2.1 Observation sites

The field campaign was conducted from 11 to 26 April 2018 on the Xianlin Campus of Nanjing University, which is situated in a suburban area approximately 20 km northeast of downtown Nanjing (see Fig. 1). The observation sites are surrounded by teaching and residential buildings, sparse roads, and vegetation cover for about 1 to 2 km, with no significant emission sources. Approximately 15 km northwest of the sampling sites are large-scale chemical and steel facilities, which can be sources of gaseous pollutants (CO, SO₂, NO_x, and VOCs) and particulate matters that may influence the site (Zhou et al., 2017). In addition, Shanghai is approximately 270 km southeast of the measurement site.

The main data reported in this study (i.e., N₂O₅, ClNO₂, and Cl₂) and the NO_x and O₃ data were obtained at the School of Atmospheric Sciences (SAS) of Nanjing University (sampling site 1). The auxiliary data – including O₃, VOCs, aerosol size distribution, and chemical composition – were obtained at the Station for Observing Regional Processes of the Earth System (SORPES, sampling site 2). Figure 1 shows the locations of the two sampling sites. Interested readers are referred to previous studies for more information about the SORPES site (e.g., Ding et al., 2013, 2019; Sun et al., 2018). A comparison of O₃ measurements at the SAS and SORPES sites shows excellent agreement during the observation period (Fig. S1 in the Supplement).

Figure 1Sampling locations. (a) Location of Nanjing city in the YRD region. (b) Location of sampling sites in Nanjing. (c) Sampling sites 1 and 2 on the Xianlin Campus of Nanjing University.

2.2 N₂O₅, ClNO₂, and Cl₂ measurements

A chemical ionization mass spectrometer coupled with a quadrupole mass analyzer (Q-CIMS, THS Instruments) was used to detect N₂O₅, ClNO₂, Cl₂, and HOCl. The Q-CIMS had been used in previous field campaigns to measure N₂O₅ and ClNO₂ (Wang et al., 2016; Tham et al., 2016). In this study, we also measured Cl₂ and HOCl and tuned the pressure of the drift tube reactor accordingly. The principles and ion chemistry of Q-CIMS were described in detail by Kercher et al. (2009). Briefly, iodide (I⁻) was adopted as the primary ion for strong affinity with our target species. Charged iodide clusters – such as ${\mathrm{IN}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}^{-}$, ${\mathrm{IClNO}}_{\mathrm{2}}^{-}$, ${\mathrm{ICl}}_{\mathrm{2}}^{-}$, and IHOCl⁻ – are formed by the ion molecular reactions shown in Reactions (R8) through (R11). Figure S3 presents an example of the CIMS spectra showing the signals of the detected species. Ion clusters with different Cl isotopes (i.e., ³⁵Cl and ³⁷Cl) were recorded to examine the identity of ClNO₂ and Cl₂, and this isotopic analysis confirmed that ClNO₂ and Cl₂ had very minor interferences (see Sect. S1 in the Supplement).

The Q-CIMS was housed on the fifth floor of the SAS building. The PFA sampling tube (length: 1.5 m; outer diameter: 0.25 in) extended out through a hole in the side wall. We took precautions to minimize the deposition of particles on the inner wall of the sampling tube and tested the possible formation and loss of N₂O₅, ClNO₂, and Cl₂ on the sampling tube (see Sect. S1 for details), which showed a negligible inlet interference on the CIMS measurement. N₂O₅ and ClNO₂ were calibrated every 2 d following established methods (Wang et al., 2016). Briefly, N₂O₅ was synthesized from the reaction of NO₂ and O₃, and ClNO₂ was produced by passing N₂O₅ through a deliquesced NaCl slurry. The dependence of N₂O₅ sensitivity on relative humidity (RH) was tested on site (see Fig. S5) and was used to account for changes in ambient RH. A Cl₂ permeation tube was used for Cl₂ calibration (Liao et al., 2014), and the permeation rate of Cl₂ (380±20 ng m⁻³) was quantified by chemical titration and ultraviolet spectrophotometry (Sect. S4). We assumed the sensitivity of HOCl to be the same as that of ClO, and we used a sensitivity ratio of ClO to Cl₂ (0.26) that was experimentally determined by Custard et al. (2016). In this study, the HOCl data were only used qualitatively. In sum, the sensitivities of N₂O₅, ClNO₂, Cl₂, and HOCl were 0.42±0.07, 0.35±0.06, 0.86±0.11, and 0.22 Hz pptv⁻¹, respectively. The detection limit (3σ) of N₂O₅, ClNO₂, and Cl₂ was 7, 2, and 5 pptv, respectively. The uncertainties of the N₂O₅ and ClNO₂ measurements were estimated to be 19 % via error propagation. The Cl₂ measurement uncertainty was estimated to be 15 %. The details of CIMS calibrations and uncertainty analysis are available in Sect. S1 and Table S3.

2.3 Auxiliary measurements

In addition to the CIMS measurement at the SAS site, meteorological factors, gaseous and aerosol chemical compositions, particle size distributions, and the NO₂ photolysis frequency (jNO₂) were simultaneously measured at the SORPES site (Table S1). The ionic compositions of PM_2.5 – including Cl⁻, ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$, and ${\mathrm{NH}}_{\mathrm{4}}^{+}$ – were measured with an Aerosol Chemical Speciation Monitor (ACSM, Aerodyne Research Inc.) and Monitor for AeRosols and GAses in ambient air (MARGA, Metrohm, Switzerland). The hourly averaged ionic compositions from the ACSM and MARGA showed good agreement (see Fig. S6). In addition, HNO₃ was also measured by MARGA. In this study, the 10 min averaged ACSM data, including total organics, were used for subsequent analysis. The mass concentration of H⁺ (µg m⁻³) was estimated to achieve electric charge balance of the cation (${\mathrm{NH}}_{\mathrm{4}}^{+}$) and anions (Cl⁻, ${\mathrm{NO}}_{\mathrm{3}}^{-}$, and ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$) of the ACSM data. The molar concentrations of inorganic ions (i.e., [Cl⁻], [${\mathrm{NO}}_{\mathrm{3}}^{-}$], [${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$], [${\mathrm{NH}}_{\mathrm{4}}^{+}$], and [H⁺]) and total organics ([Org]) were estimated using the extended aerosol inorganics model (E-AIM, model III) (Wexler, 2002). The molecular weight of the organic molecules was assumed to be 250 g mol⁻¹ (McDuffie et al., 2018b). The dry-state submicron particle size distribution was measured with a Scanning Mobility Particle Sizer (SMPS, TSI Inc.), and the data were used to estimate the aerosol surface area density (S_a) with the assumption of spherical particles. The hygroscopic growth factor of the particle size was based on an empirical parameterization, $\mathrm{GF}=\mathrm{0.582}{\left(\mathrm{8.46}+\frac{\mathrm{1}}{\mathrm{1}-\mathrm{RH}}\right)}^{\mathrm{1}/\mathrm{3}}$ (Lewis, 2008). The VOCs were measured with a proton transfer reaction time-of-flight mass spectrometer (PTR-TOF-MS, Ionicon).

2.4 Production and loss of NO₃ and N₂O₅

NO₃ radicals are primarily produced from NO₂ and O₃ (Reaction R1). The production rate equation of NO₃ (P(NO₃)) is shown as follows (Eq. 1):

where k₁ is the rate constant of Reaction (R1). NO₃ is mainly removed by gas-phase reactions with VOCs and NO (Eq. 2) and heterogeneous loss via N₂O₅ uptake (Eq. 3), where k (NO₃) and k (N₂O₅) are the first-order loss rate coefficients of NO₃ and N₂O₅, respectively.

where $k_{\mathrm{NO}+{\mathrm{NO}}_{\mathrm{3}}}$ and k_i denote the reaction rate constants of NO₃ with NO and VOC, respectively, and c(N₂O₅) is the average velocity of N₂O₅ molecules. Other minor loss pathways of NO₃ and N₂O₅ were not considered (e.g., homogeneous loss of N₂O₅).

2.5 Estimation of φ (ClNO₂) and γ (N₂O₅)

φ (ClNO₂) and γ (N₂O₅) were estimated using the observation data and parameterization. We used the observed increasing rates of ClNO₂ and total nitrate (i.e., ${\mathrm{HNO}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{3}}^{-}$) to derive the values for γ (N₂O₅) and φ (ClNO₂) in the selected cases (Phillips et al., 2016). Details of the method are described elsewhere (Tham et al., 2016; Phillips et al., 2016). Briefly, the production rate of ClNO₂ (P(ClNO₂)) is calculated as follows (Eq. 4).

The production rate of total nitrate induced by N₂O₅ uptake during the night (P(${\mathrm{NO}}_{\mathrm{3}}^{-}$)) is shown by Eq. (5).

φ (ClNO₂) is obtained by combining Eqs. (4) and (5).

And γ (N₂O₅) is derived as follows (Eq. 7).

This method assumes that (1) air masses are relatively stable and (2) N₂O₅ uptake dominates ${\mathrm{NO}}_{\mathrm{3}}^{-}$ production at night (Tham et al., 2018). Assumption (1) requires careful selection of the cases of interest. Regarding assumption (2), major nocturnal production pathways of total nitrate should be evaluated, such as comparing the reaction rate of N₂O₅ heterogeneous loss (k (N₂O₅) × [N₂O₅]) with that of NO₃ + VOC (k (NO₃) × [NO₃]), which may produce HNO₃ via H-abstraction reactions.

φ (ClNO₂) was also calculated with the parameterization shown in Eq. (8), in which the k₄∕k₃ ratio was adopted as 483±175 (Bertram and Thornton, 2009).

When considering the potential competitive effect of other species (denoted as “Y⁻”), such as sulfate or aerosol organics, for the ${\mathrm{NO}}_{\mathrm{2}}^{+}$ intermediate, the following equation (Eq. 9) was established (McDuffie et al., 2018b). Rearrangement of Eq. (9) yields Eq. (10), in which plotting $\left(\frac{\mathrm{1}}{\mathit{\phi }\left(\mathrm{ClN}{\mathrm{O}}_{\mathrm{2}}\right)}-\mathrm{1}\right)\ast \frac{\left[{\mathrm{Cl}}^{-}\right]}{\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]}$ to $\frac{\left[{\mathrm{Y}}^{-}\right]}{\left[{\mathrm{Cl}}^{-}\right]}$ should exhibit a positive correlation. k₅ represents a constant reaction rate coefficient of “Y⁻” with ${\mathrm{NO}}_{\mathrm{2}}^{+}$.

3.1 Overall observation results

Figure 2 depicts the time series of N₂O₅, ClNO₂, Cl₂, and related species. Overall, the observation sites experienced moderate levels of pollution during the study period (PM_2.5: 44.8±18.3 µg m⁻³; CO: 0.4±0.2 ppmv; SO₂: 3.1±1.8 ppbv; NO_x: 18.1±16.6 ppbv; O₃: 25.8±18.4 ppbv). The on-site observations indicated mostly stagnant weather with low wind speeds (1 m s⁻¹ in average). No precipitation was observed except for the evening of 13 April from 22:00 to 22:30 local time. The nocturnal NO mixing ratios were usually near the detection limit of the NO instrument, and the presence of abundant NO₂ and O₃ favored N₂O₅ formation and subsequent heterogeneous processes.

The most salient features of the observation were the high levels of ClNO₂ and moderate levels of Cl₂ that were present during the night. The ClNO₂ mixing ratios exceeded 1 ppbv on 12 of the 15 nights. The observed ClNO₂ levels were among the highest in the world, with a peak mixing ratio (1 min average: 3.7 ppbv) slightly higher than that of northern China (1 min average: 2.1 ppbv) (Tham et al., 2016) but lower than that reported in southern China (1 min average: 8.3 ppbv) (Yun et al., 2018). The frequent occurrence of high ClNO₂ levels was favored by several factors, including elevated levels of N₂O₅ (1 ppbv), humid weather (RH: 67.7 %±20.7 %), and chloride availability (0.36±0.31 µg m⁻³) during the field campaign. When high levels of ClNO₂ were observed, elevated concentrations of particulate nitrate as high as 40.8 µg m⁻³ (10 min average) were also present. We noticed that ClNO₂ and particulate nitrate concentrations both increased more rapidly after midnight than before midnight from 15 to 19 April, which is discussed further below.

Moderate levels of Cl₂ (up to 100 pptv) were also observed during the night. Cl₂ mixing ratios exhibited a clear diurnal pattern, peaking at night and decreasing during the day due to photolysis. The nocturnal peaks of Cl₂ mixing ratios showed discrepancies from some previous observations in which an elevated level of Cl₂ was found during the day (Liao et al., 2014; Liu et al., 2017). The Cl₂ and ClNO₂ mixing ratios reached peaks synchronously during most nights, and both species decreased in abundance or were absent in NO-rich plumes (e.g., the nights of 13 and 25 April), which suggests that Cl₂ and ClNO₂ were produced from common sources. Similar nighttime correlations of Cl₂ and ClNO₂ were also observed in the United States and in northern China (Qiu et al., 2019; Haskins et al., 2019). A subsequent analysis of the present study aims to elucidate the nighttime formation processes of ClNO₂ and Cl₂.

Figure 2Time series of ClNO₂, Cl₂, and related measurements during field observations from 11 to 26 April 2018. Data gaps were caused by technical problems or calibrations.

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3.2 High-ClNO₂ cases

Figure 3 shows the observation results from 17 and 18 April to further illustrate the ClNO₂ formation process. This case had the highest ClNO₂ observed during the campaign and shows an example of high ClNO₂ mixing ratios after midnight. As shown in Fig. 3a, the mixing ratio of ClNO₂ began to increase after sunset (18:00 LT on 17 April) and decreased after midnight. The period between 22:00 and 24:00 LT on 17 April was noted as plume 1. After midnight, the ClNO₂ mixing ratios exhibited a more rapid increase from 03:00 to 05:00 LT on 18 April (plume 3), and the particulate nitrate concentration also synchronously and significantly increased. Plumes 1 and 3 were identified as being different, resulting from an air mass shift between 00:00 and 03:00 LT on 18 April (plume 2), as indicated by abrupt changes in the RH, temperature, and O₃. We compared the backward trajectories from plume 1 to plume 3 and found no significant difference (figures not shown here). Thus, the change in the air mass from plume 1 to plume 3 was likely a local phenomenon.

The P(NO₃) and NO₃ loss pathways during plumes 1 and 3 were calculated and compared in Fig. 3b–d using the methods described in Sect. 2.4. The P(NO₃) was slightly lower during plume 3 than during plume 1, and a larger proportion of NO₃ was lost via the N₂O₅ hydrolysis pathway in plume 3. Thus, the air mass shift, in addition to the higher rate of N₂O₅ hydrolysis, was responsible for the elevated ClNO₂ levels observed after midnight.

Compared with the high levels of ClNO₂ (up to 3.5 ppbv) on the night of 17 April, the concentration of Cl⁻ was low and relatively constant (∼0.1 ppbv) during that period. The low chloride but high ClNO₂ levels were also observed in previous studies, and HCl partition was proposed to replenish particulate chloride to sustain the ClNO₂ production (Osthoff et al., 2008; Thornton et al., 2010).

Figure 3Detailed analysis of a high-ClNO₂ episode observed on 17–18 April. (a) Time series of ClNO₂ and related species. (b)–(d) Comparisons of P(NO₃) and NO₃ loss pathways in plumes 1 and 3.

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3.3 ClNO₂ production yield from N₂O₅ uptake

φ (ClNO₂) was estimated to investigate its influencing factors and the performance of parameterization in selected cases. The methods described in Sect. 2.5 were used to estimate the φ (ClNO₂) and γ (N₂O₅) using the observation data. As these methods assume a stable air mass and the dominance of N₂O₅ uptake in nitrate formation, we applied the following criteria when selecting cases for this analysis. First, the NO mixing ratios must be less than 0.1 ppbv. When significant levels of NO were present, the N₂O₅ chemistry was suppressed. Second, primary pollutants such as CO, SO₂, and meteorological factors (wind, temperature, and RH) were required to exhibit relatively constant levels or stable trends within the cases. Third, the ClNO₂ and nitrate levels had to be correlated (R²>0.6) and show increasing trends. Fifteen cases that lasted 30 min to 3 h were selected, and 10 min averaged data were used for calculation. Figure S7 shows an example of this calculation, which corresponds to plume 1 on 17 April (Fig. 3). We then evaluated the loss pathways of NO₃ in the 15 cases. The results show that the NO₃ + VOCs reactions contributed less than one-third of the total NO₃ + N₂O₅ loss (e.g., Fig. 3c, d). Nocturnal total nitrate production was thus dominated by N₂O₅ uptake, and only a small proportion of nitrate was produced by NO₃ + VOCs reactions.

The derived γ (N₂O₅) values ranged from 0.004 to 0.014 (mean: 0.008±0.004). The highest γ (N₂O₅) values (0.0135 and 0.0139) were derived between 03:00 and 05:00 LT on 18 April (i.e., plume 3 in Fig. 3), which was consistent with the rapid increase in ClNO₂ mixing ratios during that period. The variations in the γ (N₂O₅) value depended mainly on [H₂O] (R²=0.49) (see Fig. S8) but showed little correlation with other influencing factors, such as [Cl⁻], [${\mathrm{NO}}_{\mathrm{3}}^{-}$], and V_a∕S_a (figures not shown here). The dominant influence of [H₂O] on the γ (N₂O₅) value was also reported in previous studies (e.g., Tham et al., 2018).

The φ (ClNO₂) value ranged from 0.28 to 0.89 (mean: 0.56±0.15). The φ (ClNO₂) value exhibited an obvious nonlinear relationship with the [Cl⁻] / [H₂O] ratio (R²=0.52) (Fig. 4a), which is consistent with previous laboratory results (Bertram and Thornton, 2009). However, current parameterization of φ (ClNO₂) based on [Cl⁻] / [H₂O] (φ (ClNO₂)_BT) tended to overestimate the observed φ (ClNO₂) value (Fig. 4b).

Here we give two explanations for the inconsistency between the φ (ClNO₂)_BT and the field-derived φ (ClNO₂). First, the reactivity of chloride with ${\mathrm{NO}}_{\mathrm{2}}^{+}$ (i.e., k₄∕k₃ in Eq. 8) was reduced in ambient environments due to complicated issues of the mixing state, phase state, and activity coefficient. As φ (ClNO₂) is positively dependent upon [Cl⁻], a reduction in chloride reactivity could decrease the φ (ClNO₂) value in ambient particles. This explanation is supported by previous studies of γ (N₂O₅) (Morgan et al., 2015; McDuffie et al., 2018a), which showed that, when the enhancement effect of chloride on γ (N₂O₅) was neglected, the parameterized γ (N₂O₅) better matched the observed γ (N₂O₅). The second explanation deals with other unknown factors that reduce the φ (ClNO₂) value. The parameterization φ (ClNO₂)_BT only considered the [Cl⁻] / [H₂O] ratio, not other aqueous species that could suppress φ (ClNO₂), leading to the overestimation of φ (ClNO₂)_BT values.

Regarding the second explanation, we examined the possibility of sulfate and aerosol organics competing with [Cl⁻] for the ${\mathrm{NO}}_{\mathrm{2}}^{+}$ intermediate (see Sect. 2.4 and Eq. 10). The statistical results show that aerosol organics could reduce φ (ClNO₂) values (R²=0.41; Fig. S9b), but sulfate did not show such an influence (R²=0.08; Fig. S9a). The latter result contrasts with the finding of a recent laboratory study which indicated that both sulfate and some organics (e.g., carboxylate) suppress ClNO₂ formation (Staudt et al., 2019).

By incorporating the suppression effect of aerosol organics, we performed regressions of φ (ClNO₂) and obtained an improved parameterization of φ (ClNO₂) (noted as φ (ClNO₂)_BT+Org). The parameterized φ (ClNO₂)_BT+Org better matches the observed φ (ClNO₂) at low to median yields (0–0.75), and the R² and slope values in the linear regression are closer to 1 (Fig. 4b). However, the parameterized φ (ClNO₂)_BT+Org is smaller than the observed φ (ClNO₂) at high yields (0.75–0.9), which may be attributable to other unconstrained factors in the parameterization, for example mixing state and phase state issues. In Eq. (11), the factor 483 (k₄∕k₃ in Eq. 9) was adopted from Bertram and Thornton (2009), and the factor 235 (k₄∕k₅ in Eq. 9) was derived here by iterative algorithms to achieve the least-square errors between the observed and parameterized φ (ClNO₂) values. Here we assumed that the observed aerosol organics were all water-soluble and reactive toward NO${}_{\mathrm{2}}^{+}$, as previous studies did (McDuffie et al., 2018a, b). The unknown water-soluble proportion of aerosol organics is factored into k₅. Given that $k_{\mathrm{4}}/k_{\mathrm{3}}=\mathrm{483}$ and $k_{\mathrm{4}}/k_{\mathrm{5}}=\mathrm{235}$, k₅∕k₃ was calculated as 2.06, which suggests that the reaction rate constant of aerosol organics with ${\mathrm{NO}}_{\mathrm{2}}^{+}$ was twice that of the H₂O + ${\mathrm{NO}}_{\mathrm{2}}^{+}$ reaction. A recent laboratory study (Staudt et al., 2019) derived $k_{\mathrm{5}}/k_{\mathrm{3}}=\mathrm{3.7}$ for acetate, which happens to be similar to the value derived for ambient aerosol at our site.

Figure 4Influencing factors and parameterizations of φ (ClNO₂). (a) Dependence of φ (ClNO₂) on the [Cl⁻] / [H₂O] ratio. Dashed red line shows nonlinear fitting of φ (ClNO₂); “a” represents the k₄∕k₃ ratio in Eq. (8). (b) Comparison of parameterized φ (ClNO₂) and observed φ (ClNO₂), where φ (ClNO₂)_BT denotes the parameterization proposed by Bertram and Thornton (2009), and φ (ClNO₂)_BT+Org represents the revised parameterization used in this study (see Eq. 11).

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3.4 Nocturnal Cl₂ formation

3.4.1 Cl₂ as a co-product of ClNO₂ from N₂O₅ uptake

To elucidate the formation pathways of the elevated levels of Cl₂ observed during the night, we investigated the correlations of Cl₂ with the ClNO₂, HOCl, and SO₂ and the diurnal variations of these species (Fig. 5a–d). Our result suggests that Cl₂ was related to ClNO₂, but the HOCl pathway (Reaction R5) and coal burning were of minor importance at our site. ClONO₂ was not measured during our study. Recent field measurements at a rural site in northern China reported low ClONO₂ levels at night (maximum ∼15 pptv) (Breton et al., 2018). We believe that the ClONO₂ levels at our site were also low, and production pathway (Reaction R6) was insignificant given low γ (ClONO₂) ($\sim {\mathrm{10}}^{-\mathrm{3}}$) (Haskins et al., 2019). At our site, the Cl₂∕ClNO₂ ratios varied on different nights, which implies that differences exist in the production efficiencies of Cl₂ relative to those of ClNO₂.

Figure 5Correlations among Cl₂, ClNO₂, HOCl, and SO₂ and their diurnal profiles; (a), (b), and (c) show the correlations of Cl₂ with ClNO₂, HOCl, and SO₂ respectively, during the whole campaign. Dots represent 10 min averaged values colored according to campaign days. (d) exhibits the diurnal variation of Cl₂, ClNO₂, HOCl, and SO₂.

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The current mainstream interpretation of the observed correlation of ClNO₂ and Cl₂ is that Cl₂ is produced from ClNO₂ uptake (Ammann et al., 2013; Qiu et al., 2019; Wang et al., 2019; Haskins et al., 2019). We provide evidence that this interpretation does not apply to measurements from our site. We assessed the ClNO₂ uptake hypothesis by examining the magnitude of γ (ClNO₂) needed to explain the nocturnal increase in Cl₂ mixing ratios and the dependence of γ(ClNO₂) on its known influencing factors. Assuming a unity yield of Cl₂ from ClNO₂ uptake, the increasing rate of Cl₂ mixing ratios was calculated with Eq. (12). Equation (13), which was derived by rearrangement of Eq. (12), was adopted to estimate γ (ClNO₂) via the observed Cl₂ and ClNO₂ levels.

$$\begin{array}{}\text{(12)}& {\displaystyle }d\left[{\mathrm{Cl}}_{\mathrm{2}}\right]/\mathrm{d}t={\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}c\left({\mathrm{ClNO}}_{\mathrm{2}}\right)S_{\mathrm{a}}\mathit{\gamma }\left({\mathrm{ClNO}}_{\mathrm{2}}\right)\left[{\mathrm{ClNO}}_{\mathrm{2}}\right],\text{(13)}& {\displaystyle }\mathit{\gamma }({\mathrm{ClNO}}_{\mathrm{2}}{)}_{\mathrm{obs}}={\displaystyle \frac{\mathrm{4}d\left[{\mathrm{Cl}}_{\mathrm{2}}\right]/\mathrm{d}t}{c\left({\mathrm{ClNO}}_{\mathrm{2}}\right)S_{\mathrm{a}}\left[{\mathrm{ClNO}}_{\mathrm{2}}\right]}},\end{array}$$

where c(ClNO₂) is the mean molecular velocity of ClNO₂ (m s⁻¹), and [ClNO₂] represents the averaged ambient concentration of ClNO₂ in the cases of interest.

γ (ClNO₂)_obs was estimated in the selected cases following criteria 1 and 2 in Sect. 3.3, and a steady increase in Cl₂ mixing ratios was required. The resulting values of γ (ClNO₂)_obs were compiled according to the local time and are presented in box charts (Fig. 6a). Figure 6a also shows the potential factors influencing γ (ClNO₂): [Cl⁻], [H⁺], and particle diameter (D_p). Here, D_p was an influencing factor of γ (ClNO₂) because ClNO₂ uptake was regarded as a volume-limited mechanism (Ammann et al., 2013; Haskins et al., 2019). [H⁺] and [Cl⁻] were considered because the previous laboratory study proposed that H⁺ and Cl⁻ were reactants in Cl₂ production (Roberts et al., 2008). Positive correlations of γ (ClNO₂) with [Cl⁻] and D_p were also found in a field study (Haskins et al., 2019). Each box represents the γ (ClNO₂), [Cl⁻], [H⁺], or D_p of 10 min resolutions derived on individual days. For example, the box for 18:00–19:00 contains the γ (ClNO₂) estimated at 18:00–19:00 LT on 11, 12, and 14 April (Fig. 6b–d, orange lines). Figure 6b–d display the observed Cl₂ levels (blue lines) and the projected trends of Cl₂ levels from Eq. (12), where the grey lines adopted the highest γ (ClNO₂) value, $\mathrm{6.69}\times {\mathrm{10}}^{-\mathrm{5}}$, observed in the field study of Haskins et al. (2019). During early evening hours (i.e., 18:00–19:00), the γ (ClNO₂) value derived in our study was 1–2 orders of magnitude higher than those in that study. This result implies that either ClNO₂ uptake was much faster at our site or other pathways were involved in Cl₂ production. We provide evidence below that the latter is likely the case.

Figure 6γ (ClNO₂) estimated using field observation data. (a) γ (ClNO₂)_obs, [Cl⁻], [H⁺], and D_p estimated at various nighttime periods. (b)–(d) Trends of increasing trends of Cl₂ mixing ratios during the early evening hours on 11, 12, and 14 April, respectively. Orange and grey lines represent the projected trend of Cl₂ mixing ratios using Eq. (12) with constant γ (ClNO₂) values and observed ClNO₂ levels.

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If the ClNO₂ uptake were the main production channel for Cl₂, we would expect to see positive correlations between γ (ClNO₂) and factors such as [Cl⁻], [H⁺], and D_p, according to previous laboratory and field studies (Roberts et al., 2008; Haskins et al., 2019). At our site, as the increasing rate of Cl₂ concentrations (d[Cl2]∕dt) did not change significantly during the night (Fig. 5d), the γ (ClNO₂) value was constrained by a sharp decreasing trend to compensate for the increasing ClNO₂ levels after dusk (see Eq. 12). The highest γ (ClNO₂)_obs value determined during the early evening hours (18:00–19:00) was similar to the laboratory-derived γ (ClNO₂)_obs value on acidic salt films ($\mathrm{6}\times {\mathrm{10}}^{-\mathrm{3}}$) (Roberts et al., 2008). However, the lowest γ (ClNO₂)_obs value estimated during later nighttime hours (22:00–04:00) was 2 orders of magnitude lower (10⁻⁵). The large variations in the γ (ClNO₂) value contrasted with the relatively stable levels of [Cl⁻], [H⁺], and D_p at various times of night, which is in opposition to the current understanding of the relationship between the γ (ClNO₂) and these factors. In our study, the D_p was derived from the ratio of wet V_a to S_a by assuming volume-limited uptake (Ammann et al., 2013). We also calculated D_p assuming surface-limited uptake (diameter of the average surface area), and no correlation with γ (ClNO₂)_obs was indicated. Moreover, the γ (ClNO₂)_obs showed no obvious relationship with other factors such as T, RH, aerosol liquid water content (ALW), ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$, ${\mathrm{NH}}_{\mathrm{4}}^{+}$, and aerosol organics (figure not shown). To sum up, the ClNO₂ uptake pathway alone cannot explain the nocturnal increase in Cl₂ mixing ratios that we observed at our study site.

We propose another hypothesis to explain the ClNO₂–Cl₂ correlation and suggest that Cl₂ is a co-product with ClNO₂ produced from N₂O₅ uptake, in which ClNO₂ is not necessarily an intermediate of Cl₂ production. The mechanism is depicted in Fig. 7 and goes as follows. It is known that N₂O₅ hydrolysis on aerosol is responsible for the production of ${\mathrm{NO}}_{\mathrm{2}}^{+}$. According to the hybrid orbital theory, the ${\mathrm{NO}}_{\mathrm{2}}^{+}$ ion has two non-bonded π molecular orbitals due to participation of the d orbital of the central nitrogen atom (Baird and Tayler, 1981). ClNO₂ is formed via the nucleophilic addition of Cl⁻ to one of the π molecular orbitals of ${\mathrm{NO}}_{\mathrm{2}}^{+}$ (Fig. 7a) (Taylor, 1990; Behnke et al., 1997). In the same way, we propose a side reaction: the second Cl⁻ can attach to the other π molecular orbital of ${\mathrm{NO}}_{\mathrm{2}}^{+}$ and form a short-lived HNO₂Cl₂ intermediate in the presence of H⁺. It is proposed that the unstable HNO₂Cl₂ decomposes to produce Cl₂ (and HONO) (Fig. 7b). This mechanism can explain concurrent productions of Cl₂ and ClNO₂ from N₂O₅ hydrolysis but needs confirmation by additional laboratory and theoretical studies.

Figure 7Proposed formation mechanisms of ClNO₂ and Cl₂ from N₂O₅ uptake. (a) Production of ClNO₂ from ${\mathrm{NO}}_{\mathrm{2}}^{+}$ and Cl⁻. (b) Production of Cl₂ from ${\mathrm{NO}}_{\mathrm{2}}^{+}$, Cl⁻, and H⁺.

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3.4.2 Parameterizing Cl₂ formation from N₂O₅ uptake

We propose a new framework to estimate nighttime Cl₂ production by treating Cl₂, ClNO₂, and most nitrate all ultimately originating from N₂O₅ uptake. We assign a production yield to Cl₂ from the N₂O₅ uptake (φ (Cl₂)) analogous to the ClNO₂ yield and calculate this metric using Eq. (14):

$$\begin{array}{}\text{(14)}& \mathit{\phi }\left({\mathrm{Cl}}_{\mathrm{2}}\right)={\displaystyle \frac{d\left[{\mathrm{Cl}}_{\mathrm{2}}\right]/\mathrm{d}t}{k\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}}.\end{array}$$

The above formulation does not rule out the production of Cl₂ from the ClNO₂ uptake, because such production, if any, is also a result of N₂O₅ uptake and has thus been incorporated in Eq. (14). We calculated φ (Cl₂) in the same cases in which γ (N₂O₅) and φ (ClNO₂) were derived, because the availability of γ (N₂O₅) was a prerequisite of deriving φ (Cl₂). The estimated φ (Cl₂) value was 0.01–0.04 (Table S2). The dependences of φ (Cl₂) on its potential influencing factors (i.e., [Cl⁻], [H⁺], and D_p) were examined. The results show that φ (Cl₂) had positive correlations with both [Cl⁻] (R²=0.74) and [H⁺] (R²=0.75) and that the data had a high-φ (Cl₂) region and a low-φ (Cl₂) region (Fig. 8a, b). The low φ (Cl₂) values were found in continental air masses with relatively lower chloride concentrations, more alkaline ammonium, less acidic sulfate and nitrate, and thus lower acidity (Fig. 8d). In contrast, the high φ (Cl₂) values were associated with marine air masses with higher loadings of aerosol chloride, less ammonium, and more acidic compounds, and thus higher acidity (Fig. 8c). The higher acidity in the marine air masses may be explained by their passage over the industrialized cities in the YRD where large amount of SO₂ and NO_x are emitted. The average concentrations of SO₂ (3.9±0.1 ppbv) and NO_x (13.1±3.1 ppbv) in the marine air masses were higher than those (NO_x: 11.5±0.6 ppbv; SO₂: 3.3±0.3 ppbv) in the inland air masses. The dependences of the defined φ (Cl₂) on [Cl⁻] and [H⁺] indicate that nocturnal Cl₂ production requires the presence of highly acidic chloride-rich particles and sufficient levels of N₂O₅.

Figure 8Estimated φ (Cl₂) from N₂O₅ uptake and the factors influencing φ (Cl₂) (a) and (b) dependencies of φ (Cl₂) on [Cl⁻] and [H⁺] in selected cases. (c) and (d) are examples of high φ (Cl₂) values in marine air masses (e.g., 13 April) and low φ (Cl₂) values in inland air masses (e.g., 18 April) represented by 24 h backward trajectories (see Fig. S2 for trajectories during the whole observations). Inserted pie charts show average aerosol chemical compositions during 21:40 LT on 12 April to 00:40 LT on 13 April and from 22:20 to 23:40 LT on 17 April, respectively.

A parameterization scheme is derived based on the dependences of φ (Cl₂) on [Cl⁻] and [H⁺] to predict the Cl₂ formation involving N₂O₅ heterogeneous chemistry. Mechanistically, it is assumed that the nocturnal Cl₂ is produced from reactions involving ${\mathrm{NO}}_{\mathrm{2}}^{+}$ that can be produced either from uptake of N₂O₅ or ClNO₂. The production rates of nitrate, ClNO₂, and Cl₂ from the loss of ${\mathrm{NO}}_{\mathrm{2}}^{+}$ are expressed in Eq. (15) through Eq. (17). The loss rate of aerosol organics induced by ${\mathrm{NO}}_{\mathrm{2}}^{+}$ is expressed in Eq. (18) (noted as d[Org]/dt here).

$$\begin{array}{}\text{(15)}& {\displaystyle }d\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]/\mathrm{d}t=k_{\mathrm{3}}\left[{\mathrm{NO}}_{\mathrm{2}}^{+}\right]\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]\text{(16)}& {\displaystyle }d\left[{\mathrm{ClNO}}_{\mathrm{2}}\right]/\mathrm{d}t=k_{\mathrm{4}}\left[{\mathrm{NO}}_{\mathrm{2}}^{+}\right]\left[{\mathrm{Cl}}^{-}\right]\text{(17)}& {\displaystyle }d\left[{\mathrm{Cl}}_{\mathrm{2}}\right]/\mathrm{d}t=k_{\mathrm{6}}\left[{\mathrm{NO}}_{\mathrm{2}}^{+}\right]\left[{\mathrm{Cl}}^{-}\right]\left[{\mathrm{H}}^{+}\right]\text{(18)}& {\displaystyle }d\left[\mathrm{Org}\right]/\mathrm{d}t=k_{\mathrm{5}}\left[{\mathrm{NO}}_{\mathrm{2}}^{+}\right]\left[\mathrm{Org}\right]\end{array}$$

The symbol k₆ represents the rate constant of the reaction involving ${\mathrm{NO}}_{\mathrm{2}}^{+}$, Cl⁻, and H⁺. φ (Cl₂) is obtained as follows, by assuming a steady state of the ${\mathrm{NO}}_{\mathrm{2}}^{+}$ intermediate (Bertram and Thornton, 2009) (Eq. 19).

$$\begin{array}{}\text{(19)}& \begin{array}{rl}\mathit{\phi }& \left({\mathrm{Cl}}_{\mathrm{2}}\right)={\displaystyle \frac{\frac{d\left[{\mathrm{Cl}}_{\mathrm{2}}\right]}{\mathrm{d}t}}{\frac{d\left[{\mathrm{Cl}}_{\mathrm{2}}\right]}{\mathrm{d}t}+\frac{d\left[{\mathrm{ClNO}}_{\mathrm{2}}\right]}{\mathrm{d}t}+\frac{d\left[{{\mathrm{NO}}_{\mathrm{3}}}^{-}\right]}{\mathrm{d}t}+\frac{d\left[\mathrm{Org}\right]}{\mathrm{d}t}}}\\ & ={\displaystyle \frac{k_{\mathrm{6}}\left[{\mathrm{Cl}}^{-}\right]\left[{\mathrm{H}}^{+}\right]}{k_{\mathrm{6}}\left[{\mathrm{Cl}}^{-}\right]\left[{\mathrm{H}}^{+}\right]+k_{\mathrm{4}}\left[{\mathrm{Cl}}^{-}\right]+k_{\mathrm{3}}\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]+k_{\mathrm{5}}\left[\mathrm{Org}\right]}}\end{array}\end{array}$$

To remain consistent with the φ (ClNO₂) parameterization, the values 483 and 2.06 were adopted for k₄∕k₃ and k₅∕k₃, respectively, while k₆∕k₃ was estimated from the fitting of φ (Cl₂) using Eq. (19) to achieve the least-squares errors between the observed and parameterized φ (Cl₂) values. The parameterization of φ (Cl₂) was then expressed as follows (Eq. 20):

$$\begin{array}{}\text{(20)}& \begin{array}{rl}& \mathit{\phi }\left({\mathrm{Cl}}_{\mathrm{2}}\right)=\\ & {\displaystyle \frac{\mathrm{19.38}\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{Cl}}^{-}\right]}{\mathrm{19.38}\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{Cl}}^{-}\right]+\mathrm{483}\left[{\mathrm{Cl}}^{-}\right]+\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]+\mathrm{2.06}\left[\mathrm{Org}\right]}},\end{array}\end{array}$$

where the unit of [H⁺], [Cl⁻], and [Org] is mole per liter (mol L⁻¹).

The previous ClNO₂ uptake method assumed a unity Cl₂ yield from ClNO₂ uptake, but no such assumption is required in the new method for an explicit definition (Eq. 14) and parameterization (Eq. 20) of the φ (Cl₂). In addition, a quantitative relationship between φ (Cl₂) and aerosol acidity is established, which was not given in the previous parameterization. We recommend that air quality models test this parameterization for reproduction of nighttime Cl₂ observations.