Ammonium nitrate promotes sulfate formation through uptake kinetic regime

Although the anthropogenic emissions of SO2 have decreased significantly in China, the decrease in SO2− 4 in PM2.5 is much smaller than that of SO2. This implies an enhanced formation rate of SO2− 4 in the ambient air, and the mechanism is still under debate. This work investigated the formation mechanism of particulate sulfate based on statistical analysis of long-term observations in Shijiazhuang and Beijing supported with flow tube experiments. Our main finding was that the sulfur oxidation ratio (SOR) was exponentially correlated with ambient RH in Shijiazhuang (SOR= 0.15+0.0032×exp(RH/16.2)) and Beijing (SOR=−0.045+ 0.12× exp(RH/37.8)). In Shijiazhuang, the SOR is linearly correlated with the ratio of aerosol water content (AWC) in PM2.5 (SOR= 0.15+0.40×AWC/PM2.5). Our results suggest that uptake of SO2 instead of oxidation of S(IV) in the particle phase is the rate-determining step for sulfate formation. NH4NO3 plays an important role in the AWC and the change of particle state, which is a crucial factor determining the uptake kinetics of SO2 and the enhanced SOR during haze days. Our results show that NH3 significantly promoted the uptake of SO2 and subsequently the SOR, while NO2 had little influence on SO2 uptake and SOR in the presence of NH3.

the World Health Organization (WHO) (WHO, 2006). Haze events also occur with high frequency, especially, in autumn and winter.
Particulate SO 2− 4 can be formed through homogeneous oxidation of SO 2 by hydroxyl radicals (OH) and stabilized Criegee intermediates (SCIs) in the gas phase and subsequent uptake onto particles, while the OH pathway is the dominant gas-phase oxidation pathway (Seinfeld and Pandis, 2006;. Modeling studies greatly underestimated (∼ 54 %) SO 2− 4 concentration in serve pollution events in Beijing if only considering gas-phase oxidation of SO 2 , while the normalized mean bias (NMB) decreased significantly after heterogeneous oxidation of SO 2 being considered . Several heterogeneous and/or multiphase oxidation pathways, such as oxidation of SO 2 or sulfite by H 2 O 2 Maaß et al., 1999;Ye et al., 2021;Liu et al., 2021), HONO (J. F. , and O 3 (Maahs, 1983) or photochemical oxidation of SO 2 Xie et al., 2015), catalytic oxidation of SO 2 by transition metal ions (TMI) (Warneck, 2018;Martin and Good, 1991;Wang et al., 2021) and oxidation of SO 2 by NO 2 Clifton et al., 1988;Wang et al., 2016;Cheng et al., 2016;Wu et al., 2019;Spindler et al., 2003) in aqueous phase and heterogeneous oxidation of SO 2 on black carbon (Zhao et al., 2017;Zhang et al., 2020;Yao et al., 2020), have been proposed based on field measurements and laboratory and modeling studies. However, the relative contribution of these pathways to the SO 2− 4 production is still controversial. For example, the contribution of heterogeneous oxidation to SO 2− 4 production had been evaluated to be (48 ± 5) % based on oxygen iso-topic measurements , while it was 31 % even in the nighttime calculated by an observation-based modeling (OBM) (Xue et al., 2016). Gas-phase oxidation by OH could explain 33 %-36 % of SO 2− 4 production in the Beijing-Tianjin-Hebei region (L. , while it was negligible based on isotopic measurements  and OBM simulations (Xue et al., 2016). As for the oxidation of S(IV) species, which includes SO 2 , HSO − 3 and SO 2− 3 , in aqueous phase, oxidation by H 2 O 2 (T. Ye et al., 2021), NO 2 (J. F. Wang et al., 2016;Cheng et al., 2016), O 3 (Fang et al., 2019), or TMI (Mn 2+ )  was proposed as the most important pathway by different researchers. However, the relative importance of these oxidation paths varied greatly among different researches. For instance, TMI-catalyzed oxidation could explain ∼ 69 % of aqueous sulfate formation in North China Plain based on isotopic measurements and modeling (Shao et al., 2019), while oxidation by NO 2 or O 2 was the dominant oxidation path (66 %-73 %) based on isotopic measurements in another study . It should be noted that some reaction mechanisms mentioned above were proposed based on case studies in short-term observations. Thus, long-term observations at different environments are required to verify whether these mechanisms are statistically important. In addition, the previous studies mainly focused on oxidation process of SO 2 in particle phase, while it is unclear what are the controlling factors of the S(IV)-to-S(VI) conversion from the gas phase to the particle phase. In particular, it has been found that the mass fraction of NO − 3 and NH + 4 is increasing gradually (Lang et al., 2017;. This will modify its physical properties, such as morphology, phase-state and so on. The feedback between aerosol physics and aerosol chemistry is still poorly understood. In this work, 1-year field observations have been performed in Shijiazhuang and Beijing, synchronously. The formation mechanism of particulate sulfate has been statistically investigated to identify the controlling factors. The role of mass transfer of SO 2 and the oxidation of S(IV) in particle phase have been discussed based on flow tube experiments and field measurements. The conversion ratio of SO 2 to sulfate is statistically and linearly correlated to the aerosol water content (AWC), which is strongly modulated by particulate ammonium nitrate. The reaction kinetics and other factors affecting sulfate production have also been discussed. The BUCT station is on a rooftop of the main building (5 floors, ∼ 18 m above the surface), which is around 550 m from the 3rd Ring Road of Beijing. The distance between the two stations, which are the representative cities of Beijing-Tianjin-Hebei (BTH), is 260 km (Fig. S1). Both stations are surrounded by traffic and residential emissions, thus, are typical urban observation sites. The details about the observation stations have been described in our previous work (Y. Liu et al., 2020c, b, a). Ambient air was drawn from the roof of the corresponding building. At the SJZ station, the mass concentration of PM 2.5 was measured by a beta attenuation mass monitor (BAM-1020, Met One Instruments, USA) with a smart heater (model BX-830, Met One Instruments Inc., USA) to control the RH of the incoming air to 35 % and a PM 2.5 inlet (URG) to cut off the particles with diameter larger than 2.5 µm. Particle-phase total concentrations of iron and manganese were measured using a heavy-metal analyzer (EHM-X100, Skyray Instrument). Water-soluble ions (Na + , K + , Mg 2+ , Ca 2+ , NH + 4 , SO 2− 4 , Cl − and NO − 3 ) in PM 2.5 and gas pollutants (HCl, HONO, HNO 3 , SO 2 and NH 3 ) were measured using an analyzer for monitoring aerosols and gases (MARGA, ADI 2080, Applikon Analytical B.V., the Netherlands) with 1 h of time resolution. At the BUCT station, the mass concentration of PM 2.5 was the mean concentration obtained from four surrounding monitoring stations (including Wanliu, Gucheng, Wanshouxigong and Guanyuan) of China Environmental Monitoring Centre (http://www. cnemc.cn, last access: 31 December 2020). The chemical composition of PM 2.5 was measured using a time-of-flight aerosol chemical speciation monitor (ToF-ACSM, Aerodyne) after the ambient air went through a PM 2.5 inlet (URG) and a Nafion dryer (MD-700-24, Perma Pure). The configuration and the operation protocol of ToF-ACSM have been described in previous work (Fröhlich et al., 2013). The ionization efficiency (IE) calibration for ACSM was performed using 300 nm dry NH 4 NO 3 every month. Ambient air was drawn from the roof using a Teflon sampling tube (BMET-S, Beijing Saak-Mar Environmental Instrument Ltd.) with the residence time <10 s for gas-phase pollutant measurements. Trace gases including NO x , SO 2 , CO and O 3 were measured with the corresponding analyzer (Thermo Scientific, 42i, 43i, 48i and 49i) at both the SJZ and BUCT stations. Meteorological parameters including temperature, pressure, relative humidity (RH), wind speed and wind direction were measured using weather stations (WXT 520 at HAS/SJZ station and AWS 310 at AHL/BUCT station, Vaisala).

Uptake kinetics of SO 2 on dust internally mixed with NH 4 NO 3
To understand the influence of RH on uptake kinetics (γ SO 2 ), the γ SO 2 on dust internally mixed with NH 4 NO 3 was measured using a coated-wall flow tube reactor. The configuration of the reactor and data process protocol have been described in detail previously (Han et al., 2013;. The γ parameter, presenting the mass transfer kinetic of gas-phase SO 2 to particle phase, is defined by the net loss rate of SO 2 per collision onto the surface (Ravishankara, 1997;Usher et al., 2003), namely, where −dc/dt is the net loss rate of SO 2 when the surface is exposed to SO 2 (molecules s −1 ); ω is the collision frequency (s −1 ); k obs , r tube , and < c > are the first-order rate constant of SO 2 , the flow tube radius, and the average molecular velocity of SO 2 , respectively. A correction for gas-phase diffusion limitations was considered for γ obs calculations using the Cooney-Kim-Davis (CKD) method (Cooney et al., 1974;Murphy and Fahey, 1987). The Brunauer-Emmett-Teller (BET) uptake coefficient (γ SO 2 ,BET ) was obtained from the mass dependence of γ obs as follows (Han et al., 2013;: where [slope] is the slope of the plot of γ obs versus the sample mass in the linear regime (mg −1 ), A g is the inner surface area of the sample tube (cm 2 ) and S BET is the specific surface area of the particle sample (cm 2 mg −1 ). Similar to a previous work , dust internally mixed with NH 4 NO 3 was used in the kinetics study, because it was difficult to deposit enough real ambient particles onto the inner surface of the sample holder. Although the composition of the model particles is much simpler than that of ambient particles, it is still meaningful, because we mainly focused on the influence of RH or aerosol water content (AWC) on uptake kinetics of SO 2 . The mixture (mass ratio = 2 : 1) of A1 ultrafine test dust (Powder Technology Inc.) and NH 4 NO 3 (AR, Sinopharm Chemical Reagent Co. Ltd, China) were suspended in the mixture of ethanol and water (v : v = 1 : 3). The inner surface of the Pyrex quartz tube (sample holder) was uniformly coated by the above mixture and dried overnight in an oven at 393 K. The sample mass was calculated according to the weighted mass of the dry tube before and after coating. NH 4 NO 3 in the mixture was further confirmed using an ion chromatograph ( Metrohm 940, Applikon Analytical B.V., the Netherlands). Around 50 % of the NH 4 NO 3 remained in the mixture even after heating and potential evaporation. To avoid the wall loss of SO 2 on the sample holder, all the inner surface of the sample holder was covered with particles. The wall loss of SO 2 on the remained surface (the inner surface of the outside tube and the outside surface of the sample holder) was subtracted at a steady-state condition at the corresponding RH before the uptake experiment as done in our previous work . The mean concentrations of SO 2 , NO 2 and NH 3 were 8.3 ± 5.2 (0.4-49.1), 31.5 ± 13.2 (2.5-85.1) and 41.0 ± 18.4 (0.3-126.4) ppb, respectively, in polluted events (with the PM 2.5 concentration higher than 75 µg m −3 and the RH less than 90 %) in Shijiazhuang. The initial concentrations of SO 2 , NO 2 and NH 3 in the reactor were 190 ± 2.5, 100 ± 2.5 and 50 ± 2.5 ppb, respectively. The initial concentrations of NO 2 and NH 3 were close to their ambient concentrations, while a high initial SO 2 concentration was used here to obtain a good signal to noise ratio for γ SO 2 measurements. In this work, we aimed to understand the influence of AWC on the uptake kinetics of SO 2 . Therefore, we fixed the initial concentrations of pollutants and the temperature at 300 K. SO 2 and NO 2 were measured using the corresponding analyzer (Thermo 43i and 42i), and NH 3 was measured by an ammonia analyzer (EAA-22, LGR, USA). The specific surface area of the mixture of A1 dust and NH 4 NO 3 was 0.813 m 2 g −1 , measured by a nitrogen BET physisorption analyzer (Quantachrome Autosorb-1-C). RH from 0 to 80 % was adjusted by varying the ratio of dry to wet zero air (water bubbler) and measured by a RH sensor (HMP110, Humicap). Control experiments demonstrate that adsorption of SO 2 on the quartz tube is negligible. It should be noted that the wall loss of SO 2 in the presence of NH 3 and/or NO 2 would be larger in the absence of seed aerosols. Additional control experiments in the presence of NO 2 and NH 3 demonstrate that the contribution of wall loss of SO 2 should be less than 3 % to the measured γ .

Calculations of AWC, aerosol pH and production rates of sulfate in aerosol liquid water
The AWC and aerosol pH in Shijiazhuang were calculated using the ISORROPIA II model using the measured concentrations of SO 2− 4 , NH + 4 , NH 3 , NO − 3 , HNO 3 , Cl − , HCl, Na + , Ca 2+ , K + and Mg 2+ , as well as RH and temperature as input. The particles were assumed in metastable phase using a forward method (Song and Osada, 2020;Shi et al., 2019). The dataset with RH lower than 35 % was excluded (Pye et al., 2020) due to large uncertainties of aerosol pH (Ding et al., 2019;Guo et al., 2016;Pye et al., 2020). The pH was then calculated according to Pye et al. (2020) and Ding et al. (2019): where γ H + is the activity coefficient of H + , and m H + is the molality of H + . The deliquescence curves of inorganic salts were calculated at 298.5 K using the E-AIM model (Clegg et al., 1998). Then, the AWC attributed to individual salt was calculated with the mass of the salt and the mass-based growth factor at the corresponding RH. The AWC of model particles for laboratory studies was also calculated with the known composition, while the aerosol pH values in Beijing were not calculated, because the concentrations of Na + , Ca 2+ , K + and Mg 2+ were unavailable. Similar to previous studies (P. Cheng et al., 2016), four oxidation pathways of S(IV) in aqueousphase were accounted for, i.e., oxidation by O 3 , H 2 O 2 , NO 2 and TMI (Fe 3+ and Mn 2+ ), according to the following equations (Seinfeld and Pandis, 2006;Cheng et al., 2016;: where   (Seinfeld and Pandis, 2006). H 2 O 2 concentrations were unavailable during our observations. It was fitted based on temperature like in previous work (Fang et al., 2019). Figure S2 shows the derived H 2 O 2 concentrations and the diurnal curves of H 2 O 2 in winter in Shijiazhuang. The H 2 O 2 concentrations varied from 0.05 to 3.7 ppbv, with a mean value of 0.62 ± 0.52 ppbv. Overall, the wintertime H 2 O 2 concentrations derived in this work are comparable with those reported in the literature (Ye et al., 2018). The concentrations of Fe 3+ and Mn 2+ were calculated according to the measured total Fe and Mn concentrations assuming 18 % of total Fe and 30 % of total Mn were soluble Cui et al., 2008) and the precipitation equilibriums of Fe(OH) 3 and Mn(OH) 2 depending on pH. The concentrations of Fe and Mn before December 2018 were estimated according to their mean ratios to PM 2.5 mass concentration , because the instrument was unavailable.

Results and discussion
3.1 Variation of sulfate in PM 2.5 Figure 1a shows the hourly mean mass concentration of PM 2.5 measured at SJZ and BUCT stations from 15 March 2018 to 15 April 2019. The mass concentration of PM 2.5 in Shijiazhuang generally coincided with that in Beijing. This highlights the regional characteristic of air pollution in BJH. However, Shijiazhuang usually showed significantly higher PM 2.5 concentration than that in Beijing. The hourly mean PM 2.5 concentration varied in the range of 0-650 µg m −3 with an annual mean concentration of 86.4 ± 77.8 µg m −3 . The corresponding values in Beijing were 1.5-556 and 55.0 ± 51.0 µg m −3 . Particularly, the wintertime mass concentration of PM 2.5 in Shijiazhuang was around 2.4 times as that in Beijing. This is consistent with previous results that Shijiazhuang is suffering from more serious air pollution (D. Chen et al., 2019b) because of its larger density of heavy industries and more intensive emissions than in Beijing (D. Chen et al., 2019a). Like the mass concentration of PM 2.5 , both the mass concentration ( Fig. 1b) and the fraction of sulfate in PM 2.5 (Fig. 1c) in Shijiazhuang were usually higher than those in Beijing. The annual mean sulfate concentrations in Shijiazhuang and Beijing were 11.7 ± 12.7 and 5.4 ± 6.9 µg m −3 , which annually contributed 15.3 ± 8.7 % and 10.7 ± 7.3 % to the PM 2.5 mass concentrations, respectively. However, the molar ratio of NO − 3 to SO 2− 4 (3.37 ± 3.05), corresponding to the mass ratio 2.17 ± 1.97 in Beijing was significantly higher than that in Shijiazhuang (2.69 ± 1.80, corresponding to mass ratio of 1.77 ± 1.72) at the 0.05 level. This is consistent with the emission inventories of air pollutants, in which Shijiazhuang had larger SO 2 emissions than Beijing, and vice versa for NO x emissions D. Chen et al., 2019a). A decrease of sulfate concentration (5.4 ± 6.9 µg m −3 ) in Beijing was significant even when compared with that in PM 1.0 (8.1 ± 8.3 µg m −3 ) measured from July 2011 to June 2012 , while the mass ratio of NO − 3 /SO 2− 4 (2.17 ± 1.97) in Beijing showed an obvious increase compared with those in 2011-2012 (1.3-1.8)  and 2008 (0.8-1.5) . This can be ascribed to the effective reduction of SO 2 emissions but less effective reduction of traffic emissions in Beijing.
The ground surface concentrations of pollutants are prone to be affected by variation of mixing layer height (MLH) Tang et al., 2016). Sulfur oxidation ratio (SOR), which is defined as the molar ratio of sulfate to total sulfur (Wang et al., 2005;Fang et al., 2019), was calculated and should be less affected by the MLH variation. As shown in Fig. 1e, the SOR in Beijing was overall higher than that in Shijiazhuang. Thus, the annual mean SOR in Beijing (0.42 ± 0.29) was comparable with that reported in literature (Fang et al., 2019), while it was significantly higher than that in Shijiazhuang (0.31 ± 0.19) at the 0.05 level. The high primary emissions of SO 2 in Shijiazhuang should lead to a lower SOR than that in Beijing. On the other hand, secondary transformation of SO 2 to sulfate should also have an influence on the SOR. The O x (O x = NO 2 +O 3 ) concentration in Shijiazhuang was usually higher than that in Beijing (Fig. 1f). The annual mean O x concentration in Shijiazhuang was 55.2 ± 22.3 ppb, which was significantly higher than that in Beijing (50.7 ± 21.5 ppb) at the 0.05 level. This is inconsistent with the observed higher SOR in Beijing if gas-phase oxidation mainly contributed to sulfate formation. These results suggest that heterogeneous and/or multiphase reactions may also play important roles in particulate sulfate formation during transport Martin and Good, 1991;Wu et al., 2019). Figure 2a-c show the mass concentration of PM 2.5 colored according to the mass concentration of sulfate, the fraction of sulfate in the soluble PM and the SOR in Shijiazhuang. In most serve pollution events, high PM 2.5 mass concentration coincided with the high sulfate concentration, the fraction of sulfate and the SOR (colored in grey color). For example, the mean PM 2.5 concentration was 411.7 ± 98.1 µg m −3 during the pollution event that occurred from 08:00 on 12 January 2019 to 00:00 on 15 January 2019 (All times in this paper are given in local time unless stated otherwise.). The corresponding sulfate concentration, fraction of sulfate in soluble PM and SOR were 80.6 ± 24.0 µg m −3 , 39.4 ± 3.6 % and 0.79 ± 0.09, respectively. Other pollution episodes, which were highlighted in grey color in Fig. 2, showed a similar trend. The variations of the sulfate concentration, the fraction of sulfate in nonrefractory PM 2.5 and the SOR with PM 2.5 mass concentration in Beijing were similar to Shijiazhuang and shown in Fig. S3. These results confirm that the conversion rate of SO 2 to sulfate is promoted in pollution days when compared with that in clean days.

Role of aerosol water content in sulfate formation
Previous studies have found that severe pollution events are frequently accompanied with high RH Tang et al., 2016;Wu et al., 2018;Clifton et al., 1988;Maahs, 1983;Martin and Good, 1991). As shown in Fig. 2d, the high concentration of sulfate positively correlated with high RH in most cases, which are shaded in grey columns. However, some pollution events (shaded in purple columns) also occurred under high RH, but the sulfate concentration or sulfate fraction in soluble PM was not so high. This means that high RH is a necessary but not a sufficient condition for sulfate conversion in severe haze pollution events. Thus, it is difficult to fully understand the general regularity behind the dataset or overemphasize the importance of a specific process in the atmosphere based on  case studies. This might be the reason why contrary conclusions about the formation path of sulfate were drawn by different researchers. We statistically analyzed the relationship between the SOR and the RH. All the hourly mean data of the SOR and RH have been binned into 100 × 100 boxes. Then, the density of data points, which statistically indicates the occurrence of the events at given values of RH and SOR, was calculated using a bivariate kernel density estimator (Wand and Jones, 1993). Figure 3a and b show the 2D kernel density graphs between the SOR and the RH in Shijiazhuang and Beijing. The color bar shows the density of data points. Although the SOR varied obviously at a certain RH, the most probable distribution of SOR could be exponentially fitted as a function of RH in Shijiazhuang (Fig. 3a); i.e., SOR = 0.15 + 0.0032 × exp(RH/16.2) (R = 0.79). This is consistent with the dependence of SOR on RH based on previous studies Wu et al., 2019). It should be noted that both SOR and RH showed obvious diurnal variation (Fig. S4). Their diurnal variations were somewhat similar, but a 4 h time lag was observed between their minimum values. This means that the diurnal variations of SOR and RH might also contribute to the strong dependency of SOR on RH ( Fig. 3a and b). However, the exponential dependency of SOR on RH was still observable in the night or in the day ( Fig. S5a and b). It did so in winter or summer ( Fig. S5c and d). This means that aqueous reactions are important for sulfate formation even if the influence of diurnal and seasonal variations are ruled out Cheng et al., 2016).
In Fig. 3a, 72.5 % of the data points of Shijiazhuang (6509 over 8980 effective points) were in the domain with the RH range of 10 %-70 % and the SOR range of 0.05-0.42, while 10.1 % of data points were in the region with the RH greater than 70 % and the SOR greater than 0.42. The first region corresponded to a lower mean PM 2.5 concentration, sulfate concentration and SOR (76.1 ± 62.78 µg m −3 , of 8.1 ± 6.3 µg m −3 , and 0.21 ± 0.09, respectively) compared with the second one (115.7 ± 96.7 µg m −3 , 22.4 ± 20.4 µg m −3 and 0.62 ± 0.14, respectively). As shown in Fig. 3b, the SOR also exponentially increased as a function of RH in Beijing. A percentage of 74.6 % of 8169 data points were in the first region. The mean PM 2.5 concentration, sulfate concentration and SOR were 48.2 ± 44.8 µg m −3 , 2.9 ± 3.0 µg m −3 and 0.21 ± 0.10, respectively, in the low RH region, while they were 69.9 ± 50.9 µg m −3 , 9.4 ± 8.5 µg m −3 and 0.83 ± 0.15 in the high RH region. The most probable distribution of SOR in Beijing could also be exponentially fitted as a function of RH (SOR = −0.045 + 0.12 × exp(RH/37.8), R = 0.92). However, the SOR was more sensitive to RH in Beijing than that in Shijiazhuang. This might be explained by the increased importance of sulfate formation via gas-phase reactions in Beijing (Fang et al., 2019;Hollaway et al., 2019), because the PM 2.5 mass concentrations in Beijing were significantly lower than that in Shijiazhuang (Fig. 1).
Formation of particle-phase sulfate through heterogeneous or multiphase oxidations includes the uptake of SO 2 and the following oxidation in particle phase. Thus, it is meaningful to identify the rate-determining step (RDS) for understanding the evolution of the SOR. As shown in Fig. 3, the initial γ SO 2 ,BET increased exponentially from 0 to (1.13 ± 0.21) × 10 −5 when the RH increases from 2 % to 80 % in the presence of 50 ± 2.5 ppb NH 3 with or without 100 ± 2.5 ppb NO 2 . The dependence of γ SO 2 ,BET on RH was γ SO 2 ,BET = 2.44E −7+6.69E −8×exp(RH/17.4) with a correlation coefficient of 0.96. A transition region of the γ SO 2 ,BET versus the RH was observable when the RH ranged from 60 % to 80 %. When the RH was higher than 70 %, the γ SO 2 ,BET increased quickly as a function of the RH. The similar dependency on RH for the γ SO 2 ,BET and the SOR suggests that the uptake kinetic of SO 2 might determine sulfate formation.
In a previous work , it has been found that all the uptake of SO 2 on dust or nitrate-coated dust can be transformed into sulfate over the timescale of the uptake experiment using the similar coated-wall flow tube reactor. Another study also observed a quick formation of sulfate on the surface of aqueous microdroplets under acidic conditions (pH < 3.5) without the addition of other oxidants, which was explained by the direct interfacial electron transfer from SO 2 to O 2 on the aqueous microdroplets (Hung et al., 2018). The pH of deliquesced NH 4 NO 3 is 4.2 as calculated using the ISORROPIA II model. This means that oxidation of S(IV) might not be a RDS of sulfate formation. The oxidation processes can be ascribed to catalytic oxidation by O 2 in the presence of transition metals, oxidation by O 2 and nitric acid promoted by protons in the presence of nitrate  and the oxidation by other dissolved oxidants in liquid phase (T. Cheng et al., 2016;Wang et al., 2016). To further validate this assumption, the formation rates of SO 2− 4 (d[SO 2− 4 ]/dt) in aerosol liquid phase were calculated according to the method used in previous work (P. Cheng et al., 2016). If oxidation of S(IV) is the rate-determining step, the formation rate should show a similar dependence on RH like the SOR.
As shown in Fig. 4a, the relative contributions of different oxidation paths of S(IV) varied obviously case by case. In summer and autumn, oxidation by H 2 O 2 was the most important path followed by TMI. In winter, however, NO 2 , O 3 or H 2 O 2 could contribute to the major oxidation path. This might be the reason why these oxidation paths showed inconsistent relative importance of among different studies even using the same method, such as isotopic measurements (Shao et al., 2019;He et al., 2018). Figure 4b and c show the dependence of the formation rates of sulfate on RH in the range of 35 %-100 % in Shijiazhuang. The dataset for RH below 35 % was omitted due to the large uncertainty in aerosol pH calculations (Ding et al., 2019;Guo et al., 2016;Pye et al., 2020). The relative contributions of different oxidation paths of S(IV) also varied obviously as a function of RH. NO 2 and O 3 played important role in aqueous S(IV) oxidation when RH was from 35 % to 45 %, while TMI became the dominator when RH ranged from 45 % to 70 %. Above 70 % RH, the contribution of H 2 O 2 was dominant, which is consistent with several recent studies (P. . However, the total formation rate of sulfate in aerosol liquid phase slightly decreased as RH increased. A weak downward trend of the d[SO 2− 4 ]/dt rate with RH was also observable in the 2D kernel density graphs as shown in Fig. 4c. This is opposite to the dependencies of the SOR and the γ SO 2 on RH as discussed above, which means the RDS for sulfate formation should be the uptake of SO 2 instead of oxidation of S(IV) in aqueous phase. We further calculated the production rate of sulfate through uptake of SO 2 (mass transfer to aerosol Beijing and the correlation of (c) SOR in Shijiazhuang and (d) γ SO 2 ,BET with AWC/PM 2.5 . The initial concentrations of SO 2 , NO 2 and/or NH 3 in the flow tube reactor were 190 ± 2.5, 100 ± 2.5 and/or 50 ± 2.5 ppb, respectively. The grey lines are the fitting curves for the most probable SOR, and the white lines are the fitting curves for the γ SO 2 ,BET . particles) according to where A s is the surface area concentration of PM 2.5 , ω is the mean molecular velocity of SO 2 and c SO 2 is the mass concentration of SO 2 . As shown in Fig. 4c, the probabilityweighted production rate of sulfate through uptake of SO 2 (the grey line) is lower than that through aqueous oxidation of S(IV), in particular, when RH is lower than 70 %. It should be noted that the mass transfer of SO 2 was not assumed to be the RDS using a large mass accommodation coefficient of SO 2 (α = 0.11) . According to the relationship between the mass accommodation coefficient (α) and the uptake coefficient (γ ) of SO 2 (Kulmala and Wagner, 2001), the α SO 2 on particles is on the same order of the γ SO 2 . This means that mass transfer rate might have been overestimated by Cheng et al. (2016). Phase state is a crucial factor determining the mass transfer of pollutants from gas phase to particle phase (Davis et al., 2015;Marshall et al., 2018;Shiraiwa et al., 2011;, while the AWC or RH greatly affects the phase state of aerosol particles (Duan et al., 2019;Shiraiwa et al., 2017). For example, ambient particles were found to change from semisolid to liquid state when the RH was above ∼ 60 % (Y. , corresponding to the AWC higher than ∼ 15 µg m −3 (Y.  under the typical urban environment in Beijing based on rebound fractions measurements. It was also confirmed that haze particles displayed a solid-aqueous equilibrium state when the RH was around 60 %-80 % using an individual particle hygroscopicity system . As shown in Fig. S6, the most probable distribution of the AWC exponentially increased with the RH (AWC = −5.76+5.15× exp(RH/36.1), R = 0.98) in Shijiazhuang. An obvious transition region of the RH between 60 % and 80 % was also observed. These results indicate that the liquid-phase aerosol should appear when the RH is higher than ∼ 60 % (Y.  and subsequently promote the conversion of SO 2 to sulfate. The SOR increased as a power function of AWC (SOR = 0.072 + 0.043 × AWC 0.53 , R = 0.78), while it was linearly correlated with the ratio of AWC/PM 2.5 (SOR = 0.15 + 0.40 × AWC/PM 2.5 , R = 0.78) as shown in Fig. 3c. Similarly, the AWC of dust internally mixed with NH 4 NO 3 was also calculated using the ISORROPIA II model. The γ SO 2 ,BET also showed a similar trend as a function of AWC/PM 2.5 (γ SO 2 ,BET = 3.08E − 5 × AWC/PM 2.5 , R = 0.95) (Fig. 3d), although the ranges of AWC/PM 2.5 were different due to the difference in aerosol composition. This means that the fraction of aerosol liquid water governs both the conversion of SO 2 to sulfate and uptake kinetics of SO 2 .
It should be noted that although the SOR showed a similar RH dependence as the SO 2 , a deviation was observed in both Shijiazhuang and Beijing (Fig. 3). The γ SO 2 was mea- sured at a fixed temperature and initial SO 2 concentration. In the atmosphere, both of them varied obviously. This might lead to the observed deviation. On the other hand, the coexisted components such as organic aerosol and black carbon in atmospheric particles should have complicated the influence on the hygroscopicity and the phase change of particles. The difference between the model particles and the real ambient aerosol particles might also partially lead to the deviations of the RH dependence between the SOR and the γ SO 2 ,BET . In addition, it also implies that besides the reaction in aerosol liquid phase, other reaction paths such as oxidation of SO 2 by gas-phase oxidants should also play an important role in sulfate formation (Duan et al., 2019).

Influence of particle composition on AWC and sulfate formation
Besides RH, particle composition is another important factor to affect the AWC. According to the ions balance (Fig. S7a), ammonia was adequate to neutralize the anions in PM 2.5 , which is consistent with the results in the literature (Y. Wang et al., 2020b). In addition, (81.5 ± 15.9) % (with the median of 87.1 %) of ionic anions (nitrate, chloride and sulfate) were neutralized by ammonium (Fig. S7b). This means NH 4 NO 3 , (NH 4 ) 2 SO 4 and NH 4 Cl should be the dominant form of nitrate, sulfate and chloride in PM 2.5 , respectively. We further reconstructed the molecular composition from the ions based on the principles of aerosol neutralization and molecular thermodynamics (Kortelainen et al., 2017 corresponding to twice the amount of SO 2− 4 existed as (NH 4 ) 2 SO 4 , and the remaining fraction of NH + 4 was associated with NO − 3 and Cl − ; and (iv) the rest of NO − 3 , which was not neutralized by NH + 4 , was from NaNO 3 . Figure 5a and b show the variation of the molecular composition as a function of RH in Shijiazhuang. Obviously, NH 4 NO 3 and (NH 4 ) 2 SO 4 were the major molecular components. Both of them showed upward trend as the RH increased. In particular, the fraction of NH 4 NO 3 increased gradually from ∼ 10 % to ∼ 50 % when the RH increased from ∼ 30 % to 90 %. Correspondingly, the fraction of (NH 4 ) 2 SO 4 decreased as the RH increased.
It should be noted that the deliquescence RH (DRH) of NH 4 NO 3 (61.8 %) (Onasch et al., 1999) is lower than those values of NH 4 Cl (78 %) (Hu et al., 2011) and (NH 4 ) 2 SO 4 (80 %) (Lightstone et al., 2000). We further calculated the AWC attributed to the individual molecular component based on the growth factors and mass concentrations. As shown in Fig. 5c, the sum of the AWC of individual salts is underestimated by around 13 % compared to that calculated using the ISORROPIA II model (the grey line), because the mixing state was not considered in the former method. However, we can still draw a conclusion that NH 4 NO 3 and (NH 4 ) 2 SO 4 are the major contributors to the AWC. Especially NH 4 NO 3 dominated the AWC when the RH ranged from 60 % to 80 %, in which the SOR and the γ SO 2 were very sensitive to RH. These results suggest that NH 4 NO 3 should be the most important mediator to AWC and subsequently the uptake of SO 2 in the transition regime of RH in Fig. 3a. It should be noted that (NH 4 )HSO 4 has a lower DRH than NH 4 NO 3 (Y. J. . However, 98.4 % of the data points showed an R NH 4 +/SO 2− 4 higher than 2.0 in Shijiazhuang. This means that the contribution of (NH 4 )HSO 4 to PM 2.5 should be negligible because of the abundance of atmospheric NH 3 in northern China. In previous work, it has been found that SO 2 oxidation can be promoted by particulate nitrate through the accumulation of proton  and the formation of NO + NO − 3 (Kong et al., 2014). Our results further showed the importance of NH 4 NO 3 in the AWC, which possibly determines the phase state of particles and subsequently the uptake kinetics of SO 2 and the SOR as discussed above. To further confirm the role of NH 4 NO 3 in the uptake of SO 2 , uptake experiment of SO 2 on pure dust has been carried out at 2 % and 80 % RH. The corresponding γ SO 2 ,BET was 1.10 ± 1.05 × 10 −7 and 1.66 ± 0.28 × 10 −7 on pure dust sample in the presence of NH 3 and NO 2 . However, as discussed above, it was 0 and 1.12 ± 0.15 × 10 −5 on dust internally mixed with 33 % NH 4 NO 3 . This directly confirmed the role of NH 4 NO 3 in SO 2 uptake via aerosol liquid water. Figure S8 shows the dependencies of the AWC/PM 2.5 and SOR on the fraction of the individual molecular component. Both the AWC/PM 2.5 and SOR statistically increased as the fraction of NH 4 NO 3 increased ( Fig. S8a and d). A weak increase followed by a decrease was observed for the AWC/PM 2.5 as the fraction of (NH 4 ) 2 SO 4 increased, while a negative correlation between the AWC/PM 2.5 and the fraction of NH 4 Cl was observed. It did so for the SOR and the fraction of NH 4 Cl. These phenomena were overall consistent with the sequence of their hygroscopicity. In addition, chloride is a primary pollutant mainly from coal combustion and biomass burning . Besides chloride, other primary particles from combustion such as soot, which were not accounted for in this work, might also decrease the uptake capability of water and subsequently be unfavorable for SO 2 uptake.
To assess the relative importance of sulfate and nitrate (the major SIA component) to AWC, the sensitivity of their fraction to AWC in Shijiazhuang was tested using the ISOR-ROPIA II model and shown in Fig. S9. The base case means the AWC was calculated using the measured concentration of the ions. Then, we reduced the fraction of NH 4 NO 3 or (NH 4 ) 2 SO 4 from 0 to 80 % individually compared with the base case. Figure S9a shows the time series of the calculated AWC after reducing 50 % of NH 4 NO 3 or (NH 4 ) 2 SO 4 . Reduction of either NH 4 NO 3 or (NH 4 ) 2 SO 4 resulted into obvious decrease of AWC during pollution events. In most cases, the reduction amplitude of AWC was larger when reducing 50 % of NH 4 NO 3 than (NH 4 ) 2 SO 4 . Figure S9b shows the mean ratio of AWC at a certain reduction fraction of NH 4 NO 3 or (NH 4 ) 2 SO 4 to that under the base case. When NH 4 NO 3 was reduced from 0 % to 80 %, the AWC linearly reduced from 0 % to 61.1 ± 0.1 % with a slope of 0.48 %.
It varied from 0 % to 66.0 ± 0.2 % for (NH 4 ) 2 SO 4 (with a slope of 0.41 %). This means that the AWC is more sensitive to the fraction of NH 4 NO 3 than (NH 4 ) 2 SO 4 in Shijiazhuang. This also implies the importance of NH 4 NO 3 in the observed high AWC in haze days. On the other hand, reducing 10 % of NH 4 NO 3 can lead to a reduction of 5.2 ± 1.0 % AWC during haze days. Subsequently, we can roughly estimate that the SOR might be reduced by ∼ 4 % through a linear interpolation according to the equation of the SOR and the AWC/PM 2.5 (SOR = 0.15 + 0.40 × AWC/PM 2.5 ) fitted in Fig. 3c. This means reduction of NO x and NH 3 should lead to additional reduction of particulate sulfate.

Influence of other factors on sulfate formation
Several studies have proposed out that NO 2 can promote the oxidation of SO 2 on particle surfaces and in aqueous phase. For example, laboratory studies have found that parts per million (ppm) levels of NO 2 can promote sulfate formation on the surface of dust through NO + NO − 3 which is disproportionated from N 2 O 4 intermediate Liu et al., 2012;Ma et al., 2008) or parts per million levels of NO 2 can promote the oxidation of SO 2 in the deliquesced oxalic acid . This is supported by the evidence that a high fraction of sulfate in PM 2.5 is positively correlated with NO 2 concentration (Xie et al., 2015) and that a high PM 2.5 concentration is accompanied with high ratio of NO 2 /SO 2 in several case studies . The importance of the SO 2 oxidation by NO 2 in aqueous phase has also been confirmed in modeling studies Xue et al., 2016). However, this reaction path is still under debate because of the following reasons. (1) The concentration of NO 2 in laboratory studies was about 2 orders of magnitude higher than that in ambient air. This will affect the surface concentration of the intermediate (N 2 O 4 ) and the concentration of solved NO 2 in aqueous phase. (2) The dissolved NO 2 concentration is highly sensitive to pH. The pH value in aerosol was 5.6-6.2 estimated in modeling study . However, a recent work found that it varied from 3.8 to 4.5 at RH > 30 % and showed a moderate acidity because of the thermodynamic equilibrium between NH + 4 and NH 3 (Ding et al., 2019). (3) The previous calculations were conducted using a high reaction rate constant of the NO 2 reaction with dissolved S(IV) (Clifton et al., 1988;Cheng et al., 2016), while a smaller value was reported in the more recent study (Spindler et al., 2003;Tilgner et al., 2021). (4) The relative importance of each path depends on the concentration of the relevant pollutants including H 2 O 2 and TMI (P. . Therefore, it is necessary to verify the importance of this process by long-term observation at different environments. Figure 6 shows the 2D kernel density graph of the sulfate fraction in soluble PM and the SOR in Shijiazhuang as a function of the concentration of different gas-phase pollutants. It should be pointed out that the SOR or the γ SO 2 should be positively correlated to NO 2 concentration if it can promote the conversion of SO 2 to sulfate or the uptake of SO 2 . However, both sulfate fraction and SOR were negatively correlated with the concentration of NO 2 from the point of view of statistics. A same trend was observed in Beijing (Fig. S10). This is similar to recent studies that observed the opposite correlation between SOR and NO x concentration in the Sichuan Basin  and in Beijing (Fang et al., 2019). This means that NO 2 concentration is statistically not a determining factor for sulfate formation in the atmosphere. This is well supported by the uptake kinetics of SO 2 measured using a flow tube reactor. As shown in Fig. 3a and b, when 50 ± 2.5 ppb of NH 3 presenting in the reactant gases, no difference was observable for the γ SO 2 ,BET between the presence (red squares) and absence of 100 ± 2.5 ppb of NO 2 (white triangles). This is consistent with these previous studies that found NO 2 to be having no influence on SO 2 uptake when NH 3 was abundant in the atmosphere Wang et al., 2021). In addition, it is consistent with the fact that H 2 O 2 dominated the oxidation of S(IV) in aerosol liquid water when RH was higher than 60 % (Fig. 4a). It should be pointed out that the γ SO 2 at 80 % RH was 1.7 ± 0.3 × 10 −6 on the mixture of dust and NH 4 NO 3 in the absence of NH 3 and NO 2 (Fig. 3). It increased to 3.7 ± 0.2 × 10 −6 in the presence of NO 2 . This is consistent with the promotion effect of NO 2 for converting SO 2 to sulfate in the absence of NH 3 as observed in both a smog chamber  and a bubbling reactor (T. . However, the enhanced uptake of SO 2 induced by NO 2 might be too low to be measured in the presence of NH 3 . Therefore, the weak promotion effect by NO 2 alone cannot explain the negative correlation between the SOR and the concentration of NO 2 in Fig. 6f. Both the fraction of sulfate and the SOR in Shijiazhuang statistically decreased as a function of SO 2 and CO concentration, respectively (Fig. 6b, c, g and h). This might be explained by the high concentration of primary aerosol components when pollution events occurred with high concentrations of primary gas-phase pollutants. However, the fraction of sulfate increased as a function of O 3 (Fig. 6d). When the O 3 concentration was greater than 50 ppb, the SOR slightly increased with the O 3 concentration (Fig. 6i). A more obvious positive dependence of sulfate fraction on O 3 concentration was observed in Beijing (Fig. S10e). This means oxidation capacity also plays an important role in sulfate formation, especially in Beijing. This is consistent with the recent finding that O 3 plays an important role in SO 2 oxidation at different locations (Fang et al., 2019;Tian et al., 2019;Duan et al., 2019). As shown in Fig. 6j, the SOR positively correlated with the concentration of NH 3 in Shijiazhuang. This means that NH 3 can promote the conversion of SO 2 to sulfate. This is well in agreement with laboratory studies that observed the promotion effect by NH 3 to the heterogeneous reaction of SO 2 on different mineral oxides (Yang et al., 2016). In addition, flow tube experi- ments were also carried out by exposing the internal mixing sample (2 : 1 dust and NH 4 NO 3 ) to 200 ± 2.5 ppb SO 2 in the absence of NH 3 and NO 2 at 2 % and 80 % RH, respectively. As shown in Fig. 3a and b, the γ SO 2 ,BET was zero regardless of the reactants under dry condition (2 % RH), while it increased to (1.66 ± 0.28) × 10 −6 at 80 % RH. However, it was significantly smaller than the γ SO 2 ,BET ((1.13 ± 0.21) × 10 −5 ) in the presence of 50 ± 2.5 ppb NH 3 with or without 100 ± 2.5 ppb NO 2 . These results further confirm that NH 3 can promote the uptake of SO 2 at high RH, possible through enhancing the solubility of SO 2 in water (T. Cheng et al., 2016;Wang et al., 2016), because the effective solubility of SO 2 can be enhanced due to the increase of the aerosol pH.
Aerosol acidity is one of the important factors affecting the sulfate formation and the partitioning of semivolatile gases in the atmosphere . As shown in Fig. S11, when aerosol pH is lower than 4.5, the oxidation rate of S(IV) in aerosol liquid phase decreases with decreasing pH, because the oxidation of S(IV) by transition metals is the dominant path and is decreasing with aerosol pH. However, the oxidation rate of S(IV) increases when the aerosol pH is higher than 4.5. This can be explained by the fact that the solubility and effective Henry's law constant of SO 2 are positively dependent on pH Liu et al., 2021;, which is consistent with the promotion effect of sulfate formation by NH 3 .

Conclusions and atmospheric implications
Based on 1 year of observations, we confirmed that high PM 2.5 mass concentration in pollution events usually coincided with the high sulfate concentration, the fraction of sulfate, and the SOR in both Beijing and Shijiazhuang. In Shijiazhuang, the SOR exponentially increased as a function of RH from the point of view of statistics, which was similar to the RH dependence of the γ SO 2 on the model particles containing 33 % NH 4 NO 3 in the presence of NH 3 . The SOR and γ SO 2 linearly increased as a function of the fraction of aerosol water content in PM 2.5 . The enhanced uptake coefficient of SO 2 at high RH after the liquid-phase aerosol appeared might explain the increased SOR, because uptake of SO 2 was the rate-determining step for the conversion of SO 2 to particulate sulfate. NH 4 NO 3 played an important role in the AWC, the phase state of aerosol particles and subsequently the uptake kinetics of SO 2 in haze days under high RH conditions. The contribution of nitrate to PM 2.5 is increasing in China Tian et al., 2019) due to the intensive emissions of NO x from steel production and cement manufacturing Qi et al., 2017) as well as the increasing NO x emissions from traffic (Liu et al., 2007;Wang et al., 2011). The mean fraction of nitrate in PM 2.5 was 21.4 ± 12.4 % in Shijiazhuang and 15.8 ± 13.4 % in Beijing. They were close to the reported values in PM 1.0 during the summer of Beijing (24 %)  and in PM 2.5 during the winter of Chengdu (23.3 %) and Chongqing (17.5 %) . It has been found that the fraction of nitrate and ammonium usually increases as a function of PM 2.5 mass concentration . Therefore, NO x should be an urgent air pollutant in the future in China even from the point view of its contribution to PM 2.5 mass.
As observed in this work, NH 4 NO 3 has an important contribution to PM 2.5 mass concentration, the aerosol water content and subsequently the phase state of particles in the RH range of 60 %-80 %. Reduction of NO x emissions should lead to a decrease in NH 4 NO 3 concentration and subsequently the AWC during serve pollution events. This will lead to an additional reduction of SO 2 uptake and the formation of particulate sulfate through aqueous reactions. Based on our rough estimation, 4 % of sulfate might be reduced due to aqueous reaction in Shijiazhuang if the mass concentration of NH 4 NO 3 was reduced by 10 %. More work is required to quantitatively assess the contribution of nitrate to sulfate formation from aqueous reactions in the future. It should be noted that ozone pollution becomes more and more important in China (Z. Ziemke et al., 2019). This requires us to harmoniously reduce NO x and volatile organic compounds in the near future. It is also important to take actions on NH 3 emission control in the future as NH 3 can significantly promote the uptake of SO 2 in liquid-phase aerosol.
Data availability. The experimental data are available upon request to the corresponding authors.
Author contributions. YoL and XB designed the experiments. YoL and YuL wrote the paper. ZF, FZ, YZ, XF, CY, BC, YW, WD and JC carried out measurements at BUCT. XB and TJ carried out measurements at SJZ. YG, YZ and YoL carried out flow tube experiments. PL, YM and YoL performed sulfate formation calculations. YuL, FB, TP, YM, HH and MK revised the paper.
Competing interests. The authors declare that they have no conflict of interest.
Disclaimer. Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Review statement. This paper was edited by Harald Saathoff and reviewed by two anonymous referees.