Quantifying SO₂ oxidation pathways to atmospheric sulfate using stable sulfur and oxygen isotopes: laboratory simulation and field observation

The formation of secondary sulfate in the atmosphere remains controversial, and it is an urgent need to seek a new method to quantify different sulfate formation pathways. Thus, SO₂ and PM_2.5 samples were collected from 4 to 22 December 2019 in the Nanjing region. Sulfur and oxygen isotopic compositions were synchronously measured to study the contribution of SO₂ homogeneous and heterogeneous oxidation to sulfate. Meanwhile, the correlation of δ¹⁸O values between H₂O and sulfate from SO₂ oxidation by H₂O₂ and Fe³⁺ $/$ O₂ was simulatively investigated in the laboratory. Based on isotope mass equilibrium equations, the ratios of different SO₂ oxidation pathways were quantified. The results showed that secondary sulfate constituted higher than 80 % of total sulfate in PM_2.5 during the sampling period. Laboratory simulation experiments indicated that the δ¹⁸O value of sulfate was linearly dependent on the δ¹⁸O value of water, and the slopes of linear curves for SO₂ oxidation by H₂O₂ and Fe³⁺ $/$ O₂ were 0.43 and 0.65, respectively. The secondary sulfate in PM_2.5 was mainly ascribed to SO₂ homogeneous oxidation by OH radicals and heterogeneous oxidation by H₂O₂ and Fe³⁺ $/$ O₂. SO₂ heterogeneous oxidation was generally dominant during sulfate formation, and SO₂ oxidation by H₂O₂ predominated in SO₂ heterogeneous oxidation reactions, with an average ratio around 54.6 %. This study provided an insight into precisely evaluating sulfate formation by combining stable sulfur and oxygen isotopes.

1 Introduction

Sulfate is one of the prevalent components of PM_2.5 (Brüggemann et al., 2021; Huang et al., 2014; Yang et al., 2023). Sulfate makes up approximately 25 % of PM_2.5 mass in Shanghai, 23 % in Guangzhou, and 10 %–33 % in Beijing (Xue et al., 2016). The rapid sulfate formation is a crucial factor determining the explosive growth of fine particles and the frequent occurrence of severe haze events in China (Lin et al., 2022; Y. Y. Liu et al., 2020; Meng et al., 2023; Wang et al., 2021; Zhang et al., 2018). Sulfate plays an important role in the chemical and physical processes in the troposphere and lower stratosphere, and it significantly affects global climate change by scattering solar radiation and acting as cloud condensation nuclei (Gao et al., 2022; Ramanathan et al., 2001). Meanwhile, sulfate exerts a significant influence on air quality and public health (Abbatt et al., 2006).

In the past decades, numerous attempts have been made to evaluate SO₂ oxidation pathways that are involved in homogeneous and heterogeneous reactions. Traditionally, sulfate formation mechanisms mainly include SO₂ homogeneous oxidation by OH radicals and heterogeneous oxidation by H₂O₂, O₃, and O₂ catalysed by transition metal ions (TMIs) in cloud/fog water droplets. The relative importance of different sulfate formation pathways is strongly dependent on oxidant concentrations, the occurrence of fog/cloud events, and the pH of the aqueous phase (Kuang et al., 2022; Oh et al., 2023). Generally, SO₂ homogeneous oxidation by OH radicals and heterogeneous oxidation by H₂O₂ are considered the most important pathways for sulfate production on the global scale (Seinfeld and Pandis, 1998). The photochemical reactivity during the winter in Beijing has been found to be relatively high, which favours the formation of reactive species such as OH radicals and H₂O₂, thereby facilitating SO₂ oxidation (Zhang et al., 2020). Xue et al. (2014) suggested that SO₂ oxidation by O₃ and H₂O₂ in the aqueous phase contributed to the majority of total sulfate production. T. Liu et al. (2020) proposed that S(IV) oxidation by H₂O₂ in aerosol water could be an important pathway that considers the ionic strength effect. He et al. (2018) found that the contribution of SO₂ oxidation by H₂O₂ could reach 88 % during the haze period in Beijing. Ye et al. (2018) observed that the SO₂ oxidation rate by H₂O₂ was 2–5 times faster than the summed rate of the other three oxidation pathways. As a result, the actual contribution of SO₂ oxidation by H₂O₂ during the winter might be underestimated in the previous studies.

In addition, the presence of NO₂ is obviously favourable for SO₂ oxidation under the conditions of high relative humidity (RH) and NH₃. NH₃ can promote the hydrolysis of NO₂ dimers to HONO and result in more sulfate formation on the particle surface in humid conditions (He et al., 2021). However, this conclusion was doubted by Liu et al. (2017), who believed that the reaction on actual fine particles with the pH at 4.2 was too slow to account for sulfate formation. Li et al. (2020) deemed that SO₂ oxidation by NO₂ might not be a major oxidation pathway in China. Furthermore, a GEOS-Chem modelling study suggested that NO₂ oxidation contributed less than 2 % of total sulfate production. It is found that the TMI pathway was very important in highly polluted regions, and the contribution of metal-catalysed SO₂ oxidation to sulfate was as high as 49 ± 10 % in haze. Wang et al. (2021) also argued that SO₂ oxidation via TMIs on the aerosol surface could be the dominant sulfate formation pathway. They found that manganese-catalysed oxidation of SO₂ contributed 69.2 ± 5.0 % of sulfate production. Overall, the mechanisms for sulfate rapid growth remain unclear and controversial. Therefore, sulfate formation pathways need to be further explored, and it is urgent that a new method to quantify different sulfate formation processes is developed.

Generally, sulfur isotopes allow for investigating SO₂ oxidation processes in the atmosphere because of distinctive isotope fractionation associated with different oxidation reactions (Harris et al., 2013). Harris et al. (2012) presented the respective sulfur isotope fractionation factors of SO₂ oxidation by OH radicals, O₃ $/$ H₂O₂, and iron catalysis. In addition, the observed sulfur isotope fractionation of SO₂ oxidation by H₂O₂ and O₃ appeared to have no significant difference. Therefore, the results were particularly useful to determine the importance of transition metal-catalysed oxidation pathway compared to other oxidation pathways. However, other main SO₂ oxidation pathways could not be distinguished only based on stable sulfur isotope determination.

The oxygen isotope ratio (δ¹⁸O) can be used to deduce sulfate formation processes due to those SO₂ oxidation pathways affecting oxygen isotopes of the sulfate product differently. In particular, mass-independent fractionation signals of oxygen isotopes (nonzero Δ¹⁷O, where Δ¹⁷O =δ¹⁸O $-\mathrm{0.52}\times {\mathit{\delta }}^{\mathrm{17}}$O) in sulfate are usually adopted to investigate the contribution of different SO₂ oxidation pathways. This method can identify the contribution of SO₂+O₃ pathway when a high Δ¹⁷O value (> 3 ‰) is measured in sulfate. However, there is obvious uncertainty when interpreting the sulfate with a low Δ¹⁷O value (< 1 ‰). Unfortunately, most sulfate samples in the atmosphere present Δ¹⁷O< 1 ‰, suggesting a limited contribution of the SO₂+O₃ pathway during sulfate formation. It is noteworthy that the contribution of SO₂+ H₂O₂ and TMI pathway is unclear if solely using Δ¹⁷O (Li et al., 2020). Holt and Kumar (1984) found that the use of oxygen isotopes was a valuable and complementary method to determine probable mechanisms of SO₂ oxidation to sulfate in the atmosphere. This provides us an insight into precisely evaluating sulfate formation pathways by combining oxygen and sulfur isotopes.

In this contribution, PM_2.5 and SO₂ were sampled from 4 to 22 December 2019 in Nanjing. Sulfur and oxygen isotopic compositions were measured to study the contribution of SO₂ homogeneous and heterogeneous oxidation during sulfate formation. In addition, the linear relationships of δ¹⁸O values between H₂O and sulfate from SO₂ oxidation by H₂O₂ and Fe³⁺ $/$ O₂ were synchronously investigated in the laboratory. Based on sulfur and oxygen isotope mass equilibrium equations, the ratios of different SO₂ oxidation pathways during the sampling period were calculated. The study aims to seek a novel method to quantify different SO₂ oxidation processes with sulfur and oxygen isotopes.

2 Materials and methods

2.1 Sampling location

PM_2.5 and SO₂ in the atmosphere were sampled from 4 to 22 December 2019 in Nanjing, China. The sampling site was located on the roof of the library of Nanjing University of Information Science and Technology (NUIST; 32.1^∘ N, 118.5^∘ E), which is depicted in Fig. 1. The sampling location is on the side of Ningliu Road and close to Nanjing chemical industry park. There are some large-scale chemical enterprises present such as Nanjing steel plant, Nanjing thermal power plants, and Nanjing petrochemical company, which inevitably release lots of SO₂ and iron metal into the atmosphere.

Figure 1 Sampling site of NUIST in Nanjing, China. NSP: Nanjing steel plant. NTPP: Nanjing thermal power plants. NPC: Nanjing petrochemical company. NR: Ningliu Road.

2.2 PM_2.5 and SO₂ samples collection

PM_2.5 and SO₂ were sampled using a modified JCH-1000 sampler (Juchuang Co., Qingdao) with a flow rate of 1.05 m³ min⁻¹ from 08:00 to 20:00 from 4 to 22 December 2019. PM_2.5 and SO₂ were collected with a quartz filter (203 × 254 mm, Munktell, Sweden) and a glass fibre filter (203 × 254 mm, Tisch Environment INC, USA), respectively. The filters were incinerated in a muffle furnace at 450 ^∘C for 2 h and then preserved in the desiccators at room temperature. The glass fibre filters were firstly soaked in 2 % K₂CO₃ and 2 % glycerol solution for 2 h and dried in a DGG-9070A electric oven. SO₂ can be changed into sulfite immediately during the sampling.

2.3 Extractions of water-soluble sulfate

PM_2.5 sample filters were shredded and soaked in 400 mL of Milli-Q (18 MΩ) water for extractions of water-soluble sulfate. Filters were then isolated from solutions by centrifugation, and sulfate was precipitated as BaSO₄ by adding 1 mol L⁻¹ BaCl₂. After the filtration with 0.22 µm acetate membrane, BaSO₄ precipitate was rinsed with Milli-Q water to remove Cl⁻. Finally, BaSO₄ powers were calcined at 800 ^∘C for 2 h to obtain high-purity BaSO₄. In addition, a small amount of H₂O₂ solution was added to oxidize sulfite to sulfate.

2.4 Laboratory simulation of SO₂ oxidation by H₂O₂ and Fe³⁺ $/$ O₂

For SO₂ oxidation by H₂O₂, 30 mL min⁻¹ Ar was firstly introduced into three kinds of different water for about 30 min to drive out air. Sulfate was produced by adding 10 mL H₂O₂ dilute solution (0.1 mL 30 % H₂O₂ in 50 mL water) to SO₂ in the reaction chamber at 10 ^∘C. H₂O₂ solution was agitated vigorously for 1 min before admission of air. For SO₂ oxidation by Fe³⁺ $/$ O₂, 2 mL min⁻¹ SO₂ and 2 mL min⁻¹ O₂ were simultaneously put into the Fe³⁺ dilute solution at 10 ^∘C. Then, 10 mL 1 mL min⁻¹ BaCl₂ was added to prepare BaSO₄. Oxygen isotopic compositions of product sulfate and three kinds of water were measured to study their linear relationships.

2.5 Sulfur and oxygen isotope determination

Sulfur isotopic compositions in sulfate were analysed using an elemental analyser (EA; Flash 2000, Thermo) and isotope mass spectrometer (IRMS; Delta V Plus, Finningan). High-purity BaSO₄ was converted into SO₂ in EA in the presence of Cu₂O. SO₂ from EA was ionized, and the δ³⁴S value was measured using the IRMS. For the determination of δ¹⁸O, BaSO₄ pyrolysis was conducted in a graphite furnace at 1450 ^∘C, and the δ¹⁸O value was obtained in CO produced from the pyrolysis at continuous-flow mode. The results of δ³⁴S and δ¹⁸O were with respect to the international standards V-CDT and V-SMOW, and the accuracy was better than ± 0.2 ‰ and ± 0.3 ‰, respectively.

3 Results and discussion

3.1 Concentrations of PM_2.5, sulfate and SO₂

As described in Fig. 2, the mass concentrations of PM_2.5, SO${}_{\mathrm{4}}^{\mathrm{2}-}$, and SO₂ during the period from 4 to 22 December 2019 in NUIST changed from 28.1 to 67.0 µg m⁻³, 8.3 to 17.8 µg m⁻³, and 6.2 to 20.9 µg m⁻³, with an average and standard deviation at 45.7 ± 12.1, 12.7± 3.3 and 10.2 ± 4.4 µg m⁻³, respectively. It can be observed that PM_2.5 average concentration was about 1.3 times the First Grade National Ambient Air Quality Standard (35 µg m⁻³) and beyond the safety standard of the World Health Organization (10 µg m⁻³). The photochemical reactivity during the winter in Beijing has been found to be relatively high (Zhang et al., 2020), which facilitates the formation of some photooxidants. The relatively clean days during the sampling period indicate the importance of photoinduced oxidation of SO₂.

Figure 2 Variations in concentrations of PM_2.5, SO${}_{\mathrm{4}}^{\mathrm{2}-}$, and SO₂.

Meanwhile, the change trends of PM_2.5, SO${}_{\mathrm{4}}^{\mathrm{2}-}$, and SO₂ concentrations were found to be basically the same during the sampling period, indicating that sulfate was mainly from SO₂ oxidation. In particular, PM_2.5, SO${}_{\mathrm{4}}^{\mathrm{2}-}$, and SO₂ concentrations increased to the maximum values on 10 December. It is noted that NO₂ and CO concentrations were 85 and 1.60 µg m⁻³ on 10 December, which were also the maximum values during the sampling period. Based on the wind speed being lower than 3 m s⁻¹ and there being static weather during the sampling period, we believe that high CO concentration was mainly from local emissions. However, O₃ concentration on 10 December had a minimum value at 24 µg m⁻³, which preliminarily indicated that SO₂ oxidation by NO₂ might be a major pathway in sulfate formation. Previous studies showed that SO₂ oxidation by NO₂ in aerosol water dominated heterogeneous sulfate formation during wintertime at neutral aerosol pH (Wang et al., 2016; Cheng et al., 2016). However, subsequent studies showed that the calculated aerosol pH was in the range of 4.2–4.7, and the reactions between SO₂ and NO₂ during this pH range were too slow to produce sulfate. Considering low aerosol pH in the Nanjing region, we suggested that SO₂ oxidation by NO₂ was not a dominant pathway for sulfate formation during the sampling period.

In contrast, PM_2.5, SO${}_{\mathrm{4}}^{\mathrm{2}-}$, and SO₂ concentrations were observed to be at minimum values on 6 December. Similarly, NO₂ and CO concentrations were also at minimum values of 36 and 0.6 mg m⁻³, respectively. However, O₃ concentration on 6 December had a maximum value at 50 µg m⁻³. In addition, the rate of SO₂ oxidation with O₃ becomes fast only when pH > 5, and the reaction rate of SO₂ with O₃ is one-hundredth of that with H₂O₂ or TMIs when pH < 5. Therefore, pH values of actual fine particles at 4–5 in the Nanjing region could markedly restrain SO₂ oxidation by O₃. The lowest SO${}_{\mathrm{4}}^{\mathrm{2}-}$ concentration on 6 December further demonstrated that SO₂ oxidation by O₃ played an insignificant role in sulfate formation.

Generally, aqueous-phase oxidation is deemed to be a main process of sulfate formation in atmospheric environment. Shao et al. (2018) believed that heterogeneous sulfate production on aerosols occurred when RH was higher than 50 %. The RH values of the atmosphere ranging from 50.7 % to 88.9 % during the sampling period indicated that sulfate formation was closely related to SO₂ heterogeneous oxidation.

3.2 Sulfur isotopic compositions in sulfate and SO₂

It can be observed from Fig. 3 that the values of δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ were generally higher compared to those of δ³⁴S-SO₂ during the sampling period except on 16 December. The δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ values ranged from 3.1 ‰ to 4.7 ‰, with an average and standard deviation at 4.0 ± 0.6 ‰, while δ³⁴S-SO₂ values changed from −2.9 ‰ to 4.7 ‰, with an average and standard deviation at −0.2 ± 2.3 ‰. The discrepancy between the values of δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ and δ³⁴S-SO₂ was mainly related to the sulfur isotope fractionation effect during SO₂ oxidation to secondary sulfate.

Figure 3 Variations in sulfur isotopic compositions in sulfate and SO₂.

It is noteworthy that δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ values were similar to those in PM_2.5, with an average at 4.2 ‰ during the Youth Olympic Games in August 2014 in Nanjing (Guo et al., 2016). However, the average value of δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ during the sampling period was lower than 5.6 ‰ in Nanjing during a typical haze event from 21 December 2015 to 1 January 2016 (Guo et al., 2019). The higher δ³⁴S values of sulfate in haze were possibly ascribed to SO₂ heterogeneous oxidation, which typically enriched heavy sulfur isotope in sulfate. In this study, the average concentrations of PM_2.5 were 45.7 µg m⁻³, indicating a time interval that is not heavily polluted. In addition, the relatively high temperature during the sampling period was favourable for photochemical reactions and OH radicals' formation. As a result, the contribution of SO₂ homogenous oxidation increased during sulfate formation, which enriched light sulfur isotope compared to that in haze. Han et al. (2017) determined δ³⁴S values in Beijing PM_2.5, with an average at 6.0 ‰. It is observed that there was a regional difference in δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ values. The δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ value in Nanjing was generally lower than that in Beijing. The discrepancy of δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ value illustrated different sulfur sources and SO₂ oxidation pathways in these regions. In addition, δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ values presented a seasonal change. δ³⁴S values in Beijing aerosol sulfate varied from 3.4 ‰ to 7.0 ‰, with an average of 5.0 ‰ in summer, and from 7.1 ‰ to 11.3 ‰, with an average of 8.6 ‰ in winter. Generally, SO₂ homogeneous oxidation dominated in summer compared to that in winter due to strong solar irradiation (Han et al., 2016). SO₂ oxidation might lead to sulfur isotope fractionation, which was mainly attributed to equilibrium or kinetic discrimination between SO₂ and sulfate. The influence of different oxidants on sulfur isotope fractionation needed to be further investigated.

Figure 4 presents the relationship between the δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ value and atmospheric temperature during the sampling period. It can be observed that there was an obviously negative correlation. The higher temperature generally corresponded to the lower δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ value. This is mainly ascribed to the kinetic effect of sulfur isotope fractionation during SO₂ oxidation. At high temperature, more OH radicals were produced, and the contribution of SO₂ homogeneous oxidation increased. It is reported that sulfur isotope fractionation about SO₂ was −9 ‰ for homogeneous oxidation process (Tanaka et al., 1994). Therefore, a low δ³⁴S value in sulfate at high temperature was chiefly due to the elevated SO₂ homogeneous oxidation.

Figure 4 The correlation between δ³⁴S-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ values and atmospheric temperature.

3.3 Sulfur isotope fractionation during SO₂ oxidation

The secondary sulfate was generally from SO₂ homogeneous and heterogeneous oxidation (Seinfeld and Pandis, 1998). The homogeneous and heterogeneous oxidation of SO₂ might lead to sulfur isotope fractionation, which is described using the fractionation coefficient: (α)

$$\begin{array}{}\text{(1)}& \mathit{\alpha }={\displaystyle \frac{\frac{{{\mathit{\delta }}^{\mathrm{34}}\mathrm{S}}_{{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}}}{{\mathrm{10}}^{\mathrm{3}}}+\mathrm{1}}{\frac{{{\mathit{\delta }}^{\mathrm{34}}\mathrm{S}}_{{\mathrm{SO}}_{\mathrm{2}}}}{{\mathrm{10}}^{\mathrm{3}}}+\mathrm{1}}}.\end{array}$$

Sulfate enriched heavy sulfur isotope (α>1) during SO₂ heterogeneous oxidation for the presence of isotope equilibrium fractionation and kinetic fractionation. However, the light sulfur isotope enriched by sulfate (α<1) during SO₂ homogeneous oxidation due to this process was only related to kinetic fractionation. As described in Fig. 5, α values ranged from 0.9988 to 1.0201, indicating there was SO₂ homogeneous and heterogeneous oxidation during the sampling period. The α value was at a minimum of 0.9988 on 16 December, which showed SO₂ homogeneous oxidation played a crucial role.

Figure 5 Sulfur isotope fractionation coefficients during SO₂ oxidation.

It is reported that the sulfur isotope fractionation during SO₂ heterogeneous and homogeneous oxidation to sulfate was 16.5 ‰ and −9 ‰, respectively (Tanaka et al., 1994). Consequently, the contribution of SO₂ heterogeneous and homogeneous oxidation to sulfate could be calculated by sulfur isotope mass equilibrium in Eqs. (2) and (3).

$$\begin{array}{}\text{(2)}& {\displaystyle }{{\mathit{\delta }}^{\mathrm{34}}\mathrm{S}}_{{\mathrm{SO}}_{\mathrm{2}}}+\mathrm{16.5}x-\mathrm{9}y={{\mathit{\delta }}^{\mathrm{34}}\mathrm{S}}_{{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}}\text{(3)}& {\displaystyle }x+y=\mathrm{1},\end{array}$$

where x and y represent the contribution of SO₂ heterogeneous and homogeneous oxidation, respectively.

It is observed from Fig. 6 that most of the days (7 out of 11) had more than 50 % contributions from SO₂ heterogeneous oxidation, which indicated that SO₂ heterogeneous oxidation was generally dominant during sulfate formation. He et al. (2018) presented the observations of oxygen-17 excess of PM_2.5 sulfate collected in Beijing haze from October 2014 to January 2015 and found the contribution of heterogeneous sulfate production was about 41 %–54 % with a mean of 48 ± 5 %. The contribution of SO₂ heterogeneous oxidation reached a high level during 5–7 December and on 19 December, which was closely related to the temperature of the atmosphere. The low temperature of about 5 ^∘C during these days was favourable for SO₂ dissolution in water and further oxidized to sulfate. On 16 December, the contribution of SO₂ heterogeneous oxidation was at a minimum of 31.4 %. The highest temperature of 15 ^∘C on 16 December restrained SO₂ solubility in the aqueous solution and facilitated production of lots of gaseous oxidants such as OH radicals to promote SO₂ homogeneous oxidation.

Figure 6 The contributions of SO₂ heterogeneous and homogeneous oxidation to sulfate.

Overall, the temperature was an important factor in controlling SO₂ oxidation pathways. High temperature facilitated kinetic fractionation of sulfur isotope during SO₂ oxidation to sulfate, thereby decreasing the δ³⁴S value in sulfate. In addition, there was a lack of positive correlation between the contribution of SO₂ heterogeneous oxidation and O₃ or NO₂ concentration. This further demonstrated that SO₂ oxidation by O₃ and NO₂ was not an important pathway during the sampling period. Consequently, we mainly focused on SO₂ heterogeneous oxidation by H₂O₂ and Fe³⁺ $/$ O₂ in the following study.

3.4 The correlation of δ¹⁸O values between H₂O and SO${}_{\mathrm{4}}^{\mathrm{2}-}$ from SO₂ oxidation by H₂O₂ and Fe³⁺ $/$ O₂

It is known that SO₂ rapidly equilibrates with ambient water for very high molar ratios of H₂O to SO₂ in the atmosphere. As a result, the δ¹⁸O value of SO₂ is dynamically controlled by the δ¹⁸O value of water, and the δ¹⁸O value of SO₂ has no obvious effect on the δ¹⁸O value of sulfate produced from different oxidation pathways. Meanwhile, sulfate is very stable with respect to O atom exchange with ambient water. Consequently, δ¹⁸O can be adopted to distinguish SO₂ oxidation processes due to the δ¹⁸O value of product sulfate reflecting the distinctive signals of different oxidants.

We simulatively studied SO₂ heterogeneous oxidation by H₂O₂ and Fe³⁺ $/$ O₂ in the laboratory, which aims to clarify the relationship of δ¹⁸O values between product sulfate and three kinds of water at 10 ^∘C. It can be observed from Fig. 7 that the δ¹⁸O value of sulfate was linearly dependent on the δ¹⁸O value of water, and the slope of linear curve for H₂O₂ oxidation approximates a ratio of 0.43, indicating that the isotopy of about two of four oxygen atoms in sulfate was controlled by the δ¹⁸O value of water. The other two oxygen atoms were from H₂O₂ molecules, whose O–O bond remained intact during SO₂ oxidation. In addition, we noted from Fig. 7 that the slope of the linear curve for Fe³⁺ $/$ O₂ oxidation was about 0.65, which represented that the isotopy of about three of four oxygen atoms in sulfate was related to the δ¹⁸O value of water. A $\mathrm{3}/\mathrm{4}$ control of sulfate oxygens by water is also characteristic of heterogeneous oxidation mechanisms in which HSO${}_{\mathrm{3}}^{-}$ isotopically equilibrated with water prior to significant oxidation to SO${}_{\mathrm{4}}^{\mathrm{2}-}$. The other one oxygen atom in sulfate was from O₂. The higher slope suggested a higher dependence of the δ¹⁸O value of sulfate on the δ¹⁸O value of water during SO₂ heterogeneous oxidation by Fe³⁺ $/$ O₂. The discrepancy of the slopes for different SO₂ heterogeneous oxidation processes provides us with a potential method to distinguish SO₂ oxidation pathways.

Figure 7 The correlation of δ¹⁸O values between H₂O and sulfate from SO₂ oxidation by H₂O₂ and Fe³⁺ $/$ O₂, respectively.

3.5 δ¹⁸O-SO${}_{\mathrm{4}}^{\mathrm{2}-}$ values in PM_2.5 and SO₂ main oxidation pathways

As depicted in Fig. 8, δ¹⁸O values of sulfate in PM_2.5 ranged from 11.09 ‰ to 12.93 ‰, with an average and standard deviation of 12.35 ± 0.68 ‰. δ¹⁸O values of sulfate focused on a narrow scope, except those on 5 and 22 December. It should be pointed out that the δ¹⁸O value of secondary sulfate was a comprehensive result from different SO₂ oxidation processes. Sulfate in PM_2.5 usually consisted of primary sulfate and secondary sulfate. The δ¹⁸O value of primary sulfate is about 38 ‰ (Holt and Kumar, 1984), which is significantly higher than the values of secondary sulfate. The contribution of primary and secondary sulfate in the atmosphere can be calculated by the oxygen isotope mass equilibrium in Eq. (4) (Ben et al., 1982):

$$\begin{array}{}\text{(4)}& {{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{{\mathrm{PM}}_{\mathrm{2.5}}}={\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{\mathrm{PS}}\times \left(\mathrm{1}-f_{\mathrm{SS}}\right)+{\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{\mathrm{SS}}\times f_{\mathrm{SS}},\end{array}$$

where δ¹⁸O${}_{{\mathrm{PM}}_{\mathrm{2.5}}}$, δ¹⁸O_PS, and δ¹⁸O_SS mean δ¹⁸O values of PM_2.5, primary sulfate, and secondary sulfate, respectively, and f_SS is the contribution of secondary sulfate in PM_2.5.

Figure 8 δ¹⁸O values of sulfate in PM_2.5 during the sampling period.

It is noteworthy from Fig. 9 that there is a linear relationship between δ¹⁸O values in water and secondary sulfate from different SO₂ oxidation pathways, and this can be described by Eqs. (5)–(7), where the value of δ¹⁸O_water is about −6.2 ‰ in the Nanjing region. As discussed above, secondary sulfate was mainly ascribed to SO₂ homogeneous oxidation by OH radicals and heterogeneous oxidation by H₂O₂ and Fe³⁺ $/$ O₂. Therefore, the δ¹⁸O_SS value in Eq. (4) can be obtained based on Eqs. (5)–(7), respectively. As a result, the average contribution of primary and secondary sulfate in PM_2.5 is presented in Table 1. It can be observed that the majority of sulfate in PM_2.5 was secondary sulfate, which appears to constitute from 79.9 % to 86.2 % of total sulfate during the sampling period. It is admirable to quantitatively describe these formation pathways of secondary sulfate in PM_2.5.

$$\begin{array}{}\text{(5)}& {\displaystyle }\begin{array}{rl}{\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{\mathrm{SS}}& =\mathrm{0.69}\times {{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{\mathrm{water}}\\ & +\mathrm{9.5}\mathrm{‰}\left(\mathrm{OH}\right)\left(\text{Holt and Kumar, 1984}\right)\end{array}\text{(6)}& {\displaystyle }\begin{array}{rl}{\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{\mathrm{SS}}& =\mathrm{0.65}\times {{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{\mathrm{water}}\\ & +\mathrm{10.6}\mathrm{‰}\left({\mathrm{Fe}}^{\mathrm{3}+}/{\mathrm{O}}_{\mathrm{2}}\right)\left(\text{this study}\right)\end{array}\text{(7)}& {\displaystyle }\begin{array}{rl}{\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{\mathrm{SS}}& =\mathrm{0.43}\times {{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{\mathrm{water}}\\ & +\mathrm{12.5}\mathrm{‰}\left({\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}\right)\left(\text{this study}\right)\end{array}\end{array}$$

Figure 9 The correlation between δ¹⁸O values in water and sulfate in PM_2.5.

Table 1 The average contribution of primary sulfate and secondary sulfate in PM_2.5.

Table 2 The ratios of SO₂ different oxidation pathways to sulfate.

According to the percentages of SO₂ heterogeneous and homogeneous oxidation to sulfate in Fig. 6 and the average contributions of primary sulfate and secondary sulfate in PM_2.5 in Table 1, we can further calculate the ratios of different SO₂ oxidation pathways at 10 ^∘C via the oxygen isotope mass equilibrium in Eqs. (8)–(10), and the corresponding results are depicted in Table 2.

$$\begin{array}{}\text{(8)}& {\displaystyle }\begin{array}{rl}{\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{{\mathrm{PM}}_{\mathrm{2.5}}}& ={\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{\mathrm{PS}}\times f_{\mathrm{PS}}\\ & +({{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{\mathrm{SS}-\mathrm{OH}}\times f_{\mathrm{SS}-\mathrm{OH}}+{\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{\mathrm{SS}-{\mathrm{Fe}}_{\mathrm{3}}+/{\mathrm{O}}_{\mathrm{2}}}\\ & \times f_{\mathrm{SS}-{\mathrm{Fe}}_{\mathrm{3}}+/{\mathrm{O}}_{\mathrm{2}}}+{\mathit{\delta }}^{\mathrm{18}}{\mathrm{O}}_{\mathrm{SS}-{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}\\ & \times f_{\mathrm{SS}-{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}})\times f_{\mathrm{SS}}\end{array}\text{(9)}& {\displaystyle }{f}_{\mathrm{PS}}+f_{\mathrm{SS}}=\mathrm{1}\text{(10)}& {\displaystyle }{f}_{\mathrm{SS}-\mathrm{OH}}+f_{\mathrm{SS}-{\mathrm{Fe}}_{\mathrm{3}}+/{\mathrm{O}}_{\mathrm{2}}}+f_{\mathrm{SS}-{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}=\mathrm{1},\end{array}$$

where δ¹⁸O${}_{{\mathrm{PM}}_{\mathrm{2.5}}}$ and δ¹⁸O_PS are δ¹⁸O values of total sulfate and primary sulfate in PM_2.5; δ¹⁸O_SS−OH, δ¹⁸O${}_{\mathrm{SS}-{\mathrm{Fe}}_{\mathrm{3}}+/{\mathrm{O}}_{\mathrm{2}}}$ and δ¹⁸O${}_{\mathrm{SS}-{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ are δ¹⁸O values of secondary sulfate from SO₂ oxidation by OH radicals, Fe³⁺ $/$ O₂, and H₂O₂, respectively; f_PS and f_SS are the contribution of primary and secondary sulfate; and f_SS−OH, $f_{\mathrm{SS}-{\mathrm{Fe}}_{\mathrm{3}}+/{\mathrm{O}}_{\mathrm{2}}}$, and $f_{\mathrm{SS}-{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ are the ratios of secondary sulfate from SO₂ oxidation by OH radicals, Fe³⁺ $/$ O₂, and H₂O₂, respectively.

Unlike heavily polluted days with reduced solar irradiation, the photochemical reactivity can remain high in clean days during the observation period because of relatively intense solar irradiation. As a result, some photochemical reactive species such as OH radicals and H₂O₂ are deemed to be the major oxidants for sulfate formation. Generally, H₂O₂ production in the relatively clean atmosphere is ascribed to self-reaction of HO₂ radicals that mainly comes from the reactions of OH radicals with CO and volatile organic compounds. It is observed from Table 2 that the ratios of SO₂ oxidation by OH radicals ranged from 38 % to 68 %, with an average and standard deviation at 48 ± 9.7 %. The ratio reached the maximum of 68 % on 16 December, which is mainly ascribed to the highest temperature of 15 ^∘C during the sampling period. The photochemical reactions are favourable for producing more OH radicals. In contrast, the ratio of SO₂ oxidation by OH radicals decreased to the minimum of 38 % on 6 December due to the low temperature.

It is known that SO₂ oxidation by H₂O₂ and Fe³⁺ $/$ O₂ is the most important pathway during SO₂ heterogeneous oxidation. It can be observed from Table 2 that the percentage of sulfate from SO₂ oxidation by H₂O₂ in secondary sulfate from SO₂ heterogeneous oxidation changed from 38.7 % to 81.2 %, with an average and standard deviation at 54.6 ± 15.7 %, indicating that SO₂ oxidation by H₂O₂ predominated during SO₂ heterogeneous oxidation. In addition, there was an obviously positive correlation between the ratios of SO₂ oxidation by H₂O₂ and OH radicals, which was chiefly attributed to the photochemical reactions. The relatively strong solar irradiation on 16 December resulted in the maximum ratio of 81.2 % for H₂O₂ oxidation in SO₂ heterogeneous reactions. The sampling site is close to Nanjing steel plant. As companion emitters, Fe³⁺ is present in much higher concentrations than that in other areas. It is believed that SO₂ oxidation by O₂ in the presence of Fe³⁺ was not negligent in the areas where the concentrations of SO₂ and Fe³⁺ were high. This inevitably resulted in the high SO₂ oxidation ratio by Fe³⁺ $/$ O₂ in SO₂ heterogeneous oxidation processes.

4 Conclusions

There was no serious PM_2.5 pollution during the sampling period. The secondary sulfate constitutes from 79.9 % to 86.2 % of total sulfate in PM_2.5. SO₂ oxidation by O₃ and NO₂ played an insignificant role in sulfate formation. The secondary sulfate was mainly ascribed to SO₂ homogeneous oxidation by OH radicals and heterogeneous oxidation by H₂O₂ and Fe³⁺ $/$ O₂. Compared to homogeneous oxidation, SO₂ heterogeneous oxidation was generally dominant, with an average contribution of 51.6 %. SO₂ oxidation by H₂O₂ predominated in SO₂ heterogeneous oxidation reactions, the average ratio of which reached 54.6 %. Consequently, sulfur and oxygen isotopes can be used to gain an insight into sulfate formation. The determination of sulfur isotopic compositions in SO₂ and sulfate is advantageous in quantifying the contribution of SO₂ homogeneous and heterogeneous oxidation. Combining field observations of oxygen isotope in the atmosphere with the linear relationships of δ¹⁸O values between H₂O and sulfate from different SO₂ oxidation processes can obtain an increased understanding of specific sulfate formation pathways. This study is favourable for deeply investigating the sulfur cycle in the atmosphere.