfuric acid formation.

In the MCM, both MSA and sulfuric acid are formed from reactions of the CH3S(O)2O radical: R4CH3S(O)2O+HO2→CH3S(O)2OH+O2R5CH3S(O)2O+M→CH3+SO3. Reaction (R5) generates sulfur trioxide (SO3), which will quickly hydrolyze to form sulfuric acid. SO3 can also be formed by the OH oxidation of SO2, but this reaction would occur over 50 h of OH exposure, much longer than the oxidation timescale in Exp. 1. Since the measured and modeled total particulate sulfur (MSA + sulfate) agree well, the model–measurement differences in the ratio of MSA to sulfuric acid (or sulfate) may relate to the relative rates of these CH3S(O)2O reactions. It is possible that the rate constant of Reaction (R4) is underestimated in the mechanisms, but even if it is increased it to a gas-kinetic rate (3×10-10 cm3 molec.-1 s-1), MSA is still not predicted to dominate over sulfuric acid. Instead, the decomposition of CH3S(O)2O (Reaction R5), which has received little study, might be slower than the value used in the mechanism (∼0.09 s-1), leading to slower sulfuric acid formation. Alternatively, MSA might be formed by the reaction of CH3S(O)2O with species other than HO2, such as DMS or HCHO (Barnes et al., 2006; Yin et al., 1990). While such reactions are unlikely to be important in the atmosphere, they might occur in laboratory experiments, which have relatively high concentrations of organic species. However, the kinetics of such reactions are not well known and warrant future research.

Another potential source of MSA is the oxidation of MSIA by OH (Yin et al., 1990; Lucas and Prinn, 2002; von Glasow and Crutzen, 2004; Wollesen de Jonge et al., 2021; Shen et al., 2022). This pathway is currently not included in the MCM, which has MSIA reacting with OH to form SO2 and CH3 (Fig. 1). It has been suggested (Yin et al., 1990) that the reaction may occur via abstraction of the acidic hydrogen: R6CH3S(O)OH+OH→CH3S(O)O+H2O. As shown in Fig. 1, the resulting CH3S(O)O radical may react with ozone to form CH3S(O)2O, which can react further to form MSA or SO3 (Reactions R4–R5). However, inclusion of this reaction in the model increases MSA formation only slightly, and the model–measurement discrepancy remains large (Fig. S5). Alternatively, OH might add to MSIA (Lucas and Prinn, 2002; Arsene et al., 2002; Shen et al., 2022), forming the intermediate CH3SO(OH)2 that can react with O2 to produce MSA: R7CH3S(O)OH(MSIA)+OH→MCH3S(O)(OH)2R8CH3S(O)(OH)2+O2→CH3S(O)2(OH)+HO2. Including these reactions into the mechanism, using the rate constant for MSIA + OH suggested by the MCM (9×10-11 cm3 molec.-1 s-1) substantially increases the predicted MSA but at the same time decreases the predicted SO2 concentration, worsening the model–measurement agreement for SO2, and does not change predicted sulfate formation, leading to an overestimate in total aerosol production (Fig. S5). Taken together, while the OH oxidation of MSIA (Reactions R6–R8) may contribute to MSA formation, it appears not to be the only (or major) source for the MSA model–measurement discrepancy in the present experiments.

In the low-NO case (Figs. 2b and d, S4), measured and modeled concentrations also broadly agree. The predicted concentration of HPMTF is lower (by ∼30 %) than what was measured. This could be due to the uncertainty in the sensitivity of HPMTF in the I- CIMS and/or in the kisom value used in the model. The kisom value used, 0.09 s-1, is derived from our previous study (Ye et al., 2021); as discussed below, this value agrees with that determined in this work. Compared to measurements, the model also predicts somewhat higher concentrations of minor sulfur-containing products, such as DMSO, C2H6SO2 (DMSO2 + CH3SCH2OOH), MSIA, and MTF. This could be caused by overestimates of instruments' sensitivities, uncertainties in the rate constants in the model, or some losses to surfaces. Nevertheless, overall the model and measurements agree quite well, with product formation dominated by HPMTF and little aerosol formation since low-volatility species (MSA and sulfuric acid) are formed only as later-generation products.

The fate of the CH3SCH2OO radical, and hence the product distribution of DMS oxidation, relies critically on the isomerization rate constant of the CH3SCH2OO radical (kisom). In our previous work we determined kisom from a single reaction condition (at one value of τbi), and the kisom value had a large uncertainty due to the poorly constrained sensitivity of HPMTF in the CIMS. Here, we determine kisom by examining product formation at multiple values of τbi, similar to previous measurements of isomerization rates of terpene-derived RO2 radicals (Xu et al., 2019). MCM modeling suggests that RO2 + RO2 reactions represent ∼1 % of the RO2 sink in the experiments, and therefore the only bimolecular reactions considered are RO2 + NO and RO2 + HO2. HONO or NO was added to the chamber several times during the experiment (Fig. S6), perturbing the branching of the CH3SCH2OO radical (isomerization vs. bimolecular reactions). The total S measurements are shown in Fig. S8. The yield of HPMTF in the abstraction channel (Δ[HPMTF] / Δ[DMS]abs) was calculated for each perturbation as a function of τbi after taking into account the of loss via OH oxidation (kOH+HPMTF=2.1×10-11 cm3 molec.-1 s-1; see Sect. 3.4). The detailed calculation is described in the Supplement (Eqs. S1–S4). Figure 3a shows the HPMTF yield as a function of τbi. As expected, the yield increases dramatically with τbi, and fitting these data to Eq. S4 (given in the Supplement) enables the determination of kisom. The best-fit value for kisom is 0.13±0.03 s-1. The uncertainty is much smaller than in our previous determination (Ye et al., 2021) since the fit depends only on the shape (the inflection point) of the curve and not the absolute yield values and thus is insensitive to the uncertain HPMTF calibration factor. Nonetheless, since the asymptotic (high τbi) value is close to 1 (1.5), our estimated calibration factor appears to be reasonably accurate. The three data points with higher HPMTF yields (top of Fig. 3a) were collected in the latter half of the experiment, after HPMTF had built up in the chamber, and therefore correcting for OH loss resulted in an increased HPMTF yield. Because of their larger measurement uncertainties, these data points have smaller effects on the overall fit to Eq. (S4). If the OH loss is not included, kisom=0.11±0.02 s-1 (Fig. S7).

Figure 3b compares our value of kisom with previous measurements and theoretical determinations (T= 293–298 K) (Berndt et al., 2019; Jernigan et al., 2022a; Veres et al., 2020; Wu et al., 2015; Ye et al., 2021). Our measured value of kisom is consistent with our previous (single τbi) measurement (Ye et al., 2021) though with a much reduced uncertainty and is also in broad agreement with measured values from Berndt et al. (2019) (0.23±0.12 s-1) and Jernigan et al. (2022) (0.1±0.05 s-1).

Here we examine the oxidation of HPMTF and MTF, two species whose chemical fates are not well known. Both were formed only under low-NO conditions (Exp. 2a); because of the relatively low OH concentrations of that experiment, their concentrations increased throughout the entire experiment, with no subsequent decay. Thus, to estimate kOH+HPMTF and kOH+MTF, high concentrations of NO (∼70 ppb) were introduced at the end of Experiment 2 (denoted as Exp. 2b, shown in Fig. 4a). The large amount of NO essentially terminated the production of HPMTF and MTF and at the same time increased the OH concentration in the chamber. The total sulfur product distribution for Exp. 2 is shown in Fig. S9. The loss of HPMTF during this period, shown in Fig. 4b, is expected to be dominated by OH reaction because the high level of NO precluded substantial oxidation by O3 and NO3. Photolysis of HPMTF is also unlikely to contribute to the observed decay: by assuming that its photolytic cross sections are equal to the summed cross section of aldehydes and organic peroxides taken from MCM (Khan et al., 2021), we estimate that photolysis accounted for only 4 % of the HPMTF loss in our chamber. Using the cross section for MTF measured by Patroescu et al. (1996), we obtain an even lower photolysis rate, with photolysis accounting for less than 2 % of HPMTF loss in the chamber.

By calculating [OH] using the decay of DMS after the addition of NO, we fit the decay of HPMTF (Figs. 4b and S10) to derive kOH+HPMTF of 2.1 (2.0–2.2) ×10-11 cm3 molec.-1 s-1. This is in agreement with recent measurements of Jernigan et al. (2022) (1.4 (0.27–2.4) ×10-11 cm3 molec.-1 s-1); both experimental values are an order of magnitude higher than an earlier theoretical estimate of the rate (1.2×10-12 cm3 molec.-1 s-1) (Wu et al., 2015). Using this lower value, Khan et al. (2021) estimated that photolysis loss dominates HPMTF sink in the global marine sulfur budget, with OH oxidation only accounting for 10 % of HPMTF loss. This higher OH rate constant suggests that OH oxidation is in fact likely to be an important loss process for HPMTF, at least when liquid water is not present (Fung et al., 2022; Vermeuel et al., 2020; Novak et al., 2021).

MTF is formed predominantly as a second-generation DMS oxidation product from CH3SCH2OOH + OH in low-NO conditions in the mechanism. Using a similar method as kOH+HPMTF (Figs. 4b and S10), kOH+MTF is estimated to be 1.35 (1.3–1.4) ×10-11 cm3 molec.-1 s-1, which agrees with the only other measurement of kOH+MTF, 1.11±0.22×10-11 cm3 molec.-1 s-1, by Patroescu et al. (1996).

The experiments described above were carried out under dry conditions and thus focus only on homogenous gas-phase chemistry; in the atmosphere, heterogeneous and aqueous-phase processes may also be important contributors to DMS oxidation chemistry (Hoffmann et al., 2016). Thus, Experiments 4 and 5 were carried out at 65 % RH, under high- and low-NO levels, respectively. These experiments were carried out over longer timescales (higher OH exposures) than the corresponding dry experiments to better probe multi-generational product formation.

Results from Exp. 4 (in which 50–100 ppb NO was maintained in the chamber) are shown in Fig. 5a. The overall product distribution is similar to that under dry conditions (Fig. 2a), with SO2, MSA, and sulfate being the major reaction products. The modeled product distribution shown in Fig. S11a is largely the same as that in the dry experiment (Fig. 2c), as water does not play a role in the gas-phase oxidation mechanism shown in Fig. 1. Even though this experiment was carried out over longer timescales, the measured sulfur closure is quite good, 107 % (99 %–171 %) of the reacted DMS at the end of the experiment.

Figure 5c compares the evolving concentrations of major product species under high- and low-RH conditions, presented as change in product concentration relative to change in DMS concentration, over the initial OH exposure (corresponding to that of Exp. 1). Over these timescales, species such as DMSO, SO2, and MSA showed a relatively small effect of RH. By contrast, almost no C2H6SO2 (likely DMSO2) was measured in the gas phase under high-RH conditions. Within the timescale of the experiments, our measurements do not suggest conversion of MSA to sulfate in the aerosol phase, as predicted in some modeling studies (Fung et al., 2022; Chen et al., 2018). This difference may arise from low particle-phase OH concentrations in our experiments.

Figure 5b shows products from Exp. 5 (65% RH, low-NO conditions, τbi>1 s). As in the low-RH, long-τbi case (Exp. 2a, Fig. 2b), HPMTF and SO2 are the dominant measured products, and little aerosol formation is observed. One minor new product, with formula SO6, was detected in the I- CIMS in this experiment; it is likely an adduct (i.e., O3 ⚫ SO3 ⚫ I-) or a fragment formed in the instrument, but the parent species is unknown. In contrast to the high-NO experiment (Exp. 4), sulfur closure was markedly worse than under dry conditions. In the first 6 h of equivalent OH exposure (the timescale of the dry experiment), only 74 % (53 %–97%) of the reacted sulfur was detected as products. This sulfur closure degraded still further as the experiment proceeded and was only 23 % (18 %–31 %) at the end of the experiment. Here, I- CIMS sensitivities derived from the dry calibration were used for species quantification and therefore may underestimate the concentration under high-RH conditions (Lee et al., 2014; Veres et al., 2020). However, these differences would have to be dramatic (by factor of 5 or more) to account for all the reacted sulfur, and therefore such calibration errors are unlikely to explain the decreased sulfur closure.

Figure 5d shows differences for key product species formed in the long-τbi experiments under the high- and low-RH conditions, again over the timescales of the dry experiment (the first 6 h of equivalent OH exposure). Over these timescales, the initial yields of DMSO, C2H6SO2, and HPMTF are not substantially different in the humid and dry cases. SO2 concentrations were lower under humid conditions but with an absolute difference of only ∼2 ppb. Thus the production rates of these species are not affected dramatically by RH level. Instead the poor sulfur closure at high-RH conditions suggests that extra losses over longer timescales may be most likely by uptake to surfaces. The low aerosol concentration towards the end of the experiment (due to particle wall loss over the long experimental time, ∼17 h) could lead to substantial chamber wall loss of low-volatility products, which would contribute to this gap in measured sulfur. Such surface losses are likely exacerbated at high-RH conditions, due to uptake into the aqueous phase. The initial aerosol liquid water content (LWC) in the high-RH experiment was 10–100 µg m3, orders of magnitude lower than LWC in maritime clouds (Wallace and Hobbs, 2006). Therefore, such losses may play an even more important role in the real atmosphere. Indeed, studies have suggested that uptake to cloud water may be an important sink of gas-phase HPMTF. Using in situ measurements, Vermeuel et al. (2020) and Novak et al. (2021) have shown that HPMTF is lost to clouds and aerosols effectively in the marine boundary layer. Similarly, using a global model, Fung et al. (2022) found that including cloud uptake into a global model substantially decreases the global burden of HPMTF, by up to 86 %. This uptake of water-soluble intermediate species (e.g., MSIA, DMSO2, and HPMTF) into cloud droplets may then contribute to the condensed-phase production of MSA and sulfate (Hoffmann et al., 2021; Novak et al., 2021), but such processes are not accessed in the present chamber experiment.