The synthesis of αpOS-249 was through the monosulfation of α-pinene diol with sulfur trioxide-pyridine complex directly (Wang et al., 2017). The purity of αpOS-249 was higher than 99 % based on nuclear magnetic resonance (NMR) spectra. Pure standard was stored in a freezer at -20 °C prior to the experiments. The experimental overview and conditions of aqueous-phase ^⚫OH oxidation of αpOS-249 were summarized in Scheme S1 and Table S2, respectively. The experiments included kinetic experiments (αpOS-249 + reference compound (i.e., benzonic acid (BA)) +⚫OH), product-capture experiments (αpOS-249 +⚫OH), and control experiments (αpOS-249 + UV light only and αpOS-249 + H₂O₂ only). All experiments were performed in a photoreactor with a volume of 150 mL (Witkowski and Gierczak, 2017; Witkowski et al., 2018; Witkowski et al., 2023; Witkowski et al., 2024). A quartz plate covered the top of the reactor and was sealed with flange clamps. The inner layer of the reactor held the reaction mixture, and circulating cooling water flowed through the outer layer to maintain a temperature of 298 ± 1 K, regulated by a refrigerated bath circulator (SD15R-30-A12E, PolyScience). The reaction mixture was continuously stirred with a magnetic stirrer to ensure homogeneity during the oxidation. A 300 W Xenon lamp (HSX-UV300, Beijing NBeT) equipped with a quartz UV filter maintained peak emission at 313 nm, which was used to generate ^⚫OH radicals through the photolysis of H₂O₂. The photoreactor was housed in a dark box to prevent interference from external light sources.

A typical kinetic experiment commenced (time zero) by activating the Xenon lamp to irradiate the reaction solution containing αpOS-249, BA, and H₂O₂. BA was added as a reference compound to track ^⚫OH. Under irradiation, a steady-state concentration of ^⚫OH ([^⚫OH]_ss) of around (4–9) × 10⁻¹⁴ mol L⁻¹was generated, as calculated from the simulations using a box model (Sect. S3) (Witkowski and Gierczak, 2017; Otto et al., 2019). This concentration is in good agreement with previously reported [^⚫OH]_ss levels in cloud and fog water (Choudhary et al., 2023). The reaction progress was monitored by sampling 1.5 mL aliquots from the reactor at regular time intervals over a total duration of 3 h (every 15 min in the initial hour and every 30 min in the subsequent two hours). Each sample was instantly mixed with 0.3 mL catalase solution (2 mg mL⁻¹) to decompose the residual H₂O₂ and stop further reactions (Witkowski and Gierczak, 2017; Witkowski et al., 2018). These samples were incubated at 298 K for 20 min and then filtered through a PTFE syringe filter (45 mm, 0.2 µm pore size, Pall Corporation) before subsequent chemical analysis. The pH values of the reaction mixtures were monitored using an electrochemical meter (Orion Versastar Pro, Thermo Scientific) pre-calibrated with pH buffer solutions. The procedure for product-capture experiments was the same as the kinetic experiments, except that BA was not added. Two sets of control experiments were conducted. One involved irradiating a solution of αpOS-249 alone to examine the effects of light only. The other set combined αpOS-249 and H₂O₂ in the dark to isolate the effects of H₂O₂.

The decay of αpOS-249 and BA upon oxidation was quantified by a UHPLC system (Dionex Ultimate 3000, Thermo Fisher Scientific) coupled with an Orbitrap mass spectrometer (IQ-X Tribrid, Thermo Fisher Scientific) employing calibration curves. The calibration curves were established using the synthesized αpOS-249 and commercially available BA as standards. The uncertainties in the measurements of αpOS-249 and BA were determined by the reproducibility of integrated peak areas across multiple measurements at the same concentration. In addition, reaction products (e.g., OS products) formed upon oxidation were detected by the same system. Experimental details can be found in previous publications (Brüggemann et al., 2019; Wang et al., 2022). Briefly, chromatographic separation was performed by an Acquity UPLC HSS T3 column (2.1 mm × 100 mm, 1.8 µm; Waters) with a gradient elution program as follow: mobile phase consisting of eluent A (H₂O with 0.1 % formic acid) and eluent B (acetonitrile with 0.1 % formic acid), at a flow rate of 0.3 mL min⁻¹. Eluent B was initially set at 5 % for 1.0 min, gradually increased to 99 % in 8.0 min, held at 99 % for 2.0 min, and then rapidly decreased back to 5 % within 0.1 min, and maintained at 5 % for the final 2.9 min, resulting in a total run time of 13.0 min. The injection volume was 3 µL. The Orbitrap MS detection was performed in negative electrospray ionization mode, under the following settings: spray voltage at 2300 V, sheath gas at 40 Arb, auxiliary gas at 10 Arb, sweep gas at 2 Arb, RF Lens of 30 %, ion transfer tube temperature of 300 °C, and the vaporizer temperature of 320 °C. The analysis began with a full MS scan. For MS/MS data acquisition, the MS was operated in data-dependent acquisition mode with stepped HCD collision energy of 15 %, 25 %, and 40 %. The intensity threshold for triggering MS/MS data acquisition was set at 1 × 10⁵. The MS resolution was configured to 120 000 and 30 000 for full MS scan and MS/MS scan, respectively. The m/z range for the full MS scan was 50–1200 and 50–500 for the MS/MS scan. The data were analyzed using Xcalibur (version 4.1) as well as the open-source software package MZmine 2.38, following the workflows and methods previously described (Brüggemann et al., 2019; Wang et al., 2022).

The formation of inorganic sulfates (HSO4- / SO42-) during the aqueous ^⚫OH oxidation of αpOS-249 was determined using ion chromatography (IC). The details have been given in previous studies (Xu et al., 2022; Lai et al., 2023). Briefly, the samples were analyzed with a Dionex ICS-1100 IC system (Thermo Fisher Scientific). Inorganic sulfate anions were separated using an IonPac AS11-HC analytical column (4 mm × 250 mm) and an IonPac AG11-HC guard column (4 mm × 50 mm). The IC system operated in negative mode with 15 mmol L⁻¹ NaOH as the eluent at a flow rate of 0.8 mL min⁻¹. Moreover, the concentration of SO42- anions quantified by IC represents the total amount of HSO4- and SO42- (Xu et al., 2022; Lai et al., 2023). In this work, the quantity of inorganic sulfates was measured based on its peak area in the chromatogram and quantified using a calibration curve based on Na₂SO₄ standard, with a retention time (RT) of 4.0 min. The uncertainty of inorganic sulfate measurements was found to be 2.5 % from repeated measurements.

Control experiments were conducted to account for any non ^⚫OH losses, including αpOS-249 photolysis due to UV radiation alone and the reaction of αpOS-249 with H₂O₂ in the absence of light (Sect. S4). Figure S1 reveals that αpOS-249 neither photolyzes nor reacts with H₂O₂ unless light is present to generate ^⚫OH. Furthermore, as discussed in Sect. S5, the aqueous-phase ^⚫OH oxidation kinetics of αpOS-249 is likely insensitive to solution pH under typical atmospheric conditions.

Relative rate method was adopted to determine the second-order rate constants for ^⚫OH oxidation of αpOS-249 (kOS) by comparing the measured rate constants to that of a reference compound (BA) with a well-known ^⚫OH reaction rate of kRef= (5.5 ± 0.3) × 10⁹ L mol⁻¹ s⁻¹ at a solution pH of 4.5 (Hems and Abbatt, 2018), a condition that is the same as our experiments (Sect. S5). In the reaction mixture, ^⚫OH reacts with both αpOS-249 (Reaction R1) and BA (Reaction R2) as described in the reactions shown below (Hems and Abbatt, 2018). The second-order rate constants for the ^⚫OH oxidation of αpOS-249 (kOS) were calculated using Eq. (1), where [αpOS-249] and [BA] are the concentrations of αpOS-249 and BA, respectively, at the initial (time = 0) and intermediate (time =t) time: R1⚫OH+αpOS-249⟶kOSproductsR2⚫OH+BA⟶kRefproducts 1ln[αpOS-249]0[αpOS-249]t=kOSkRefln[BA]0[BA]t

Figure 1a illustrates the relative kinetic plot, yielding a kOS value of (2.2 ± 0.2) × 10⁹ L mol⁻¹ s⁻¹ at 298 K. The uncertainty of kOS was calculated by propagating the two standard deviations (2σ) from multiple experiments, the reported uncertainty of the rate constant for the reference compound, and the uncertainties from measurements of αpOS-249 and BA (Witkowski and Gierczak, 2017). The rate constant is compared with that predicted by the structure-activity relationship (SAR) model which has been widely used to estimate the reactivity of various organic compounds towards ^⚫OH radicals in aqueous phase (Monod and Doussin, 2008; Doussin and Monod, 2013). Our recent laboratory work revealed the strong deactivating effect of the sulfate group (-OSO3-) on aqueous-phase ^⚫OH radicals oxidation kinetics, and extended the SAR model to include OSs (Lai et al., 2024), by introducing new interaction parameters for the -OSO3- group (F (α-position) = 0.22 and G(β-position) = 0.44). Here, we predicted the second-order rate constant for the aqueous-phase ^⚫OH oxidation of αpOS-249 to be 3.1 × 10⁹ L mol⁻¹ s⁻¹ (Sect. S6 and Fig. S2 in the Supplement), which is higher than our measured value of (2.2 ± 0.2) × 10⁹ L mol⁻¹ s⁻¹. This difference is within an acceptable range when considering the performance of the SAR model (58 % of simulated rates within ± 20 % and 76 % within ± 40 % of experimental data) (Monod and Doussin, 2008; Doussin and Monod, 2013). This suggests that the SAR model is a valuable tool for predicting the aqueous-phase ^⚫OH oxidation rate constants of a variety of atmospheric OSs.

We also assessed the significance of aqueous-phase ^⚫OH oxidation in its atmospheric fate by estimating the atmospheric lifetimes (Fig. 1b), τ=1/(kOS × [^⚫OH]) (Wen et al., 2021). The estimated lifetimes based on the newly obtained experimental data varied from approximately 3 min in remote aerosol conditions ([^⚫OH] = 3 × 10⁻¹² mol L⁻¹) to about 2 d in urban cloud conditions ([^⚫OH] = 3.5 × 10⁻¹⁵ mol L⁻¹) (Herrmann et al., 2010). In addition, using SAR predictions with higher rate constant yield shorter lifetimes, ranging from about 2 min in remote aerosol conditions to about 1 d in urban cloud conditions. Given these relatively short atmospheric lifetimes, the aqueous-phase ^⚫OH oxidation could likely serve as a significant transformation pathway for αpOS-249.

Figure S3 shows the total ion chromatograms (TICs) obtained from the product-capture experiments. Before oxidation (Fig. S3a, t0), a dominant peak corresponding to the [M–H]⁻ ion of αpOS-249 (m/z=249.08, C₁₀H₁₇O₅S⁻) is observed at a retention time (RT) of 4.7 min. After 45 min of ^⚫OH oxidation (Fig. S3b, t45), the intensity of αpOS-249 significantly decreases, accompanied by the emergence of new product peaks with low intensities. After 3 h of oxidation (Fig. S3c, t180), αpOS-249 is almost completely consumed. Notably, some new product peaks observed at t45 exhibit a declining trend, suggesting their susceptibility to ^⚫OH oxidation. A number of new OS products were detected based on two primary criteria: (i) their absence prior to oxidation (t0), and ii) the presence of fragmentation patterns in their MS² spectra, primarily showing the bisulfate anion (HSO4-, m/z=96.96), and often accompanied by other sulfur-containing ions such as the sulfite ion radical (SO3⚫-, m/z=79.96), and bisulfite anion (HSO3-, m/z=80.97) (Surratt et al., 2008; Huang et al., 2018; Xu et al., 2022). These identified OS products were summarized in Table S5 and were grouped into two categories: more oxygenated C₁₀ OS products, formed through functionalization processes via the addition of oxygenated functional groups, and smaller OS (< C₁₀) products, which result from fragmentation processes.

Figure 2a shows the time-dependent evolution of intensities for more oxygenated C₁₀ OS products from different generations. These products were grouped according to the number of added oxygen atoms (e.g., +1× O, +2 × O, etc). The highest intensity of first-generation products (+1 × O) peaked at 45 mins into the reaction, followed by a noticeable decrease, while the second-generation products (+2× O) showed a gradual increase, lagged their peak at 90 min before gradually declining. Third (+ 3 × O) and fourth-generation (+4 × O) products followed a similar pattern, with a relatively lower intensity compared to the first and second-generation products. They showed a slow increase, peaking at 120 min with a minimal decrease. Additionally, fifth-generation (+5 × O) products had even lower intensity, peaking at 150 min, while sixth-generation (+6 × O) products showed the lowest intensity and a continued slow increasing trend. This evolution pattern can be well described as multi-generation sequential oxygenation processes (Kroll et al., 2015).

The intensities of smaller OS (< C₁₀) products are categorized by their carbon atoms (e.g., C₉, C₈, C₇ etc), and their time-dependent evolutions are shown in Fig. 2b. C₉ OS products show the highest intensity, peaking at 120 min before a slight decrease. Meanwhile, C₇ OS products show the second highest intensity, but significantly lower than C₉ OS products, displaying a consistent upward trend. The other OS groups all demonstrate a continued increasing trend with low intensities. Unlike more oxygenated C₁₀ OS products, the evolution of smaller OS products always keep increasing with reaction time, suggesting that fragmentation likely begins to gain increased significance as oxidation proceeds.

Figure 2c shows the variation in absolute intensity of αpOS-249 and its oxidation products with different carbon atoms before (t0) and after (t45 and t180) oxidation. The total intensity of C₁₀ OS products initially exhibits a significant increase followed by a decline. Meanwhile, the intensity of smaller OS (< C₁₀) products steadily increases throughout the reaction. This implies that functionalization processes likely dominate over the fragmentation processes in the early oxidation stages (e.g., within the initial hour). However, as oxidation proceeds, fragmentation processes begin to gain comparable significance (Fig. S4). It is important to note that this simple comparison assumes that OS products have the same ionization efficiency as αpOS-249. However, differences in ionization efficiency among OS products relative to the parent OS are not well understood. As a result, the findings from this simple analysis should be interpreted with caution. Authentic standards are important for accurately quantifying more oxygenated C₁₀ OS products and smaller OS products. In the absence of these standards, quantification becomes challenging, and both overestimation and underestimation are possible depending on the specific molecular structures involved. Furthermore, this observed trend agrees with the hypothesis that as oxidation continues, the addition of functional groups to the parent compound increases, leading to a higher probability of alkoxy radicals' formation with functional groups on the β-carbon (Kroll et al., 2011; Kessler et al., 2012; Lambe et al., 2012; Wiegel et al., 2015; Hems and Abbatt, 2018; Jiang et al., 2023). This, in turn, enhances the fragmentation processes, as the addition of oxygenated functional groups on the β-carbon plays an activating role and reduces the energy barrier for decomposition (Wiegel et al., 2015). Furthermore, other factors such as higher O/C ratios and increased polarity can enhance the alkoxy decomposition, thereby favoring the fragmentation process at later stages of oxidation (Wiegel et al., 2015).

Upon oxidation, the ^⚫OH radical can initially attack different reaction sites. Table S4 and Fig. S2 show the partial rate constants for hydrogen abstraction at various reaction sites, as derived from the SAR model. The model predicts that the relative reactivity ranges from 2.3 % at 5-C to 21.2 % at 3-C. ^⚫OH radicals do not exhibit an overall strong preference for specific carbon types (primary carbons: 34.8 %, secondary carbons: 29.7 %, and tertiary carbons: 32.6 %) (Table S4). For simplicity and clarity, we proposed the mechanisms involving the three types of carbon atoms with the highest predicted partial rate constants in Scheme 1. A generic reaction scheme outlining the formation of the identified OS products was shown in Scheme S2, based on well-established reaction pathways reported in the literatures (Russell, 1957; Bennett and Summers, 1974; Hearn et al., 2007; Smith et al., 2009; George and Abbatt, 2010; Kroll et al., 2015).